From 68ac6731cbea6db9677e1a26f673f53d964245ee Mon Sep 17 00:00:00 2001
From: Matt Borland <matt@mattborland.com>
Date: Tue, 13 Aug 2024 11:18:56 -0400
Subject: [PATCH 01/24] Add NVRTC support to cos_pi

---
 .../boost/math/special_functions/cos_pi.hpp   | 40 ++++++++++++++++++-
 1 file changed, 39 insertions(+), 1 deletion(-)

diff --git a/include/boost/math/special_functions/cos_pi.hpp b/include/boost/math/special_functions/cos_pi.hpp
index 5a7c742b4..7c33614de 100644
--- a/include/boost/math/special_functions/cos_pi.hpp
+++ b/include/boost/math/special_functions/cos_pi.hpp
@@ -11,9 +11,12 @@
 #pragma once
 #endif
 
+#include <boost/math/tools/config.hpp>
+
+#ifndef BOOST_MATH_HAS_NVRTC
+
 #include <cmath>
 #include <limits>
-#include <boost/math/tools/config.hpp>
 #include <boost/math/tools/numeric_limits.hpp>
 #include <boost/math/special_functions/math_fwd.hpp>
 #include <boost/math/special_functions/trunc.hpp>
@@ -86,5 +89,40 @@ BOOST_MATH_GPU_ENABLED inline typename tools::promote_args<T>::type cos_pi(T x)
 
 } // namespace math
 } // namespace boost
+
+#else // Special handling for NVRTC
+
+namespace boost {
+namespace math {
+
+template <typename T>
+BOOST_MATH_GPU_ENABLED auto cos_pi(T x)
+{
+   return ::cospi(x);
+}
+
+template <>
+BOOST_MATH_GPU_ENABLED auto cos_pi(float x)
+{
+   return ::cospif(x);
+}
+
+template <typename T, typename Policy>
+BOOST_MATH_GPU_ENABLED auto cos_pi(T x, const Policy&)
+{
+   return ::cospi(x);
+}
+
+template <typename Policy>
+BOOST_MATH_GPU_ENABLED auto cos_pi(float x, const Policy&)
+{
+   return ::cospif(x);
+}
+
+} // namespace math
+} // namespace boost
+
+#endif // BOOST_MATH_HAS_NVRTC
+
 #endif
 

From dae8f3ad2753815a37c166e5fe3e050b939e19da Mon Sep 17 00:00:00 2001
From: Matt Borland <matt@mattborland.com>
Date: Tue, 13 Aug 2024 11:19:10 -0400
Subject: [PATCH 02/24] Add cos_pi NVRTC testing

---
 test/nvrtc_jamfile                |   2 +
 test/test_cos_pi_nvrtc_double.cpp | 186 ++++++++++++++++++++++++++++++
 test/test_cos_pi_nvrtc_float.cpp  | 186 ++++++++++++++++++++++++++++++
 3 files changed, 374 insertions(+)
 create mode 100644 test/test_cos_pi_nvrtc_double.cpp
 create mode 100644 test/test_cos_pi_nvrtc_float.cpp

diff --git a/test/nvrtc_jamfile b/test/nvrtc_jamfile
index 703bf8099..38f9f2476 100644
--- a/test/nvrtc_jamfile
+++ b/test/nvrtc_jamfile
@@ -12,6 +12,8 @@ project : requirements
 # Special Functions
 run test_cbrt_nvrtc_double.cpp ;
 run test_cbrt_nvrtc_float.cpp ;
+run test_cos_pi_nvrtc_double.cpp ;
+run test_cos_pi_nvrtc_float.cpp ;
 run test_expm1_nvrtc_double.cpp ;
 run test_expm1_nvrtc_float.cpp ;
 run test_fpclassify_nvrtc_double.cpp ;
diff --git a/test/test_cos_pi_nvrtc_double.cpp b/test/test_cos_pi_nvrtc_double.cpp
new file mode 100644
index 000000000..459524bbe
--- /dev/null
+++ b/test/test_cos_pi_nvrtc_double.cpp
@@ -0,0 +1,186 @@
+//  Copyright John Maddock 2016.
+//  Copyright Matt Borland 2024.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+#define BOOST_MATH_PROMOTE_DOUBLE_POLICY false
+
+#include <iostream>
+#include <iomanip>
+#include <vector>
+#include <random>
+#include <exception>
+#include <boost/math/special_functions/cos_pi.hpp>
+#include <boost/math/special_functions/relative_difference.hpp>
+#include <cuda.h>
+#include <cuda_runtime.h>
+#include <nvrtc.h>
+
+typedef double float_type;
+
+const char* cuda_kernel = R"(
+typedef double float_type;
+#include <boost/math/special_functions/cos_pi.hpp>
+extern "C" __global__ 
+void test_cos_pi_kernel(const float_type *in1, const float_type*, float_type *out, int numElements)
+{
+    int i = blockDim.x * blockIdx.x + threadIdx.x;
+    if (i < numElements)
+    {
+        out[i] = boost::math::cos_pi(in1[i]);
+    }
+}
+)";
+
+void checkCUDAError(cudaError_t result, const char* msg)
+{
+    if (result != cudaSuccess)
+    {
+        std::cerr << msg << ": " << cudaGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkCUError(CUresult result, const char* msg)
+{
+    if (result != CUDA_SUCCESS)
+    {
+        const char* errorStr;
+        cuGetErrorString(result, &errorStr);
+        std::cerr << msg << ": " << errorStr << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkNVRTCError(nvrtcResult result, const char* msg)
+{
+    if (result != NVRTC_SUCCESS)
+    {
+        std::cerr << msg << ": " << nvrtcGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+int main() 
+{
+    try
+    {
+        // Initialize CUDA driver API
+        checkCUError(cuInit(0), "Failed to initialize CUDA");
+
+        // Create CUDA context
+        CUcontext context;
+        CUdevice device;
+        checkCUError(cuDeviceGet(&device, 0), "Failed to get CUDA device");
+        checkCUError(cuCtxCreate(&context, 0, device), "Failed to create CUDA context");
+
+        nvrtcProgram prog;
+        nvrtcResult res;
+
+        res = nvrtcCreateProgram(&prog, cuda_kernel, "test_cos_pi_kernel.cu", 0, nullptr, nullptr);
+        checkNVRTCError(res, "Failed to create NVRTC program");
+
+        nvrtcAddNameExpression(prog, "test_cos_pi_kernel");
+
+        #ifdef BOOST_MATH_NVRTC_CI_RUN
+        const char* opts[] = {"--std=c++14", "--gpu-architecture=compute_75", "--include-path=/home/runner/work/cuda-math/boost-root/libs/cuda-math/include/"};
+        #else
+        const char* opts[] = {"--std=c++14", "--include-path=/home/mborland/Documents/boost/libs/cuda-math/include/"};
+        #endif
+
+        // Compile the program
+        res = nvrtcCompileProgram(prog, sizeof(opts) / sizeof(const char*), opts);
+        if (res != NVRTC_SUCCESS) 
+        {
+            size_t log_size;
+            nvrtcGetProgramLogSize(prog, &log_size);
+            char* log = new char[log_size];
+            nvrtcGetProgramLog(prog, log);
+            std::cerr << "Compilation failed:\n" << log << std::endl;
+            delete[] log;
+            exit(EXIT_FAILURE);
+        }
+
+        // Get PTX from the program
+        size_t ptx_size;
+        nvrtcGetPTXSize(prog, &ptx_size);
+        char* ptx = new char[ptx_size];
+        nvrtcGetPTX(prog, ptx);
+
+        // Load PTX into CUDA module
+        CUmodule module;
+        CUfunction kernel;
+        checkCUError(cuModuleLoadDataEx(&module, ptx, 0, 0, 0), "Failed to load module");
+        checkCUError(cuModuleGetFunction(&kernel, module, "test_cos_pi_kernel"), "Failed to get kernel function");
+
+        int numElements = 5000;
+        float_type *h_in1, *h_in2, *h_out;
+        float_type *d_in1, *d_in2, *d_out;
+
+        // Allocate memory on the host
+        h_in1 = new float_type[numElements];
+        h_in2 = new float_type[numElements];
+        h_out = new float_type[numElements];
+
+        // Initialize input arrays
+        std::mt19937_64 rng(42);
+        std::uniform_real_distribution<float_type> dist(0.0f, 1.0f);
+        for (int i = 0; i < numElements; ++i) 
+        {
+            h_in1[i] = static_cast<float_type>(dist(rng));
+            h_in2[i] = static_cast<float_type>(dist(rng));
+        }
+
+        checkCUDAError(cudaMalloc(&d_in1, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in1");
+        checkCUDAError(cudaMalloc(&d_in2, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in2");
+        checkCUDAError(cudaMalloc(&d_out, numElements * sizeof(float_type)), "Failed to allocate device memory for d_out");
+
+        checkCUDAError(cudaMemcpy(d_in1, h_in1, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in1");
+        checkCUDAError(cudaMemcpy(d_in2, h_in2, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in2");
+
+        int blockSize = 256;
+        int numBlocks = (numElements + blockSize - 1) / blockSize;
+        void* args[] = { &d_in1, &d_in2, &d_out, &numElements };
+        checkCUError(cuLaunchKernel(kernel, numBlocks, 1, 1, blockSize, 1, 1, 0, 0, args, 0), "Kernel launch failed");
+
+        checkCUDAError(cudaMemcpy(h_out, d_out, numElements * sizeof(float_type), cudaMemcpyDeviceToHost), "Failed to copy data back to host for h_out");
+
+        // Verify Result
+        for (int i = 0; i < numElements; ++i) 
+        {
+            auto res = boost::math::cos_pi(h_in1[i]);
+            if (std::isfinite(res))
+            {
+                if (boost::math::epsilon_difference(res, h_out[i]) > 300)
+                {
+                    std::cout << "error at line: " << i
+                            << "\nParallel: " << h_out[i]
+                            << "\n  Serial: " << res
+                            << "\n    Dist: " << boost::math::epsilon_difference(res, h_out[i]) << std::endl;
+                }
+            }
+        }
+
+        cudaFree(d_in1);
+        cudaFree(d_in2);
+        cudaFree(d_out);
+        delete[] h_in1;
+        delete[] h_in2;
+        delete[] h_out;
+
+        nvrtcDestroyProgram(&prog);
+        delete[] ptx;
+
+        cuCtxDestroy(context);
+
+        std::cout << "Kernel executed successfully." << std::endl;
+        return 0;
+    }
+    catch(const std::exception& e)
+    {
+        std::cerr << "Stopped with exception: " << e.what() << std::endl;
+        return EXIT_FAILURE;
+    }
+}
diff --git a/test/test_cos_pi_nvrtc_float.cpp b/test/test_cos_pi_nvrtc_float.cpp
new file mode 100644
index 000000000..7c1eef3fa
--- /dev/null
+++ b/test/test_cos_pi_nvrtc_float.cpp
@@ -0,0 +1,186 @@
+//  Copyright John Maddock 2016.
+//  Copyright Matt Borland 2024.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+#define BOOST_MATH_PROMOTE_DOUBLE_POLICY false
+
+#include <iostream>
+#include <iomanip>
+#include <vector>
+#include <random>
+#include <exception>
+#include <boost/math/special_functions/cos_pi.hpp>
+#include <boost/math/special_functions/relative_difference.hpp>
+#include <cuda.h>
+#include <cuda_runtime.h>
+#include <nvrtc.h>
+
+typedef float float_type;
+
+const char* cuda_kernel = R"(
+typedef double float_type;
+#include <boost/math/special_functions/cos_pi.hpp>
+extern "C" __global__ 
+void test_cos_pi_kernel(const float_type *in1, const float_type*, float_type *out, int numElements)
+{
+    int i = blockDim.x * blockIdx.x + threadIdx.x;
+    if (i < numElements)
+    {
+        out[i] = boost::math::cos_pi(in1[i]);
+    }
+}
+)";
+
+void checkCUDAError(cudaError_t result, const char* msg)
+{
+    if (result != cudaSuccess)
+    {
+        std::cerr << msg << ": " << cudaGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkCUError(CUresult result, const char* msg)
+{
+    if (result != CUDA_SUCCESS)
+    {
+        const char* errorStr;
+        cuGetErrorString(result, &errorStr);
+        std::cerr << msg << ": " << errorStr << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkNVRTCError(nvrtcResult result, const char* msg)
+{
+    if (result != NVRTC_SUCCESS)
+    {
+        std::cerr << msg << ": " << nvrtcGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+int main() 
+{
+    try
+    {
+        // Initialize CUDA driver API
+        checkCUError(cuInit(0), "Failed to initialize CUDA");
+
+        // Create CUDA context
+        CUcontext context;
+        CUdevice device;
+        checkCUError(cuDeviceGet(&device, 0), "Failed to get CUDA device");
+        checkCUError(cuCtxCreate(&context, 0, device), "Failed to create CUDA context");
+
+        nvrtcProgram prog;
+        nvrtcResult res;
+
+        res = nvrtcCreateProgram(&prog, cuda_kernel, "test_cos_pi_kernel.cu", 0, nullptr, nullptr);
+        checkNVRTCError(res, "Failed to create NVRTC program");
+
+        nvrtcAddNameExpression(prog, "test_cos_pi_kernel");
+
+        #ifdef BOOST_MATH_NVRTC_CI_RUN
+        const char* opts[] = {"--std=c++14", "--gpu-architecture=compute_75", "--include-path=/home/runner/work/cuda-math/boost-root/libs/cuda-math/include/"};
+        #else
+        const char* opts[] = {"--std=c++14", "--include-path=/home/mborland/Documents/boost/libs/cuda-math/include/"};
+        #endif
+
+        // Compile the program
+        res = nvrtcCompileProgram(prog, sizeof(opts) / sizeof(const char*), opts);
+        if (res != NVRTC_SUCCESS) 
+        {
+            size_t log_size;
+            nvrtcGetProgramLogSize(prog, &log_size);
+            char* log = new char[log_size];
+            nvrtcGetProgramLog(prog, log);
+            std::cerr << "Compilation failed:\n" << log << std::endl;
+            delete[] log;
+            exit(EXIT_FAILURE);
+        }
+
+        // Get PTX from the program
+        size_t ptx_size;
+        nvrtcGetPTXSize(prog, &ptx_size);
+        char* ptx = new char[ptx_size];
+        nvrtcGetPTX(prog, ptx);
+
+        // Load PTX into CUDA module
+        CUmodule module;
+        CUfunction kernel;
+        checkCUError(cuModuleLoadDataEx(&module, ptx, 0, 0, 0), "Failed to load module");
+        checkCUError(cuModuleGetFunction(&kernel, module, "test_cos_pi_kernel"), "Failed to get kernel function");
+
+        int numElements = 5000;
+        float_type *h_in1, *h_in2, *h_out;
+        float_type *d_in1, *d_in2, *d_out;
+
+        // Allocate memory on the host
+        h_in1 = new float_type[numElements];
+        h_in2 = new float_type[numElements];
+        h_out = new float_type[numElements];
+
+        // Initialize input arrays
+        std::mt19937_64 rng(42);
+        std::uniform_real_distribution<float_type> dist(0.0f, 1.0f);
+        for (int i = 0; i < numElements; ++i) 
+        {
+            h_in1[i] = static_cast<float_type>(dist(rng));
+            h_in2[i] = static_cast<float_type>(dist(rng));
+        }
+
+        checkCUDAError(cudaMalloc(&d_in1, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in1");
+        checkCUDAError(cudaMalloc(&d_in2, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in2");
+        checkCUDAError(cudaMalloc(&d_out, numElements * sizeof(float_type)), "Failed to allocate device memory for d_out");
+
+        checkCUDAError(cudaMemcpy(d_in1, h_in1, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in1");
+        checkCUDAError(cudaMemcpy(d_in2, h_in2, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in2");
+
+        int blockSize = 256;
+        int numBlocks = (numElements + blockSize - 1) / blockSize;
+        void* args[] = { &d_in1, &d_in2, &d_out, &numElements };
+        checkCUError(cuLaunchKernel(kernel, numBlocks, 1, 1, blockSize, 1, 1, 0, 0, args, 0), "Kernel launch failed");
+
+        checkCUDAError(cudaMemcpy(h_out, d_out, numElements * sizeof(float_type), cudaMemcpyDeviceToHost), "Failed to copy data back to host for h_out");
+
+        // Verify Result
+        for (int i = 0; i < numElements; ++i) 
+        {
+            auto res = boost::math::cos_pi(h_in1[i]);
+            if (std::isfinite(res))
+            {
+                if (boost::math::epsilon_difference(res, h_out[i]) > 300)
+                {
+                    std::cout << "error at line: " << i
+                            << "\nParallel: " << h_out[i]
+                            << "\n  Serial: " << res
+                            << "\n    Dist: " << boost::math::epsilon_difference(res, h_out[i]) << std::endl;
+                }
+            }
+        }
+
+        cudaFree(d_in1);
+        cudaFree(d_in2);
+        cudaFree(d_out);
+        delete[] h_in1;
+        delete[] h_in2;
+        delete[] h_out;
+
+        nvrtcDestroyProgram(&prog);
+        delete[] ptx;
+
+        cuCtxDestroy(context);
+
+        std::cout << "Kernel executed successfully." << std::endl;
+        return 0;
+    }
+    catch(const std::exception& e)
+    {
+        std::cerr << "Stopped with exception: " << e.what() << std::endl;
+        return EXIT_FAILURE;
+    }
+}

From 6100af43339680dd1ea88626f4a8533dfd2718bd Mon Sep 17 00:00:00 2001
From: Matt Borland <matt@mattborland.com>
Date: Tue, 13 Aug 2024 11:23:35 -0400
Subject: [PATCH 03/24] Add NVRTC support to sin_pi

---
 .../boost/math/special_functions/sin_pi.hpp   | 40 ++++++++++++++++++-
 1 file changed, 39 insertions(+), 1 deletion(-)

diff --git a/include/boost/math/special_functions/sin_pi.hpp b/include/boost/math/special_functions/sin_pi.hpp
index 3e16bfc96..e59e232e6 100644
--- a/include/boost/math/special_functions/sin_pi.hpp
+++ b/include/boost/math/special_functions/sin_pi.hpp
@@ -11,10 +11,13 @@
 #pragma once
 #endif
 
+#include <boost/math/tools/config.hpp>
+
+#ifndef BOOST_MATH_HAS_NVRTC
+
 #include <cmath>
 #include <limits>
 #include <type_traits>
-#include <boost/math/tools/config.hpp>
 #include <boost/math/tools/numeric_limits.hpp>
 #include <boost/math/special_functions/math_fwd.hpp>
 #include <boost/math/special_functions/trunc.hpp>
@@ -94,5 +97,40 @@ inline typename tools::promote_args<T>::type sin_pi(T x)
 
 } // namespace math
 } // namespace boost
+
+#else // Special handling for NVRTC
+
+namespace boost {
+namespace math {
+
+template <typename T>
+BOOST_MATH_GPU_ENABLED auto sin_pi(T x)
+{
+   return ::sinpi(x);
+}
+
+template <>
+BOOST_MATH_GPU_ENABLED auto sin_pi(float x)
+{
+   return ::sinpif(x);
+}
+
+template <typename T, typename Policy>
+BOOST_MATH_GPU_ENABLED auto sin_pi(T x, const Policy&)
+{
+   return ::sinpi(x);
+}
+
+template <typename Policy>
+BOOST_MATH_GPU_ENABLED auto sin_pi(float x, const Policy&)
+{
+   return ::sinpif(x);
+}
+
+} // namespace math
+} // namespace boost
+
+#endif // BOOST_MATH_HAS_NVRTC
+
 #endif
 

From 566c5a1422bbe87b01696886088d77ec49d2e9f1 Mon Sep 17 00:00:00 2001
From: Matt Borland <matt@mattborland.com>
Date: Tue, 13 Aug 2024 11:23:46 -0400
Subject: [PATCH 04/24] Add sin_pi NVRTC testing

---
 test/nvrtc_jamfile                |   2 +
 test/test_sin_pi_nvrtc_double.cpp | 186 ++++++++++++++++++++++++++++++
 test/test_sin_pi_nvrtc_float.cpp  | 186 ++++++++++++++++++++++++++++++
 3 files changed, 374 insertions(+)
 create mode 100644 test/test_sin_pi_nvrtc_double.cpp
 create mode 100644 test/test_sin_pi_nvrtc_float.cpp

diff --git a/test/nvrtc_jamfile b/test/nvrtc_jamfile
index 38f9f2476..9eebb3df5 100644
--- a/test/nvrtc_jamfile
+++ b/test/nvrtc_jamfile
@@ -26,4 +26,6 @@ run test_round_nvrtc_double.cpp ;
 run test_round_nvrtc_float.cpp ;
 run test_sign_nvrtc_double.cpp ;
 run test_sign_nvrtc_float.cpp ;
+run test_sin_pi_nvrtc_double.cpp ;
+run test_sin_pi_nvrtc_float.cpp ;
 run test_trunc_nvrtc_double.cpp ;
diff --git a/test/test_sin_pi_nvrtc_double.cpp b/test/test_sin_pi_nvrtc_double.cpp
new file mode 100644
index 000000000..b6cff9798
--- /dev/null
+++ b/test/test_sin_pi_nvrtc_double.cpp
@@ -0,0 +1,186 @@
+//  Copyright John Maddock 2016.
+//  Copyright Matt Borland 2024.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+#define BOOST_MATH_PROMOTE_DOUBLE_POLICY false
+
+#include <iostream>
+#include <iomanip>
+#include <vector>
+#include <random>
+#include <exception>
+#include <boost/math/special_functions/sin_pi.hpp>
+#include <boost/math/special_functions/relative_difference.hpp>
+#include <cuda.h>
+#include <cuda_runtime.h>
+#include <nvrtc.h>
+
+typedef double float_type;
+
+const char* cuda_kernel = R"(
+typedef double float_type;
+#include <boost/math/special_functions/sin_pi.hpp>
+extern "C" __global__ 
+void test_sin_pi_kernel(const float_type *in1, const float_type*, float_type *out, int numElements)
+{
+    int i = blockDim.x * blockIdx.x + threadIdx.x;
+    if (i < numElements)
+    {
+        out[i] = boost::math::sin_pi(in1[i]);
+    }
+}
+)";
+
+void checkCUDAError(cudaError_t result, const char* msg)
+{
+    if (result != cudaSuccess)
+    {
+        std::cerr << msg << ": " << cudaGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkCUError(CUresult result, const char* msg)
+{
+    if (result != CUDA_SUCCESS)
+    {
+        const char* errorStr;
+        cuGetErrorString(result, &errorStr);
+        std::cerr << msg << ": " << errorStr << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkNVRTCError(nvrtcResult result, const char* msg)
+{
+    if (result != NVRTC_SUCCESS)
+    {
+        std::cerr << msg << ": " << nvrtcGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+int main() 
+{
+    try
+    {
+        // Initialize CUDA driver API
+        checkCUError(cuInit(0), "Failed to initialize CUDA");
+
+        // Create CUDA context
+        CUcontext context;
+        CUdevice device;
+        checkCUError(cuDeviceGet(&device, 0), "Failed to get CUDA device");
+        checkCUError(cuCtxCreate(&context, 0, device), "Failed to create CUDA context");
+
+        nvrtcProgram prog;
+        nvrtcResult res;
+
+        res = nvrtcCreateProgram(&prog, cuda_kernel, "test_sin_pi_kernel.cu", 0, nullptr, nullptr);
+        checkNVRTCError(res, "Failed to create NVRTC program");
+
+        nvrtcAddNameExpression(prog, "test_sin_pi_kernel");
+
+        #ifdef BOOST_MATH_NVRTC_CI_RUN
+        const char* opts[] = {"--std=c++14", "--gpu-architecture=compute_75", "--include-path=/home/runner/work/cuda-math/boost-root/libs/cuda-math/include/"};
+        #else
+        const char* opts[] = {"--std=c++14", "--include-path=/home/mborland/Documents/boost/libs/cuda-math/include/"};
+        #endif
+
+        // Compile the program
+        res = nvrtcCompileProgram(prog, sizeof(opts) / sizeof(const char*), opts);
+        if (res != NVRTC_SUCCESS) 
+        {
+            size_t log_size;
+            nvrtcGetProgramLogSize(prog, &log_size);
+            char* log = new char[log_size];
+            nvrtcGetProgramLog(prog, log);
+            std::cerr << "Compilation failed:\n" << log << std::endl;
+            delete[] log;
+            exit(EXIT_FAILURE);
+        }
+
+        // Get PTX from the program
+        size_t ptx_size;
+        nvrtcGetPTXSize(prog, &ptx_size);
+        char* ptx = new char[ptx_size];
+        nvrtcGetPTX(prog, ptx);
+
+        // Load PTX into CUDA module
+        CUmodule module;
+        CUfunction kernel;
+        checkCUError(cuModuleLoadDataEx(&module, ptx, 0, 0, 0), "Failed to load module");
+        checkCUError(cuModuleGetFunction(&kernel, module, "test_sin_pi_kernel"), "Failed to get kernel function");
+
+        int numElements = 5000;
+        float_type *h_in1, *h_in2, *h_out;
+        float_type *d_in1, *d_in2, *d_out;
+
+        // Allocate memory on the host
+        h_in1 = new float_type[numElements];
+        h_in2 = new float_type[numElements];
+        h_out = new float_type[numElements];
+
+        // Initialize input arrays
+        std::mt19937_64 rng(42);
+        std::uniform_real_distribution<float_type> dist(0.0f, 1.0f);
+        for (int i = 0; i < numElements; ++i) 
+        {
+            h_in1[i] = static_cast<float_type>(dist(rng));
+            h_in2[i] = static_cast<float_type>(dist(rng));
+        }
+
+        checkCUDAError(cudaMalloc(&d_in1, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in1");
+        checkCUDAError(cudaMalloc(&d_in2, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in2");
+        checkCUDAError(cudaMalloc(&d_out, numElements * sizeof(float_type)), "Failed to allocate device memory for d_out");
+
+        checkCUDAError(cudaMemcpy(d_in1, h_in1, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in1");
+        checkCUDAError(cudaMemcpy(d_in2, h_in2, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in2");
+
+        int blockSize = 256;
+        int numBlocks = (numElements + blockSize - 1) / blockSize;
+        void* args[] = { &d_in1, &d_in2, &d_out, &numElements };
+        checkCUError(cuLaunchKernel(kernel, numBlocks, 1, 1, blockSize, 1, 1, 0, 0, args, 0), "Kernel launch failed");
+
+        checkCUDAError(cudaMemcpy(h_out, d_out, numElements * sizeof(float_type), cudaMemcpyDeviceToHost), "Failed to copy data back to host for h_out");
+
+        // Verify Result
+        for (int i = 0; i < numElements; ++i) 
+        {
+            auto res = boost::math::sin_pi(h_in1[i]);
+            if (std::isfinite(res))
+            {
+                if (boost::math::epsilon_difference(res, h_out[i]) > 300)
+                {
+                    std::cout << "error at line: " << i
+                            << "\nParallel: " << h_out[i]
+                            << "\n  Serial: " << res
+                            << "\n    Dist: " << boost::math::epsilon_difference(res, h_out[i]) << std::endl;
+                }
+            }
+        }
+
+        cudaFree(d_in1);
+        cudaFree(d_in2);
+        cudaFree(d_out);
+        delete[] h_in1;
+        delete[] h_in2;
+        delete[] h_out;
+
+        nvrtcDestroyProgram(&prog);
+        delete[] ptx;
+
+        cuCtxDestroy(context);
+
+        std::cout << "Kernel executed successfully." << std::endl;
+        return 0;
+    }
+    catch(const std::exception& e)
+    {
+        std::cerr << "Stopped with exception: " << e.what() << std::endl;
+        return EXIT_FAILURE;
+    }
+}
diff --git a/test/test_sin_pi_nvrtc_float.cpp b/test/test_sin_pi_nvrtc_float.cpp
new file mode 100644
index 000000000..32cc38059
--- /dev/null
+++ b/test/test_sin_pi_nvrtc_float.cpp
@@ -0,0 +1,186 @@
+//  Copyright John Maddock 2016.
+//  Copyright Matt Borland 2024.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+#define BOOST_MATH_PROMOTE_DOUBLE_POLICY false
+
+#include <iostream>
+#include <iomanip>
+#include <vector>
+#include <random>
+#include <exception>
+#include <boost/math/special_functions/sin_pi.hpp>
+#include <boost/math/special_functions/relative_difference.hpp>
+#include <cuda.h>
+#include <cuda_runtime.h>
+#include <nvrtc.h>
+
+typedef float float_type;
+
+const char* cuda_kernel = R"(
+typedef double float_type;
+#include <boost/math/special_functions/sin_pi.hpp>
+extern "C" __global__ 
+void test_sin_pi_kernel(const float_type *in1, const float_type*, float_type *out, int numElements)
+{
+    int i = blockDim.x * blockIdx.x + threadIdx.x;
+    if (i < numElements)
+    {
+        out[i] = boost::math::sin_pi(in1[i]);
+    }
+}
+)";
+
+void checkCUDAError(cudaError_t result, const char* msg)
+{
+    if (result != cudaSuccess)
+    {
+        std::cerr << msg << ": " << cudaGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkCUError(CUresult result, const char* msg)
+{
+    if (result != CUDA_SUCCESS)
+    {
+        const char* errorStr;
+        cuGetErrorString(result, &errorStr);
+        std::cerr << msg << ": " << errorStr << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkNVRTCError(nvrtcResult result, const char* msg)
+{
+    if (result != NVRTC_SUCCESS)
+    {
+        std::cerr << msg << ": " << nvrtcGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+int main() 
+{
+    try
+    {
+        // Initialize CUDA driver API
+        checkCUError(cuInit(0), "Failed to initialize CUDA");
+
+        // Create CUDA context
+        CUcontext context;
+        CUdevice device;
+        checkCUError(cuDeviceGet(&device, 0), "Failed to get CUDA device");
+        checkCUError(cuCtxCreate(&context, 0, device), "Failed to create CUDA context");
+
+        nvrtcProgram prog;
+        nvrtcResult res;
+
+        res = nvrtcCreateProgram(&prog, cuda_kernel, "test_sin_pi_kernel.cu", 0, nullptr, nullptr);
+        checkNVRTCError(res, "Failed to create NVRTC program");
+
+        nvrtcAddNameExpression(prog, "test_sin_pi_kernel");
+
+        #ifdef BOOST_MATH_NVRTC_CI_RUN
+        const char* opts[] = {"--std=c++14", "--gpu-architecture=compute_75", "--include-path=/home/runner/work/cuda-math/boost-root/libs/cuda-math/include/"};
+        #else
+        const char* opts[] = {"--std=c++14", "--include-path=/home/mborland/Documents/boost/libs/cuda-math/include/"};
+        #endif
+
+        // Compile the program
+        res = nvrtcCompileProgram(prog, sizeof(opts) / sizeof(const char*), opts);
+        if (res != NVRTC_SUCCESS) 
+        {
+            size_t log_size;
+            nvrtcGetProgramLogSize(prog, &log_size);
+            char* log = new char[log_size];
+            nvrtcGetProgramLog(prog, log);
+            std::cerr << "Compilation failed:\n" << log << std::endl;
+            delete[] log;
+            exit(EXIT_FAILURE);
+        }
+
+        // Get PTX from the program
+        size_t ptx_size;
+        nvrtcGetPTXSize(prog, &ptx_size);
+        char* ptx = new char[ptx_size];
+        nvrtcGetPTX(prog, ptx);
+
+        // Load PTX into CUDA module
+        CUmodule module;
+        CUfunction kernel;
+        checkCUError(cuModuleLoadDataEx(&module, ptx, 0, 0, 0), "Failed to load module");
+        checkCUError(cuModuleGetFunction(&kernel, module, "test_sin_pi_kernel"), "Failed to get kernel function");
+
+        int numElements = 5000;
+        float_type *h_in1, *h_in2, *h_out;
+        float_type *d_in1, *d_in2, *d_out;
+
+        // Allocate memory on the host
+        h_in1 = new float_type[numElements];
+        h_in2 = new float_type[numElements];
+        h_out = new float_type[numElements];
+
+        // Initialize input arrays
+        std::mt19937_64 rng(42);
+        std::uniform_real_distribution<float_type> dist(0.0f, 1.0f);
+        for (int i = 0; i < numElements; ++i) 
+        {
+            h_in1[i] = static_cast<float_type>(dist(rng));
+            h_in2[i] = static_cast<float_type>(dist(rng));
+        }
+
+        checkCUDAError(cudaMalloc(&d_in1, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in1");
+        checkCUDAError(cudaMalloc(&d_in2, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in2");
+        checkCUDAError(cudaMalloc(&d_out, numElements * sizeof(float_type)), "Failed to allocate device memory for d_out");
+
+        checkCUDAError(cudaMemcpy(d_in1, h_in1, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in1");
+        checkCUDAError(cudaMemcpy(d_in2, h_in2, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in2");
+
+        int blockSize = 256;
+        int numBlocks = (numElements + blockSize - 1) / blockSize;
+        void* args[] = { &d_in1, &d_in2, &d_out, &numElements };
+        checkCUError(cuLaunchKernel(kernel, numBlocks, 1, 1, blockSize, 1, 1, 0, 0, args, 0), "Kernel launch failed");
+
+        checkCUDAError(cudaMemcpy(h_out, d_out, numElements * sizeof(float_type), cudaMemcpyDeviceToHost), "Failed to copy data back to host for h_out");
+
+        // Verify Result
+        for (int i = 0; i < numElements; ++i) 
+        {
+            auto res = boost::math::sin_pi(h_in1[i]);
+            if (std::isfinite(res))
+            {
+                if (boost::math::epsilon_difference(res, h_out[i]) > 300)
+                {
+                    std::cout << "error at line: " << i
+                            << "\nParallel: " << h_out[i]
+                            << "\n  Serial: " << res
+                            << "\n    Dist: " << boost::math::epsilon_difference(res, h_out[i]) << std::endl;
+                }
+            }
+        }
+
+        cudaFree(d_in1);
+        cudaFree(d_in2);
+        cudaFree(d_out);
+        delete[] h_in1;
+        delete[] h_in2;
+        delete[] h_out;
+
+        nvrtcDestroyProgram(&prog);
+        delete[] ptx;
+
+        cuCtxDestroy(context);
+
+        std::cout << "Kernel executed successfully." << std::endl;
+        return 0;
+    }
+    catch(const std::exception& e)
+    {
+        std::cerr << "Stopped with exception: " << e.what() << std::endl;
+        return EXIT_FAILURE;
+    }
+}

From c9b230422c2b0d3dec4af4765cf853605d6a594d Mon Sep 17 00:00:00 2001
From: Matt Borland <matt@mattborland.com>
Date: Tue, 13 Aug 2024 11:38:14 -0400
Subject: [PATCH 05/24] Add NVRTC support to erf and erfc

---
 include/boost/math/special_functions/erf.hpp | 63 +++++++++++++++++++-
 1 file changed, 62 insertions(+), 1 deletion(-)

diff --git a/include/boost/math/special_functions/erf.hpp b/include/boost/math/special_functions/erf.hpp
index 0b311c464..d56fc58dc 100644
--- a/include/boost/math/special_functions/erf.hpp
+++ b/include/boost/math/special_functions/erf.hpp
@@ -11,8 +11,11 @@
 #pragma once
 #endif
 
-#include <boost/math/special_functions/math_fwd.hpp>
 #include <boost/math/tools/config.hpp>
+
+#ifndef BOOST_MATH_HAS_NVRTC
+
+#include <boost/math/special_functions/math_fwd.hpp>
 #include <boost/math/special_functions/gamma.hpp>
 #include <boost/math/tools/roots.hpp>
 #include <boost/math/policies/error_handling.hpp>
@@ -1273,6 +1276,64 @@ BOOST_MATH_GPU_ENABLED inline typename tools::promote_args<T>::type erfc(T z)
 } // namespace math
 } // namespace boost
 
+#else // Special handling for NVRTC platform
+
+namespace boost {
+namespace math {
+
+template <typename T>
+BOOST_MATH_GPU_ENABLED auto erf(T x)
+{
+   return ::erf(x);
+}
+
+template <>
+BOOST_MATH_GPU_ENABLED auto erf(float x)
+{
+   return ::erff(x);
+}
+
+template <typename T, typename Policy>
+BOOST_MATH_GPU_ENABLED auto erf(T x, const Policy&)
+{
+   return ::erf(x);
+}
+
+template <typename Policy>
+BOOST_MATH_GPU_ENABLED auto erf(float x, const Policy&)
+{
+   return ::erff(x);
+}
+
+template <typename T>
+BOOST_MATH_GPU_ENABLED auto erfc(T x)
+{
+   return ::erfc(x);
+}
+
+template <>
+BOOST_MATH_GPU_ENABLED auto erfc(float x)
+{
+   return ::erfcf(x);
+}
+
+template <typename T, typename Policy>
+BOOST_MATH_GPU_ENABLED auto erfc(T x, const Policy&)
+{
+   return ::erfc(x);
+}
+
+template <typename Policy>
+BOOST_MATH_GPU_ENABLED auto erfc(float x, const Policy&)
+{
+   return ::erfcf(x);
+}
+
+} // namespace math
+} // namespace boost
+
+#endif // BOOST_MATH_HAS_NVRTC
+
 #include <boost/math/special_functions/detail/erf_inv.hpp>
 
 #endif // BOOST_MATH_SPECIAL_ERF_HPP

From 781f6604ea85811a9ed1f9c63a6fdcb19a16e4dc Mon Sep 17 00:00:00 2001
From: Matt Borland <matt@mattborland.com>
Date: Tue, 13 Aug 2024 11:38:27 -0400
Subject: [PATCH 06/24] Add erf NVRTC testing

---
 test/nvrtc_jamfile             |   2 +
 test/test_erf_nvrtc_double.cpp | 186 +++++++++++++++++++++++++++++++++
 test/test_erf_nvrtc_float.cpp  | 186 +++++++++++++++++++++++++++++++++
 3 files changed, 374 insertions(+)
 create mode 100644 test/test_erf_nvrtc_double.cpp
 create mode 100644 test/test_erf_nvrtc_float.cpp

diff --git a/test/nvrtc_jamfile b/test/nvrtc_jamfile
index 9eebb3df5..5b19c4bd2 100644
--- a/test/nvrtc_jamfile
+++ b/test/nvrtc_jamfile
@@ -14,6 +14,8 @@ run test_cbrt_nvrtc_double.cpp ;
 run test_cbrt_nvrtc_float.cpp ;
 run test_cos_pi_nvrtc_double.cpp ;
 run test_cos_pi_nvrtc_float.cpp ;
+run test_erf_nvrtc_double.cpp ;
+run test_erf_nvrtc_float.cpp ;
 run test_expm1_nvrtc_double.cpp ;
 run test_expm1_nvrtc_float.cpp ;
 run test_fpclassify_nvrtc_double.cpp ;
diff --git a/test/test_erf_nvrtc_double.cpp b/test/test_erf_nvrtc_double.cpp
new file mode 100644
index 000000000..e20d0188d
--- /dev/null
+++ b/test/test_erf_nvrtc_double.cpp
@@ -0,0 +1,186 @@
+//  Copyright John Maddock 2016.
+//  Copyright Matt Borland 2024.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+#define BOOST_MATH_PROMOTE_DOUBLE_POLICY false
+
+#include <iostream>
+#include <iomanip>
+#include <vector>
+#include <random>
+#include <exception>
+#include <boost/math/special_functions/erf.hpp>
+#include <boost/math/special_functions/relative_difference.hpp>
+#include <cuda.h>
+#include <cuda_runtime.h>
+#include <nvrtc.h>
+
+typedef double float_type;
+
+const char* cuda_kernel = R"(
+typedef double float_type;
+#include <boost/math/special_functions/erf.hpp>
+extern "C" __global__ 
+void test_erf_kernel(const float_type *in1, const float_type*, float_type *out, int numElements)
+{
+    int i = blockDim.x * blockIdx.x + threadIdx.x;
+    if (i < numElements)
+    {
+        out[i] = boost::math::erf(in1[i]);
+    }
+}
+)";
+
+void checkCUDAError(cudaError_t result, const char* msg)
+{
+    if (result != cudaSuccess)
+    {
+        std::cerr << msg << ": " << cudaGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkCUError(CUresult result, const char* msg)
+{
+    if (result != CUDA_SUCCESS)
+    {
+        const char* errorStr;
+        cuGetErrorString(result, &errorStr);
+        std::cerr << msg << ": " << errorStr << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkNVRTCError(nvrtcResult result, const char* msg)
+{
+    if (result != NVRTC_SUCCESS)
+    {
+        std::cerr << msg << ": " << nvrtcGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+int main() 
+{
+    try
+    {
+        // Initialize CUDA driver API
+        checkCUError(cuInit(0), "Failed to initialize CUDA");
+
+        // Create CUDA context
+        CUcontext context;
+        CUdevice device;
+        checkCUError(cuDeviceGet(&device, 0), "Failed to get CUDA device");
+        checkCUError(cuCtxCreate(&context, 0, device), "Failed to create CUDA context");
+
+        nvrtcProgram prog;
+        nvrtcResult res;
+
+        res = nvrtcCreateProgram(&prog, cuda_kernel, "test_erf_kernel.cu", 0, nullptr, nullptr);
+        checkNVRTCError(res, "Failed to create NVRTC program");
+
+        nvrtcAddNameExpression(prog, "test_erf_kernel");
+
+        #ifdef BOOST_MATH_NVRTC_CI_RUN
+        const char* opts[] = {"--std=c++14", "--gpu-architecture=compute_75", "--include-path=/home/runner/work/cuda-math/boost-root/libs/cuda-math/include/"};
+        #else
+        const char* opts[] = {"--std=c++14", "--include-path=/home/mborland/Documents/boost/libs/cuda-math/include/"};
+        #endif
+
+        // Compile the program
+        res = nvrtcCompileProgram(prog, sizeof(opts) / sizeof(const char*), opts);
+        if (res != NVRTC_SUCCESS) 
+        {
+            size_t log_size;
+            nvrtcGetProgramLogSize(prog, &log_size);
+            char* log = new char[log_size];
+            nvrtcGetProgramLog(prog, log);
+            std::cerr << "Compilation failed:\n" << log << std::endl;
+            delete[] log;
+            exit(EXIT_FAILURE);
+        }
+
+        // Get PTX from the program
+        size_t ptx_size;
+        nvrtcGetPTXSize(prog, &ptx_size);
+        char* ptx = new char[ptx_size];
+        nvrtcGetPTX(prog, ptx);
+
+        // Load PTX into CUDA module
+        CUmodule module;
+        CUfunction kernel;
+        checkCUError(cuModuleLoadDataEx(&module, ptx, 0, 0, 0), "Failed to load module");
+        checkCUError(cuModuleGetFunction(&kernel, module, "test_erf_kernel"), "Failed to get kernel function");
+
+        int numElements = 5000;
+        float_type *h_in1, *h_in2, *h_out;
+        float_type *d_in1, *d_in2, *d_out;
+
+        // Allocate memory on the host
+        h_in1 = new float_type[numElements];
+        h_in2 = new float_type[numElements];
+        h_out = new float_type[numElements];
+
+        // Initialize input arrays
+        std::mt19937_64 rng(42);
+        std::uniform_real_distribution<float_type> dist(0.0f, 1.0f);
+        for (int i = 0; i < numElements; ++i) 
+        {
+            h_in1[i] = static_cast<float_type>(dist(rng));
+            h_in2[i] = static_cast<float_type>(dist(rng));
+        }
+
+        checkCUDAError(cudaMalloc(&d_in1, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in1");
+        checkCUDAError(cudaMalloc(&d_in2, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in2");
+        checkCUDAError(cudaMalloc(&d_out, numElements * sizeof(float_type)), "Failed to allocate device memory for d_out");
+
+        checkCUDAError(cudaMemcpy(d_in1, h_in1, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in1");
+        checkCUDAError(cudaMemcpy(d_in2, h_in2, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in2");
+
+        int blockSize = 256;
+        int numBlocks = (numElements + blockSize - 1) / blockSize;
+        void* args[] = { &d_in1, &d_in2, &d_out, &numElements };
+        checkCUError(cuLaunchKernel(kernel, numBlocks, 1, 1, blockSize, 1, 1, 0, 0, args, 0), "Kernel launch failed");
+
+        checkCUDAError(cudaMemcpy(h_out, d_out, numElements * sizeof(float_type), cudaMemcpyDeviceToHost), "Failed to copy data back to host for h_out");
+
+        // Verify Result
+        for (int i = 0; i < numElements; ++i) 
+        {
+            auto res = boost::math::erf(h_in1[i]);
+            if (std::isfinite(res))
+            {
+                if (boost::math::epsilon_difference(res, h_out[i]) > 300)
+                {
+                    std::cout << "error at line: " << i
+                            << "\nParallel: " << h_out[i]
+                            << "\n  Serial: " << res
+                            << "\n    Dist: " << boost::math::epsilon_difference(res, h_out[i]) << std::endl;
+                }
+            }
+        }
+
+        cudaFree(d_in1);
+        cudaFree(d_in2);
+        cudaFree(d_out);
+        delete[] h_in1;
+        delete[] h_in2;
+        delete[] h_out;
+
+        nvrtcDestroyProgram(&prog);
+        delete[] ptx;
+
+        cuCtxDestroy(context);
+
+        std::cout << "Kernel executed successfully." << std::endl;
+        return 0;
+    }
+    catch(const std::exception& e)
+    {
+        std::cerr << "Stopped with exception: " << e.what() << std::endl;
+        return EXIT_FAILURE;
+    }
+}
diff --git a/test/test_erf_nvrtc_float.cpp b/test/test_erf_nvrtc_float.cpp
new file mode 100644
index 000000000..913b1a14c
--- /dev/null
+++ b/test/test_erf_nvrtc_float.cpp
@@ -0,0 +1,186 @@
+//  Copyright John Maddock 2016.
+//  Copyright Matt Borland 2024.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+#define BOOST_MATH_PROMOTE_DOUBLE_POLICY false
+
+#include <iostream>
+#include <iomanip>
+#include <vector>
+#include <random>
+#include <exception>
+#include <boost/math/special_functions/erf.hpp>
+#include <boost/math/special_functions/relative_difference.hpp>
+#include <cuda.h>
+#include <cuda_runtime.h>
+#include <nvrtc.h>
+
+typedef float float_type;
+
+const char* cuda_kernel = R"(
+typedef double float_type;
+#include <boost/math/special_functions/erf.hpp>
+extern "C" __global__ 
+void test_erf_kernel(const float_type *in1, const float_type*, float_type *out, int numElements)
+{
+    int i = blockDim.x * blockIdx.x + threadIdx.x;
+    if (i < numElements)
+    {
+        out[i] = boost::math::erf(in1[i]);
+    }
+}
+)";
+
+void checkCUDAError(cudaError_t result, const char* msg)
+{
+    if (result != cudaSuccess)
+    {
+        std::cerr << msg << ": " << cudaGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkCUError(CUresult result, const char* msg)
+{
+    if (result != CUDA_SUCCESS)
+    {
+        const char* errorStr;
+        cuGetErrorString(result, &errorStr);
+        std::cerr << msg << ": " << errorStr << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkNVRTCError(nvrtcResult result, const char* msg)
+{
+    if (result != NVRTC_SUCCESS)
+    {
+        std::cerr << msg << ": " << nvrtcGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+int main() 
+{
+    try
+    {
+        // Initialize CUDA driver API
+        checkCUError(cuInit(0), "Failed to initialize CUDA");
+
+        // Create CUDA context
+        CUcontext context;
+        CUdevice device;
+        checkCUError(cuDeviceGet(&device, 0), "Failed to get CUDA device");
+        checkCUError(cuCtxCreate(&context, 0, device), "Failed to create CUDA context");
+
+        nvrtcProgram prog;
+        nvrtcResult res;
+
+        res = nvrtcCreateProgram(&prog, cuda_kernel, "test_erf_kernel.cu", 0, nullptr, nullptr);
+        checkNVRTCError(res, "Failed to create NVRTC program");
+
+        nvrtcAddNameExpression(prog, "test_erf_kernel");
+
+        #ifdef BOOST_MATH_NVRTC_CI_RUN
+        const char* opts[] = {"--std=c++14", "--gpu-architecture=compute_75", "--include-path=/home/runner/work/cuda-math/boost-root/libs/cuda-math/include/"};
+        #else
+        const char* opts[] = {"--std=c++14", "--include-path=/home/mborland/Documents/boost/libs/cuda-math/include/"};
+        #endif
+
+        // Compile the program
+        res = nvrtcCompileProgram(prog, sizeof(opts) / sizeof(const char*), opts);
+        if (res != NVRTC_SUCCESS) 
+        {
+            size_t log_size;
+            nvrtcGetProgramLogSize(prog, &log_size);
+            char* log = new char[log_size];
+            nvrtcGetProgramLog(prog, log);
+            std::cerr << "Compilation failed:\n" << log << std::endl;
+            delete[] log;
+            exit(EXIT_FAILURE);
+        }
+
+        // Get PTX from the program
+        size_t ptx_size;
+        nvrtcGetPTXSize(prog, &ptx_size);
+        char* ptx = new char[ptx_size];
+        nvrtcGetPTX(prog, ptx);
+
+        // Load PTX into CUDA module
+        CUmodule module;
+        CUfunction kernel;
+        checkCUError(cuModuleLoadDataEx(&module, ptx, 0, 0, 0), "Failed to load module");
+        checkCUError(cuModuleGetFunction(&kernel, module, "test_erf_kernel"), "Failed to get kernel function");
+
+        int numElements = 5000;
+        float_type *h_in1, *h_in2, *h_out;
+        float_type *d_in1, *d_in2, *d_out;
+
+        // Allocate memory on the host
+        h_in1 = new float_type[numElements];
+        h_in2 = new float_type[numElements];
+        h_out = new float_type[numElements];
+
+        // Initialize input arrays
+        std::mt19937_64 rng(42);
+        std::uniform_real_distribution<float_type> dist(0.0f, 1.0f);
+        for (int i = 0; i < numElements; ++i) 
+        {
+            h_in1[i] = static_cast<float_type>(dist(rng));
+            h_in2[i] = static_cast<float_type>(dist(rng));
+        }
+
+        checkCUDAError(cudaMalloc(&d_in1, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in1");
+        checkCUDAError(cudaMalloc(&d_in2, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in2");
+        checkCUDAError(cudaMalloc(&d_out, numElements * sizeof(float_type)), "Failed to allocate device memory for d_out");
+
+        checkCUDAError(cudaMemcpy(d_in1, h_in1, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in1");
+        checkCUDAError(cudaMemcpy(d_in2, h_in2, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in2");
+
+        int blockSize = 256;
+        int numBlocks = (numElements + blockSize - 1) / blockSize;
+        void* args[] = { &d_in1, &d_in2, &d_out, &numElements };
+        checkCUError(cuLaunchKernel(kernel, numBlocks, 1, 1, blockSize, 1, 1, 0, 0, args, 0), "Kernel launch failed");
+
+        checkCUDAError(cudaMemcpy(h_out, d_out, numElements * sizeof(float_type), cudaMemcpyDeviceToHost), "Failed to copy data back to host for h_out");
+
+        // Verify Result
+        for (int i = 0; i < numElements; ++i) 
+        {
+            auto res = boost::math::erf(h_in1[i]);
+            if (std::isfinite(res))
+            {
+                if (boost::math::epsilon_difference(res, h_out[i]) > 300)
+                {
+                    std::cout << "error at line: " << i
+                            << "\nParallel: " << h_out[i]
+                            << "\n  Serial: " << res
+                            << "\n    Dist: " << boost::math::epsilon_difference(res, h_out[i]) << std::endl;
+                }
+            }
+        }
+
+        cudaFree(d_in1);
+        cudaFree(d_in2);
+        cudaFree(d_out);
+        delete[] h_in1;
+        delete[] h_in2;
+        delete[] h_out;
+
+        nvrtcDestroyProgram(&prog);
+        delete[] ptx;
+
+        cuCtxDestroy(context);
+
+        std::cout << "Kernel executed successfully." << std::endl;
+        return 0;
+    }
+    catch(const std::exception& e)
+    {
+        std::cerr << "Stopped with exception: " << e.what() << std::endl;
+        return EXIT_FAILURE;
+    }
+}

From abd0618942f5c77e35b9605f338e46a3d6530a2b Mon Sep 17 00:00:00 2001
From: Matt Borland <matt@mattborland.com>
Date: Tue, 13 Aug 2024 11:40:23 -0400
Subject: [PATCH 07/24] Add erfc NVRTC testing

---
 test/nvrtc_jamfile              |   2 +
 test/test_erfc_nvrtc_double.cpp | 186 ++++++++++++++++++++++++++++++++
 test/test_erfc_nvrtc_float.cpp  | 186 ++++++++++++++++++++++++++++++++
 3 files changed, 374 insertions(+)
 create mode 100644 test/test_erfc_nvrtc_double.cpp
 create mode 100644 test/test_erfc_nvrtc_float.cpp

diff --git a/test/nvrtc_jamfile b/test/nvrtc_jamfile
index 5b19c4bd2..fa04990e5 100644
--- a/test/nvrtc_jamfile
+++ b/test/nvrtc_jamfile
@@ -16,6 +16,8 @@ run test_cos_pi_nvrtc_double.cpp ;
 run test_cos_pi_nvrtc_float.cpp ;
 run test_erf_nvrtc_double.cpp ;
 run test_erf_nvrtc_float.cpp ;
+run test_erfc_nvrtc_double.cpp ;
+run test_erfc_nvrtc_float.cpp ;
 run test_expm1_nvrtc_double.cpp ;
 run test_expm1_nvrtc_float.cpp ;
 run test_fpclassify_nvrtc_double.cpp ;
diff --git a/test/test_erfc_nvrtc_double.cpp b/test/test_erfc_nvrtc_double.cpp
new file mode 100644
index 000000000..c43a469ac
--- /dev/null
+++ b/test/test_erfc_nvrtc_double.cpp
@@ -0,0 +1,186 @@
+//  Copyright John Maddock 2016.
+//  Copyright Matt Borland 2024.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+#define BOOST_MATH_PROMOTE_DOUBLE_POLICY false
+
+#include <iostream>
+#include <iomanip>
+#include <vector>
+#include <random>
+#include <exception>
+#include <boost/math/special_functions/erf.hpp>
+#include <boost/math/special_functions/relative_difference.hpp>
+#include <cuda.h>
+#include <cuda_runtime.h>
+#include <nvrtc.h>
+
+typedef double float_type;
+
+const char* cuda_kernel = R"(
+typedef double float_type;
+#include <boost/math/special_functions/erf.hpp>
+extern "C" __global__ 
+void test_erf_kernel(const float_type *in1, const float_type*, float_type *out, int numElements)
+{
+    int i = blockDim.x * blockIdx.x + threadIdx.x;
+    if (i < numElements)
+    {
+        out[i] = boost::math::erfc(in1[i]);
+    }
+}
+)";
+
+void checkCUDAError(cudaError_t result, const char* msg)
+{
+    if (result != cudaSuccess)
+    {
+        std::cerr << msg << ": " << cudaGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkCUError(CUresult result, const char* msg)
+{
+    if (result != CUDA_SUCCESS)
+    {
+        const char* errorStr;
+        cuGetErrorString(result, &errorStr);
+        std::cerr << msg << ": " << errorStr << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkNVRTCError(nvrtcResult result, const char* msg)
+{
+    if (result != NVRTC_SUCCESS)
+    {
+        std::cerr << msg << ": " << nvrtcGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+int main() 
+{
+    try
+    {
+        // Initialize CUDA driver API
+        checkCUError(cuInit(0), "Failed to initialize CUDA");
+
+        // Create CUDA context
+        CUcontext context;
+        CUdevice device;
+        checkCUError(cuDeviceGet(&device, 0), "Failed to get CUDA device");
+        checkCUError(cuCtxCreate(&context, 0, device), "Failed to create CUDA context");
+
+        nvrtcProgram prog;
+        nvrtcResult res;
+
+        res = nvrtcCreateProgram(&prog, cuda_kernel, "test_erf_kernel.cu", 0, nullptr, nullptr);
+        checkNVRTCError(res, "Failed to create NVRTC program");
+
+        nvrtcAddNameExpression(prog, "test_erf_kernel");
+
+        #ifdef BOOST_MATH_NVRTC_CI_RUN
+        const char* opts[] = {"--std=c++14", "--gpu-architecture=compute_75", "--include-path=/home/runner/work/cuda-math/boost-root/libs/cuda-math/include/"};
+        #else
+        const char* opts[] = {"--std=c++14", "--include-path=/home/mborland/Documents/boost/libs/cuda-math/include/"};
+        #endif
+
+        // Compile the program
+        res = nvrtcCompileProgram(prog, sizeof(opts) / sizeof(const char*), opts);
+        if (res != NVRTC_SUCCESS) 
+        {
+            size_t log_size;
+            nvrtcGetProgramLogSize(prog, &log_size);
+            char* log = new char[log_size];
+            nvrtcGetProgramLog(prog, log);
+            std::cerr << "Compilation failed:\n" << log << std::endl;
+            delete[] log;
+            exit(EXIT_FAILURE);
+        }
+
+        // Get PTX from the program
+        size_t ptx_size;
+        nvrtcGetPTXSize(prog, &ptx_size);
+        char* ptx = new char[ptx_size];
+        nvrtcGetPTX(prog, ptx);
+
+        // Load PTX into CUDA module
+        CUmodule module;
+        CUfunction kernel;
+        checkCUError(cuModuleLoadDataEx(&module, ptx, 0, 0, 0), "Failed to load module");
+        checkCUError(cuModuleGetFunction(&kernel, module, "test_erf_kernel"), "Failed to get kernel function");
+
+        int numElements = 5000;
+        float_type *h_in1, *h_in2, *h_out;
+        float_type *d_in1, *d_in2, *d_out;
+
+        // Allocate memory on the host
+        h_in1 = new float_type[numElements];
+        h_in2 = new float_type[numElements];
+        h_out = new float_type[numElements];
+
+        // Initialize input arrays
+        std::mt19937_64 rng(42);
+        std::uniform_real_distribution<float_type> dist(0.0f, 1.0f);
+        for (int i = 0; i < numElements; ++i) 
+        {
+            h_in1[i] = static_cast<float_type>(dist(rng));
+            h_in2[i] = static_cast<float_type>(dist(rng));
+        }
+
+        checkCUDAError(cudaMalloc(&d_in1, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in1");
+        checkCUDAError(cudaMalloc(&d_in2, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in2");
+        checkCUDAError(cudaMalloc(&d_out, numElements * sizeof(float_type)), "Failed to allocate device memory for d_out");
+
+        checkCUDAError(cudaMemcpy(d_in1, h_in1, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in1");
+        checkCUDAError(cudaMemcpy(d_in2, h_in2, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in2");
+
+        int blockSize = 256;
+        int numBlocks = (numElements + blockSize - 1) / blockSize;
+        void* args[] = { &d_in1, &d_in2, &d_out, &numElements };
+        checkCUError(cuLaunchKernel(kernel, numBlocks, 1, 1, blockSize, 1, 1, 0, 0, args, 0), "Kernel launch failed");
+
+        checkCUDAError(cudaMemcpy(h_out, d_out, numElements * sizeof(float_type), cudaMemcpyDeviceToHost), "Failed to copy data back to host for h_out");
+
+        // Verify Result
+        for (int i = 0; i < numElements; ++i) 
+        {
+            auto res = boost::math::erfc(h_in1[i]);
+            if (std::isfinite(res))
+            {
+                if (boost::math::epsilon_difference(res, h_out[i]) > 300)
+                {
+                    std::cout << "error at line: " << i
+                            << "\nParallel: " << h_out[i]
+                            << "\n  Serial: " << res
+                            << "\n    Dist: " << boost::math::epsilon_difference(res, h_out[i]) << std::endl;
+                }
+            }
+        }
+
+        cudaFree(d_in1);
+        cudaFree(d_in2);
+        cudaFree(d_out);
+        delete[] h_in1;
+        delete[] h_in2;
+        delete[] h_out;
+
+        nvrtcDestroyProgram(&prog);
+        delete[] ptx;
+
+        cuCtxDestroy(context);
+
+        std::cout << "Kernel executed successfully." << std::endl;
+        return 0;
+    }
+    catch(const std::exception& e)
+    {
+        std::cerr << "Stopped with exception: " << e.what() << std::endl;
+        return EXIT_FAILURE;
+    }
+}
diff --git a/test/test_erfc_nvrtc_float.cpp b/test/test_erfc_nvrtc_float.cpp
new file mode 100644
index 000000000..f8756045a
--- /dev/null
+++ b/test/test_erfc_nvrtc_float.cpp
@@ -0,0 +1,186 @@
+//  Copyright John Maddock 2016.
+//  Copyright Matt Borland 2024.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+#define BOOST_MATH_PROMOTE_DOUBLE_POLICY false
+
+#include <iostream>
+#include <iomanip>
+#include <vector>
+#include <random>
+#include <exception>
+#include <boost/math/special_functions/erf.hpp>
+#include <boost/math/special_functions/relative_difference.hpp>
+#include <cuda.h>
+#include <cuda_runtime.h>
+#include <nvrtc.h>
+
+typedef float float_type;
+
+const char* cuda_kernel = R"(
+typedef float float_type;
+#include <boost/math/special_functions/erf.hpp>
+extern "C" __global__ 
+void test_erf_kernel(const float_type *in1, const float_type*, float_type *out, int numElements)
+{
+    int i = blockDim.x * blockIdx.x + threadIdx.x;
+    if (i < numElements)
+    {
+        out[i] = boost::math::erfc(in1[i]);
+    }
+}
+)";
+
+void checkCUDAError(cudaError_t result, const char* msg)
+{
+    if (result != cudaSuccess)
+    {
+        std::cerr << msg << ": " << cudaGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkCUError(CUresult result, const char* msg)
+{
+    if (result != CUDA_SUCCESS)
+    {
+        const char* errorStr;
+        cuGetErrorString(result, &errorStr);
+        std::cerr << msg << ": " << errorStr << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkNVRTCError(nvrtcResult result, const char* msg)
+{
+    if (result != NVRTC_SUCCESS)
+    {
+        std::cerr << msg << ": " << nvrtcGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+int main() 
+{
+    try
+    {
+        // Initialize CUDA driver API
+        checkCUError(cuInit(0), "Failed to initialize CUDA");
+
+        // Create CUDA context
+        CUcontext context;
+        CUdevice device;
+        checkCUError(cuDeviceGet(&device, 0), "Failed to get CUDA device");
+        checkCUError(cuCtxCreate(&context, 0, device), "Failed to create CUDA context");
+
+        nvrtcProgram prog;
+        nvrtcResult res;
+
+        res = nvrtcCreateProgram(&prog, cuda_kernel, "test_erf_kernel.cu", 0, nullptr, nullptr);
+        checkNVRTCError(res, "Failed to create NVRTC program");
+
+        nvrtcAddNameExpression(prog, "test_erf_kernel");
+
+        #ifdef BOOST_MATH_NVRTC_CI_RUN
+        const char* opts[] = {"--std=c++14", "--gpu-architecture=compute_75", "--include-path=/home/runner/work/cuda-math/boost-root/libs/cuda-math/include/"};
+        #else
+        const char* opts[] = {"--std=c++14", "--include-path=/home/mborland/Documents/boost/libs/cuda-math/include/"};
+        #endif
+
+        // Compile the program
+        res = nvrtcCompileProgram(prog, sizeof(opts) / sizeof(const char*), opts);
+        if (res != NVRTC_SUCCESS) 
+        {
+            size_t log_size;
+            nvrtcGetProgramLogSize(prog, &log_size);
+            char* log = new char[log_size];
+            nvrtcGetProgramLog(prog, log);
+            std::cerr << "Compilation failed:\n" << log << std::endl;
+            delete[] log;
+            exit(EXIT_FAILURE);
+        }
+
+        // Get PTX from the program
+        size_t ptx_size;
+        nvrtcGetPTXSize(prog, &ptx_size);
+        char* ptx = new char[ptx_size];
+        nvrtcGetPTX(prog, ptx);
+
+        // Load PTX into CUDA module
+        CUmodule module;
+        CUfunction kernel;
+        checkCUError(cuModuleLoadDataEx(&module, ptx, 0, 0, 0), "Failed to load module");
+        checkCUError(cuModuleGetFunction(&kernel, module, "test_erf_kernel"), "Failed to get kernel function");
+
+        int numElements = 5000;
+        float_type *h_in1, *h_in2, *h_out;
+        float_type *d_in1, *d_in2, *d_out;
+
+        // Allocate memory on the host
+        h_in1 = new float_type[numElements];
+        h_in2 = new float_type[numElements];
+        h_out = new float_type[numElements];
+
+        // Initialize input arrays
+        std::mt19937_64 rng(42);
+        std::uniform_real_distribution<float_type> dist(0.0f, 1.0f);
+        for (int i = 0; i < numElements; ++i) 
+        {
+            h_in1[i] = static_cast<float_type>(dist(rng));
+            h_in2[i] = static_cast<float_type>(dist(rng));
+        }
+
+        checkCUDAError(cudaMalloc(&d_in1, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in1");
+        checkCUDAError(cudaMalloc(&d_in2, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in2");
+        checkCUDAError(cudaMalloc(&d_out, numElements * sizeof(float_type)), "Failed to allocate device memory for d_out");
+
+        checkCUDAError(cudaMemcpy(d_in1, h_in1, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in1");
+        checkCUDAError(cudaMemcpy(d_in2, h_in2, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in2");
+
+        int blockSize = 256;
+        int numBlocks = (numElements + blockSize - 1) / blockSize;
+        void* args[] = { &d_in1, &d_in2, &d_out, &numElements };
+        checkCUError(cuLaunchKernel(kernel, numBlocks, 1, 1, blockSize, 1, 1, 0, 0, args, 0), "Kernel launch failed");
+
+        checkCUDAError(cudaMemcpy(h_out, d_out, numElements * sizeof(float_type), cudaMemcpyDeviceToHost), "Failed to copy data back to host for h_out");
+
+        // Verify Result
+        for (int i = 0; i < numElements; ++i) 
+        {
+            auto res = boost::math::erfc(h_in1[i]);
+            if (std::isfinite(res))
+            {
+                if (boost::math::epsilon_difference(res, h_out[i]) > 300)
+                {
+                    std::cout << "error at line: " << i
+                            << "\nParallel: " << h_out[i]
+                            << "\n  Serial: " << res
+                            << "\n    Dist: " << boost::math::epsilon_difference(res, h_out[i]) << std::endl;
+                }
+            }
+        }
+
+        cudaFree(d_in1);
+        cudaFree(d_in2);
+        cudaFree(d_out);
+        delete[] h_in1;
+        delete[] h_in2;
+        delete[] h_out;
+
+        nvrtcDestroyProgram(&prog);
+        delete[] ptx;
+
+        cuCtxDestroy(context);
+
+        std::cout << "Kernel executed successfully." << std::endl;
+        return 0;
+    }
+    catch(const std::exception& e)
+    {
+        std::cerr << "Stopped with exception: " << e.what() << std::endl;
+        return EXIT_FAILURE;
+    }
+}

From cc4cf74edf17f7fc846db825e16a4cc284dbcbd5 Mon Sep 17 00:00:00 2001
From: Matt Borland <matt@mattborland.com>
Date: Tue, 13 Aug 2024 11:47:55 -0400
Subject: [PATCH 08/24] Fix types in NVRTC testing

---
 test/test_cos_pi_nvrtc_float.cpp | 2 +-
 test/test_sin_pi_nvrtc_float.cpp | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/test/test_cos_pi_nvrtc_float.cpp b/test/test_cos_pi_nvrtc_float.cpp
index 7c1eef3fa..2f541e217 100644
--- a/test/test_cos_pi_nvrtc_float.cpp
+++ b/test/test_cos_pi_nvrtc_float.cpp
@@ -21,7 +21,7 @@
 typedef float float_type;
 
 const char* cuda_kernel = R"(
-typedef double float_type;
+typedef float float_type;
 #include <boost/math/special_functions/cos_pi.hpp>
 extern "C" __global__ 
 void test_cos_pi_kernel(const float_type *in1, const float_type*, float_type *out, int numElements)
diff --git a/test/test_sin_pi_nvrtc_float.cpp b/test/test_sin_pi_nvrtc_float.cpp
index 32cc38059..f67079774 100644
--- a/test/test_sin_pi_nvrtc_float.cpp
+++ b/test/test_sin_pi_nvrtc_float.cpp
@@ -21,7 +21,7 @@
 typedef float float_type;
 
 const char* cuda_kernel = R"(
-typedef double float_type;
+typedef float float_type;
 #include <boost/math/special_functions/sin_pi.hpp>
 extern "C" __global__ 
 void test_sin_pi_kernel(const float_type *in1, const float_type*, float_type *out, int numElements)

From 4d59bbd38c02a8749a70f0dba77b57deaf39f9f8 Mon Sep 17 00:00:00 2001
From: Matt Borland <matt@mattborland.com>
Date: Tue, 13 Aug 2024 11:48:12 -0400
Subject: [PATCH 09/24] Add NVRTC support to erf_inv and erfc_inv

---
 .../math/special_functions/detail/erf_inv.hpp | 61 +++++++++++++++++++
 1 file changed, 61 insertions(+)

diff --git a/include/boost/math/special_functions/detail/erf_inv.hpp b/include/boost/math/special_functions/detail/erf_inv.hpp
index 69a08abe6..cb65cffbc 100644
--- a/include/boost/math/special_functions/detail/erf_inv.hpp
+++ b/include/boost/math/special_functions/detail/erf_inv.hpp
@@ -15,6 +15,9 @@
 #endif
 
 #include <boost/math/tools/config.hpp>
+
+#ifndef BOOST_MATH_HAS_NVRTC
+
 #include <type_traits>
 
 namespace boost{ namespace math{
@@ -490,6 +493,64 @@ BOOST_MATH_GPU_ENABLED inline typename tools::promote_args<T>::type erf_inv(T z)
 } // namespace math
 } // namespace boost
 
+#else // Special handling for NVRTC
+
+namespace boost {
+namespace math {
+
+template <typename T>
+BOOST_MATH_GPU_ENABLED auto erf_inv(T x)
+{
+   return ::erfinv(x);
+}
+
+template <>
+BOOST_MATH_GPU_ENABLED auto erf_inv(float x)
+{
+   return ::erfinvf(x);
+}
+
+template <typename T, typename Policy>
+BOOST_MATH_GPU_ENABLED auto erf_inv(T x, const Policy&)
+{
+   return ::erfinv(x);
+}
+
+template <typename Policy>
+BOOST_MATH_GPU_ENABLED auto erf_inv(float x, const Policy&)
+{
+   return ::erfinvf(x);
+}
+
+template <typename T>
+BOOST_MATH_GPU_ENABLED auto erfc_inv(T x)
+{
+   return ::erfcinv(x);
+}
+
+template <>
+BOOST_MATH_GPU_ENABLED auto erfc_inv(float x)
+{
+   return ::erfcinvf(x);
+}
+
+template <typename T, typename Policy>
+BOOST_MATH_GPU_ENABLED auto erfc_inv(T x, const Policy&)
+{
+   return ::erfcinv(x);
+}
+
+template <typename Policy>
+BOOST_MATH_GPU_ENABLED auto erfc_inv(float x, const Policy&)
+{
+   return ::erfcinvf(x);
+}
+
+} // namespace math
+} // namespace boost
+
+#endif // BOOST_MATH_HAS_NVRTV
+
 #ifdef _MSC_VER
 #pragma warning(pop)
 #endif

From 54d5ff8b8111af5a91bc956c865b10e6c6c6b3ef Mon Sep 17 00:00:00 2001
From: Matt Borland <matt@mattborland.com>
Date: Tue, 13 Aug 2024 11:48:26 -0400
Subject: [PATCH 10/24] Add erf_inv NVRTC testing

---
 test/nvrtc_jamfile                 |   2 +
 test/test_erf_inv_nvrtc_double.cpp | 186 +++++++++++++++++++++++++++++
 test/test_erf_inv_nvrtc_float.cpp  | 186 +++++++++++++++++++++++++++++
 3 files changed, 374 insertions(+)
 create mode 100644 test/test_erf_inv_nvrtc_double.cpp
 create mode 100644 test/test_erf_inv_nvrtc_float.cpp

diff --git a/test/nvrtc_jamfile b/test/nvrtc_jamfile
index fa04990e5..d36a3381d 100644
--- a/test/nvrtc_jamfile
+++ b/test/nvrtc_jamfile
@@ -18,6 +18,8 @@ run test_erf_nvrtc_double.cpp ;
 run test_erf_nvrtc_float.cpp ;
 run test_erfc_nvrtc_double.cpp ;
 run test_erfc_nvrtc_float.cpp ;
+run test_erf_inv_nvrtc_double.cpp ;
+run test_erf_inv_nvrtc_float.cpp ;
 run test_expm1_nvrtc_double.cpp ;
 run test_expm1_nvrtc_float.cpp ;
 run test_fpclassify_nvrtc_double.cpp ;
diff --git a/test/test_erf_inv_nvrtc_double.cpp b/test/test_erf_inv_nvrtc_double.cpp
new file mode 100644
index 000000000..5588b7668
--- /dev/null
+++ b/test/test_erf_inv_nvrtc_double.cpp
@@ -0,0 +1,186 @@
+//  Copyright John Maddock 2016.
+//  Copyright Matt Borland 2024.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+#define BOOST_MATH_PROMOTE_DOUBLE_POLICY false
+
+#include <iostream>
+#include <iomanip>
+#include <vector>
+#include <random>
+#include <exception>
+#include <boost/math/special_functions/erf.hpp>
+#include <boost/math/special_functions/relative_difference.hpp>
+#include <cuda.h>
+#include <cuda_runtime.h>
+#include <nvrtc.h>
+
+typedef double float_type;
+
+const char* cuda_kernel = R"(
+typedef double float_type;
+#include <boost/math/special_functions/erf.hpp>
+extern "C" __global__ 
+void test_erf_kernel(const float_type *in1, const float_type*, float_type *out, int numElements)
+{
+    int i = blockDim.x * blockIdx.x + threadIdx.x;
+    if (i < numElements)
+    {
+        out[i] = boost::math::erf_inv(in1[i]);
+    }
+}
+)";
+
+void checkCUDAError(cudaError_t result, const char* msg)
+{
+    if (result != cudaSuccess)
+    {
+        std::cerr << msg << ": " << cudaGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkCUError(CUresult result, const char* msg)
+{
+    if (result != CUDA_SUCCESS)
+    {
+        const char* errorStr;
+        cuGetErrorString(result, &errorStr);
+        std::cerr << msg << ": " << errorStr << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkNVRTCError(nvrtcResult result, const char* msg)
+{
+    if (result != NVRTC_SUCCESS)
+    {
+        std::cerr << msg << ": " << nvrtcGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+int main() 
+{
+    try
+    {
+        // Initialize CUDA driver API
+        checkCUError(cuInit(0), "Failed to initialize CUDA");
+
+        // Create CUDA context
+        CUcontext context;
+        CUdevice device;
+        checkCUError(cuDeviceGet(&device, 0), "Failed to get CUDA device");
+        checkCUError(cuCtxCreate(&context, 0, device), "Failed to create CUDA context");
+
+        nvrtcProgram prog;
+        nvrtcResult res;
+
+        res = nvrtcCreateProgram(&prog, cuda_kernel, "test_erf_kernel.cu", 0, nullptr, nullptr);
+        checkNVRTCError(res, "Failed to create NVRTC program");
+
+        nvrtcAddNameExpression(prog, "test_erf_kernel");
+
+        #ifdef BOOST_MATH_NVRTC_CI_RUN
+        const char* opts[] = {"--std=c++14", "--gpu-architecture=compute_75", "--include-path=/home/runner/work/cuda-math/boost-root/libs/cuda-math/include/"};
+        #else
+        const char* opts[] = {"--std=c++14", "--include-path=/home/mborland/Documents/boost/libs/cuda-math/include/"};
+        #endif
+
+        // Compile the program
+        res = nvrtcCompileProgram(prog, sizeof(opts) / sizeof(const char*), opts);
+        if (res != NVRTC_SUCCESS) 
+        {
+            size_t log_size;
+            nvrtcGetProgramLogSize(prog, &log_size);
+            char* log = new char[log_size];
+            nvrtcGetProgramLog(prog, log);
+            std::cerr << "Compilation failed:\n" << log << std::endl;
+            delete[] log;
+            exit(EXIT_FAILURE);
+        }
+
+        // Get PTX from the program
+        size_t ptx_size;
+        nvrtcGetPTXSize(prog, &ptx_size);
+        char* ptx = new char[ptx_size];
+        nvrtcGetPTX(prog, ptx);
+
+        // Load PTX into CUDA module
+        CUmodule module;
+        CUfunction kernel;
+        checkCUError(cuModuleLoadDataEx(&module, ptx, 0, 0, 0), "Failed to load module");
+        checkCUError(cuModuleGetFunction(&kernel, module, "test_erf_kernel"), "Failed to get kernel function");
+
+        int numElements = 5000;
+        float_type *h_in1, *h_in2, *h_out;
+        float_type *d_in1, *d_in2, *d_out;
+
+        // Allocate memory on the host
+        h_in1 = new float_type[numElements];
+        h_in2 = new float_type[numElements];
+        h_out = new float_type[numElements];
+
+        // Initialize input arrays
+        std::mt19937_64 rng(42);
+        std::uniform_real_distribution<float_type> dist(0.0f, 1.0f);
+        for (int i = 0; i < numElements; ++i) 
+        {
+            h_in1[i] = static_cast<float_type>(dist(rng));
+            h_in2[i] = static_cast<float_type>(dist(rng));
+        }
+
+        checkCUDAError(cudaMalloc(&d_in1, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in1");
+        checkCUDAError(cudaMalloc(&d_in2, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in2");
+        checkCUDAError(cudaMalloc(&d_out, numElements * sizeof(float_type)), "Failed to allocate device memory for d_out");
+
+        checkCUDAError(cudaMemcpy(d_in1, h_in1, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in1");
+        checkCUDAError(cudaMemcpy(d_in2, h_in2, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in2");
+
+        int blockSize = 256;
+        int numBlocks = (numElements + blockSize - 1) / blockSize;
+        void* args[] = { &d_in1, &d_in2, &d_out, &numElements };
+        checkCUError(cuLaunchKernel(kernel, numBlocks, 1, 1, blockSize, 1, 1, 0, 0, args, 0), "Kernel launch failed");
+
+        checkCUDAError(cudaMemcpy(h_out, d_out, numElements * sizeof(float_type), cudaMemcpyDeviceToHost), "Failed to copy data back to host for h_out");
+
+        // Verify Result
+        for (int i = 0; i < numElements; ++i) 
+        {
+            auto res = boost::math::erf_inv(h_in1[i]);
+            if (std::isfinite(res))
+            {
+                if (boost::math::epsilon_difference(res, h_out[i]) > 300)
+                {
+                    std::cout << "error at line: " << i
+                            << "\nParallel: " << h_out[i]
+                            << "\n  Serial: " << res
+                            << "\n    Dist: " << boost::math::epsilon_difference(res, h_out[i]) << std::endl;
+                }
+            }
+        }
+
+        cudaFree(d_in1);
+        cudaFree(d_in2);
+        cudaFree(d_out);
+        delete[] h_in1;
+        delete[] h_in2;
+        delete[] h_out;
+
+        nvrtcDestroyProgram(&prog);
+        delete[] ptx;
+
+        cuCtxDestroy(context);
+
+        std::cout << "Kernel executed successfully." << std::endl;
+        return 0;
+    }
+    catch(const std::exception& e)
+    {
+        std::cerr << "Stopped with exception: " << e.what() << std::endl;
+        return EXIT_FAILURE;
+    }
+}
diff --git a/test/test_erf_inv_nvrtc_float.cpp b/test/test_erf_inv_nvrtc_float.cpp
new file mode 100644
index 000000000..ff7f6db98
--- /dev/null
+++ b/test/test_erf_inv_nvrtc_float.cpp
@@ -0,0 +1,186 @@
+//  Copyright John Maddock 2016.
+//  Copyright Matt Borland 2024.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+#define BOOST_MATH_PROMOTE_DOUBLE_POLICY false
+
+#include <iostream>
+#include <iomanip>
+#include <vector>
+#include <random>
+#include <exception>
+#include <boost/math/special_functions/erf.hpp>
+#include <boost/math/special_functions/relative_difference.hpp>
+#include <cuda.h>
+#include <cuda_runtime.h>
+#include <nvrtc.h>
+
+typedef float float_type;
+
+const char* cuda_kernel = R"(
+typedef float float_type;
+#include <boost/math/special_functions/erf.hpp>
+extern "C" __global__ 
+void test_erf_kernel(const float_type *in1, const float_type*, float_type *out, int numElements)
+{
+    int i = blockDim.x * blockIdx.x + threadIdx.x;
+    if (i < numElements)
+    {
+        out[i] = boost::math::erf_inv(in1[i]);
+    }
+}
+)";
+
+void checkCUDAError(cudaError_t result, const char* msg)
+{
+    if (result != cudaSuccess)
+    {
+        std::cerr << msg << ": " << cudaGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkCUError(CUresult result, const char* msg)
+{
+    if (result != CUDA_SUCCESS)
+    {
+        const char* errorStr;
+        cuGetErrorString(result, &errorStr);
+        std::cerr << msg << ": " << errorStr << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkNVRTCError(nvrtcResult result, const char* msg)
+{
+    if (result != NVRTC_SUCCESS)
+    {
+        std::cerr << msg << ": " << nvrtcGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+int main() 
+{
+    try
+    {
+        // Initialize CUDA driver API
+        checkCUError(cuInit(0), "Failed to initialize CUDA");
+
+        // Create CUDA context
+        CUcontext context;
+        CUdevice device;
+        checkCUError(cuDeviceGet(&device, 0), "Failed to get CUDA device");
+        checkCUError(cuCtxCreate(&context, 0, device), "Failed to create CUDA context");
+
+        nvrtcProgram prog;
+        nvrtcResult res;
+
+        res = nvrtcCreateProgram(&prog, cuda_kernel, "test_erf_kernel.cu", 0, nullptr, nullptr);
+        checkNVRTCError(res, "Failed to create NVRTC program");
+
+        nvrtcAddNameExpression(prog, "test_erf_kernel");
+
+        #ifdef BOOST_MATH_NVRTC_CI_RUN
+        const char* opts[] = {"--std=c++14", "--gpu-architecture=compute_75", "--include-path=/home/runner/work/cuda-math/boost-root/libs/cuda-math/include/"};
+        #else
+        const char* opts[] = {"--std=c++14", "--include-path=/home/mborland/Documents/boost/libs/cuda-math/include/"};
+        #endif
+
+        // Compile the program
+        res = nvrtcCompileProgram(prog, sizeof(opts) / sizeof(const char*), opts);
+        if (res != NVRTC_SUCCESS) 
+        {
+            size_t log_size;
+            nvrtcGetProgramLogSize(prog, &log_size);
+            char* log = new char[log_size];
+            nvrtcGetProgramLog(prog, log);
+            std::cerr << "Compilation failed:\n" << log << std::endl;
+            delete[] log;
+            exit(EXIT_FAILURE);
+        }
+
+        // Get PTX from the program
+        size_t ptx_size;
+        nvrtcGetPTXSize(prog, &ptx_size);
+        char* ptx = new char[ptx_size];
+        nvrtcGetPTX(prog, ptx);
+
+        // Load PTX into CUDA module
+        CUmodule module;
+        CUfunction kernel;
+        checkCUError(cuModuleLoadDataEx(&module, ptx, 0, 0, 0), "Failed to load module");
+        checkCUError(cuModuleGetFunction(&kernel, module, "test_erf_kernel"), "Failed to get kernel function");
+
+        int numElements = 5000;
+        float_type *h_in1, *h_in2, *h_out;
+        float_type *d_in1, *d_in2, *d_out;
+
+        // Allocate memory on the host
+        h_in1 = new float_type[numElements];
+        h_in2 = new float_type[numElements];
+        h_out = new float_type[numElements];
+
+        // Initialize input arrays
+        std::mt19937_64 rng(42);
+        std::uniform_real_distribution<float_type> dist(0.0f, 1.0f);
+        for (int i = 0; i < numElements; ++i) 
+        {
+            h_in1[i] = static_cast<float_type>(dist(rng));
+            h_in2[i] = static_cast<float_type>(dist(rng));
+        }
+
+        checkCUDAError(cudaMalloc(&d_in1, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in1");
+        checkCUDAError(cudaMalloc(&d_in2, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in2");
+        checkCUDAError(cudaMalloc(&d_out, numElements * sizeof(float_type)), "Failed to allocate device memory for d_out");
+
+        checkCUDAError(cudaMemcpy(d_in1, h_in1, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in1");
+        checkCUDAError(cudaMemcpy(d_in2, h_in2, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in2");
+
+        int blockSize = 256;
+        int numBlocks = (numElements + blockSize - 1) / blockSize;
+        void* args[] = { &d_in1, &d_in2, &d_out, &numElements };
+        checkCUError(cuLaunchKernel(kernel, numBlocks, 1, 1, blockSize, 1, 1, 0, 0, args, 0), "Kernel launch failed");
+
+        checkCUDAError(cudaMemcpy(h_out, d_out, numElements * sizeof(float_type), cudaMemcpyDeviceToHost), "Failed to copy data back to host for h_out");
+
+        // Verify Result
+        for (int i = 0; i < numElements; ++i) 
+        {
+            auto res = boost::math::erf_inv(h_in1[i]);
+            if (std::isfinite(res))
+            {
+                if (boost::math::epsilon_difference(res, h_out[i]) > 300)
+                {
+                    std::cout << "error at line: " << i
+                            << "\nParallel: " << h_out[i]
+                            << "\n  Serial: " << res
+                            << "\n    Dist: " << boost::math::epsilon_difference(res, h_out[i]) << std::endl;
+                }
+            }
+        }
+
+        cudaFree(d_in1);
+        cudaFree(d_in2);
+        cudaFree(d_out);
+        delete[] h_in1;
+        delete[] h_in2;
+        delete[] h_out;
+
+        nvrtcDestroyProgram(&prog);
+        delete[] ptx;
+
+        cuCtxDestroy(context);
+
+        std::cout << "Kernel executed successfully." << std::endl;
+        return 0;
+    }
+    catch(const std::exception& e)
+    {
+        std::cerr << "Stopped with exception: " << e.what() << std::endl;
+        return EXIT_FAILURE;
+    }
+}

From 79d555677659fc10cb743cc163971b6f03295bbf Mon Sep 17 00:00:00 2001
From: Matt Borland <matt@mattborland.com>
Date: Tue, 13 Aug 2024 11:49:56 -0400
Subject: [PATCH 11/24] Add erfc_inv NVRTC testing

---
 test/nvrtc_jamfile                  |   2 +
 test/test_erfc_inv_nvrtc_double.cpp | 186 ++++++++++++++++++++++++++++
 test/test_erfc_inv_nvrtc_float.cpp  | 186 ++++++++++++++++++++++++++++
 3 files changed, 374 insertions(+)
 create mode 100644 test/test_erfc_inv_nvrtc_double.cpp
 create mode 100644 test/test_erfc_inv_nvrtc_float.cpp

diff --git a/test/nvrtc_jamfile b/test/nvrtc_jamfile
index d36a3381d..9e59740e6 100644
--- a/test/nvrtc_jamfile
+++ b/test/nvrtc_jamfile
@@ -20,6 +20,8 @@ run test_erfc_nvrtc_double.cpp ;
 run test_erfc_nvrtc_float.cpp ;
 run test_erf_inv_nvrtc_double.cpp ;
 run test_erf_inv_nvrtc_float.cpp ;
+run test_erfc_inv_nvrtc_double.cpp ;
+run test_erfc_inv_nvrtc_float.cpp ;
 run test_expm1_nvrtc_double.cpp ;
 run test_expm1_nvrtc_float.cpp ;
 run test_fpclassify_nvrtc_double.cpp ;
diff --git a/test/test_erfc_inv_nvrtc_double.cpp b/test/test_erfc_inv_nvrtc_double.cpp
new file mode 100644
index 000000000..ae961d657
--- /dev/null
+++ b/test/test_erfc_inv_nvrtc_double.cpp
@@ -0,0 +1,186 @@
+//  Copyright John Maddock 2016.
+//  Copyright Matt Borland 2024.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+#define BOOST_MATH_PROMOTE_DOUBLE_POLICY false
+
+#include <iostream>
+#include <iomanip>
+#include <vector>
+#include <random>
+#include <exception>
+#include <boost/math/special_functions/erf.hpp>
+#include <boost/math/special_functions/relative_difference.hpp>
+#include <cuda.h>
+#include <cuda_runtime.h>
+#include <nvrtc.h>
+
+typedef double float_type;
+
+const char* cuda_kernel = R"(
+typedef double float_type;
+#include <boost/math/special_functions/erf.hpp>
+extern "C" __global__ 
+void test_erf_kernel(const float_type *in1, const float_type*, float_type *out, int numElements)
+{
+    int i = blockDim.x * blockIdx.x + threadIdx.x;
+    if (i < numElements)
+    {
+        out[i] = boost::math::erfc_inv(in1[i]);
+    }
+}
+)";
+
+void checkCUDAError(cudaError_t result, const char* msg)
+{
+    if (result != cudaSuccess)
+    {
+        std::cerr << msg << ": " << cudaGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkCUError(CUresult result, const char* msg)
+{
+    if (result != CUDA_SUCCESS)
+    {
+        const char* errorStr;
+        cuGetErrorString(result, &errorStr);
+        std::cerr << msg << ": " << errorStr << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkNVRTCError(nvrtcResult result, const char* msg)
+{
+    if (result != NVRTC_SUCCESS)
+    {
+        std::cerr << msg << ": " << nvrtcGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+int main() 
+{
+    try
+    {
+        // Initialize CUDA driver API
+        checkCUError(cuInit(0), "Failed to initialize CUDA");
+
+        // Create CUDA context
+        CUcontext context;
+        CUdevice device;
+        checkCUError(cuDeviceGet(&device, 0), "Failed to get CUDA device");
+        checkCUError(cuCtxCreate(&context, 0, device), "Failed to create CUDA context");
+
+        nvrtcProgram prog;
+        nvrtcResult res;
+
+        res = nvrtcCreateProgram(&prog, cuda_kernel, "test_erf_kernel.cu", 0, nullptr, nullptr);
+        checkNVRTCError(res, "Failed to create NVRTC program");
+
+        nvrtcAddNameExpression(prog, "test_erf_kernel");
+
+        #ifdef BOOST_MATH_NVRTC_CI_RUN
+        const char* opts[] = {"--std=c++14", "--gpu-architecture=compute_75", "--include-path=/home/runner/work/cuda-math/boost-root/libs/cuda-math/include/"};
+        #else
+        const char* opts[] = {"--std=c++14", "--include-path=/home/mborland/Documents/boost/libs/cuda-math/include/"};
+        #endif
+
+        // Compile the program
+        res = nvrtcCompileProgram(prog, sizeof(opts) / sizeof(const char*), opts);
+        if (res != NVRTC_SUCCESS) 
+        {
+            size_t log_size;
+            nvrtcGetProgramLogSize(prog, &log_size);
+            char* log = new char[log_size];
+            nvrtcGetProgramLog(prog, log);
+            std::cerr << "Compilation failed:\n" << log << std::endl;
+            delete[] log;
+            exit(EXIT_FAILURE);
+        }
+
+        // Get PTX from the program
+        size_t ptx_size;
+        nvrtcGetPTXSize(prog, &ptx_size);
+        char* ptx = new char[ptx_size];
+        nvrtcGetPTX(prog, ptx);
+
+        // Load PTX into CUDA module
+        CUmodule module;
+        CUfunction kernel;
+        checkCUError(cuModuleLoadDataEx(&module, ptx, 0, 0, 0), "Failed to load module");
+        checkCUError(cuModuleGetFunction(&kernel, module, "test_erf_kernel"), "Failed to get kernel function");
+
+        int numElements = 5000;
+        float_type *h_in1, *h_in2, *h_out;
+        float_type *d_in1, *d_in2, *d_out;
+
+        // Allocate memory on the host
+        h_in1 = new float_type[numElements];
+        h_in2 = new float_type[numElements];
+        h_out = new float_type[numElements];
+
+        // Initialize input arrays
+        std::mt19937_64 rng(42);
+        std::uniform_real_distribution<float_type> dist(0.0f, 1.0f);
+        for (int i = 0; i < numElements; ++i) 
+        {
+            h_in1[i] = static_cast<float_type>(dist(rng));
+            h_in2[i] = static_cast<float_type>(dist(rng));
+        }
+
+        checkCUDAError(cudaMalloc(&d_in1, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in1");
+        checkCUDAError(cudaMalloc(&d_in2, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in2");
+        checkCUDAError(cudaMalloc(&d_out, numElements * sizeof(float_type)), "Failed to allocate device memory for d_out");
+
+        checkCUDAError(cudaMemcpy(d_in1, h_in1, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in1");
+        checkCUDAError(cudaMemcpy(d_in2, h_in2, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in2");
+
+        int blockSize = 256;
+        int numBlocks = (numElements + blockSize - 1) / blockSize;
+        void* args[] = { &d_in1, &d_in2, &d_out, &numElements };
+        checkCUError(cuLaunchKernel(kernel, numBlocks, 1, 1, blockSize, 1, 1, 0, 0, args, 0), "Kernel launch failed");
+
+        checkCUDAError(cudaMemcpy(h_out, d_out, numElements * sizeof(float_type), cudaMemcpyDeviceToHost), "Failed to copy data back to host for h_out");
+
+        // Verify Result
+        for (int i = 0; i < numElements; ++i) 
+        {
+            auto res = boost::math::erfc_inv(h_in1[i]);
+            if (std::isfinite(res))
+            {
+                if (boost::math::epsilon_difference(res, h_out[i]) > 300)
+                {
+                    std::cout << "error at line: " << i
+                            << "\nParallel: " << h_out[i]
+                            << "\n  Serial: " << res
+                            << "\n    Dist: " << boost::math::epsilon_difference(res, h_out[i]) << std::endl;
+                }
+            }
+        }
+
+        cudaFree(d_in1);
+        cudaFree(d_in2);
+        cudaFree(d_out);
+        delete[] h_in1;
+        delete[] h_in2;
+        delete[] h_out;
+
+        nvrtcDestroyProgram(&prog);
+        delete[] ptx;
+
+        cuCtxDestroy(context);
+
+        std::cout << "Kernel executed successfully." << std::endl;
+        return 0;
+    }
+    catch(const std::exception& e)
+    {
+        std::cerr << "Stopped with exception: " << e.what() << std::endl;
+        return EXIT_FAILURE;
+    }
+}
diff --git a/test/test_erfc_inv_nvrtc_float.cpp b/test/test_erfc_inv_nvrtc_float.cpp
new file mode 100644
index 000000000..b676330ce
--- /dev/null
+++ b/test/test_erfc_inv_nvrtc_float.cpp
@@ -0,0 +1,186 @@
+//  Copyright John Maddock 2016.
+//  Copyright Matt Borland 2024.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+#define BOOST_MATH_PROMOTE_DOUBLE_POLICY false
+
+#include <iostream>
+#include <iomanip>
+#include <vector>
+#include <random>
+#include <exception>
+#include <boost/math/special_functions/erf.hpp>
+#include <boost/math/special_functions/relative_difference.hpp>
+#include <cuda.h>
+#include <cuda_runtime.h>
+#include <nvrtc.h>
+
+typedef float float_type;
+
+const char* cuda_kernel = R"(
+typedef float float_type;
+#include <boost/math/special_functions/erf.hpp>
+extern "C" __global__ 
+void test_erf_kernel(const float_type *in1, const float_type*, float_type *out, int numElements)
+{
+    int i = blockDim.x * blockIdx.x + threadIdx.x;
+    if (i < numElements)
+    {
+        out[i] = boost::math::erfc_inv(in1[i]);
+    }
+}
+)";
+
+void checkCUDAError(cudaError_t result, const char* msg)
+{
+    if (result != cudaSuccess)
+    {
+        std::cerr << msg << ": " << cudaGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkCUError(CUresult result, const char* msg)
+{
+    if (result != CUDA_SUCCESS)
+    {
+        const char* errorStr;
+        cuGetErrorString(result, &errorStr);
+        std::cerr << msg << ": " << errorStr << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkNVRTCError(nvrtcResult result, const char* msg)
+{
+    if (result != NVRTC_SUCCESS)
+    {
+        std::cerr << msg << ": " << nvrtcGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+int main() 
+{
+    try
+    {
+        // Initialize CUDA driver API
+        checkCUError(cuInit(0), "Failed to initialize CUDA");
+
+        // Create CUDA context
+        CUcontext context;
+        CUdevice device;
+        checkCUError(cuDeviceGet(&device, 0), "Failed to get CUDA device");
+        checkCUError(cuCtxCreate(&context, 0, device), "Failed to create CUDA context");
+
+        nvrtcProgram prog;
+        nvrtcResult res;
+
+        res = nvrtcCreateProgram(&prog, cuda_kernel, "test_erf_kernel.cu", 0, nullptr, nullptr);
+        checkNVRTCError(res, "Failed to create NVRTC program");
+
+        nvrtcAddNameExpression(prog, "test_erf_kernel");
+
+        #ifdef BOOST_MATH_NVRTC_CI_RUN
+        const char* opts[] = {"--std=c++14", "--gpu-architecture=compute_75", "--include-path=/home/runner/work/cuda-math/boost-root/libs/cuda-math/include/"};
+        #else
+        const char* opts[] = {"--std=c++14", "--include-path=/home/mborland/Documents/boost/libs/cuda-math/include/"};
+        #endif
+
+        // Compile the program
+        res = nvrtcCompileProgram(prog, sizeof(opts) / sizeof(const char*), opts);
+        if (res != NVRTC_SUCCESS) 
+        {
+            size_t log_size;
+            nvrtcGetProgramLogSize(prog, &log_size);
+            char* log = new char[log_size];
+            nvrtcGetProgramLog(prog, log);
+            std::cerr << "Compilation failed:\n" << log << std::endl;
+            delete[] log;
+            exit(EXIT_FAILURE);
+        }
+
+        // Get PTX from the program
+        size_t ptx_size;
+        nvrtcGetPTXSize(prog, &ptx_size);
+        char* ptx = new char[ptx_size];
+        nvrtcGetPTX(prog, ptx);
+
+        // Load PTX into CUDA module
+        CUmodule module;
+        CUfunction kernel;
+        checkCUError(cuModuleLoadDataEx(&module, ptx, 0, 0, 0), "Failed to load module");
+        checkCUError(cuModuleGetFunction(&kernel, module, "test_erf_kernel"), "Failed to get kernel function");
+
+        int numElements = 5000;
+        float_type *h_in1, *h_in2, *h_out;
+        float_type *d_in1, *d_in2, *d_out;
+
+        // Allocate memory on the host
+        h_in1 = new float_type[numElements];
+        h_in2 = new float_type[numElements];
+        h_out = new float_type[numElements];
+
+        // Initialize input arrays
+        std::mt19937_64 rng(42);
+        std::uniform_real_distribution<float_type> dist(0.0f, 1.0f);
+        for (int i = 0; i < numElements; ++i) 
+        {
+            h_in1[i] = static_cast<float_type>(dist(rng));
+            h_in2[i] = static_cast<float_type>(dist(rng));
+        }
+
+        checkCUDAError(cudaMalloc(&d_in1, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in1");
+        checkCUDAError(cudaMalloc(&d_in2, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in2");
+        checkCUDAError(cudaMalloc(&d_out, numElements * sizeof(float_type)), "Failed to allocate device memory for d_out");
+
+        checkCUDAError(cudaMemcpy(d_in1, h_in1, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in1");
+        checkCUDAError(cudaMemcpy(d_in2, h_in2, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in2");
+
+        int blockSize = 256;
+        int numBlocks = (numElements + blockSize - 1) / blockSize;
+        void* args[] = { &d_in1, &d_in2, &d_out, &numElements };
+        checkCUError(cuLaunchKernel(kernel, numBlocks, 1, 1, blockSize, 1, 1, 0, 0, args, 0), "Kernel launch failed");
+
+        checkCUDAError(cudaMemcpy(h_out, d_out, numElements * sizeof(float_type), cudaMemcpyDeviceToHost), "Failed to copy data back to host for h_out");
+
+        // Verify Result
+        for (int i = 0; i < numElements; ++i) 
+        {
+            auto res = boost::math::erfc_inv(h_in1[i]);
+            if (std::isfinite(res))
+            {
+                if (boost::math::epsilon_difference(res, h_out[i]) > 300)
+                {
+                    std::cout << "error at line: " << i
+                            << "\nParallel: " << h_out[i]
+                            << "\n  Serial: " << res
+                            << "\n    Dist: " << boost::math::epsilon_difference(res, h_out[i]) << std::endl;
+                }
+            }
+        }
+
+        cudaFree(d_in1);
+        cudaFree(d_in2);
+        cudaFree(d_out);
+        delete[] h_in1;
+        delete[] h_in2;
+        delete[] h_out;
+
+        nvrtcDestroyProgram(&prog);
+        delete[] ptx;
+
+        cuCtxDestroy(context);
+
+        std::cout << "Kernel executed successfully." << std::endl;
+        return 0;
+    }
+    catch(const std::exception& e)
+    {
+        std::cerr << "Stopped with exception: " << e.what() << std::endl;
+        return EXIT_FAILURE;
+    }
+}

From 090735e915f156a078d9533b8d3b678cbb247ce7 Mon Sep 17 00:00:00 2001
From: Matt Borland <matt@mattborland.com>
Date: Tue, 13 Aug 2024 14:04:17 -0400
Subject: [PATCH 12/24] Update polynomial evaluation for NVRTC

---
 .../tools/detail/polynomial_horner1_10.hpp    | 22 +++----
 .../tools/detail/polynomial_horner1_11.hpp    | 24 ++++----
 .../tools/detail/polynomial_horner1_12.hpp    | 26 ++++----
 .../tools/detail/polynomial_horner1_13.hpp    | 28 ++++-----
 .../tools/detail/polynomial_horner1_14.hpp    | 30 +++++-----
 .../tools/detail/polynomial_horner1_15.hpp    | 32 +++++-----
 .../tools/detail/polynomial_horner1_16.hpp    | 34 +++++------
 .../tools/detail/polynomial_horner1_17.hpp    | 36 +++++------
 .../tools/detail/polynomial_horner1_18.hpp    | 38 ++++++------
 .../tools/detail/polynomial_horner1_19.hpp    | 40 ++++++-------
 .../tools/detail/polynomial_horner1_2.hpp     |  6 +-
 .../tools/detail/polynomial_horner1_20.hpp    | 42 ++++++-------
 .../tools/detail/polynomial_horner1_3.hpp     |  8 +--
 .../tools/detail/polynomial_horner1_4.hpp     | 10 ++--
 .../tools/detail/polynomial_horner1_5.hpp     | 12 ++--
 .../tools/detail/polynomial_horner1_6.hpp     | 14 ++---
 .../tools/detail/polynomial_horner1_7.hpp     | 16 ++---
 .../tools/detail/polynomial_horner1_8.hpp     | 18 +++---
 .../tools/detail/polynomial_horner1_9.hpp     | 20 +++----
 .../tools/detail/polynomial_horner2_10.hpp    | 22 +++----
 .../tools/detail/polynomial_horner2_11.hpp    | 24 ++++----
 .../tools/detail/polynomial_horner2_12.hpp    | 26 ++++----
 .../tools/detail/polynomial_horner2_13.hpp    | 28 ++++-----
 .../tools/detail/polynomial_horner2_14.hpp    | 30 +++++-----
 .../tools/detail/polynomial_horner2_15.hpp    | 32 +++++-----
 .../tools/detail/polynomial_horner2_16.hpp    | 34 +++++------
 .../tools/detail/polynomial_horner2_17.hpp    | 36 +++++------
 .../tools/detail/polynomial_horner2_18.hpp    | 38 ++++++------
 .../tools/detail/polynomial_horner2_19.hpp    | 40 ++++++-------
 .../tools/detail/polynomial_horner2_2.hpp     | 10 ++--
 .../tools/detail/polynomial_horner2_20.hpp    | 42 ++++++-------
 .../tools/detail/polynomial_horner2_3.hpp     | 10 ++--
 .../tools/detail/polynomial_horner2_4.hpp     | 10 ++--
 .../tools/detail/polynomial_horner2_5.hpp     | 12 ++--
 .../tools/detail/polynomial_horner2_6.hpp     | 14 ++---
 .../tools/detail/polynomial_horner2_7.hpp     | 16 ++---
 .../tools/detail/polynomial_horner2_8.hpp     | 18 +++---
 .../tools/detail/polynomial_horner2_9.hpp     | 20 +++----
 .../tools/detail/polynomial_horner3_10.hpp    | 22 +++----
 .../tools/detail/polynomial_horner3_11.hpp    | 24 ++++----
 .../tools/detail/polynomial_horner3_12.hpp    | 26 ++++----
 .../tools/detail/polynomial_horner3_13.hpp    | 28 ++++-----
 .../tools/detail/polynomial_horner3_14.hpp    | 30 +++++-----
 .../tools/detail/polynomial_horner3_15.hpp    | 32 +++++-----
 .../tools/detail/polynomial_horner3_16.hpp    | 34 +++++------
 .../tools/detail/polynomial_horner3_17.hpp    | 36 +++++------
 .../tools/detail/polynomial_horner3_18.hpp    | 38 ++++++------
 .../tools/detail/polynomial_horner3_19.hpp    | 40 ++++++-------
 .../tools/detail/polynomial_horner3_2.hpp     | 10 ++--
 .../tools/detail/polynomial_horner3_20.hpp    | 42 ++++++-------
 .../tools/detail/polynomial_horner3_3.hpp     | 10 ++--
 .../tools/detail/polynomial_horner3_4.hpp     | 10 ++--
 .../tools/detail/polynomial_horner3_5.hpp     | 12 ++--
 .../tools/detail/polynomial_horner3_6.hpp     | 14 ++---
 .../tools/detail/polynomial_horner3_7.hpp     | 16 ++---
 .../tools/detail/polynomial_horner3_8.hpp     | 18 +++---
 .../tools/detail/polynomial_horner3_9.hpp     | 20 +++----
 .../math/tools/detail/rational_horner1_10.hpp | 22 +++----
 .../math/tools/detail/rational_horner1_11.hpp | 24 ++++----
 .../math/tools/detail/rational_horner1_12.hpp | 26 ++++----
 .../math/tools/detail/rational_horner1_13.hpp | 28 ++++-----
 .../math/tools/detail/rational_horner1_14.hpp | 30 +++++-----
 .../math/tools/detail/rational_horner1_15.hpp | 32 +++++-----
 .../math/tools/detail/rational_horner1_16.hpp | 34 +++++------
 .../math/tools/detail/rational_horner1_17.hpp | 36 +++++------
 .../math/tools/detail/rational_horner1_18.hpp | 38 ++++++------
 .../math/tools/detail/rational_horner1_19.hpp | 40 ++++++-------
 .../math/tools/detail/rational_horner1_2.hpp  |  6 +-
 .../math/tools/detail/rational_horner1_20.hpp | 42 ++++++-------
 .../math/tools/detail/rational_horner1_3.hpp  |  8 +--
 .../math/tools/detail/rational_horner1_4.hpp  | 10 ++--
 .../math/tools/detail/rational_horner1_5.hpp  | 12 ++--
 .../math/tools/detail/rational_horner1_6.hpp  | 14 ++---
 .../math/tools/detail/rational_horner1_7.hpp  | 16 ++---
 .../math/tools/detail/rational_horner1_8.hpp  | 18 +++---
 .../math/tools/detail/rational_horner1_9.hpp  | 20 +++----
 .../math/tools/detail/rational_horner2_10.hpp | 22 +++----
 .../math/tools/detail/rational_horner2_11.hpp | 24 ++++----
 .../math/tools/detail/rational_horner2_12.hpp | 26 ++++----
 .../math/tools/detail/rational_horner2_13.hpp | 28 ++++-----
 .../math/tools/detail/rational_horner2_14.hpp | 30 +++++-----
 .../math/tools/detail/rational_horner2_15.hpp | 32 +++++-----
 .../math/tools/detail/rational_horner2_16.hpp | 34 +++++------
 .../math/tools/detail/rational_horner2_17.hpp | 36 +++++------
 .../math/tools/detail/rational_horner2_18.hpp | 38 ++++++------
 .../math/tools/detail/rational_horner2_19.hpp | 40 ++++++-------
 .../math/tools/detail/rational_horner2_2.hpp  | 10 ++--
 .../math/tools/detail/rational_horner2_20.hpp | 42 ++++++-------
 .../math/tools/detail/rational_horner2_3.hpp  | 10 ++--
 .../math/tools/detail/rational_horner2_4.hpp  | 10 ++--
 .../math/tools/detail/rational_horner2_5.hpp  | 12 ++--
 .../math/tools/detail/rational_horner2_6.hpp  | 14 ++---
 .../math/tools/detail/rational_horner2_7.hpp  | 16 ++---
 .../math/tools/detail/rational_horner2_8.hpp  | 18 +++---
 .../math/tools/detail/rational_horner2_9.hpp  | 20 +++----
 .../math/tools/detail/rational_horner3_10.hpp | 22 +++----
 .../math/tools/detail/rational_horner3_11.hpp | 24 ++++----
 .../math/tools/detail/rational_horner3_12.hpp | 26 ++++----
 .../math/tools/detail/rational_horner3_13.hpp | 28 ++++-----
 .../math/tools/detail/rational_horner3_14.hpp | 30 +++++-----
 .../math/tools/detail/rational_horner3_15.hpp | 32 +++++-----
 .../math/tools/detail/rational_horner3_16.hpp | 34 +++++------
 .../math/tools/detail/rational_horner3_17.hpp | 36 +++++------
 .../math/tools/detail/rational_horner3_18.hpp | 38 ++++++------
 .../math/tools/detail/rational_horner3_19.hpp | 40 ++++++-------
 .../math/tools/detail/rational_horner3_2.hpp  | 10 ++--
 .../math/tools/detail/rational_horner3_20.hpp | 42 ++++++-------
 .../math/tools/detail/rational_horner3_3.hpp  | 10 ++--
 .../math/tools/detail/rational_horner3_4.hpp  | 10 ++--
 .../math/tools/detail/rational_horner3_5.hpp  | 12 ++--
 .../math/tools/detail/rational_horner3_6.hpp  | 14 ++---
 .../math/tools/detail/rational_horner3_7.hpp  | 16 ++---
 .../math/tools/detail/rational_horner3_8.hpp  | 18 +++---
 .../math/tools/detail/rational_horner3_9.hpp  | 20 +++----
 include/boost/math/tools/rational.hpp         | 54 ++++++++++-------
 tools/generate_rational_code.cpp              | 60 +++++++++----------
 116 files changed, 1443 insertions(+), 1431 deletions(-)

diff --git a/include/boost/math/tools/detail/polynomial_horner1_10.hpp b/include/boost/math/tools/detail/polynomial_horner1_10.hpp
index 37e4cba01..04ad90b69 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_10.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_10.hpp
@@ -12,67 +12,67 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_11.hpp b/include/boost/math/tools/detail/polynomial_horner1_11.hpp
index 885490f22..f99ab8250 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_11.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_11.hpp
@@ -12,73 +12,73 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_12.hpp b/include/boost/math/tools/detail/polynomial_horner1_12.hpp
index f54034592..3006ebe51 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_12.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_12.hpp
@@ -12,79 +12,79 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_13.hpp b/include/boost/math/tools/detail/polynomial_horner1_13.hpp
index e9e13bd52..0f1118909 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_13.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_13.hpp
@@ -12,85 +12,85 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_14.hpp b/include/boost/math/tools/detail/polynomial_horner1_14.hpp
index eaa18bdc5..caba4b97e 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_14.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_14.hpp
@@ -12,91 +12,91 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_15.hpp b/include/boost/math/tools/detail/polynomial_horner1_15.hpp
index c4a880449..c8f42ac81 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_15.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_15.hpp
@@ -12,97 +12,97 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_16.hpp b/include/boost/math/tools/detail/polynomial_horner1_16.hpp
index 5c262cc63..2ed591ccf 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_16.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_16.hpp
@@ -12,103 +12,103 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_17.hpp b/include/boost/math/tools/detail/polynomial_horner1_17.hpp
index 90d49a0bd..5e9fc8cd7 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_17.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_17.hpp
@@ -12,109 +12,109 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((((a[16] * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_18.hpp b/include/boost/math/tools/detail/polynomial_horner1_18.hpp
index 58fb83fd3..ffb62ff04 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_18.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_18.hpp
@@ -12,115 +12,115 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((((a[16] * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((((((a[17] * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_19.hpp b/include/boost/math/tools/detail/polynomial_horner1_19.hpp
index 18a6af2d3..56df108ac 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_19.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_19.hpp
@@ -12,121 +12,121 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((((a[16] * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((((((a[17] * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((((((a[18] * x + a[17]) * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_2.hpp b/include/boost/math/tools/detail/polynomial_horner1_2.hpp
index 645e3f878..63091ebdd 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_2.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_2.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_20.hpp b/include/boost/math/tools/detail/polynomial_horner1_20.hpp
index 47584e787..c16e5143e 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_20.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_20.hpp
@@ -12,127 +12,127 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((((a[16] * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((((((a[17] * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((((((a[18] * x + a[17]) * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 20>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 20>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((((((((a[19] * x + a[18]) * x + a[17]) * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_3.hpp b/include/boost/math/tools/detail/polynomial_horner1_3.hpp
index 420bbcc28..0aeccc111 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_3.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_3.hpp
@@ -12,25 +12,25 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_4.hpp b/include/boost/math/tools/detail/polynomial_horner1_4.hpp
index 930798e74..61058fce8 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_4.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_4.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_5.hpp b/include/boost/math/tools/detail/polynomial_horner1_5.hpp
index b97a8f9eb..47021bc50 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_5.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_5.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_6.hpp b/include/boost/math/tools/detail/polynomial_horner1_6.hpp
index 6a699f517..bfd24371d 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_6.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_6.hpp
@@ -12,43 +12,43 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_7.hpp b/include/boost/math/tools/detail/polynomial_horner1_7.hpp
index 2aceeeca1..50ddca63f 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_7.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_7.hpp
@@ -12,49 +12,49 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_8.hpp b/include/boost/math/tools/detail/polynomial_horner1_8.hpp
index 0486d642f..3be7ba4d1 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_8.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_8.hpp
@@ -12,55 +12,55 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_9.hpp b/include/boost/math/tools/detail/polynomial_horner1_9.hpp
index b0838014b..4ec53c48b 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_9.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_9.hpp
@@ -12,61 +12,61 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner2_10.hpp b/include/boost/math/tools/detail/polynomial_horner2_10.hpp
index 2a680d756..f242d7464 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_10.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_10.hpp
@@ -12,72 +12,72 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_11.hpp b/include/boost/math/tools/detail/polynomial_horner2_11.hpp
index 7036eec3f..edf7f86c5 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_11.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_11.hpp
@@ -12,79 +12,79 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_12.hpp b/include/boost/math/tools/detail/polynomial_horner2_12.hpp
index fbbf2a3fa..969c9c4dd 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_12.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_12.hpp
@@ -12,86 +12,86 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_13.hpp b/include/boost/math/tools/detail/polynomial_horner2_13.hpp
index 46fb3859d..ed4559d11 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_13.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_13.hpp
@@ -12,93 +12,93 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_14.hpp b/include/boost/math/tools/detail/polynomial_horner2_14.hpp
index d1c326e0f..4b79eb78a 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_14.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_14.hpp
@@ -12,100 +12,100 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_15.hpp b/include/boost/math/tools/detail/polynomial_horner2_15.hpp
index d679cfeaf..28b62eee7 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_15.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_15.hpp
@@ -12,107 +12,107 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_16.hpp b/include/boost/math/tools/detail/polynomial_horner2_16.hpp
index 0f3ed8f6c..6368b4054 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_16.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_16.hpp
@@ -12,114 +12,114 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((a[15] * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_17.hpp b/include/boost/math/tools/detail/polynomial_horner2_17.hpp
index 7783c4c81..551e6191c 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_17.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_17.hpp
@@ -12,121 +12,121 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((a[15] * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((a[16] * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((((a[15] * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_18.hpp b/include/boost/math/tools/detail/polynomial_horner2_18.hpp
index 4e3b57f98..19cfdc19e 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_18.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_18.hpp
@@ -12,128 +12,128 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((a[15] * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((a[16] * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((((a[15] * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((((a[17] * x2 + a[15]) * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((((a[16] * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_19.hpp b/include/boost/math/tools/detail/polynomial_horner2_19.hpp
index 9eca8ef11..9ea87fd93 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_19.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_19.hpp
@@ -12,135 +12,135 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((a[15] * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((a[16] * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((((a[15] * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((((a[17] * x2 + a[15]) * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((((a[16] * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((((a[18] * x2 + a[16]) * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((((((a[17] * x2 + a[15]) * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_2.hpp b/include/boost/math/tools/detail/polynomial_horner2_2.hpp
index 857d43fdb..1982a81f3 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_2.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_2.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner2_20.hpp b/include/boost/math/tools/detail/polynomial_horner2_20.hpp
index 2a8359025..23afe55e0 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_20.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_20.hpp
@@ -12,142 +12,142 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((a[15] * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((a[16] * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((((a[15] * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((((a[17] * x2 + a[15]) * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((((a[16] * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((((a[18] * x2 + a[16]) * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((((((a[17] * x2 + a[15]) * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 20>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 20>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((((a[19] * x2 + a[17]) * x2 + a[15]) * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((((((a[18] * x2 + a[16]) * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_3.hpp b/include/boost/math/tools/detail/polynomial_horner2_3.hpp
index b5956cdaf..f9d6953b8 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_3.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_3.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner2_4.hpp b/include/boost/math/tools/detail/polynomial_horner2_4.hpp
index 9194a1868..8f11de5b3 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_4.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_4.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner2_5.hpp b/include/boost/math/tools/detail/polynomial_horner2_5.hpp
index 4e20c214a..eba9ee9e6 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_5.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_5.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_6.hpp b/include/boost/math/tools/detail/polynomial_horner2_6.hpp
index a33168d5e..ef77c6255 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_6.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_6.hpp
@@ -12,44 +12,44 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_7.hpp b/include/boost/math/tools/detail/polynomial_horner2_7.hpp
index 2f135756c..fe8d21b95 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_7.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_7.hpp
@@ -12,51 +12,51 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_8.hpp b/include/boost/math/tools/detail/polynomial_horner2_8.hpp
index 4c59602f9..de1810a94 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_8.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_8.hpp
@@ -12,58 +12,58 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_9.hpp b/include/boost/math/tools/detail/polynomial_horner2_9.hpp
index 0b60c3c04..5c53b7329 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_9.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_9.hpp
@@ -12,65 +12,65 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
diff --git a/include/boost/math/tools/detail/polynomial_horner3_10.hpp b/include/boost/math/tools/detail/polynomial_horner3_10.hpp
index 3386fcae4..7fb5bb474 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_10.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_10.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_11.hpp b/include/boost/math/tools/detail/polynomial_horner3_11.hpp
index f24ebb024..9f22820de 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_11.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_11.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_12.hpp b/include/boost/math/tools/detail/polynomial_horner3_12.hpp
index 73916940d..b04961376 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_12.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_12.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -175,7 +175,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_13.hpp b/include/boost/math/tools/detail/polynomial_horner3_13.hpp
index 44ec9a84c..f39a33cc9 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_13.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_13.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -175,7 +175,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_14.hpp b/include/boost/math/tools/detail/polynomial_horner3_14.hpp
index 4d4e9e21c..32b9e7db2 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_14.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_14.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -175,7 +175,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -231,7 +231,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_15.hpp b/include/boost/math/tools/detail/polynomial_horner3_15.hpp
index b7cf83dd1..55325c84b 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_15.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_15.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -175,7 +175,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -231,7 +231,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -262,7 +262,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_16.hpp b/include/boost/math/tools/detail/polynomial_horner3_16.hpp
index fbf504f3f..f71d62f50 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_16.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_16.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -175,7 +175,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -231,7 +231,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -262,7 +262,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -295,7 +295,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_17.hpp b/include/boost/math/tools/detail/polynomial_horner3_17.hpp
index c7af11b65..783a34558 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_17.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_17.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -175,7 +175,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -231,7 +231,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -262,7 +262,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -295,7 +295,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -330,7 +330,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_18.hpp b/include/boost/math/tools/detail/polynomial_horner3_18.hpp
index feceac694..b10b270c4 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_18.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_18.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -175,7 +175,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -231,7 +231,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -262,7 +262,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -295,7 +295,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -330,7 +330,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -367,7 +367,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_19.hpp b/include/boost/math/tools/detail/polynomial_horner3_19.hpp
index 6a9a4ea6f..21147591c 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_19.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_19.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -175,7 +175,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -231,7 +231,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -262,7 +262,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -295,7 +295,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -330,7 +330,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -367,7 +367,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -406,7 +406,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_2.hpp b/include/boost/math/tools/detail/polynomial_horner3_2.hpp
index 69925be1c..ee3e35e6c 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_2.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_2.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner3_20.hpp b/include/boost/math/tools/detail/polynomial_horner3_20.hpp
index 8dda51139..338aeb7db 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_20.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_20.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -175,7 +175,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -231,7 +231,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -262,7 +262,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -295,7 +295,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -330,7 +330,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -367,7 +367,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -406,7 +406,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -447,7 +447,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 20>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 20>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_3.hpp b/include/boost/math/tools/detail/polynomial_horner3_3.hpp
index 30e68ac2a..1eee0cfac 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_3.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_3.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner3_4.hpp b/include/boost/math/tools/detail/polynomial_horner3_4.hpp
index e3c9b16f3..efa7fba48 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_4.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_4.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner3_5.hpp b/include/boost/math/tools/detail/polynomial_horner3_5.hpp
index c02467da0..f150e2a4a 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_5.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_5.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_6.hpp b/include/boost/math/tools/detail/polynomial_horner3_6.hpp
index ad71255bf..fe679e74d 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_6.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_6.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_7.hpp b/include/boost/math/tools/detail/polynomial_horner3_7.hpp
index 31e0afa66..76f080ad9 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_7.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_7.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_8.hpp b/include/boost/math/tools/detail/polynomial_horner3_8.hpp
index 33121b204..75634bdfc 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_8.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_8.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_9.hpp b/include/boost/math/tools/detail/polynomial_horner3_9.hpp
index c9f717133..63a40580d 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_9.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_9.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/rational_horner1_10.hpp b/include/boost/math/tools/detail/rational_horner1_10.hpp
index 346ac34ec..e2f6c6d2f 100644
--- a/include/boost/math/tools/detail/rational_horner1_10.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_10.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_11.hpp b/include/boost/math/tools/detail/rational_horner1_11.hpp
index 74ed24a74..31d480a65 100644
--- a/include/boost/math/tools/detail/rational_horner1_11.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_11.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_12.hpp b/include/boost/math/tools/detail/rational_horner1_12.hpp
index 9072d1698..c08a85b3a 100644
--- a/include/boost/math/tools/detail/rational_horner1_12.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_12.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -144,7 +144,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((b[11] * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_13.hpp b/include/boost/math/tools/detail/rational_horner1_13.hpp
index 1e5c75092..cc87ec2dc 100644
--- a/include/boost/math/tools/detail/rational_horner1_13.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_13.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -144,7 +144,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((b[11] * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -156,7 +156,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((b[12] * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_14.hpp b/include/boost/math/tools/detail/rational_horner1_14.hpp
index 75b9bde42..256473710 100644
--- a/include/boost/math/tools/detail/rational_horner1_14.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_14.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -144,7 +144,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((b[11] * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -156,7 +156,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((b[12] * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -168,7 +168,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((b[13] * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_15.hpp b/include/boost/math/tools/detail/rational_horner1_15.hpp
index 47f18a3c4..2ab24814e 100644
--- a/include/boost/math/tools/detail/rational_horner1_15.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_15.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -144,7 +144,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((b[11] * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -156,7 +156,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((b[12] * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -168,7 +168,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((b[13] * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((b[14] * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_16.hpp b/include/boost/math/tools/detail/rational_horner1_16.hpp
index fec9a51a2..dce0b5e9b 100644
--- a/include/boost/math/tools/detail/rational_horner1_16.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_16.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -144,7 +144,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((b[11] * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -156,7 +156,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((b[12] * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -168,7 +168,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((b[13] * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((b[14] * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -192,7 +192,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((((b[15] * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_17.hpp b/include/boost/math/tools/detail/rational_horner1_17.hpp
index b26dac95c..8e875d657 100644
--- a/include/boost/math/tools/detail/rational_horner1_17.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_17.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -144,7 +144,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((b[11] * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -156,7 +156,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((b[12] * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -168,7 +168,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((b[13] * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((b[14] * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -192,7 +192,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((((b[15] * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -204,7 +204,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((((((a[16] * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((((b[16] * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_18.hpp b/include/boost/math/tools/detail/rational_horner1_18.hpp
index 074a6359b..ab67a970b 100644
--- a/include/boost/math/tools/detail/rational_horner1_18.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_18.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -144,7 +144,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((b[11] * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -156,7 +156,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((b[12] * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -168,7 +168,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((b[13] * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((b[14] * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -192,7 +192,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((((b[15] * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -204,7 +204,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((((((a[16] * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((((b[16] * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -216,7 +216,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((((((a[17] * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((((((b[17] * x + b[16]) * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_19.hpp b/include/boost/math/tools/detail/rational_horner1_19.hpp
index a1cceaeab..dc300343a 100644
--- a/include/boost/math/tools/detail/rational_horner1_19.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_19.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -144,7 +144,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((b[11] * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -156,7 +156,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((b[12] * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -168,7 +168,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((b[13] * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((b[14] * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -192,7 +192,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((((b[15] * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -204,7 +204,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((((((a[16] * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((((b[16] * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -216,7 +216,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((((((a[17] * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((((((b[17] * x + b[16]) * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -228,7 +228,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((((((((a[18] * x + a[17]) * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((((((b[18] * x + b[17]) * x + b[16]) * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_2.hpp b/include/boost/math/tools/detail/rational_horner1_2.hpp
index 81250ba10..c6b1ef9ef 100644
--- a/include/boost/math/tools/detail/rational_horner1_2.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_2.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_20.hpp b/include/boost/math/tools/detail/rational_horner1_20.hpp
index 63763fd8c..5b8b170c1 100644
--- a/include/boost/math/tools/detail/rational_horner1_20.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_20.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -144,7 +144,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((b[11] * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -156,7 +156,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((b[12] * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -168,7 +168,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((b[13] * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((b[14] * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -192,7 +192,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((((b[15] * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -204,7 +204,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((((((a[16] * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((((b[16] * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -216,7 +216,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((((((a[17] * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((((((b[17] * x + b[16]) * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -228,7 +228,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((((((((a[18] * x + a[17]) * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((((((b[18] * x + b[17]) * x + b[16]) * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -240,7 +240,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 20>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 20>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((((((((a[19] * x + a[18]) * x + a[17]) * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((((((((b[19] * x + b[18]) * x + b[17]) * x + b[16]) * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_3.hpp b/include/boost/math/tools/detail/rational_horner1_3.hpp
index 1aebe20d3..6933e22bf 100644
--- a/include/boost/math/tools/detail/rational_horner1_3.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_3.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_4.hpp b/include/boost/math/tools/detail/rational_horner1_4.hpp
index 8175f348c..49b983577 100644
--- a/include/boost/math/tools/detail/rational_horner1_4.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_4.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_5.hpp b/include/boost/math/tools/detail/rational_horner1_5.hpp
index 93c11c1ef..91e97ff44 100644
--- a/include/boost/math/tools/detail/rational_horner1_5.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_5.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_6.hpp b/include/boost/math/tools/detail/rational_horner1_6.hpp
index a59cceb24..876b026cd 100644
--- a/include/boost/math/tools/detail/rational_horner1_6.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_6.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_7.hpp b/include/boost/math/tools/detail/rational_horner1_7.hpp
index eaa023a50..bcac18293 100644
--- a/include/boost/math/tools/detail/rational_horner1_7.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_7.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_8.hpp b/include/boost/math/tools/detail/rational_horner1_8.hpp
index 5624c814f..55e30a53e 100644
--- a/include/boost/math/tools/detail/rational_horner1_8.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_8.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_9.hpp b/include/boost/math/tools/detail/rational_horner1_9.hpp
index c94e7ed42..c7087de50 100644
--- a/include/boost/math/tools/detail/rational_horner1_9.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_9.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner2_10.hpp b/include/boost/math/tools/detail/rational_horner2_10.hpp
index 0e4fd54ea..4d74a714d 100644
--- a/include/boost/math/tools/detail/rational_horner2_10.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_10.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -90,7 +90,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -122,7 +122,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_11.hpp b/include/boost/math/tools/detail/rational_horner2_11.hpp
index 841c8bd49..15f1cf255 100644
--- a/include/boost/math/tools/detail/rational_horner2_11.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_11.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -90,7 +90,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -122,7 +122,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -138,7 +138,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_12.hpp b/include/boost/math/tools/detail/rational_horner2_12.hpp
index 3e783c577..24e9d9e7f 100644
--- a/include/boost/math/tools/detail/rational_horner2_12.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_12.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -90,7 +90,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -122,7 +122,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -138,7 +138,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -154,7 +154,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_13.hpp b/include/boost/math/tools/detail/rational_horner2_13.hpp
index a3afa653d..495f88525 100644
--- a/include/boost/math/tools/detail/rational_horner2_13.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_13.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -90,7 +90,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -122,7 +122,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -138,7 +138,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -154,7 +154,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -170,7 +170,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_14.hpp b/include/boost/math/tools/detail/rational_horner2_14.hpp
index 377c1ad42..273e723b6 100644
--- a/include/boost/math/tools/detail/rational_horner2_14.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_14.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -90,7 +90,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -122,7 +122,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -138,7 +138,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -154,7 +154,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -170,7 +170,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -186,7 +186,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_15.hpp b/include/boost/math/tools/detail/rational_horner2_15.hpp
index 9082d03f8..c7e24ec7d 100644
--- a/include/boost/math/tools/detail/rational_horner2_15.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_15.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -90,7 +90,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -122,7 +122,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -138,7 +138,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -154,7 +154,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -170,7 +170,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -186,7 +186,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_16.hpp b/include/boost/math/tools/detail/rational_horner2_16.hpp
index 64173bffe..2eebd702b 100644
--- a/include/boost/math/tools/detail/rational_horner2_16.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_16.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -90,7 +90,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -122,7 +122,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -138,7 +138,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -154,7 +154,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -170,7 +170,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -186,7 +186,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -218,7 +218,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_17.hpp b/include/boost/math/tools/detail/rational_horner2_17.hpp
index 5ae8cb428..1fee63047 100644
--- a/include/boost/math/tools/detail/rational_horner2_17.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_17.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -90,7 +90,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -122,7 +122,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -138,7 +138,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -154,7 +154,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -170,7 +170,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -186,7 +186,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -218,7 +218,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -234,7 +234,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_18.hpp b/include/boost/math/tools/detail/rational_horner2_18.hpp
index ebe440e62..7aedbf2aa 100644
--- a/include/boost/math/tools/detail/rational_horner2_18.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_18.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -90,7 +90,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -122,7 +122,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -138,7 +138,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -154,7 +154,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -170,7 +170,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -186,7 +186,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -218,7 +218,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -234,7 +234,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -250,7 +250,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_19.hpp b/include/boost/math/tools/detail/rational_horner2_19.hpp
index c1a2d4383..1c36a267c 100644
--- a/include/boost/math/tools/detail/rational_horner2_19.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_19.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -90,7 +90,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -122,7 +122,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -138,7 +138,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -154,7 +154,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -170,7 +170,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -186,7 +186,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -218,7 +218,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -234,7 +234,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -250,7 +250,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -266,7 +266,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_2.hpp b/include/boost/math/tools/detail/rational_horner2_2.hpp
index e1dd400ae..bb2e2c4dc 100644
--- a/include/boost/math/tools/detail/rational_horner2_2.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_2.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
diff --git a/include/boost/math/tools/detail/rational_horner2_20.hpp b/include/boost/math/tools/detail/rational_horner2_20.hpp
index 50a63c128..a591b901c 100644
--- a/include/boost/math/tools/detail/rational_horner2_20.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_20.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -90,7 +90,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -122,7 +122,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -138,7 +138,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -154,7 +154,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -170,7 +170,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -186,7 +186,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -218,7 +218,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -234,7 +234,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -250,7 +250,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -266,7 +266,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -282,7 +282,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 20>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 20>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_3.hpp b/include/boost/math/tools/detail/rational_horner2_3.hpp
index ab0d029aa..0b410d8bb 100644
--- a/include/boost/math/tools/detail/rational_horner2_3.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_3.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
diff --git a/include/boost/math/tools/detail/rational_horner2_4.hpp b/include/boost/math/tools/detail/rational_horner2_4.hpp
index 147f5d1da..07a9a2c5a 100644
--- a/include/boost/math/tools/detail/rational_horner2_4.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_4.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
diff --git a/include/boost/math/tools/detail/rational_horner2_5.hpp b/include/boost/math/tools/detail/rational_horner2_5.hpp
index db5907b6f..0933ddfbc 100644
--- a/include/boost/math/tools/detail/rational_horner2_5.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_5.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_6.hpp b/include/boost/math/tools/detail/rational_horner2_6.hpp
index b71bc150a..dee9c6e16 100644
--- a/include/boost/math/tools/detail/rational_horner2_6.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_6.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_7.hpp b/include/boost/math/tools/detail/rational_horner2_7.hpp
index da5b1476a..6f9a85838 100644
--- a/include/boost/math/tools/detail/rational_horner2_7.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_7.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_8.hpp b/include/boost/math/tools/detail/rational_horner2_8.hpp
index b047ad948..33dda23bb 100644
--- a/include/boost/math/tools/detail/rational_horner2_8.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_8.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -90,7 +90,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_9.hpp b/include/boost/math/tools/detail/rational_horner2_9.hpp
index 4eed1c430..a9025a890 100644
--- a/include/boost/math/tools/detail/rational_horner2_9.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_9.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -90,7 +90,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_10.hpp b/include/boost/math/tools/detail/rational_horner3_10.hpp
index 1fe94f8e3..b7cec124e 100644
--- a/include/boost/math/tools/detail/rational_horner3_10.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_10.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -242,7 +242,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -312,7 +312,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_11.hpp b/include/boost/math/tools/detail/rational_horner3_11.hpp
index 1a4277a82..579f0e486 100644
--- a/include/boost/math/tools/detail/rational_horner3_11.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_11.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -242,7 +242,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -312,7 +312,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -390,7 +390,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_12.hpp b/include/boost/math/tools/detail/rational_horner3_12.hpp
index 5deb0f374..54300dd08 100644
--- a/include/boost/math/tools/detail/rational_horner3_12.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_12.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -242,7 +242,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -312,7 +312,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -390,7 +390,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -476,7 +476,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_13.hpp b/include/boost/math/tools/detail/rational_horner3_13.hpp
index 6c6857f31..d2fc7b633 100644
--- a/include/boost/math/tools/detail/rational_horner3_13.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_13.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -242,7 +242,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -312,7 +312,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -390,7 +390,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -476,7 +476,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -570,7 +570,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_14.hpp b/include/boost/math/tools/detail/rational_horner3_14.hpp
index 1aadb35de..0b7675f49 100644
--- a/include/boost/math/tools/detail/rational_horner3_14.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_14.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -242,7 +242,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -312,7 +312,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -390,7 +390,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -476,7 +476,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -570,7 +570,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -672,7 +672,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_15.hpp b/include/boost/math/tools/detail/rational_horner3_15.hpp
index 0f79e5b0d..8286caed0 100644
--- a/include/boost/math/tools/detail/rational_horner3_15.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_15.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -242,7 +242,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -312,7 +312,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -390,7 +390,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -476,7 +476,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -570,7 +570,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -672,7 +672,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -782,7 +782,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_16.hpp b/include/boost/math/tools/detail/rational_horner3_16.hpp
index b7c6e96c1..fc823e416 100644
--- a/include/boost/math/tools/detail/rational_horner3_16.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_16.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -242,7 +242,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -312,7 +312,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -390,7 +390,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -476,7 +476,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -570,7 +570,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -672,7 +672,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -782,7 +782,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -900,7 +900,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_17.hpp b/include/boost/math/tools/detail/rational_horner3_17.hpp
index 25328e7ff..cf7f75a70 100644
--- a/include/boost/math/tools/detail/rational_horner3_17.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_17.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -242,7 +242,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -312,7 +312,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -390,7 +390,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -476,7 +476,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -570,7 +570,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -672,7 +672,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -782,7 +782,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -900,7 +900,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -1026,7 +1026,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_18.hpp b/include/boost/math/tools/detail/rational_horner3_18.hpp
index 335b895c4..f853ed3e0 100644
--- a/include/boost/math/tools/detail/rational_horner3_18.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_18.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -242,7 +242,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -312,7 +312,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -390,7 +390,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -476,7 +476,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -570,7 +570,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -672,7 +672,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -782,7 +782,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -900,7 +900,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -1026,7 +1026,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -1160,7 +1160,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_19.hpp b/include/boost/math/tools/detail/rational_horner3_19.hpp
index 22d24403e..d44e22c90 100644
--- a/include/boost/math/tools/detail/rational_horner3_19.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_19.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -242,7 +242,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -312,7 +312,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -390,7 +390,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -476,7 +476,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -570,7 +570,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -672,7 +672,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -782,7 +782,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -900,7 +900,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -1026,7 +1026,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -1160,7 +1160,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -1302,7 +1302,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_2.hpp b/include/boost/math/tools/detail/rational_horner3_2.hpp
index e1dd400ae..bb2e2c4dc 100644
--- a/include/boost/math/tools/detail/rational_horner3_2.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_2.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
diff --git a/include/boost/math/tools/detail/rational_horner3_20.hpp b/include/boost/math/tools/detail/rational_horner3_20.hpp
index f97124afb..967edf083 100644
--- a/include/boost/math/tools/detail/rational_horner3_20.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_20.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -242,7 +242,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -312,7 +312,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -390,7 +390,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -476,7 +476,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -570,7 +570,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -672,7 +672,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -782,7 +782,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -900,7 +900,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -1026,7 +1026,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -1160,7 +1160,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -1302,7 +1302,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -1452,7 +1452,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 20>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 20>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_3.hpp b/include/boost/math/tools/detail/rational_horner3_3.hpp
index ab0d029aa..0b410d8bb 100644
--- a/include/boost/math/tools/detail/rational_horner3_3.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_3.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
diff --git a/include/boost/math/tools/detail/rational_horner3_4.hpp b/include/boost/math/tools/detail/rational_horner3_4.hpp
index 147f5d1da..07a9a2c5a 100644
--- a/include/boost/math/tools/detail/rational_horner3_4.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_4.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
diff --git a/include/boost/math/tools/detail/rational_horner3_5.hpp b/include/boost/math/tools/detail/rational_horner3_5.hpp
index af1c76f1c..62c76dd50 100644
--- a/include/boost/math/tools/detail/rational_horner3_5.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_5.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_6.hpp b/include/boost/math/tools/detail/rational_horner3_6.hpp
index 05d626ac8..f81a068ac 100644
--- a/include/boost/math/tools/detail/rational_horner3_6.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_6.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_7.hpp b/include/boost/math/tools/detail/rational_horner3_7.hpp
index 2d91a5c50..fea457ccf 100644
--- a/include/boost/math/tools/detail/rational_horner3_7.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_7.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_8.hpp b/include/boost/math/tools/detail/rational_horner3_8.hpp
index 3a6ea4ff0..306e2a41d 100644
--- a/include/boost/math/tools/detail/rational_horner3_8.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_8.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_9.hpp b/include/boost/math/tools/detail/rational_horner3_9.hpp
index d20149b22..93a3527c1 100644
--- a/include/boost/math/tools/detail/rational_horner3_9.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_9.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -242,7 +242,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/rational.hpp b/include/boost/math/tools/rational.hpp
index b65700f62..e3c3e7e33 100644
--- a/include/boost/math/tools/rational.hpp
+++ b/include/boost/math/tools/rational.hpp
@@ -10,9 +10,13 @@
 #pragma once
 #endif
 
-#include <array>
 #include <boost/math/tools/config.hpp>
 #include <boost/math/tools/assert.hpp>
+#include <boost/math/tools/type_traits.hpp>
+
+#ifndef BOOST_MATH_HAS_NVRTC
+#include <array>
+#endif
 
 #if BOOST_MATH_POLY_METHOD == 1
 #  define BOOST_HEADER() <BOOST_MATH_JOIN(boost/math/tools/detail/polynomial_horner1_, BOOST_MATH_MAX_POLY_ORDER).hpp>
@@ -168,7 +172,7 @@ namespace boost{ namespace math{ namespace tools{
 // Forward declaration to keep two phase lookup happy:
 //
 template <class T, class U>
-BOOST_MATH_GPU_ENABLED U evaluate_polynomial(const T* poly, U const& z, std::size_t count) BOOST_MATH_NOEXCEPT(U);
+BOOST_MATH_GPU_ENABLED U evaluate_polynomial(const T* poly, U const& z, BOOST_MATH_SIZE_T count) BOOST_MATH_NOEXCEPT(U);
 
 namespace detail{
 
@@ -186,7 +190,7 @@ BOOST_MATH_GPU_ENABLED BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp
 // the loop expanded versions above:
 //
 template <class T, class U>
-BOOST_MATH_GPU_ENABLED inline U evaluate_polynomial(const T* poly, U const& z, std::size_t count) BOOST_MATH_NOEXCEPT(U)
+BOOST_MATH_GPU_ENABLED inline U evaluate_polynomial(const T* poly, U const& z, BOOST_MATH_SIZE_T count) BOOST_MATH_NOEXCEPT(U)
 {
    BOOST_MATH_ASSERT(count > 0);
    U sum = static_cast<U>(poly[count - 1]);
@@ -201,64 +205,70 @@ BOOST_MATH_GPU_ENABLED inline U evaluate_polynomial(const T* poly, U const& z, s
 // Compile time sized polynomials, just inline forwarders to the
 // implementations above:
 //
-template <std::size_t N, class T, class V>
+template <BOOST_MATH_SIZE_T N, class T, class V>
 BOOST_MATH_GPU_ENABLED BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial(const T(&a)[N], const V& val) BOOST_MATH_NOEXCEPT(V)
 {
-   typedef std::integral_constant<int, N> tag_type;
+   typedef boost::math::integral_constant<int, N> tag_type;
    return detail::evaluate_polynomial_c_imp(static_cast<const T*>(a), val, static_cast<tag_type const*>(nullptr));
 }
 
-template <std::size_t N, class T, class V>
+#ifndef BOOST_MATH_HAS_NVRTC
+template <BOOST_MATH_SIZE_T N, class T, class V>
 BOOST_MATH_GPU_ENABLED BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial(const std::array<T,N>& a, const V& val) BOOST_MATH_NOEXCEPT(V)
 {
-   typedef std::integral_constant<int, N> tag_type;
+   typedef boost::math::integral_constant<int, N> tag_type;
    return detail::evaluate_polynomial_c_imp(static_cast<const T*>(a.data()), val, static_cast<tag_type const*>(nullptr));
 }
+#endif
 //
 // Even polynomials are trivial: just square the argument!
 //
 template <class T, class U>
-BOOST_MATH_GPU_ENABLED inline U evaluate_even_polynomial(const T* poly, U z, std::size_t count) BOOST_MATH_NOEXCEPT(U)
+BOOST_MATH_GPU_ENABLED inline U evaluate_even_polynomial(const T* poly, U z, BOOST_MATH_SIZE_T count) BOOST_MATH_NOEXCEPT(U)
 {
    return evaluate_polynomial(poly, U(z*z), count);
 }
 
-template <std::size_t N, class T, class V>
+template <BOOST_MATH_SIZE_T N, class T, class V>
 BOOST_MATH_GPU_ENABLED BOOST_MATH_GPU_ENABLED inline V evaluate_even_polynomial(const T(&a)[N], const V& z) BOOST_MATH_NOEXCEPT(V)
 {
    return evaluate_polynomial(a, V(z*z));
 }
 
-template <std::size_t N, class T, class V>
+#ifndef BOOST_MATH_HAS_NVRTC
+template <BOOST_MATH_SIZE_T N, class T, class V>
 BOOST_MATH_GPU_ENABLED BOOST_MATH_GPU_ENABLED inline V evaluate_even_polynomial(const std::array<T,N>& a, const V& z) BOOST_MATH_NOEXCEPT(V)
 {
    return evaluate_polynomial(a, V(z*z));
 }
+#endif
 //
 // Odd polynomials come next:
 //
 template <class T, class U>
-BOOST_MATH_GPU_ENABLED inline U evaluate_odd_polynomial(const T* poly, U z, std::size_t count) BOOST_MATH_NOEXCEPT(U)
+BOOST_MATH_GPU_ENABLED inline U evaluate_odd_polynomial(const T* poly, U z, BOOST_MATH_SIZE_T count) BOOST_MATH_NOEXCEPT(U)
 {
    return poly[0] + z * evaluate_polynomial(poly+1, U(z*z), count-1);
 }
 
-template <std::size_t N, class T, class V>
+template <BOOST_MATH_SIZE_T N, class T, class V>
 BOOST_MATH_GPU_ENABLED BOOST_MATH_GPU_ENABLED inline V evaluate_odd_polynomial(const T(&a)[N], const V& z) BOOST_MATH_NOEXCEPT(V)
 {
-   typedef std::integral_constant<int, N-1> tag_type;
+   typedef boost::math::integral_constant<int, N-1> tag_type;
    return a[0] + z * detail::evaluate_polynomial_c_imp(static_cast<const T*>(a) + 1, V(z*z), static_cast<tag_type const*>(nullptr));
 }
 
-template <std::size_t N, class T, class V>
+#ifndef BOOST_MATH_HAS_NVRTC
+template <BOOST_MATH_SIZE_T N, class T, class V>
 BOOST_MATH_GPU_ENABLED BOOST_MATH_GPU_ENABLED inline V evaluate_odd_polynomial(const std::array<T,N>& a, const V& z) BOOST_MATH_NOEXCEPT(V)
 {
-   typedef std::integral_constant<int, N-1> tag_type;
+   typedef boost::math::integral_constant<int, N-1> tag_type;
    return a[0] + z * detail::evaluate_polynomial_c_imp(static_cast<const T*>(a.data()) + 1, V(z*z), static_cast<tag_type const*>(nullptr));
 }
+#endif
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED V evaluate_rational(const T* num, const U* denom, const V& z_, std::size_t count) BOOST_MATH_NOEXCEPT(V);
+BOOST_MATH_GPU_ENABLED V evaluate_rational(const T* num, const U* denom, const V& z_, BOOST_MATH_SIZE_T count) BOOST_MATH_NOEXCEPT(V);
 
 namespace detail{
 
@@ -278,7 +288,7 @@ BOOST_MATH_GPU_ENABLED BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(c
 // in our Lanczos code for example.
 //
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED V evaluate_rational(const T* num, const U* denom, const V& z_, std::size_t count) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED V evaluate_rational(const T* num, const U* denom, const V& z_, BOOST_MATH_SIZE_T count) BOOST_MATH_NOEXCEPT(V)
 {
    V z(z_);
    V s1, s2;
@@ -310,17 +320,19 @@ BOOST_MATH_GPU_ENABLED V evaluate_rational(const T* num, const U* denom, const V
    return s1 / s2;
 }
 
-template <std::size_t N, class T, class U, class V>
+template <BOOST_MATH_SIZE_T N, class T, class U, class V>
 BOOST_MATH_GPU_ENABLED BOOST_MATH_GPU_ENABLED inline V evaluate_rational(const T(&a)[N], const U(&b)[N], const V& z) BOOST_MATH_NOEXCEPT(V)
 {
-   return detail::evaluate_rational_c_imp(a, b, z, static_cast<const std::integral_constant<int, N>*>(nullptr));
+   return detail::evaluate_rational_c_imp(a, b, z, static_cast<const boost::math::integral_constant<int, N>*>(nullptr));
 }
 
-template <std::size_t N, class T, class U, class V>
+#ifndef BOOST_MATH_HAS_NVRTC
+template <BOOST_MATH_SIZE_T N, class T, class U, class V>
 BOOST_MATH_GPU_ENABLED BOOST_MATH_GPU_ENABLED inline V evaluate_rational(const std::array<T,N>& a, const std::array<U,N>& b, const V& z) BOOST_MATH_NOEXCEPT(V)
 {
-   return detail::evaluate_rational_c_imp(a.data(), b.data(), z, static_cast<std::integral_constant<int, N>*>(nullptr));
+   return detail::evaluate_rational_c_imp(a.data(), b.data(), z, static_cast<boost::math::integral_constant<int, N>*>(nullptr));
 }
+#endif
 
 } // namespace tools
 } // namespace math
diff --git a/tools/generate_rational_code.cpp b/tools/generate_rational_code.cpp
index 92b7da9a1..20ffde850 100644
--- a/tools/generate_rational_code.cpp
+++ b/tools/generate_rational_code.cpp
@@ -40,13 +40,13 @@ void print_polynomials(int max_order)
          "#define BOOST_MATH_TOOLS_POLY_EVAL_" << i << "_HPP\n\n"
          "namespace boost{ namespace math{ namespace tools{ namespace detail{\n\n"
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*)\n"
          "{\n"
          "   return static_cast<V>(0);\n"
          "}\n"
          "\n"
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*)\n"
          "{\n"
          "   return static_cast<V>(a[0]);\n"
          "}\n\n";
@@ -55,7 +55,7 @@ void print_polynomials(int max_order)
       {
          ofs << 
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, " << order << ">*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, " << order << ">*)\n"
          "{\n"
          "   return static_cast<V>(";
          
@@ -90,28 +90,28 @@ void print_polynomials(int max_order)
          "#define BOOST_MATH_TOOLS_POLY_EVAL_" << i << "_HPP\n\n"
          "namespace boost{ namespace math{ namespace tools{ namespace detail{\n\n"
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*)\n"
          "{\n"
          "   return static_cast<V>(0);\n"
          "}\n"
          "\n"
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*)\n"
          "{\n"
          "   return static_cast<V>(a[0]);\n"
          "}\n\n"
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*)\n"
          "{\n"
          "   return static_cast<V>(a[1] * x + a[0]);\n"
          "}\n\n"
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*)\n"
          "{\n"
          "   return static_cast<V>((a[2] * x + a[1]) * x + a[0]);\n"
          "}\n\n"
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*)\n"
          "{\n"
          "   return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);\n"
          "}\n\n";
@@ -120,7 +120,7 @@ void print_polynomials(int max_order)
       {
          ofs << 
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, " << order << ">*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, " << order << ">*)\n"
          "{\n"
          "   V x2 = x * x;\n"
          "   return static_cast<V>(";
@@ -186,28 +186,28 @@ void print_polynomials(int max_order)
          "#define BOOST_MATH_TOOLS_POLY_EVAL_" << i << "_HPP\n\n"
          "namespace boost{ namespace math{ namespace tools{ namespace detail{\n\n"
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*)\n"
          "{\n"
          "   return static_cast<V>(0);\n"
          "}\n"
          "\n"
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*)\n"
          "{\n"
          "   return static_cast<V>(a[0]);\n"
          "}\n\n"
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*)\n"
          "{\n"
          "   return static_cast<V>(a[1] * x + a[0]);\n"
          "}\n\n"
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*)\n"
          "{\n"
          "   return static_cast<V>((a[2] * x + a[1]) * x + a[0]);\n"
          "}\n\n"
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*)\n"
          "{\n"
          "   return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);\n"
          "}\n\n";
@@ -216,7 +216,7 @@ void print_polynomials(int max_order)
       {
          ofs << 
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, " << order << ">*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, " << order << ">*)\n"
          "{\n"
          "   V x2 = x * x;\n"
          "   V t[2];\n";
@@ -281,13 +281,13 @@ void print_rationals(int max_order)
          "#define BOOST_MATH_TOOLS_POLY_RAT_" << i << "_HPP\n\n"
          "namespace boost{ namespace math{ namespace tools{ namespace detail{\n\n"
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*)\n"
          "{\n"
          "   return static_cast<V>(0);\n"
          "}\n"
          "\n"
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*)\n"
          "{\n"
          "   return static_cast<V>(a[0]) / static_cast<V>(b[0]);\n"
          "}\n\n";
@@ -296,7 +296,7 @@ void print_rationals(int max_order)
       {
          ofs << 
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, " << order << ">*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, " << order << ">*)\n"
          "{\n"
          "   if((-1 <= x) && (x <= 1))\n"
          "     return static_cast<V>((";
@@ -361,28 +361,28 @@ void print_rationals(int max_order)
          "#define BOOST_MATH_TOOLS_RAT_EVAL_" << i << "_HPP\n\n"
          "namespace boost{ namespace math{ namespace tools{ namespace detail{\n\n"
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*)\n"
          "{\n"
          "   return static_cast<V>(0);\n"
          "}\n"
          "\n"
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*)\n"
          "{\n"
          "   return static_cast<V>(a[0]) / static_cast<V>(b[0]);\n"
          "}\n\n"
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*)\n"
          "{\n"
          "   return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));\n"
          "}\n\n"
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*)\n"
          "{\n"
          "   return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));\n"
          "}\n\n"
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*)\n"
          "{\n"
          "   return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));\n"
          "}\n\n";
@@ -391,7 +391,7 @@ void print_rationals(int max_order)
       {
          ofs << 
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, " << order << ">*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, " << order << ">*)\n"
          "{\n"
          "   if((-1 <= x) && (x <= 1))\n   {\n"
          "      V x2 = x * x;\n"
@@ -577,28 +577,28 @@ void print_rationals(int max_order)
          "#define BOOST_MATH_TOOLS_RAT_EVAL_" << i << "_HPP\n\n"
          "namespace boost{ namespace math{ namespace tools{ namespace detail{\n\n"
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*)\n"
          "{\n"
          "   return static_cast<V>(0);\n"
          "}\n"
          "\n"
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*)\n"
          "{\n"
          "   return static_cast<V>(a[0]) / static_cast<V>(b[0]);\n"
          "}\n\n"
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*)\n"
          "{\n"
          "   return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));\n"
          "}\n\n"
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*)\n"
          "{\n"
          "   return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));\n"
          "}\n\n"
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*)\n"
          "{\n"
          "   return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));\n"
          "}\n\n";
@@ -607,7 +607,7 @@ void print_rationals(int max_order)
       {
          ofs << 
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, " << order << ">*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, " << order << ">*)\n"
          "{\n"
          "   if((-1 <= x) && (x <= 1))\n   {\n"
          "      V x2 = x * x;\n"

From da6abf9fb3700e51584c964dcd513373dee9a55d Mon Sep 17 00:00:00 2001
From: Matt Borland <matt@mattborland.com>
Date: Tue, 13 Aug 2024 14:16:42 -0400
Subject: [PATCH 13/24] Add GPU definition of assertions

---
 include/boost/math/tools/assert.hpp | 17 ++++++++++++++++-
 1 file changed, 16 insertions(+), 1 deletion(-)

diff --git a/include/boost/math/tools/assert.hpp b/include/boost/math/tools/assert.hpp
index 3d5655923..3f57351fc 100644
--- a/include/boost/math/tools/assert.hpp
+++ b/include/boost/math/tools/assert.hpp
@@ -10,6 +10,19 @@
 #ifndef BOOST_MATH_TOOLS_ASSERT_HPP
 #define BOOST_MATH_TOOLS_ASSERT_HPP
 
+#include <boost/math/tools/config.hpp>
+
+#ifdef BOOST_MATH_HAS_GPU_SUPPORT
+
+// Run time asserts are generally unsupported
+
+#define BOOST_MATH_ASSERT(expr)
+#define BOOST_MATH_ASSERT_MSG(expr, msg)
+#define BOOST_MATH_STATIC_ASSERT(expr) static_assert(expr, #expr " failed")
+#define BOOST_MATH_STATIC_ASSERT_MSG(expr, msg) static_assert(expr, msg)
+
+#else
+
 #include <boost/math/tools/is_standalone.hpp>
 
 #ifndef BOOST_MATH_STANDALONE
@@ -29,6 +42,8 @@
 #define BOOST_MATH_STATIC_ASSERT(expr) static_assert(expr, #expr " failed")
 #define BOOST_MATH_STATIC_ASSERT_MSG(expr, msg) static_assert(expr, msg)
 
-#endif
+#endif // Is standalone
+
+#endif // BOOST_MATH_HAS_GPU_SUPPORT
 
 #endif // BOOST_MATH_TOOLS_ASSERT_HPP

From 865eacb8c78dc1e8f3966c09b2359696503f84a0 Mon Sep 17 00:00:00 2001
From: Matt Borland <matt@mattborland.com>
Date: Tue, 13 Aug 2024 14:37:51 -0400
Subject: [PATCH 14/24] Apply promotion changes from
 https://github.com/boostorg/math/pull/1022

---
 include/boost/math/tools/promotion.hpp | 318 ++++++-------------------
 1 file changed, 71 insertions(+), 247 deletions(-)

diff --git a/include/boost/math/tools/promotion.hpp b/include/boost/math/tools/promotion.hpp
index c117e9575..a65f3703f 100644
--- a/include/boost/math/tools/promotion.hpp
+++ b/include/boost/math/tools/promotion.hpp
@@ -3,6 +3,7 @@
 // Copyright John Maddock 2006.
 // Copyright Paul A. Bristow 2006.
 // Copyright Matt Borland 2023.
+// Copyright Ryan Elandt 2023.
 
 // Use, modification and distribution are subject to the
 // Boost Software License, Version 1.0.
@@ -24,15 +25,7 @@
 #endif
 
 #include <boost/math/tools/config.hpp>
-#include <type_traits>
-
-#if defined __has_include
-#  if __cplusplus > 202002L || (defined(_MSVC_LANG) && _MSVC_LANG > 202002L)
-#    if __has_include (<stdfloat>)
-#    include <stdfloat>
-#    endif
-#  endif
-#endif
+#include <boost/math/tools/type_traits.hpp>
 
 namespace boost
 {
@@ -40,272 +33,103 @@ namespace boost
   {
     namespace tools
     {
+      ///// This promotion system works as follows:
+      // 
+      // Rule<T1> (one argument promotion rule):
+      //   - Promotes `T` to `double` if `T` is an integer type as identified by
+      //     `std::is_integral`, otherwise is `T`
+      //
+      // Rule<T1, T2_to_TN...> (two or more argument promotion rule):
+      //   - 1. Calculates type using applying Rule<T1>.
+      //   - 2. Calculates type using applying Rule<T2_to_TN...> 
+      //   - If the type calculated in 1 and 2 are both floating point types, as
+      //     identified by `std::is_floating_point`, then return the type
+      //     determined by `std::common_type`. Otherwise return the type using
+      //     an asymmetric convertibility rule.
+      //
+      ///// Discussion:
+      //
       // If either T1 or T2 is an integer type,
       // pretend it was a double (for the purposes of further analysis).
       // Then pick the wider of the two floating-point types
       // as the actual signature to forward to.
       // For example:
-      // foo(int, short) -> double foo(double, double);
-      // foo(int, float) -> double foo(double, double);
-      // Note: NOT float foo(float, float)
-      // foo(int, double) -> foo(double, double);
-      // foo(double, float) -> double foo(double, double);
-      // foo(double, float) -> double foo(double, double);
-      // foo(any-int-or-float-type, long double) -> foo(long double, long double);
-      // but ONLY float foo(float, float) is unchanged.
-      // So the only way to get an entirely float version is to call foo(1.F, 2.F),
-      // But since most (all?) the math functions convert to double internally,
-      // probably there would not be the hoped-for gain by using float here.
-
+      //    foo(int, short) -> double foo(double, double);  // ***NOT*** float foo(float, float)
+      //    foo(int, float) -> double foo(double, double);  // ***NOT*** float foo(float, float)
+      //    foo(int, double) -> foo(double, double);
+      //    foo(double, float) -> double foo(double, double);
+      //    foo(double, float) -> double foo(double, double);
+      //    foo(any-int-or-float-type, long double) -> foo(long double, long double);
+      // ONLY float foo(float, float) is unchanged, so the only way to get an
+      // entirely float version is to call foo(1.F, 2.F). But since most (all?) the
+      // math functions convert to double internally, probably there would not be the
+      // hoped-for gain by using float here.
+      //
       // This follows the C-compatible conversion rules of pow, etc
       // where pow(int, float) is converted to pow(double, double).
 
+
+      // Promotes a single argument to double if it is an integer type
       template <class T>
-      struct promote_arg
-      { // If T is integral type, then promote to double.
-        using type = typename std::conditional<std::is_integral<T>::value, double, T>::type;
+      struct promote_arg {
+         using type = typename boost::math::conditional<boost::math::is_integral<T>::value, double, T>::type;
       };
-      // These full specialisations reduce std::conditional usage and speed up
-      // compilation:
-      template <> struct promote_arg<float> { using type = float; };
-      template <> struct promote_arg<double>{ using type = double; };
-      template <> struct promote_arg<long double> { using type = long double; };
-      template <> struct promote_arg<int> {  using type = double; };
 
-      #ifdef __STDCPP_FLOAT16_T__
-      template <> struct promote_arg<std::float16_t> { using type = std::float16_t; };
-      #endif
-      #ifdef __STDCPP_FLOAT32_T__
-      template <> struct promote_arg<std::float32_t> { using type = std::float32_t; };
-      #endif
-      #ifdef __STDCPP_FLOAT64_T__
-      template <> struct promote_arg<std::float64_t> { using type = std::float64_t; };
-      #endif
-      #ifdef __STDCPP_FLOAT128_T__
-      template <> struct promote_arg<std::float128_t> { using type = std::float128_t; };
-      #endif
-
-      template <typename T>
-      using promote_arg_t = typename promote_arg<T>::type;
 
+      // Promotes two arguments, neither of which is an integer type using an asymmetric
+      // convertibility rule.
+      template <class T1, class T2, bool = (boost::math::is_floating_point<T1>::value && boost::math::is_floating_point<T2>::value)>
+      struct pa2_integral_already_removed {
+         using type = typename boost::math::conditional<
+            !boost::math::is_floating_point<T2>::value && boost::math::is_convertible<T1, T2>::value, 
+            T2, T1>::type;
+      };
+      // For two floating point types, promotes using `std::common_type` functionality 
       template <class T1, class T2>
-      struct promote_args_2
-      { // Promote, if necessary, & pick the wider of the two floating-point types.
-        // for both parameter types, if integral promote to double.
-        using T1P = typename promote_arg<T1>::type; // T1 perhaps promoted.
-        using T2P = typename promote_arg<T2>::type; // T2 perhaps promoted.
-        using intermediate_type = typename std::conditional<
-          std::is_floating_point<T1P>::value && std::is_floating_point<T2P>::value, // both T1P and T2P are floating-point?
-#ifdef __STDCPP_FLOAT128_T__
-           typename std::conditional<std::is_same<std::float128_t, T1P>::value || std::is_same<std::float128_t, T2P>::value, // either long double?
-            std::float128_t,
-#endif 
-#ifdef BOOST_MATH_USE_FLOAT128
-           typename std::conditional<std::is_same<__float128, T1P>::value || std::is_same<__float128, T2P>::value, // either long double?
-            __float128,
-#endif 
-             typename std::conditional<std::is_same<long double, T1P>::value || std::is_same<long double, T2P>::value, // either long double?
-               long double, // then result type is long double.
-#ifdef __STDCPP_FLOAT64_T__
-             typename std::conditional<std::is_same<std::float64_t, T1P>::value || std::is_same<std::float64_t, T2P>::value, // either float64?
-               std::float64_t, // then result type is float64_t.
-#endif
-               typename std::conditional<std::is_same<double, T1P>::value || std::is_same<double, T2P>::value, // either double?
-                  double, // result type is double.
-#ifdef __STDCPP_FLOAT32_T__
-             typename std::conditional<std::is_same<std::float32_t, T1P>::value || std::is_same<std::float32_t, T2P>::value, // either float32?
-               std::float32_t, // then result type is float32_t.
-#endif
-                  float // else result type is float.
-             >::type
-#ifdef BOOST_MATH_USE_FLOAT128
-             >::type
-#endif
-#ifdef __STDCPP_FLOAT128_T__
-             >::type
-#endif
-#ifdef __STDCPP_FLOAT64_T__
-             >::type
-#endif
-#ifdef __STDCPP_FLOAT32_T__
-             >::type
-#endif
-             >::type,
-          // else one or the other is a user-defined type:
-          typename std::conditional<!std::is_floating_point<T2P>::value && std::is_convertible<T1P, T2P>::value, T2P, T1P>::type>::type;
-
-#ifdef __STDCPP_FLOAT64_T__
-          // If long doubles are doubles then we should prefer to use std::float64_t when available
-          using type = std::conditional_t<(sizeof(double) == sizeof(long double) && std::is_same<intermediate_type, long double>::value), std::float64_t, intermediate_type>;
-#else
-          using type = intermediate_type;
-#endif
-      }; // promote_arg2
-      // These full specialisations reduce std::conditional usage and speed up
-      // compilation:
-      template <> struct promote_args_2<float, float> { using type = float; };
-      template <> struct promote_args_2<double, double>{ using type = double; };
-      template <> struct promote_args_2<long double, long double> { using type = long double; };
-      template <> struct promote_args_2<int, int> {  using type = double; };
-      template <> struct promote_args_2<int, float> {  using type = double; };
-      template <> struct promote_args_2<float, int> {  using type = double; };
-      template <> struct promote_args_2<int, double> {  using type = double; };
-      template <> struct promote_args_2<double, int> {  using type = double; };
-      template <> struct promote_args_2<int, long double> {  using type = long double; };
-      template <> struct promote_args_2<long double, int> {  using type = long double; };
-      template <> struct promote_args_2<float, double> {  using type = double; };
-      template <> struct promote_args_2<double, float> {  using type = double; };
-      template <> struct promote_args_2<float, long double> {  using type = long double; };
-      template <> struct promote_args_2<long double, float> {  using type = long double; };
-      template <> struct promote_args_2<double, long double> {  using type = long double; };
-      template <> struct promote_args_2<long double, double> {  using type = long double; };
-
-      #ifdef __STDCPP_FLOAT128_T__
-      template <> struct promote_args_2<int, std::float128_t> { using type = std::float128_t; };
-      template <> struct promote_args_2<std::float128_t, int> { using type = std::float128_t; };
-      template <> struct promote_args_2<std::float128_t, float> { using type = std::float128_t; };
-      template <> struct promote_args_2<float, std::float128_t> { using type = std::float128_t; };
-      template <> struct promote_args_2<std::float128_t, double> { using type = std::float128_t; };
-      template <> struct promote_args_2<double, std::float128_t> { using type = std::float128_t; };
-      template <> struct promote_args_2<std::float128_t, long double> { using type = std::float128_t; };
-      template <> struct promote_args_2<long double, std::float128_t> { using type = std::float128_t; };
-
-      #ifdef __STDCPP_FLOAT16_T__
-      template <> struct promote_args_2<std::float128_t, std::float16_t> { using type = std::float128_t; };
-      template <> struct promote_args_2<std::float16_t, std::float128_t> { using type = std::float128_t; };
-      #endif
-
-      #ifdef __STDCPP_FLOAT32_T__
-      template <> struct promote_args_2<std::float128_t, std::float32_t> { using type = std::float128_t; };
-      template <> struct promote_args_2<std::float32_t, std::float128_t> { using type = std::float128_t; };
-      #endif
-
-      #ifdef __STDCPP_FLOAT64_T__
-      template <> struct promote_args_2<std::float128_t, std::float64_t> { using type = std::float128_t; };
-      template <> struct promote_args_2<std::float64_t, std::float128_t> { using type = std::float128_t; };
-      #endif
-
-      template <> struct promote_args_2<std::float128_t, std::float128_t> { using type = std::float128_t; };
-      #endif
-
-      #ifdef __STDCPP_FLOAT64_T__
-      template <> struct promote_args_2<int, std::float64_t> { using type = std::float64_t; };
-      template <> struct promote_args_2<std::float64_t, int> { using type = std::float64_t; };
-      template <> struct promote_args_2<std::float64_t, float> { using type = std::float64_t; };
-      template <> struct promote_args_2<float, std::float64_t> { using type = std::float64_t; };
-      template <> struct promote_args_2<std::float64_t, double> { using type = std::float64_t; };
-      template <> struct promote_args_2<double, std::float64_t> { using type = std::float64_t; };
-      template <> struct promote_args_2<std::float64_t, long double> { using type = long double; };
-      template <> struct promote_args_2<long double, std::float64_t> { using type = long double; };
-
-      #ifdef __STDCPP_FLOAT16_T__
-      template <> struct promote_args_2<std::float64_t, std::float16_t> { using type = std::float64_t; };
-      template <> struct promote_args_2<std::float16_t, std::float64_t> { using type = std::float64_t; };
-      #endif
-
-      #ifdef __STDCPP_FLOAT32_T__
-      template <> struct promote_args_2<std::float64_t, std::float32_t> { using type = std::float64_t; };
-      template <> struct promote_args_2<std::float32_t, std::float64_t> { using type = std::float64_t; };
-      #endif
-
-      template <> struct promote_args_2<std::float64_t, std::float64_t> { using type = std::float64_t; };
-      #endif
-
-      #ifdef __STDCPP_FLOAT32_T__
-      template <> struct promote_args_2<int, std::float32_t> { using type = std::float32_t; };
-      template <> struct promote_args_2<std::float32_t, int> { using type = std::float32_t; };
-      template <> struct promote_args_2<std::float32_t, float> { using type = std::float32_t; };
-      template <> struct promote_args_2<float, std::float32_t> { using type = std::float32_t; };
-      template <> struct promote_args_2<std::float32_t, double> { using type = double; };
-      template <> struct promote_args_2<double, std::float32_t> { using type = double; };
-      template <> struct promote_args_2<std::float32_t, long double> { using type = long double; };
-      template <> struct promote_args_2<long double, std::float32_t> { using type = long double; };
-
-      #ifdef __STDCPP_FLOAT16_T__
-      template <> struct promote_args_2<std::float32_t, std::float16_t> { using type = std::float32_t; };
-      template <> struct promote_args_2<std::float16_t, std::float32_t> { using type = std::float32_t; };
-      #endif
-
-      template <> struct promote_args_2<std::float32_t, std::float32_t> { using type = std::float32_t; };
-      #endif
+      struct pa2_integral_already_removed<T1, T2, true> {
+         using type = boost::math::common_type_t<T1, T2, float>;
+      };
 
-      #ifdef __STDCPP_FLOAT16_T__
-      template <> struct promote_args_2<int, std::float16_t> { using type = std::float16_t; };
-      template <> struct promote_args_2<std::float16_t, int> { using type = std::float16_t; };
-      template <> struct promote_args_2<std::float16_t, float> { using type = float; };
-      template <> struct promote_args_2<float, std::float16_t> { using type = float; };
-      template <> struct promote_args_2<std::float16_t, double> { using type = double; };
-      template <> struct promote_args_2<double, std::float16_t> { using type = double; };
-      template <> struct promote_args_2<std::float16_t, long double> { using type = long double; };
-      template <> struct promote_args_2<long double, std::float16_t> { using type = long double; };
 
-      template <> struct promote_args_2<std::float16_t, std::float16_t> { using type = std::float16_t; };
-      #endif
+      // Template definition for promote_args_permissive
+      template <typename... Args>
+      struct promote_args_permissive;
+      // Specialization for one argument
+      template <typename T>
+      struct promote_args_permissive<T> {
+         using type = typename promote_arg<typename boost::math::remove_cv<T>::type>::type;
+      };
+      // Specialization for two or more arguments
+      template <typename T1, typename... T2_to_TN>
+      struct promote_args_permissive<T1, T2_to_TN...> {
+         using type = typename pa2_integral_already_removed<
+                  typename promote_args_permissive<T1>::type,
+                  typename promote_args_permissive<T2_to_TN...>::type
+               >::type;
+      };
 
-      template <typename T, typename U>
-      using promote_args_2_t = typename promote_args_2<T, U>::type;
+      template <class... Args>
+      using promote_args_permissive_t = typename promote_args_permissive<Args...>::type;
 
-      template <class T1, class T2=float, class T3=float, class T4=float, class T5=float, class T6=float>
-      struct promote_args
-      {
-         using type = typename promote_args_2<
-            typename std::remove_cv<T1>::type,
-            typename promote_args_2<
-               typename std::remove_cv<T2>::type,
-               typename promote_args_2<
-                  typename std::remove_cv<T3>::type,
-                  typename promote_args_2<
-                     typename std::remove_cv<T4>::type,
-                     typename promote_args_2<
-                        typename std::remove_cv<T5>::type, typename std::remove_cv<T6>::type
-                     >::type
-                  >::type
-               >::type
-            >::type
-         >::type;
 
+      // Same as `promote_args_permissive` but with a static assertion that the promoted type
+      // is not `long double` if `BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS` is defined
+      template <class... Args>
+      struct promote_args {
+         using type = typename promote_args_permissive<Args...>::type;
 #if defined(BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS)
          //
          // Guard against use of long double if it's not supported:
          //
-         static_assert((0 == std::is_same<type, long double>::value), "Sorry, but this platform does not have sufficient long double support for the special functions to be reliably implemented.");
+         static_assert((0 == boost::math::is_same<type, long double>::value), "Sorry, but this platform does not have sufficient long double support for the special functions to be reliably implemented.");
 #endif
       };
 
-      template <class T1, class T2=float, class T3=float, class T4=float, class T5=float, class T6=float>
-      using promote_args_t = typename promote_args<T1, T2, T3, T4, T5, T6>::type;
-
-      //
-      // This struct is the same as above, but has no static assert on long double usage,
-      // it should be used only on functions that can be implemented for long double
-      // even when std lib support is missing or broken for that type.
-      //
-      template <class T1, class T2=float, class T3=float, class T4=float, class T5=float, class T6=float>
-      struct promote_args_permissive
-      {
-         using type = typename promote_args_2<
-            typename std::remove_cv<T1>::type,
-            typename promote_args_2<
-               typename std::remove_cv<T2>::type,
-               typename promote_args_2<
-                  typename std::remove_cv<T3>::type,
-                  typename promote_args_2<
-                     typename std::remove_cv<T4>::type,
-                     typename promote_args_2<
-                        typename std::remove_cv<T5>::type, typename std::remove_cv<T6>::type
-                     >::type
-                  >::type
-               >::type
-            >::type
-         >::type;
-      };
-
-      template <class T1, class T2=float, class T3=float, class T4=float, class T5=float, class T6=float>
-      using promote_args_permissive_t = typename promote_args_permissive<T1, T2, T3, T4, T5, T6>::type;
+      template <class... Args>
+      using promote_args_t = typename promote_args<Args...>::type;
 
     } // namespace tools
   } // namespace math
 } // namespace boost
 
 #endif // BOOST_MATH_PROMOTION_HPP
-

From 5261cf3dfe914e7ce92415712b2148b35c4cab0b Mon Sep 17 00:00:00 2001
From: Matt Borland <matt@mattborland.com>
Date: Tue, 13 Aug 2024 14:38:07 -0400
Subject: [PATCH 15/24] Fix old promotion args

---
 include/boost/math/ccmath/copysign.hpp          |  2 +-
 include/boost/math/ccmath/fdim.hpp              |  2 +-
 include/boost/math/ccmath/fmax.hpp              |  2 +-
 include/boost/math/ccmath/fmin.hpp              |  2 +-
 include/boost/math/ccmath/hypot.hpp             |  2 +-
 include/boost/math/differentiation/autodiff.hpp | 14 +++++++-------
 6 files changed, 12 insertions(+), 12 deletions(-)

diff --git a/include/boost/math/ccmath/copysign.hpp b/include/boost/math/ccmath/copysign.hpp
index 90a58102b..e117e57fa 100644
--- a/include/boost/math/ccmath/copysign.hpp
+++ b/include/boost/math/ccmath/copysign.hpp
@@ -54,7 +54,7 @@ constexpr auto copysign(T1 mag, T2 sgn) noexcept
 {
     if (BOOST_MATH_IS_CONSTANT_EVALUATED(mag))
     {        
-        using promoted_type = boost::math::tools::promote_args_2_t<T1, T2>;
+        using promoted_type = boost::math::tools::promote_args_t<T1, T2>;
         return boost::math::ccmath::copysign(static_cast<promoted_type>(mag), static_cast<promoted_type>(sgn));
     }
     else
diff --git a/include/boost/math/ccmath/fdim.hpp b/include/boost/math/ccmath/fdim.hpp
index cdcbc223c..d6b4e25ce 100644
--- a/include/boost/math/ccmath/fdim.hpp
+++ b/include/boost/math/ccmath/fdim.hpp
@@ -66,7 +66,7 @@ constexpr auto fdim(T1 x, T2 y) noexcept
 {
     if (BOOST_MATH_IS_CONSTANT_EVALUATED(x))
     {
-        using promoted_type = boost::math::tools::promote_args_2_t<T1, T2>;
+        using promoted_type = boost::math::tools::promote_args_t<T1, T2>;
         return boost::math::ccmath::fdim(promoted_type(x), promoted_type(y));
     }
     else
diff --git a/include/boost/math/ccmath/fmax.hpp b/include/boost/math/ccmath/fmax.hpp
index 237355275..8a0d17d03 100644
--- a/include/boost/math/ccmath/fmax.hpp
+++ b/include/boost/math/ccmath/fmax.hpp
@@ -62,7 +62,7 @@ constexpr auto fmax(T1 x, T2 y) noexcept
 {
     if (BOOST_MATH_IS_CONSTANT_EVALUATED(x))
     {
-        using promoted_type = boost::math::tools::promote_args_2_t<T1, T2>;
+        using promoted_type = boost::math::tools::promote_args_t<T1, T2>;
         return boost::math::ccmath::fmax(static_cast<promoted_type>(x), static_cast<promoted_type>(y));
     }
     else
diff --git a/include/boost/math/ccmath/fmin.hpp b/include/boost/math/ccmath/fmin.hpp
index 1c113e0d6..29885b69c 100644
--- a/include/boost/math/ccmath/fmin.hpp
+++ b/include/boost/math/ccmath/fmin.hpp
@@ -62,7 +62,7 @@ constexpr auto fmin(T1 x, T2 y) noexcept
 {
     if (BOOST_MATH_IS_CONSTANT_EVALUATED(x))
     {
-        using promoted_type = boost::math::tools::promote_args_2_t<T1, T2>;
+        using promoted_type = boost::math::tools::promote_args_t<T1, T2>;
         return boost::math::ccmath::fmin(static_cast<promoted_type>(x), static_cast<promoted_type>(y));
     }
     else
diff --git a/include/boost/math/ccmath/hypot.hpp b/include/boost/math/ccmath/hypot.hpp
index 4e0e245b4..34dd5ab2c 100644
--- a/include/boost/math/ccmath/hypot.hpp
+++ b/include/boost/math/ccmath/hypot.hpp
@@ -89,7 +89,7 @@ constexpr auto hypot(T1 x, T2 y) noexcept
 {
     if(BOOST_MATH_IS_CONSTANT_EVALUATED(x))
     {
-        using promoted_type = boost::math::tools::promote_args_2_t<T1, T2>;
+        using promoted_type = boost::math::tools::promote_args_t<T1, T2>;
         return boost::math::ccmath::hypot(static_cast<promoted_type>(x), static_cast<promoted_type>(y));
     }
     else
diff --git a/include/boost/math/differentiation/autodiff.hpp b/include/boost/math/differentiation/autodiff.hpp
index 7a57aa2f9..b8880f24d 100644
--- a/include/boost/math/differentiation/autodiff.hpp
+++ b/include/boost/math/differentiation/autodiff.hpp
@@ -39,7 +39,7 @@ namespace detail {
 
 template <typename RealType, typename... RealTypes>
 struct promote_args_n {
-  using type = typename tools::promote_args_2<RealType, typename promote_args_n<RealTypes...>::type>::type;
+  using type = typename tools::promote_args<RealType, typename promote_args_n<RealTypes...>::type>::type;
 };
 
 template <typename RealType>
@@ -2002,9 +2002,9 @@ using autodiff_root_type = typename autodiff_fvar_type<RealType, Order>::root_ty
 
 // See boost/math/tools/promotion.hpp
 template <typename RealType0, size_t Order0, typename RealType1, size_t Order1>
-struct promote_args_2<detail::autodiff_fvar_type<RealType0, Order0>,
+struct promote_args<detail::autodiff_fvar_type<RealType0, Order0>,
                       detail::autodiff_fvar_type<RealType1, Order1>> {
-  using type = detail::autodiff_fvar_type<typename promote_args_2<RealType0, RealType1>::type,
+  using type = detail::autodiff_fvar_type<typename promote_args<RealType0, RealType1>::type,
 #ifndef BOOST_MATH_NO_CXX14_CONSTEXPR
                                           (std::max)(Order0, Order1)>;
 #else
@@ -2018,13 +2018,13 @@ struct promote_args<detail::autodiff_fvar_type<RealType, Order>> {
 };
 
 template <typename RealType0, size_t Order0, typename RealType1>
-struct promote_args_2<detail::autodiff_fvar_type<RealType0, Order0>, RealType1> {
-  using type = detail::autodiff_fvar_type<typename promote_args_2<RealType0, RealType1>::type, Order0>;
+struct promote_args<detail::autodiff_fvar_type<RealType0, Order0>, RealType1> {
+  using type = detail::autodiff_fvar_type<typename promote_args<RealType0, RealType1>::type, Order0>;
 };
 
 template <typename RealType0, typename RealType1, size_t Order1>
-struct promote_args_2<RealType0, detail::autodiff_fvar_type<RealType1, Order1>> {
-  using type = detail::autodiff_fvar_type<typename promote_args_2<RealType0, RealType1>::type, Order1>;
+struct promote_args<RealType0, detail::autodiff_fvar_type<RealType1, Order1>> {
+  using type = detail::autodiff_fvar_type<typename promote_args<RealType0, RealType1>::type, Order1>;
 };
 
 template <typename destination_t, typename RealType, std::size_t Order>

From cbdb7207a8e947bbb87a31f79cdf4f2313cf8404 Mon Sep 17 00:00:00 2001
From: Matt Borland <matt@mattborland.com>
Date: Tue, 13 Aug 2024 14:38:30 -0400
Subject: [PATCH 16/24] Add NVRTC definition of BOOST_MATH_NOEXCEPT

---
 include/boost/math/tools/config.hpp | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/include/boost/math/tools/config.hpp b/include/boost/math/tools/config.hpp
index eeee11671..2048cfbc1 100644
--- a/include/boost/math/tools/config.hpp
+++ b/include/boost/math/tools/config.hpp
@@ -793,6 +793,8 @@ BOOST_MATH_GPU_ENABLED constexpr T cuda_safe_max(const T& a, const T& b) { retur
 
 #define BOOST_MATH_STATIC static
 
+#define BOOST_MATH_NOEXCEPT(T) noexcept(boost::math::is_floating_point_v<T>)
+
 template <class T>
 BOOST_MATH_GPU_ENABLED constexpr void gpu_safe_swap(T& a, T& b) { T t(a); a = b; b = t; }
 

From 0089d4cb9d1fa2fa0055aa1154e7ca05d4725b4b Mon Sep 17 00:00:00 2001
From: Matt Borland <matt@mattborland.com>
Date: Tue, 13 Aug 2024 14:59:05 -0400
Subject: [PATCH 17/24] Add GPU to macro definitions

---
 include/boost/math/policies/policy.hpp | 28 +++++++++++++-------------
 1 file changed, 14 insertions(+), 14 deletions(-)

diff --git a/include/boost/math/policies/policy.hpp b/include/boost/math/policies/policy.hpp
index a17dfe6db..432191362 100644
--- a/include/boost/math/policies/policy.hpp
+++ b/include/boost/math/policies/policy.hpp
@@ -135,16 +135,16 @@ namespace policies{
                                                                                                 \
    namespace detail{                                                                            \
    template <Type N>                                                                            \
-   char test_is_valid_arg(const name<N>* = nullptr);                                            \
-   char test_is_default_arg(const name<Default>* = nullptr);                                    \
+   BOOST_MATH_GPU_ENABLED char test_is_valid_arg(const name<N>* = nullptr);                     \
+   BOOST_MATH_GPU_ENABLED char test_is_default_arg(const name<Default>* = nullptr);             \
                                                                                                 \
    template <typename T>                                                                        \
    class is_##name##_imp                                                                        \
    {                                                                                            \
    private:                                                                                     \
       template <Type N>                                                                         \
-      static char test(const name<N>* = nullptr);                                               \
-      static double test(...);                                                                  \
+      BOOST_MATH_GPU_ENABLED static char test(const name<N>* = nullptr);                        \
+      BOOST_MATH_GPU_ENABLED static double test(...);                                           \
    public:                                                                                      \
       static constexpr bool value = sizeof(test(static_cast<T*>(nullptr))) == sizeof(char);     \
    };                                                                                           \
@@ -164,16 +164,16 @@ namespace policies{
                                                                                                 \
    namespace detail{                                                                            \
    template <bool N>                                                                            \
-   char test_is_valid_arg(const name<N>* = nullptr);                                            \
-   char test_is_default_arg(const name<Default>* = nullptr);                                    \
+   BOOST_MATH_GPU_ENABLED char test_is_valid_arg(const name<N>* = nullptr);                     \
+   BOOST_MATH_GPU_ENABLED char test_is_default_arg(const name<Default>* = nullptr);             \
                                                                                                 \
    template <typename T>                                                                        \
    class is_##name##_imp                                                                        \
    {                                                                                            \
    private:                                                                                     \
       template <bool N>                                                                         \
-      static char test(const name<N>* = nullptr);                                               \
-      static double test(...);                                                                  \
+      BOOST_MATH_GPU_ENABLED static char test(const name<N>* = nullptr);                        \
+      BOOST_MATH_GPU_ENABLED static double test(...);                                           \
    public:                                                                                      \
       static constexpr bool value = sizeof(test(static_cast<T*>(nullptr))) == sizeof(char);     \
    };                                                                                           \
@@ -273,10 +273,10 @@ struct precision
 #endif
 };
 
-double test_is_valid_arg(...);
-double test_is_default_arg(...);
-char test_is_valid_arg(const default_policy*);
-char test_is_default_arg(const default_policy*);
+BOOST_MATH_GPU_ENABLED double test_is_valid_arg(...);
+BOOST_MATH_GPU_ENABLED double test_is_default_arg(...);
+BOOST_MATH_GPU_ENABLED char test_is_valid_arg(const default_policy*);
+BOOST_MATH_GPU_ENABLED char test_is_default_arg(const default_policy*);
 
 template <typename T>
 class is_valid_policy_imp
@@ -934,8 +934,8 @@ template <class A1,
           class A9,
           class A10,
           class A11>
-char test_is_policy(const policy<A1,A2,A3,A4,A5,A6,A7,A8,A9,A10,A11>*);
-double test_is_policy(...);
+BOOST_MATH_GPU_ENABLED char test_is_policy(const policy<A1,A2,A3,A4,A5,A6,A7,A8,A9,A10,A11>*);
+BOOST_MATH_GPU_ENABLED double test_is_policy(...);
 
 template <typename P>
 class is_policy_imp

From 7818b0648013d0f5cf91b6cdf2756613ea4a9e28 Mon Sep 17 00:00:00 2001
From: Matt Borland <matt@mattborland.com>
Date: Tue, 13 Aug 2024 14:59:21 -0400
Subject: [PATCH 18/24] Add more macro definitions

---
 include/boost/math/tools/config.hpp | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/include/boost/math/tools/config.hpp b/include/boost/math/tools/config.hpp
index 2048cfbc1..dc358852b 100644
--- a/include/boost/math/tools/config.hpp
+++ b/include/boost/math/tools/config.hpp
@@ -794,6 +794,8 @@ BOOST_MATH_GPU_ENABLED constexpr T cuda_safe_max(const T& a, const T& b) { retur
 #define BOOST_MATH_STATIC static
 
 #define BOOST_MATH_NOEXCEPT(T) noexcept(boost::math::is_floating_point_v<T>)
+#define BOOST_MATH_EXPLICIT_TEMPLATE_TYPE(T) 
+#define BOOST_MATH_BIG_CONSTANT(T, N, V) static_cast<T>(V)
 
 template <class T>
 BOOST_MATH_GPU_ENABLED constexpr void gpu_safe_swap(T& a, T& b) { T t(a); a = b; b = t; }

From f060ae2260747d96fd1c57d64bc3af0b77955d3d Mon Sep 17 00:00:00 2001
From: Matt Borland <matt@mattborland.com>
Date: Tue, 13 Aug 2024 15:53:53 -0400
Subject: [PATCH 19/24] Remove old workaround

---
 .../boost/math/policies/error_handling.hpp    | 26 -------------------
 1 file changed, 26 deletions(-)

diff --git a/include/boost/math/policies/error_handling.hpp b/include/boost/math/policies/error_handling.hpp
index 0f85023be..b1c0d8e3e 100644
--- a/include/boost/math/policies/error_handling.hpp
+++ b/include/boost/math/policies/error_handling.hpp
@@ -336,32 +336,6 @@ BOOST_MATH_GPU_ENABLED constexpr T raise_overflow_error(
    return boost::math::numeric_limits<T>::has_infinity ? boost::math::numeric_limits<T>::infinity() : boost::math::tools::max_value<T>();
 }
 
-#ifdef BOOST_MATH_HAS_GPU_SUPPORT
-
-template <>
-BOOST_MATH_GPU_ENABLED constexpr float raise_overflow_error<float>(
-           const char* ,
-           const char* ,
-           const  ::boost::math::policies::overflow_error< ::boost::math::policies::ignore_error>&) BOOST_MATH_NOEXCEPT(float)
-{
-   // This may or may not do the right thing, but the user asked for the error
-   // to be ignored so here we go anyway:
-   return static_cast<float>(INFINITY);
-}
-
-template <>
-BOOST_MATH_GPU_ENABLED constexpr double raise_overflow_error<double>(
-           const char* ,
-           const char* ,
-           const  ::boost::math::policies::overflow_error< ::boost::math::policies::ignore_error>&) BOOST_MATH_NOEXCEPT(double)
-{
-   // This may or may not do the right thing, but the user asked for the error
-   // to be ignored so here we go anyway:
-   return INFINITY;
-}
-
-#endif
-
 template <class T>
 BOOST_MATH_GPU_ENABLED constexpr T raise_overflow_error(
            const char* ,

From dc8469f346c653190dceab4829a1b0b1fd87ba16 Mon Sep 17 00:00:00 2001
From: Matt Borland <matt@mattborland.com>
Date: Tue, 13 Aug 2024 16:19:12 -0400
Subject: [PATCH 20/24] Add NVRTC capable error handling

---
 .../boost/math/policies/error_handling.hpp    | 147 ++++++++++++++++++
 1 file changed, 147 insertions(+)

diff --git a/include/boost/math/policies/error_handling.hpp b/include/boost/math/policies/error_handling.hpp
index b1c0d8e3e..d1d74c534 100644
--- a/include/boost/math/policies/error_handling.hpp
+++ b/include/boost/math/policies/error_handling.hpp
@@ -10,6 +10,9 @@
 
 #include <boost/math/tools/config.hpp>
 #include <boost/math/tools/numeric_limits.hpp>
+
+#ifndef BOOST_MATH_HAS_NVRTC
+
 #include <iomanip>
 #include <string>
 #include <cstring>
@@ -892,5 +895,149 @@ BOOST_MATH_GPU_ENABLED std::pair<T, T> pair_from_single(const T& val) BOOST_MATH
 
 }} // namespaces boost/math
 
+#else // Special values for NVRTC
+
+namespace boost {
+namespace math {
+namespace policies {
+
+template <class T, class Policy>
+BOOST_MATH_GPU_ENABLED constexpr T raise_domain_error(
+           const char* ,
+           const char* ,
+           const T& ,
+           const Policy&) BOOST_MATH_NOEXCEPT(T)
+{
+   // This may or may not do the right thing, but the user asked for the error
+   // to be ignored so here we go anyway:
+   return boost::math::numeric_limits<T>::quiet_NaN();
+}
+
+template <class T, class Policy>
+BOOST_MATH_GPU_ENABLED constexpr T raise_pole_error(
+           const char* function,
+           const char* message,
+           const T& val,
+           const  Policy&) BOOST_MATH_NOEXCEPT(T)
+{
+   return boost::math::numeric_limits<T>::quiet_NaN();
+}
+
+template <class T, class Policy>
+BOOST_MATH_GPU_ENABLED constexpr T raise_overflow_error(
+           const char* ,
+           const char* ,
+           const Policy&) BOOST_MATH_NOEXCEPT(T)
+{
+   // This may or may not do the right thing, but the user asked for the error
+   // to be ignored so here we go anyway:
+   return boost::math::numeric_limits<T>::has_infinity ? boost::math::numeric_limits<T>::infinity() : (boost::math::numeric_limits<T>::max)();
+}
+
+template <class T, class Policy>
+BOOST_MATH_GPU_ENABLED constexpr T raise_overflow_error(
+           const char* ,
+           const char* ,
+           const T&,
+           const Policy&) BOOST_MATH_NOEXCEPT(T)
+{
+   // This may or may not do the right thing, but the user asked for the error
+   // to be ignored so here we go anyway:
+   return boost::math::numeric_limits<T>::has_infinity ? boost::math::numeric_limits<T>::infinity() : (boost::math::numeric_limits<T>::max)();
+}
+
+template <class T, class Policy>
+BOOST_MATH_GPU_ENABLED constexpr T raise_underflow_error(
+           const char* ,
+           const char* ,
+           const Policy&) BOOST_MATH_NOEXCEPT(T)
+{
+   // This may or may not do the right thing, but the user asked for the error
+   // to be ignored so here we go anyway:
+   return static_cast<T>(0);
+}
+
+template <class T, class Policy>
+BOOST_MATH_GPU_ENABLED inline constexpr T raise_denorm_error(
+           const char* ,
+           const char* ,
+           const T& val,
+           const Policy&) BOOST_MATH_NOEXCEPT(T)
+{
+   // This may or may not do the right thing, but the user asked for the error
+   // to be ignored so here we go anyway:
+   return val;
+}
+
+template <class T, class Policy>
+BOOST_MATH_GPU_ENABLED constexpr T raise_evaluation_error(
+           const char* ,
+           const char* ,
+           const T& val,
+           const Policy&) BOOST_MATH_NOEXCEPT(T)
+{
+   // This may or may not do the right thing, but the user asked for the error
+   // to be ignored so here we go anyway:
+   return val;
+}
+
+template <class T, class TargetType, class Policy>
+BOOST_MATH_GPU_ENABLED constexpr TargetType raise_rounding_error(
+           const char* ,
+           const char* ,
+           const T& val,
+           const TargetType&,
+           const Policy&) BOOST_MATH_NOEXCEPT(T)
+{
+   // This may or may not do the right thing, but the user asked for the error
+   // to be ignored so here we go anyway:
+   static_assert(boost::math::numeric_limits<TargetType>::is_specialized, "The target type must have std::numeric_limits specialized.");
+   return  val > 0 ? (boost::math::numeric_limits<TargetType>::max)() : (boost::math::numeric_limits<TargetType>::is_integer ? (boost::math::numeric_limits<TargetType>::min)() : -(boost::math::numeric_limits<TargetType>::max)());
+}
+
+template <class T, class R, class Policy>
+BOOST_MATH_GPU_ENABLED inline constexpr T raise_indeterminate_result_error(
+           const char* ,
+           const char* ,
+           const T& ,
+           const R& result,
+           const Policy&) BOOST_MATH_NOEXCEPT(T)
+{
+   // This may or may not do the right thing, but the user asked for the error
+   // to be ignored so here we go anyway:
+   return result;
+}
+
+template <class R, class Policy, class T>
+BOOST_MATH_GPU_ENABLED BOOST_MATH_FORCEINLINE R checked_narrowing_cast(T val, const char* function) noexcept(boost::math::is_floating_point_v<R> && boost::math::is_floating_point_v<T>)
+{
+   // We only have ignore error policy so no reason to check
+   return static_cast<R>(val);
+}
+
+template <class T, class Policy>
+BOOST_MATH_GPU_ENABLED inline void check_series_iterations(const char* function, BOOST_MATH_UINTMAX_T max_iter, const Policy& pol) noexcept(boost::math::is_floating_point_v<T>)
+{
+   if(max_iter >= policies::get_max_series_iterations<Policy>())
+      raise_evaluation_error<T>(
+         function,
+         "Series evaluation exceeded %1% iterations, giving up now.", static_cast<T>(static_cast<double>(max_iter)), pol);
+}
+
+template <class T, class Policy>
+BOOST_MATH_GPU_ENABLED inline void check_root_iterations(const char* function, BOOST_MATH_UINTMAX_T max_iter, const Policy& pol) noexcept(boost::math::is_floating_point_v<T>)
+{
+   if(max_iter >= policies::get_max_root_iterations<Policy>())
+      raise_evaluation_error<T>(
+         function,
+         "Root finding evaluation exceeded %1% iterations, giving up now.", static_cast<T>(static_cast<double>(max_iter)), pol);
+}
+
+} // namespace policies
+} // namespace math
+} // namespace boost
+
+#endif
+
 #endif // BOOST_MATH_POLICY_ERROR_HANDLING_HPP
 

From 333e85f6826695e0d69d1403f5a75d860dd84625 Mon Sep 17 00:00:00 2001
From: Matt Borland <matt@mattborland.com>
Date: Tue, 13 Aug 2024 16:19:24 -0400
Subject: [PATCH 21/24] Add missing macros

---
 include/boost/math/tools/config.hpp | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/include/boost/math/tools/config.hpp b/include/boost/math/tools/config.hpp
index dc358852b..4c8e3dcf3 100644
--- a/include/boost/math/tools/config.hpp
+++ b/include/boost/math/tools/config.hpp
@@ -796,6 +796,8 @@ BOOST_MATH_GPU_ENABLED constexpr T cuda_safe_max(const T& a, const T& b) { retur
 #define BOOST_MATH_NOEXCEPT(T) noexcept(boost::math::is_floating_point_v<T>)
 #define BOOST_MATH_EXPLICIT_TEMPLATE_TYPE(T) 
 #define BOOST_MATH_BIG_CONSTANT(T, N, V) static_cast<T>(V)
+#define BOOST_MATH_FORCEINLINE __forceinline__
+#define BOOST_MATH_STD_USING  
 
 template <class T>
 BOOST_MATH_GPU_ENABLED constexpr void gpu_safe_swap(T& a, T& b) { T t(a); a = b; b = t; }

From 067efe69f7dd9b705af898a422eaeeace9b8b574 Mon Sep 17 00:00:00 2001
From: Matt Borland <matt@mattborland.com>
Date: Tue, 13 Aug 2024 16:27:36 -0400
Subject: [PATCH 22/24] Add NVRTC support to constants

---
 include/boost/math/constants/constants.hpp | 20 ++++++++++++++++++--
 1 file changed, 18 insertions(+), 2 deletions(-)

diff --git a/include/boost/math/constants/constants.hpp b/include/boost/math/constants/constants.hpp
index bd2afd714..df702bf89 100644
--- a/include/boost/math/constants/constants.hpp
+++ b/include/boost/math/constants/constants.hpp
@@ -1,5 +1,6 @@
 //  Copyright John Maddock 2005-2006, 2011.
 //  Copyright Paul A. Bristow 2006-2011.
+//  Copyright Matt Borland 2024.
 //  Use, modification and distribution are subject to the
 //  Boost Software License, Version 1.0. (See accompanying file
 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
@@ -8,6 +9,9 @@
 #define BOOST_MATH_CONSTANTS_CONSTANTS_INCLUDED
 
 #include <boost/math/tools/config.hpp>
+
+#ifndef BOOST_MATH_HAS_NVRTC
+
 #include <boost/math/tools/cxx03_warn.hpp>
 #include <boost/math/policies/policy.hpp>
 #include <boost/math/tools/precision.hpp>
@@ -243,6 +247,16 @@ namespace boost{ namespace math
    namespace long_double_constants{ static constexpr long double name = BOOST_MATH_JOIN(x, L); }\
    namespace constants{
 
+#else // NVRTC simplified macro definition
+
+#define BOOST_DEFINE_MATH_CONSTANT(name, value, str_value) template <typename T> BOOST_MATH_GPU_ENABLED constexpr T name() noexcept { return static_cast<T>(value); }
+
+namespace boost {
+namespace math {
+namespace constants {
+
+#endif
+
   BOOST_DEFINE_MATH_CONSTANT(half, 5.000000000000000000000000000000000000e-01, "5.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01")
   BOOST_DEFINE_MATH_CONSTANT(third, 3.333333333333333333333333333333333333e-01, "3.33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333e-01")
   BOOST_DEFINE_MATH_CONSTANT(twothirds, 6.666666666666666666666666666666666666e-01, "6.66666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667e-01")
@@ -318,14 +332,12 @@ namespace boost{ namespace math
   BOOST_DEFINE_MATH_CONSTANT(one_div_pi, 0.3183098861837906715377675267450287240689192, "0.31830988618379067153776752674502872406891929148091289749533468811779359526845307018022760553250617191214568545351")
   BOOST_DEFINE_MATH_CONSTANT(two_div_root_pi, 1.12837916709551257389615890312154517168810125, "1.12837916709551257389615890312154517168810125865799771368817144342128493688298682897348732040421472688605669581272")
 
-#if __cplusplus >= 201103L || (defined(_MSC_VER) && _MSC_VER >= 1900)
   BOOST_DEFINE_MATH_CONSTANT(first_feigenbaum, 4.66920160910299067185320382046620161725818557747576863274,  "4.6692016091029906718532038204662016172581855774757686327456513430041343302113147371386897440239480138171")
   BOOST_DEFINE_MATH_CONSTANT(plastic, 1.324717957244746025960908854478097340734404056901733364534, "1.32471795724474602596090885447809734073440405690173336453401505030282785124554759405469934798178728032991")
   BOOST_DEFINE_MATH_CONSTANT(gauss, 0.834626841674073186281429732799046808993993013490347002449, "0.83462684167407318628142973279904680899399301349034700244982737010368199270952641186969116035127532412906785")
   BOOST_DEFINE_MATH_CONSTANT(dottie, 0.739085133215160641655312087673873404013411758900757464965, "0.739085133215160641655312087673873404013411758900757464965680635773284654883547594599376106931766531849801246")
   BOOST_DEFINE_MATH_CONSTANT(reciprocal_fibonacci, 3.35988566624317755317201130291892717968890513, "3.35988566624317755317201130291892717968890513373196848649555381532513031899668338361541621645679008729704")
   BOOST_DEFINE_MATH_CONSTANT(laplace_limit, 0.662743419349181580974742097109252907056233549115022417, "0.66274341934918158097474209710925290705623354911502241752039253499097185308651127724965480259895818168")
-#endif
 
 template <typename T>
 BOOST_MATH_GPU_ENABLED inline constexpr T tau() {  return two_pi<T>(); }
@@ -338,7 +350,11 @@ BOOST_MATH_GPU_ENABLED inline constexpr T tau() {  return two_pi<T>(); }
 // We deliberately include this *after* all the declarations above,
 // that way the calculation routines can call on other constants above:
 //
+// NVRTC will not have a type that needs runtime calculation
+//
+#ifndef BOOST_MATH_HAS_NVRTC
 #include <boost/math/constants/calculate_constants.hpp>
+#endif
 
 #endif // BOOST_MATH_CONSTANTS_CONSTANTS_INCLUDED
 

From 74a2138a436981096ef3287d77852e38b67b8b36 Mon Sep 17 00:00:00 2001
From: Matt Borland <matt@mattborland.com>
Date: Tue, 13 Aug 2024 16:27:46 -0400
Subject: [PATCH 23/24] Add NVRTC support to digamma

---
 .../boost/math/special_functions/digamma.hpp  | 50 +++++++++++++------
 1 file changed, 35 insertions(+), 15 deletions(-)

diff --git a/include/boost/math/special_functions/digamma.hpp b/include/boost/math/special_functions/digamma.hpp
index bde80f7dd..382ad0d6b 100644
--- a/include/boost/math/special_functions/digamma.hpp
+++ b/include/boost/math/special_functions/digamma.hpp
@@ -14,13 +14,20 @@
 #endif
 
 #include <boost/math/tools/config.hpp>
-#include <boost/math/special_functions/math_fwd.hpp>
+#include <boost/math/tools/type_traits.hpp>
 #include <boost/math/tools/rational.hpp>
-#include <boost/math/tools/series.hpp>
 #include <boost/math/tools/promotion.hpp>
+#include <boost/math/policies/policy.hpp>
+#include <boost/math/policies/error_handling.hpp>
+#include <boost/math/constants/constants.hpp>
+
+#ifndef BOOST_MATH_HAS_NVRTC
+#include <boost/math/special_functions/math_fwd.hpp>
+#include <boost/math/tools/series.hpp>
 #include <boost/math/policies/error_handling.hpp>
 #include <boost/math/constants/constants.hpp>
 #include <boost/math/tools/big_constant.hpp>
+#endif
 
 #if defined(__GNUC__) && defined(BOOST_MATH_USE_FLOAT128)
 //
@@ -39,9 +46,9 @@ namespace detail{
 // Begin by defining the smallest value for which it is safe to
 // use the asymptotic expansion for digamma:
 //
-BOOST_MATH_GPU_ENABLED inline unsigned digamma_large_lim(const std::integral_constant<int, 0>*)
+BOOST_MATH_GPU_ENABLED inline unsigned digamma_large_lim(const boost::math::integral_constant<int, 0>*)
 {  return 20;  }
-BOOST_MATH_GPU_ENABLED inline unsigned digamma_large_lim(const std::integral_constant<int, 113>*)
+BOOST_MATH_GPU_ENABLED inline unsigned digamma_large_lim(const boost::math::integral_constant<int, 113>*)
 {  return 20;  }
 BOOST_MATH_GPU_ENABLED inline unsigned digamma_large_lim(const void*)
 {  return 10;  }
@@ -55,8 +62,10 @@ BOOST_MATH_GPU_ENABLED inline unsigned digamma_large_lim(const void*)
 //
 // This first one gives 34-digit precision for x >= 20:
 //
+
+#ifndef BOOST_MATH_HAS_NVRTC
 template <class T>
-inline T digamma_imp_large(T x, const std::integral_constant<int, 113>*)
+inline T digamma_imp_large(T x, const boost::math::integral_constant<int, 113>*)
 {
    BOOST_MATH_STD_USING // ADL of std functions.
    static const T P[] = {
@@ -89,7 +98,7 @@ inline T digamma_imp_large(T x, const std::integral_constant<int, 113>*)
 // 19-digit precision for x >= 10:
 //
 template <class T>
-inline T digamma_imp_large(T x, const std::integral_constant<int, 64>*)
+inline T digamma_imp_large(T x, const boost::math::integral_constant<int, 64>*)
 {
    BOOST_MATH_STD_USING // ADL of std functions.
    static const T P[] = {
@@ -112,11 +121,12 @@ inline T digamma_imp_large(T x, const std::integral_constant<int, 64>*)
    result -= z * tools::evaluate_polynomial(P, z);
    return result;
 }
+#endif
 //
 // 17-digit precision for x >= 10:
 //
 template <class T>
-BOOST_MATH_GPU_ENABLED inline T digamma_imp_large(T x, const std::integral_constant<int, 53>*)
+BOOST_MATH_GPU_ENABLED inline T digamma_imp_large(T x, const boost::math::integral_constant<int, 53>*)
 {
    BOOST_MATH_STD_USING // ADL of std functions.
    BOOST_MATH_STATIC const T P[] = {
@@ -140,7 +150,7 @@ BOOST_MATH_GPU_ENABLED inline T digamma_imp_large(T x, const std::integral_const
 // 9-digit precision for x >= 10:
 //
 template <class T>
-BOOST_MATH_GPU_ENABLED inline T digamma_imp_large(T x, const std::integral_constant<int, 24>*)
+BOOST_MATH_GPU_ENABLED inline T digamma_imp_large(T x, const boost::math::integral_constant<int, 24>*)
 {
    BOOST_MATH_STD_USING // ADL of std functions.
    BOOST_MATH_STATIC const T P[] = {
@@ -155,6 +165,8 @@ BOOST_MATH_GPU_ENABLED inline T digamma_imp_large(T x, const std::integral_const
    result -= z * tools::evaluate_polynomial(P, z);
    return result;
 }
+
+#ifndef BOOST_MATH_HAS_NVRTC
 //
 // Fully generic asymptotic expansion in terms of Bernoulli numbers, see:
 // http://functions.wolfram.com/06.14.06.0012.01
@@ -179,7 +191,7 @@ struct digamma_series_func
 };
 
 template <class T, class Policy>
-inline T digamma_imp_large(T x, const Policy& pol, const std::integral_constant<int, 0>*)
+inline T digamma_imp_large(T x, const Policy& pol, const boost::math::integral_constant<int, 0>*)
 {
    BOOST_MATH_STD_USING
    digamma_series_func<T> s(x);
@@ -196,7 +208,7 @@ inline T digamma_imp_large(T x, const Policy& pol, const std::integral_constant<
 // 35-digit precision:
 //
 template <class T>
-T digamma_imp_1_2(T x, const std::integral_constant<int, 113>*)
+T digamma_imp_1_2(T x, const boost::math::integral_constant<int, 113>*)
 {
    //
    // Now the approximation, we use the form:
@@ -260,7 +272,7 @@ T digamma_imp_1_2(T x, const std::integral_constant<int, 113>*)
 // 19-digit precision:
 //
 template <class T>
-T digamma_imp_1_2(T x, const std::integral_constant<int, 64>*)
+T digamma_imp_1_2(T x, const boost::math::integral_constant<int, 64>*)
 {
    //
    // Now the approximation, we use the form:
@@ -308,11 +320,13 @@ T digamma_imp_1_2(T x, const std::integral_constant<int, 64>*)
 
    return result;
 }
+
+#endif
 //
 // 18-digit precision:
 //
 template <class T>
-BOOST_MATH_GPU_ENABLED T digamma_imp_1_2(T x, const std::integral_constant<int, 53>*)
+BOOST_MATH_GPU_ENABLED T digamma_imp_1_2(T x, const boost::math::integral_constant<int, 53>*)
 {
    //
    // Now the approximation, we use the form:
@@ -363,7 +377,7 @@ BOOST_MATH_GPU_ENABLED T digamma_imp_1_2(T x, const std::integral_constant<int,
 // 9-digit precision:
 //
 template <class T>
-BOOST_MATH_GPU_ENABLED inline T digamma_imp_1_2(T x, const std::integral_constant<int, 24>*)
+BOOST_MATH_GPU_ENABLED inline T digamma_imp_1_2(T x, const boost::math::integral_constant<int, 24>*)
 {
    //
    // Now the approximation, we use the form:
@@ -441,11 +455,13 @@ BOOST_MATH_GPU_ENABLED T digamma_imp(T x, const Tag* t, const Policy& pol)
    // If we're above the lower-limit for the
    // asymptotic expansion then use it:
    //
+   #ifndef BOOST_MATH_HAS_NVRTC
    if(x >= digamma_large_lim(t))
    {
       result += digamma_imp_large(x, t);
    }
    else
+   #endif
    {
       //
       // If x > 2 reduce to the interval [1,2]:
@@ -468,8 +484,10 @@ BOOST_MATH_GPU_ENABLED T digamma_imp(T x, const Tag* t, const Policy& pol)
    return result;
 }
 
+#ifndef BOOST_MATH_HAS_NVRTC
+
 template <class T, class Policy>
-T digamma_imp(T x, const std::integral_constant<int, 0>* t, const Policy& pol)
+T digamma_imp(T x, const boost::math::integral_constant<int, 0>* t, const Policy& pol)
 {
    //
    // This handles reflection of negative arguments, and all our
@@ -566,6 +584,8 @@ T digamma_imp(T x, const std::integral_constant<int, 0>* t, const Policy& pol)
    // LCOV_EXCL_STOP
 }
 
+#endif
+
 } // namespace detail
 
 template <class T, class Policy>
@@ -575,7 +595,7 @@ BOOST_MATH_GPU_ENABLED inline typename tools::promote_args<T>::type
    typedef typename tools::promote_args<T>::type result_type;
    typedef typename policies::evaluation<result_type, Policy>::type value_type;
    typedef typename policies::precision<T, Policy>::type precision_type;
-   typedef std::integral_constant<int,
+   typedef boost::math::integral_constant<int,
       (precision_type::value <= 0) || (precision_type::value > 113) ? 0 :
       precision_type::value <= 24 ? 24 :
       precision_type::value <= 53 ? 53 :

From ce0f99eb98d99569c6695107e98a62e275c9f0db Mon Sep 17 00:00:00 2001
From: Matt Borland <matt@mattborland.com>
Date: Tue, 13 Aug 2024 16:39:53 -0400
Subject: [PATCH 24/24] Add NVRTC digamma tests

---
 test/nvrtc_jamfile                 |   2 +
 test/test_digamma_nvrtc_double.cpp | 190 +++++++++++++++++++++++++++++
 test/test_digamma_nvrtc_float.cpp  | 190 +++++++++++++++++++++++++++++
 3 files changed, 382 insertions(+)
 create mode 100644 test/test_digamma_nvrtc_double.cpp
 create mode 100644 test/test_digamma_nvrtc_float.cpp

diff --git a/test/nvrtc_jamfile b/test/nvrtc_jamfile
index 9e59740e6..434ca002b 100644
--- a/test/nvrtc_jamfile
+++ b/test/nvrtc_jamfile
@@ -14,6 +14,8 @@ run test_cbrt_nvrtc_double.cpp ;
 run test_cbrt_nvrtc_float.cpp ;
 run test_cos_pi_nvrtc_double.cpp ;
 run test_cos_pi_nvrtc_float.cpp ;
+run test_digamma_nvrtc_double.cpp ;
+run test_digamma_nvrtc_float.cpp ;
 run test_erf_nvrtc_double.cpp ;
 run test_erf_nvrtc_float.cpp ;
 run test_erfc_nvrtc_double.cpp ;
diff --git a/test/test_digamma_nvrtc_double.cpp b/test/test_digamma_nvrtc_double.cpp
new file mode 100644
index 000000000..d3da10188
--- /dev/null
+++ b/test/test_digamma_nvrtc_double.cpp
@@ -0,0 +1,190 @@
+//  Copyright John Maddock 2016.
+//  Copyright Matt Borland 2024.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+#define BOOST_MATH_PROMOTE_DOUBLE_POLICY false
+
+// Must be included first
+#include <nvrtc.h>
+#include <cuda.h>
+#include <cuda_runtime.h>
+
+#include <iostream>
+#include <iomanip>
+#include <vector>
+#include <random>
+#include <exception>
+#include <boost/math/special_functions/digamma.hpp>
+#include <boost/math/special_functions/relative_difference.hpp>
+
+typedef double float_type;
+
+const char* cuda_kernel = R"(
+typedef double float_type;
+#include <cuda/std/type_traits>
+#include <boost/math/special_functions/digamma.hpp>
+extern "C" __global__ 
+void test_digamma_kernel(const float_type *in1, const float_type*, float_type *out, int numElements)
+{
+    int i = blockDim.x * blockIdx.x + threadIdx.x;
+    if (i < numElements)
+    {
+        out[i] = boost::math::digamma(in1[i]);
+    }
+}
+)";
+
+void checkCUDAError(cudaError_t result, const char* msg)
+{
+    if (result != cudaSuccess)
+    {
+        std::cerr << msg << ": " << cudaGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkCUError(CUresult result, const char* msg)
+{
+    if (result != CUDA_SUCCESS)
+    {
+        const char* errorStr;
+        cuGetErrorString(result, &errorStr);
+        std::cerr << msg << ": " << errorStr << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkNVRTCError(nvrtcResult result, const char* msg)
+{
+    if (result != NVRTC_SUCCESS)
+    {
+        std::cerr << msg << ": " << nvrtcGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+int main() 
+{
+    try
+    {
+        // Initialize CUDA driver API
+        checkCUError(cuInit(0), "Failed to initialize CUDA");
+
+        // Create CUDA context
+        CUcontext context;
+        CUdevice device;
+        checkCUError(cuDeviceGet(&device, 0), "Failed to get CUDA device");
+        checkCUError(cuCtxCreate(&context, 0, device), "Failed to create CUDA context");
+
+        nvrtcProgram prog;
+        nvrtcResult res;
+
+        res = nvrtcCreateProgram(&prog, cuda_kernel, "test_digamma_kernel.cu", 0, nullptr, nullptr);
+        checkNVRTCError(res, "Failed to create NVRTC program");
+
+        nvrtcAddNameExpression(prog, "test_digamma_kernel");
+
+        #ifdef BOOST_MATH_NVRTC_CI_RUN
+        const char* opts[] = {"--std=c++14", "--gpu-architecture=compute_75", "--include-path=/home/runner/work/cuda-math/boost-root/libs/cuda-math/include/", "-I/usr/local/cuda/include"};
+        #else
+        const char* opts[] = {"--std=c++14", "--include-path=/home/mborland/Documents/boost/libs/cuda-math/include/", "-I/usr/local/cuda/include"};
+        #endif
+
+        // Compile the program
+        res = nvrtcCompileProgram(prog, sizeof(opts) / sizeof(const char*), opts);
+        if (res != NVRTC_SUCCESS) 
+        {
+            size_t log_size;
+            nvrtcGetProgramLogSize(prog, &log_size);
+            char* log = new char[log_size];
+            nvrtcGetProgramLog(prog, log);
+            std::cerr << "Compilation failed:\n" << log << std::endl;
+            delete[] log;
+            exit(EXIT_FAILURE);
+        }
+
+        // Get PTX from the program
+        size_t ptx_size;
+        nvrtcGetPTXSize(prog, &ptx_size);
+        char* ptx = new char[ptx_size];
+        nvrtcGetPTX(prog, ptx);
+
+        // Load PTX into CUDA module
+        CUmodule module;
+        CUfunction kernel;
+        checkCUError(cuModuleLoadDataEx(&module, ptx, 0, 0, 0), "Failed to load module");
+        checkCUError(cuModuleGetFunction(&kernel, module, "test_digamma_kernel"), "Failed to get kernel function");
+
+        int numElements = 5000;
+        float_type *h_in1, *h_in2, *h_out;
+        float_type *d_in1, *d_in2, *d_out;
+
+        // Allocate memory on the host
+        h_in1 = new float_type[numElements];
+        h_in2 = new float_type[numElements];
+        h_out = new float_type[numElements];
+
+        // Initialize input arrays
+        std::mt19937_64 rng(42);
+        std::uniform_real_distribution<float_type> dist(0.0f, 1000.0f);
+        for (int i = 0; i < numElements; ++i) 
+        {
+            h_in1[i] = static_cast<float_type>(dist(rng));
+            h_in2[i] = static_cast<float_type>(dist(rng));
+        }
+
+        checkCUDAError(cudaMalloc(&d_in1, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in1");
+        checkCUDAError(cudaMalloc(&d_in2, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in2");
+        checkCUDAError(cudaMalloc(&d_out, numElements * sizeof(float_type)), "Failed to allocate device memory for d_out");
+
+        checkCUDAError(cudaMemcpy(d_in1, h_in1, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in1");
+        checkCUDAError(cudaMemcpy(d_in2, h_in2, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in2");
+
+        int blockSize = 256;
+        int numBlocks = (numElements + blockSize - 1) / blockSize;
+        void* args[] = { &d_in1, &d_in2, &d_out, &numElements };
+        checkCUError(cuLaunchKernel(kernel, numBlocks, 1, 1, blockSize, 1, 1, 0, 0, args, 0), "Kernel launch failed");
+
+        checkCUDAError(cudaMemcpy(h_out, d_out, numElements * sizeof(float_type), cudaMemcpyDeviceToHost), "Failed to copy data back to host for h_out");
+
+        // Verify Result
+        for (int i = 0; i < numElements; ++i) 
+        {
+            const auto res = boost::math::digamma(h_in1[i]);
+            
+            if (std::isfinite(res))
+            {
+                if (boost::math::epsilon_difference(res, h_out[i]) > 300)
+                {
+                    std::cout << "error at line: " << i
+                            << "\nParallel: " << h_out[i]
+                            << "\n  Serial: " << res
+                            << "\n    Dist: " << boost::math::epsilon_difference(res, h_out[i]) << std::endl;
+                }
+            }
+        }
+
+        cudaFree(d_in1);
+        cudaFree(d_in2);
+        cudaFree(d_out);
+        delete[] h_in1;
+        delete[] h_in2;
+        delete[] h_out;
+
+        nvrtcDestroyProgram(&prog);
+        delete[] ptx;
+
+        cuCtxDestroy(context);
+
+        std::cout << "Kernel executed successfully." << std::endl;
+        return 0;
+    }
+    catch(const std::exception& e)
+    {
+        std::cerr << "Stopped with exception: " << e.what() << std::endl;
+        return EXIT_FAILURE;
+    }
+}
diff --git a/test/test_digamma_nvrtc_float.cpp b/test/test_digamma_nvrtc_float.cpp
new file mode 100644
index 000000000..a698cbd56
--- /dev/null
+++ b/test/test_digamma_nvrtc_float.cpp
@@ -0,0 +1,190 @@
+//  Copyright John Maddock 2016.
+//  Copyright Matt Borland 2024.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+#define BOOST_MATH_PROMOTE_DOUBLE_POLICY false
+
+// Must be included first
+#include <nvrtc.h>
+#include <cuda.h>
+#include <cuda_runtime.h>
+
+#include <iostream>
+#include <iomanip>
+#include <vector>
+#include <random>
+#include <exception>
+#include <boost/math/special_functions/digamma.hpp>
+#include <boost/math/special_functions/relative_difference.hpp>
+
+typedef float float_type;
+
+const char* cuda_kernel = R"(
+typedef float float_type;
+#include <cuda/std/type_traits>
+#include <boost/math/special_functions/digamma.hpp>
+extern "C" __global__ 
+void test_digamma_kernel(const float_type *in1, const float_type*, float_type *out, int numElements)
+{
+    int i = blockDim.x * blockIdx.x + threadIdx.x;
+    if (i < numElements)
+    {
+        out[i] = boost::math::digamma(in1[i]);
+    }
+}
+)";
+
+void checkCUDAError(cudaError_t result, const char* msg)
+{
+    if (result != cudaSuccess)
+    {
+        std::cerr << msg << ": " << cudaGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkCUError(CUresult result, const char* msg)
+{
+    if (result != CUDA_SUCCESS)
+    {
+        const char* errorStr;
+        cuGetErrorString(result, &errorStr);
+        std::cerr << msg << ": " << errorStr << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+void checkNVRTCError(nvrtcResult result, const char* msg)
+{
+    if (result != NVRTC_SUCCESS)
+    {
+        std::cerr << msg << ": " << nvrtcGetErrorString(result) << std::endl;
+        exit(EXIT_FAILURE);
+    }
+}
+
+int main() 
+{
+    try
+    {
+        // Initialize CUDA driver API
+        checkCUError(cuInit(0), "Failed to initialize CUDA");
+
+        // Create CUDA context
+        CUcontext context;
+        CUdevice device;
+        checkCUError(cuDeviceGet(&device, 0), "Failed to get CUDA device");
+        checkCUError(cuCtxCreate(&context, 0, device), "Failed to create CUDA context");
+
+        nvrtcProgram prog;
+        nvrtcResult res;
+
+        res = nvrtcCreateProgram(&prog, cuda_kernel, "test_digamma_kernel.cu", 0, nullptr, nullptr);
+        checkNVRTCError(res, "Failed to create NVRTC program");
+
+        nvrtcAddNameExpression(prog, "test_digamma_kernel");
+
+        #ifdef BOOST_MATH_NVRTC_CI_RUN
+        const char* opts[] = {"--std=c++14", "--gpu-architecture=compute_75", "--include-path=/home/runner/work/cuda-math/boost-root/libs/cuda-math/include/", "-I/usr/local/cuda/include"};
+        #else
+        const char* opts[] = {"--std=c++14", "--include-path=/home/mborland/Documents/boost/libs/cuda-math/include/", "-I/usr/local/cuda/include"};
+        #endif
+
+        // Compile the program
+        res = nvrtcCompileProgram(prog, sizeof(opts) / sizeof(const char*), opts);
+        if (res != NVRTC_SUCCESS) 
+        {
+            size_t log_size;
+            nvrtcGetProgramLogSize(prog, &log_size);
+            char* log = new char[log_size];
+            nvrtcGetProgramLog(prog, log);
+            std::cerr << "Compilation failed:\n" << log << std::endl;
+            delete[] log;
+            exit(EXIT_FAILURE);
+        }
+
+        // Get PTX from the program
+        size_t ptx_size;
+        nvrtcGetPTXSize(prog, &ptx_size);
+        char* ptx = new char[ptx_size];
+        nvrtcGetPTX(prog, ptx);
+
+        // Load PTX into CUDA module
+        CUmodule module;
+        CUfunction kernel;
+        checkCUError(cuModuleLoadDataEx(&module, ptx, 0, 0, 0), "Failed to load module");
+        checkCUError(cuModuleGetFunction(&kernel, module, "test_digamma_kernel"), "Failed to get kernel function");
+
+        int numElements = 5000;
+        float_type *h_in1, *h_in2, *h_out;
+        float_type *d_in1, *d_in2, *d_out;
+
+        // Allocate memory on the host
+        h_in1 = new float_type[numElements];
+        h_in2 = new float_type[numElements];
+        h_out = new float_type[numElements];
+
+        // Initialize input arrays
+        std::mt19937_64 rng(42);
+        std::uniform_real_distribution<float_type> dist(0.0f, 1000.0f);
+        for (int i = 0; i < numElements; ++i) 
+        {
+            h_in1[i] = static_cast<float_type>(dist(rng));
+            h_in2[i] = static_cast<float_type>(dist(rng));
+        }
+
+        checkCUDAError(cudaMalloc(&d_in1, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in1");
+        checkCUDAError(cudaMalloc(&d_in2, numElements * sizeof(float_type)), "Failed to allocate device memory for d_in2");
+        checkCUDAError(cudaMalloc(&d_out, numElements * sizeof(float_type)), "Failed to allocate device memory for d_out");
+
+        checkCUDAError(cudaMemcpy(d_in1, h_in1, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in1");
+        checkCUDAError(cudaMemcpy(d_in2, h_in2, numElements * sizeof(float_type), cudaMemcpyHostToDevice), "Failed to copy data to device for d_in2");
+
+        int blockSize = 256;
+        int numBlocks = (numElements + blockSize - 1) / blockSize;
+        void* args[] = { &d_in1, &d_in2, &d_out, &numElements };
+        checkCUError(cuLaunchKernel(kernel, numBlocks, 1, 1, blockSize, 1, 1, 0, 0, args, 0), "Kernel launch failed");
+
+        checkCUDAError(cudaMemcpy(h_out, d_out, numElements * sizeof(float_type), cudaMemcpyDeviceToHost), "Failed to copy data back to host for h_out");
+
+        // Verify Result
+        for (int i = 0; i < numElements; ++i) 
+        {
+            const auto res = boost::math::digamma(h_in1[i]);
+            
+            if (std::isfinite(res))
+            {
+                if (boost::math::epsilon_difference(res, h_out[i]) > 300)
+                {
+                    std::cout << "error at line: " << i
+                            << "\nParallel: " << h_out[i]
+                            << "\n  Serial: " << res
+                            << "\n    Dist: " << boost::math::epsilon_difference(res, h_out[i]) << std::endl;
+                }
+            }
+        }
+
+        cudaFree(d_in1);
+        cudaFree(d_in2);
+        cudaFree(d_out);
+        delete[] h_in1;
+        delete[] h_in2;
+        delete[] h_out;
+
+        nvrtcDestroyProgram(&prog);
+        delete[] ptx;
+
+        cuCtxDestroy(context);
+
+        std::cout << "Kernel executed successfully." << std::endl;
+        return 0;
+    }
+    catch(const std::exception& e)
+    {
+        std::cerr << "Stopped with exception: " << e.what() << std::endl;
+        return EXIT_FAILURE;
+    }
+}