feat: adds affine_sigmoid() and affine_sigmoid_approx()

refactor: removes sigmoid_fast()

core/math/math_funcs.h

@@ -764,8 +764,19 @@ class Math {
 	static _ALWAYS_INLINE_ double sigmoid_approx(double p_x) { return 0.5 + p_x / (4.0 + fabs(p_x)); }
 	static _ALWAYS_INLINE_ float sigmoid_approx(float p_x) { return 0.5f + p_x / (4.0f + fabsf(p_x)); }
 
-	static _ALWAYS_INLINE_ double sigmoid_fast(double p_x) { return p_x / (1.0 + fabs(p_x)); }
-	static _ALWAYS_INLINE_ float sigmoid_fast(float p_x) { return p_x / (1.0f + fabsf(p_x)); }
+	static _ALWAYS_INLINE_ double sigmoid_affine(double p_x, double p_amplitude, double p_y_translation) {
+		return p_amplitude / (1.0 + ::exp(-p_x)) + p_y_translation;
+	}
+	static _ALWAYS_INLINE_ float sigmoid_affine(float p_x, float p_amplitude, float p_y_translation) {
+		return p_amplitude / (1.0f + expf(-p_x)) + p_y_translation;
+	}
+
+	static _ALWAYS_INLINE_ double sigmoid_affine_approx(double p_x, double p_amplitude, double p_y_translation) {
+		return p_amplitude * (0.5 + p_x / (4.0 + fabs(p_x))) + p_y_translation;
+	}
+	static _ALWAYS_INLINE_ float sigmoid_affine_approx(float p_x, float p_amplitude, float p_y_translation) {
+		return p_amplitude * (0.5f + p_x / (4.0f + fabsf(p_x))) + p_y_translation;
+	}
 };
 
 #endif // MATH_FUNCS_H

core/variant/variant_utility.cpp

@@ -647,8 +647,12 @@ double VariantUtilityFunctions::sigmoid_approx(double x) {
 	return Math::sigmoid_approx(x);
 }
 
-double VariantUtilityFunctions::sigmoid_fast(double x) {
-	return Math::sigmoid_fast(x);
+double VariantUtilityFunctions::sigmoid_affine(double x, double amplitude, double y_translation) {
+	return Math::sigmoid_affine(x, amplitude, y_translation);
+}
+
+double VariantUtilityFunctions::sigmoid_affine_approx(double x, double amplitude, double y_translation) {
+	return Math::sigmoid_affine_approx(x, amplitude, y_translation);
 }
 
 Variant VariantUtilityFunctions::max(const Variant **p_args, int p_argcount, Callable::CallError &r_error) {
@@ -1801,7 +1805,8 @@ void Variant::_register_variant_utility_functions() {
 
 	FUNCBINDR(sigmoid, sarray("x"), Variant::UTILITY_FUNC_TYPE_MATH);
 	FUNCBINDR(sigmoid_approx, sarray("x"), Variant::UTILITY_FUNC_TYPE_MATH);
-	FUNCBINDR(sigmoid_fast, sarray("x"), Variant::UTILITY_FUNC_TYPE_MATH);
+	FUNCBINDR(sigmoid_affine, sarray("x", "amplitude", "y_translation"), Variant::UTILITY_FUNC_TYPE_MATH);
+	FUNCBINDR(sigmoid_affine_approx, sarray("x", "amplitude", "y_translation"), Variant::UTILITY_FUNC_TYPE_MATH);
 
 	// Random
 

core/variant/variant_utility.h

@@ -117,7 +117,8 @@ struct VariantUtilityFunctions {
 	static int64_t nearest_po2(int64_t x);
 	static double sigmoid(double x);
 	static double sigmoid_approx(double x);
-	static double sigmoid_fast(double x);
+	static double sigmoid_affine(double x, double amplitude, double y_translation);
+	static double sigmoid_affine_approx(double x, double amplitude, double y_translation);
 	// Random
 	static void randomize();
 	static int64_t randi();

doc/classes/@GlobalScope.xml

@@ -1194,41 +1194,63 @@
 				[b]Note:[/b] For faster but less accurate approximation, see [method sigmoid_approx] or [method sigmoid_fast].
 			</description>
 		</method>
-		<method name="sigmoid_approx">
+		<method name="sigmoid_affine">
 			<return type="float" />
 			<param index="0" name="x" type="float" />
+			<param index="1" name="amplitude" type="float" />
+			<param index="2" name="y_translation" type="float" />
 			<description>
-				Computes an approximation of the sigmoid function for [param x], which maps the input value into the range (0, 1).
+				Computes an affine-transformed sigmoid for [param x], which allows scaling by [param amplitude] and translation by [param y_translate].
+				The affine sigmoid function is defined as:
+				[codeblock]
+				affine_sigmoid(x, amplitude, y_translate) = (amplitude / (1 + exp(-x))) + y_translate
+				[/codeblock]
+				This function modifies the standard sigmoid by introducing scaling and vertical translation.
+				[codeblock]
+				var result = affine_sigmoid(0.0, 1.0, 0.0)  # result is 0.5
+				var result = affine_sigmoid(1.0, 2.0, -1.0) # result is approximately 0.46
+				var result = affine_sigmoid(-1.0, 3.0, 2.0) # result is approximately 2.81
+				var result = affine_sigmoid(1.0, 2.0, 2.5) # result is approximately 3.96
+				[/codeblock]
+				[b]Note:[/b] This is a more accurate but computationally heavier version of the affine sigmoid. For faster approximations, see [method affine_sigmoid_approx].
+			</description>
+		</method>
+		<method name="sigmoid_affine_approx">
+			<return type="float" />
+			<param index="0" name="x" type="float" />
+			<param index="1" name="amplitude" type="float" />
+			<param index="2" name="y_translation" type="float" />
+			<description>
+				Computes an approximation of the affine-transformed sigmoid function for [param x], allowing scaling by [param amplitude] and translation by [param y_translate].
 				The approximation function is defined as:
 				[codeblock]
-				sigmoid_approx(x) = 0.5 + (x / (4 + abs(x)))
+				affine_sigmoid_approx(x, amplitude, y_translate) = amplitude * (0.5 + (x / (4 + abs(x)))) + y_translate
 				[/codeblock]
-				This function is faster than the standard [method sigmoid], especially useful in performance-sensitive environments where a balance between accuracy and speed is desired.
-				It provides a closer approximation to the sigmoid than the [method sigmoid_fast] function, especially around [param x] = 0.
+				This function approximates the affine sigmoid, offering faster computation at the cost of some precision. It is useful in performance-sensitive environments where both transformation and speed are needed.
 				[codeblock]
-				var result = sigmoid_approx(0.0)  # result is 0.5
-				var result = sigmoid_approx(2.0)  # result is approximately 0.83
-				var result = sigmoid_approx(-1.0) # result is approximately 0.3
-				var result = sigmoid_approx(5.0)  # result is approximately 1.05
+				var result = affine_sigmoid_approx(0.0, 1.0, 0.0)  # result is 0.5
+				var result = affine_sigmoid_approx(2.0, 2.0, 1.0)  # result is approximately 2.67
+				var result = affine_sigmoid_approx(-1.0, 3.0, 0.5) # result is approximately 1.4
+				var result = affine_sigmoid_approx(1.0, 2.0, 2.5) # result is approximately 3.9
 				[/codeblock]
 			</description>
 		</method>
-		<method name="sigmoid_fast">
+		<method name="sigmoid_approx">
 			<return type="float" />
 			<param index="0" name="x" type="float" />
 			<description>
-				Computes a fast approximation of the sigmoid function for [param x], which maps the input value into the range (-1, 1).
-				The fast sigmoid function is defined as:
+				Computes an approximation of the sigmoid function for [param x], which maps the input value into the range (0, 1).
+				The approximation function is defined as:
 				[codeblock]
-				fast_sigmoid(x) = x / (1 + abs(x))
+				sigmoid_approx(x) = 0.5 + (x / (4 + abs(x)))
 				[/codeblock]
-				This function is faster to compute than the standard [method sigmoid] and [method sigmoid_approx], but is less accurate, particularly in the steep transition area around 0.
-				It is commonly used in real-time systems and machine learning where performance is critical.
+				This function is faster than the standard [method sigmoid], especially useful in performance-sensitive environments where a balance between accuracy and speed is desired.
+				It provides a closer approximation to the sigmoid than the [method sigmoid_fast] function, especially around [param x] = 0.
 				[codeblock]
-				var result = sigmoid_fast(0.0)  # result is 0
-				var result = sigmoid_fast(2.0)  # result is approximately 0.67
-				var result = sigmoid_fast(-1.0) # result is approximately -0.5
-				var result = sigmoid_fast(5.0)  # result is approximately 0.83
+				var result = sigmoid_approx(0.0)  # result is 0.5
+				var result = sigmoid_approx(2.0)  # result is approximately 0.83
+				var result = sigmoid_approx(-1.0) # result is approximately 0.3
+				var result = sigmoid_approx(5.0)  # result is approximately 1.05
 				[/codeblock]
 			</description>
 		</method>