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[RFC] Microscaling data types (f4E2M1FN, f6E2M3FN, f6E3M2FN, f8E8M0FNU)
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| # [RFC] Microscaling data types (f4E2M1FN, f6E2M3FN, f6E3M2FN, f8E8M0FNU) | ||
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| Status: Review<br/> | ||
| Initial version: 10/01/2024<br/> | ||
| Last updated: 10/07/2024<br/> | ||
| Discussion thread: TODO | ||
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| ## Overview | ||
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| This RFC proposes adding new primitive data types, which will allow representing | ||
| block scaled data as described in _OCP Microscaling Formats (MX) Specification | ||
| v1.0_[^1]. | ||
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| Dot operation on MXFP8/MXFP6/MXFP4 inputs can be hardware-accelerated on | ||
| Blackwell (NVidia architecture). | ||
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| The proposed primitive types are added to LLVM APFloat[^2] [^3] [^4], MLIR | ||
| builtin types[^5] [^6] [^7] [^8], and to JAX-ML dtypes[^9] [^10], the latter | ||
| also makes them available in NumPy. | ||
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| ## Summary | ||
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| The new types follow a convention similar to IEEE 754, but with some significant | ||
| differences. | ||
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| The sub-byte data types (f4E2M1FN, f6E2M3FN, f6E3M2FN) cannot represent | ||
| infinity or NaN. | ||
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| The scaling data type (f8E8M0FNU) has no mantissa and no sign bit, and it cannot | ||
| represent infinity, negative numbers or zeros. | ||
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| ### Float4E2M1FN | ||
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| 4-bit floating point type with 1 sign bit, 2 bits exponent and 1 bit mantissa. | ||
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| ```c | ||
| f4E2M1FN | ||
| - Exponent bias: 1 | ||
| - Minimum stored exponent value: 1 (binary 01) | ||
| - Maximum stored exponent value: 3 (binary 11) | ||
| - Minimum unbiased exponent value: 1 − 1 = 0 | ||
| - Maximum unbiased exponent value: 3 - 1 = 2 | ||
| - Precision specifies the total number of bits used for the significand | ||
| (mantissa), including implicit leading integer bit = 1 + 1 = 2 | ||
| - Has positive and negative zero | ||
| - Doesn't have infinity | ||
| - Doesn't have NaN | ||
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| Additional details: | ||
| - Zeros (+/-): S.00.0 | ||
| - Max normal number (+/-): S.11.1 = 2^2 x (1+0.5) = ±6 | ||
| - Min normal number (+/-): S.01.0 = 2^0 x (1+0) = ±1 | ||
| - Min subnormal number (+/-): S.00.1 = 2^0 x 0.5 = ±0.5 | ||
| ``` | ||
| List of representable absolute values: [0, 0.5, 1, 1.5, 2, 3, 4, 6] | ||
| When converting an IEEE-754 floating-point number to `f4E2M1FN`, infinities are | ||
| clamped to the minimum (-6) or maximum (6) value, depending on the sign. | ||
| Conversion from NaN is undefined. | ||
| ### Float6E2M3FN | ||
| 6-bit floating point type with 1 sign bit, 2 bits exponent and 3 bits mantissa. | ||
| ```c | ||
| f6E2M3FN | ||
| - Exponent bias: 1 | ||
| - Minimum stored exponent value: 1 (binary 01) | ||
| - Maximum stored exponent value: 3 (binary 11) | ||
| - Minimum unbiased exponent value: 1 − 1 = 0 | ||
| - Maximum unbiased exponent value: 3 - 1 = 2 | ||
| - Precision specifies the total number of bits used for the significand | ||
| (mantissa), including implicit leading integer bit = 3 + 1 = 4 | ||
| - Has positive and negative zero | ||
| - Doesn't have infinity | ||
| - Doesn't have NaN | ||
| Additional details: | ||
| - Zeros (+/-): S.00.000 | ||
| - Max normal number (+/-): S.11.111 = 2^2 x (1+0.875) = ±7.5 | ||
| - Min normal number (+/-): S.01.000 = 2^0 x (1+0) = ±1 | ||
| - Max subnormal number (+/-): S.00.111 = 2^0 x 0.875 = ±0.875 | ||
| - Min subnormal number (+/-): S.00.001 = 2^0 x 0.125 = ±0.125 | ||
| ``` | ||
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| When converting an IEEE-754 floating-point number to `f6E2M3FN`, infinities are | ||
| clamped to the minimum (-7.5) or maximum (7.5) value, depending on the sign. | ||
| Conversion from NaN is undefined. | ||
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| ### Float6E3M2FN | ||
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| 6-bit floating point type with 1 sign bit, 3 bits exponent and 2 bits mantissa. | ||
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| ```c | ||
| f6E2M3FN | ||
| - Exponent bias: 3 | ||
| - Minimum stored exponent value: 1 (binary 001) | ||
| - Maximum stored exponent value: 7 (binary 111) | ||
| - Minimum unbiased exponent value: 1 − 3 = -2 | ||
| - Maximum unbiased exponent value: 7 - 3 = 4 | ||
| - Precision specifies the total number of bits used for the significand | ||
| (mantissa), including implicit leading integer bit = 2 + 1 = 3 | ||
| - Has positive and negative zero | ||
| - Doesn't have infinity | ||
| - Doesn't have NaN | ||
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| Additional details: | ||
| - Zeros (+/-): S.000.00 | ||
| - Max normal number (+/-): S.111.11 = 2^4 x (1+0.75) = ±28 | ||
| - Min normal number (+/-): S.001.00 = 2^(-2) x (1+0) = ±0.25 | ||
| - Max subnormal number (+/-): S.000.11 = 2^(-2) x 0.75 = ±0.1875 | ||
| - Min subnormal number (+/-): S.000.01 = 2^(-2) x 0.25 = ±0.0625 | ||
| ``` | ||
| When converting an IEEE-754 floating-point number to `f6E3M2FN`, infinities are | ||
| clamped to the minimum (-28) or maximum (28) value, depending on the sign. | ||
| Conversion from NaN is undefined. | ||
| ### Float8E8M0FNU | ||
| 8-bit floating point type with no sign bit, 8 bits exponent and no mantissa. | ||
| ```c | ||
| f8E8M0FNU | ||
| - Exponent bias: 127 | ||
| - Minimum stored exponent value: 0 (binary 0000'0000) | ||
| - Maximum stored exponent value: 254 (binary 1111'1110) | ||
| - Minimum unbiased exponent value: 0 − 127 = -127 | ||
| - Maximum unbiased exponent value: 254 - 127 = 127 | ||
| - Precision specifies the total number of bits used for the significand | ||
| (mantissa), including implicit leading integer bit = 0 + 1 = 1 | ||
| - Doesn't have zeros | ||
| - Doesn't have infinity | ||
| - NaN is represented as binary 1111'1111 | ||
| Additional details: | ||
| - Max normal number: 1111'1110 = 2^127 | ||
| - Min normal number: 0000'0000 = 2^(-127) | ||
| ``` | ||
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| This type is intended to represent scaling factors, so there's no point of | ||
| having the sign bit or the zero value. | ||
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| Converting from a 32-bit IEEE-754 floating point number (FP32) to `f8E8M0FNU` | ||
| in RTZ (round-to-zero) mode is a simple bit shift of the exponent bits. | ||
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| ## Microscaling formats | ||
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| Microscaling format (MX) data consists of two tensors: element data as a | ||
| low-precision data type divided into equal blocks and scale data (one scaling | ||
| factor per block). | ||
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| The OCP MX specification[^1] defines several floating-point formats: `MXFP8`, | ||
| `MXFP6` and `MXFP4` (described below). | ||
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| ### MXFP8 | ||
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| Block scaled data with `f8E4M3FN` or `f8E5M2` element data type and `f8E8M0FNU` | ||
| scaling data type using block size of 32 elements. | ||
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| Every block of data takes 33 bytes of memory, a 48% reduction in size compared | ||
| to FP16, and a 3% overhead compared to FP8. Mean relative error of quantizing | ||
| a normal distribution of values as MXFP8 (E4M3) is ~2.5%. | ||
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| The element data types already exist in StableHLO[^11] so they're not covered in | ||
| this RFC. | ||
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| ### MXFP6 | ||
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| Block scaled data with `f6E2M3FN` or `f6E3M2FN` element data type and | ||
| `f8E8M0FNU` scaling data type using block size of 32 elements. | ||
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| Every block of data takes 25 bytes of memory, a 61% reduction in size compared | ||
| to FP16, and a 22% reduction compared to FP8. Mean relative error of quantizing | ||
| a normal distribution of values as MXFP6 (E2M3) is ~5%. | ||
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| ### MXFP4 | ||
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| Block scaled data with `f4E2M1FN` element data type and `f8E8M0FNU` scaling data | ||
| type using block size of 32 elements. | ||
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| Every block of data takes 17 bytes of memory, a 73% reduction in size compared | ||
| to FP16, and a 47% reduction compared to FP8. Mean relative error of quantizing | ||
| a normal distribution of values as MXFP4 is ~16%. | ||
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| ## References | ||
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| [^1]: Open Compute Project [Microscaling Formats (MX) Specification v1.0](https://www.opencompute.org/documents/ocp-microscaling-formats-mx-v1-0-spec-final-pdf) | ||
| [^2]: LLVM [PR#95392](https://github.com/llvm/llvm-project/pull/95392) [APFloat] Add APFloat support for FP4 data type | ||
| [^3]: LLVM [PR#94735](https://github.com/llvm/llvm-project/pull/94735) [APFloat] Add APFloat support for FP6 data types | ||
| [^4]: LLVM [PR#107127](https://github.com/llvm/llvm-project/pull/107127) [APFloat] Add APFloat support for E8M0 type | ||
| [^5]: LLVM [PR#108877](https://github.com/llvm/llvm-project/pull/108877) [MLIR] Add f4E2M1FN type | ||
| [^6]: LLVM [PR#107999](https://github.com/llvm/llvm-project/pull/107999) [MLIR] Add f6E2M3FN type | ||
| [^7]: LLVM [PR#105573](https://github.com/llvm/llvm-project/pull/105573) [MLIR] Add f6E3M2FN type | ||
| [^8]: LLVM [PR#111028](https://github.com/llvm/llvm-project/pull/111028) [MLIR] Add f8E8M0FNU type | ||
| [^9]: JAX-ML [PR#181](https://github.com/jax-ml/ml_dtypes/pull/181) Add sub-byte data types: float4_e2m1fn, float6_e2m3fn, float6_e3m2fn | ||
| [^10]: JAX-ML [PR#166](https://github.com/jax-ml/ml_dtypes/pull/181) Add float8_e8m0_fnu (E8M0) OCP MX scale format | ||
| [^11]: [RFC: FP8 in StableHLO](https://github.com/openxla/stablehlo/blob/main/rfcs/20221031-fp8.md) |