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Add f8E4M3 and f8E3M4 types support (#2482)
This PR adds f8E4M3 and f8E3M4 types support. f8E4M3 and f8E3M4 types follow IEEE 754 convention. ```c f8E4M3 (IEEE 754) - Exponent bias: 7 - Maximum stored exponent value: 14 (binary 1110) - Maximum unbiased exponent value: 14 - 7 = 7 - Minimum stored exponent value: 1 (binary 0001) - Minimum unbiased exponent value: 1 − 7 = −6 - Precision specifies the total number of bits used for the significand (mantisa), including implicit leading integer bit = 3 + 1 = 4 - Follows IEEE 754 conventions for representation of special values - Has Positive and Negative zero - Has Positive and Negative infinity - Has NaNs Additional details: - Max exp (unbiased): 7 - Min exp (unbiased): -6 - Infinities (+/-): S.1111.000 - Zeros (+/-): S.0000.000 - NaNs: S.1111.{001, 010, 011, 100, 101, 110, 111} - Max normal number: S.1110.111 = +/-2^(7) x (1 + 0.875) = +/-240 - Min normal number: S.0001.000 = +/-2^(-6) - Max subnormal number: S.0000.111 = +/-2^(-6) x 0.875 = +/-2^(-9) x 7 - Min subnormal number: S.0000.001 = +/-2^(-6) x 0.125 = +/-2^(-9) ``` ```c f8E3M4 (IEEE 754) - Exponent bias: 3 - Maximum stored exponent value: 6 (binary 110) - Maximum unbiased exponent value: 6 - 3 = 3 - Minimum stored exponent value: 1 (binary 001) - Minimum unbiased exponent value: 1 − 3 = −2 - Precision specifies the total number of bits used for the significand (mantissa), including implicit leading integer bit = 4 + 1 = 5 - Follows IEEE 754 conventions for representation of special values - Has Positive and Negative zero - Has Positive and Negative infinity - Has NaNs Additional details: - Max exp (unbiased): 3 - Min exp (unbiased): -2 - Infinities (+/-): S.111.0000 - Zeros (+/-): S.000.0000 - NaNs: S.111.{0,1}⁴ except S.111.0000 - Max normal number: S.110.1111 = +/-2^(6-3) x (1 + 15/16) = +/-2^3 x 31 x 2^(-4) = +/-15.5 - Min normal number: S.001.0000 = +/-2^(1-3) x (1 + 0) = +/-2^(-2) - Max subnormal number: S.000.1111 = +/-2^(-2) x 15/16 = +/-2^(-2) x 15 x 2^(-4) = +/-15 x 2^(-6) - Min subnormal number: S.000.0001 = +/-2^(-2) x 1/16 = +/-2^(-2) x 2^(-4) = +/-2^(-6) ``` Related PRs: - LLVM [PR-97179](llvm/llvm-project#97179) [APFloat] Add support for f8E4M3 IEEE 754 type (Merged) - LLVM [PR-97118](llvm/llvm-project#97118) [MLIR] Add f8E4M3 IEEE 754 type (Merged) - LLVM [PR-99698](llvm/llvm-project#99698) [APFloat] Add support for f8E3M4 IEEE 754 type (Merged) - LLVM [PR-101230](llvm/llvm-project#101230) [MLIR] Add f8E3M4 IEEE 754 type (Merged) - StableHLO [PR-2486](#2486) [RFC] Add f8E4M3 and f8E3M4 types support - ml_dtypes [PR-161](jax-ml/ml_dtypes#161) Add float8_e4m3 (Merged) - ml_dtypes [PR-171](jax-ml/ml_dtypes#171) Add float8_e3m4 (Merged) - XLA [PR-16585](openxla/xla#16585) Add support for float8_e4m3
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