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5b90392 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | """Reference implementation — the CORRECTNESS SPEC for `mixed_precision_gemm_split`.
This is correct but slow. It defines exactly what your kernel must reproduce; its speed has no
bearing on your score, which is an absolute TFLOP/s number. GENERATED by _factory/build.py.
"""
import torch
def mixed_precision_gemm_split(a_q, a_scale, b_q, b_scale, a_hi, b_hi):
"""Exact int32 branch + affine rescale, plus a plain bf16 branch. The numerical SPECIFICATION.
The int8 contraction is done in float64 purely as a convenient EXACT integer accumulator: every partial
sum is bounded by 127*127*K < 2^53, so fp64 reproduces the int32 dot product bit for bit (this is
checked against torch._int_mm). fp32 would NOT be exact here -- the sums exceed 2^24.
The outlier branch is a plain fp32-accumulated contraction of the two bf16 operands. It carries NO
scales: a_hi and b_hi are already real values.
"""
acc = a_q.double() @ b_q.double().t() # (M, N), exact integers
lo = acc * a_scale.double().unsqueeze(1) * b_scale.double().unsqueeze(0)
hi = (a_hi.float() @ b_hi.float().t()).double() # the bf16 outlier branch
return (lo + hi).float()
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