| """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() | |