Use a better error bound for fp16 tests of the rsum microkernel.
#6431
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PiperOrigin-RevId: 634519272
fbarchard
reviewed
May 16, 2024
| // We don't use the usual hard bound $\gamma_n = \frac{nu}{1 - nu}$ since | ||
| // for `fp16` $nu > 1$ already for $n > 2000$, rendering the bound | ||
| // meaningless. | ||
| const float fp16_u = |
fbarchard
reviewed
May 16, 2024
| const float fp16_u = | ||
| 4.88281e-4; // Half of the ULP, max relative rounding error. | ||
| const float n = batch_size() - 1; | ||
| const float gamma_n = std::expm1(5.0f * std::sqrt(n) * fp16_u + |
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this is really complicated/obscure and different than all other testers, making it hard to maintain.
is rsum fp16 different than other testers?
assuming this is better, can we apply it to float and all other testers?
does it need to change for bf16 or qs8 comparisons?
it looks slow... did you benchmark?
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Use a better error bound for
fp16tests of thersummicrokernel.