gh-140443: Use fma in loghelper to improve accuracy of log for very large integers#140469
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…ery large integers
Replaced the expression computing the final result in loghelper with an
fma() call:
result = fma(func(2.0), (double)e, func(x));
This change reduces rounding error and improves the ULP distribution of
math.log10() for very large integer inputs.
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tim-one
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It's been a joy! Thank you for your efforts and patience. It's amazing how much "busy work" there is to make a 1-line change 🤣, eh?
It all looks good to me. I'll merge it tomorrow. Perhaps @StanFromIreland knows more than me about what kind of markup decorations are wanted in NEWS entries. I can never remember that stuff
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Thank you, @tim-one and @StanFromIreland, for your guidance throughout this PR (and thank you for pointing out my mistakes.) I’ve learned a great deal from your feedback and reviews. |
StanFromIreland
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…e-140443.wT5i1A.rst Co-authored-by: Stan Ulbrych <89152624+StanFromIreland@users.noreply.github.com>
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…for very large integers (python#140469) * pythongh-140443:use fma in loghelper to improve accuracy of log for very large integers Use fused multiply-add in log_helper() for huge ints. Saving a rounding here is remarkably effective. Across some millions of randomized test cases with ints up to a billion bits, on Windows and using log10, the ULP error distribution was dramatically flattened, and its range was nearly cut in half. In fact, the largest error Tim saw was under 0.6 ULP. --------- Co-authored-by: abhi210 <27881020+Abhi210@users.noreply.github.com> Co-authored-by: Stan Ulbrych <89152624+StanFromIreland@users.noreply.github.com>
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Replaced the expression computing the final result in loghelper with an fma() call:
This change reduces rounding error and improves the ULP distribution of math.log for very large integer inputs.