Improve precision of horner_polynomial #280
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The common use of horner_polynomial is to take an array of coefficients, and to specify that all coefficients in the array are used. This commit changes horner_polynomial to allow inference of the size.
We were previously implicitly relying on LLVM's behaviour of promoting f16 operations to f32 and getting extra precision that amounts to getting the same results as FMA. We never did that consistently (it varied between platforms) and we now consistently do not do that, resulting in incorrect results for at least half-precision pow. Use FMA to fix that. tanpi and tgamma have hardcoded exceptions where the approximation was known to not be sufficiently precise. These exceptions are updated.
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coldav
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Jan 8, 2024
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Overview
Improve precision of horner_polynomial
Reason for change
We were previously implicitly relying on LLVM's behaviour of promoting f16 operations to f32 and getting extra precision that amounts to getting the same results as FMA. We never did that consistently (it varied between platforms) and we now consistently do not do that, resulting in incorrect results for at least half-precision pow. Use FMA to fix that.
Description of change
This MR consists of two commits that are not intended to be squashed, and are best reviewed separately. There is a large mostly mechanical NFC commit to simplify how
horner_polynomialis used, followed by a small commit that fixes its implementation.Anything else we should know?
With this change, we pass OpenCL CTS
fp16-stagingbranch's testing for half-precisionpow.Checklist
recent version available through
pip) on all modified code.