gemini-code-assist[bot] commented on PR #18582:
URL: https://github.com/apache/tvm/pull/18582#issuecomment-3644810592
## Summary of Changes
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this pull request and will post my feedback shortly. In the meantime, here's a
summary to help you and other reviewers quickly get up to speed!
This pull request significantly enhances the accuracy of the ACOS and ASIN
trigonometric functions, particularly at their domain boundaries. By
strategically switching to system library functions for extreme input values
while retaining the efficient Taylor series for central values, the change
ensures robust and precise mathematical computations without sacrificing
performance where the series remains effective.
### Highlights
* **Precision Improvement for ACOS and ASIN**: This pull request resolves a
precision issue in the ACOS operator, which previously produced incorrect
results for boundary values like x=±1.0. The root cause was identified as the
poor convergence of ASIN's 6-term Taylor series expansion near these
boundaries, affecting ACOS due to its implementation as "π/2 - asin(x)".
* **Hybrid Implementation for ASIN and ACOS**: A hybrid approach has been
implemented for both ASIN and ACOS. For input values where "|x| >= 0.9", the
system library functions ("asinf" and "acosf") are now utilized to ensure high
precision. For values where "|x| < 0.9", the existing Taylor series expansion,
which is accurate in this range, continues to be used.
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