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authorPaul Zimmermann <Paul.Zimmermann@inria.fr>2021-04-01 08:14:10 +0200
committerPaul Zimmermann <Paul.Zimmermann@inria.fr>2021-04-02 06:15:48 +0200
commit9acda61d94acc5348c2330f2519a14d1a4a37e73 (patch)
treedcad90e95870279c37b5be7c646b3a3f6edc15cb /sysdeps/sh
parent595c22ecd8e87a27fd19270ed30fdbae9ad25426 (diff)
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Fix the inaccuracy of j0f/j1f/y0f/y1f [BZ #14469, #14470, #14471, #14472]
For j0f/j1f/y0f/y1f, the largest error for all binary32
inputs is reduced to at most 9 ulps for all rounding modes.

The new code is enabled only when there is a cancellation at the very end of
the j0f/j1f/y0f/y1f computation, or for very large inputs, thus should not
give any visible slowdown on average.  Two different algorithms are used:

* around the first 64 zeros of j0/j1/y0/y1, approximation polynomials of
  degree 3 are used, computed using the Sollya tool (https://www.sollya.org/)

* for large inputs, an asymptotic formula from [1] is used

[1] Fast and Accurate Bessel Function Computation,
    John Harrison, Proceedings of Arith 19, 2009.

Inputs yielding the new largest errors are added to auto-libm-test-in,
and ulps are regenerated for various targets (thanks Adhemerval Zanella).

Tested on x86_64 with --disable-multi-arch and on powerpc64le-linux-gnu.
Reviewed-by: Adhemerval Zanella  <adhemerval.zanella@linaro.org>
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