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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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The corner cases included were generated using exhaustive search
for all float/binary32 values on x86_64 (comparing to MPFR for
correct rounding to nearest).
For the j0/j1/y0 functions, only cases with ulp error <= 9 were
included.
Reviewed-by: Carlos O'Donell <carlos@redhat.com>
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math/auto-libm-test-out is, at over 30 MB, by far the largest file in
the glibc source tree. This patch splits it by function, so reducing
it to auto-libm-test-out-<func> files that are all under 5 MB in size.
This is preliminary to splitting up libm-test.inc as well so that each
function's tests can also be processed separately by
gen-libm-test.pl. As a preliminary patch it doesn't actually
implement that step; rather, all the separate files get concatenated
by the Makefile to produce the monolithic auto-libm-test-out file
again as an input to gen-libm-test.pl. (The concatentation is
identical to the file in the source tree before this patch.)
Even this preliminary step, however, is of use independent of
splitting up libm-test.inc: some tests for csin and csinh have not
been moved to auto-libm-test-in because they result in
auto-libm-test-out generation taking several minutes rather than a few
seconds (all released MPC versions are very slow for certain sin /
sinh inputs; there are some old improvements in MPC mainline which
should eventually become MPC 1.1, but the complex inverse trig and
hyperbolic functions are slow even in MPC mainline and have yet to be
moved to auto-libm-test-in at all), and it seems much more reasonable
to add such inputs to auto-libm-test-in when it will only slow down
regeneration for particular functions than when it will slow down
regeneration globally.
gen-auto-libm-tests still parses the whole input file, but only
generates output for the requested function. This ensures bad syntax
in the file is always detected, and parsing the whole file is quick;
it's output generation that is comparatively slow for some functions.
Tested for x86_64.
* math/gen-auto-libm-tests.c: Update comment about use of program.
(generate_output): Add argument FUNCTION.
(main): Require extra argument. Pass function name to
generate_output.
* math/Makefile (generated): Add auto-libm-test-out.
(libm-test-funcs-auto): New variable.
(auto-libm-test-out-files): New variable.
($(objpfx)libm-test.c): Depend on $(auto-libm-test-out-files).
Concatenate those files to form $(objpfx)auto-libm-test-out and
use it as input to gen-libm-test.pl.
* math/README.libm-test: Update.
* math/auto-libm-test-out: Remove.
* math/auto-libm-test-out-acos: New generated file.
* math/auto-libm-test-out-acosh: Likewise.
* math/auto-libm-test-out-asin: Likewise.
* math/auto-libm-test-out-asinh: Likewise.
* math/auto-libm-test-out-atan: Likewise.
* math/auto-libm-test-out-atan2: Likewise.
* math/auto-libm-test-out-atanh: Likewise.
* math/auto-libm-test-out-cabs: Likewise.
* math/auto-libm-test-out-carg: Likewise.
* math/auto-libm-test-out-cbrt: Likewise.
* math/auto-libm-test-out-ccos: Likewise.
* math/auto-libm-test-out-ccosh: Likewise.
* math/auto-libm-test-out-cexp: Likewise.
* math/auto-libm-test-out-clog: Likewise.
* math/auto-libm-test-out-clog10: Likewise.
* math/auto-libm-test-out-cos: Likewise.
* math/auto-libm-test-out-cosh: Likewise.
* math/auto-libm-test-out-cpow: Likewise.
* math/auto-libm-test-out-csin: Likewise.
* math/auto-libm-test-out-csinh: Likewise.
* math/auto-libm-test-out-csqrt: Likewise.
* math/auto-libm-test-out-ctan: Likewise.
* math/auto-libm-test-out-ctanh: Likewise.
* math/auto-libm-test-out-erf: Likewise.
* math/auto-libm-test-out-erfc: Likewise.
* math/auto-libm-test-out-exp: Likewise.
* math/auto-libm-test-out-exp10: Likewise.
* math/auto-libm-test-out-exp2: Likewise.
* math/auto-libm-test-out-expm1: Likewise.
* math/auto-libm-test-out-fma: Likewise.
* math/auto-libm-test-out-hypot: Likewise.
* math/auto-libm-test-out-j0: Likewise.
* math/auto-libm-test-out-j1: Likewise.
* math/auto-libm-test-out-jn: Likewise.
* math/auto-libm-test-out-lgamma: Likewise.
* math/auto-libm-test-out-log: Likewise.
* math/auto-libm-test-out-log10: Likewise.
* math/auto-libm-test-out-log1p: Likewise.
* math/auto-libm-test-out-log2: Likewise.
* math/auto-libm-test-out-pow: Likewise.
* math/auto-libm-test-out-sin: Likewise.
* math/auto-libm-test-out-sincos: Likewise.
* math/auto-libm-test-out-sinh: Likewise.
* math/auto-libm-test-out-sqrt: Likewise.
* math/auto-libm-test-out-tan: Likewise.
* math/auto-libm-test-out-tanh: Likewise.
* math/auto-libm-test-out-tgamma: Likewise.
* math/auto-libm-test-out-y0: Likewise.
* math/auto-libm-test-out-y1: Likewise.
* math/auto-libm-test-out-yn: Likewise.
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