Bug 21094 reports 3ulp errors of cosf and tanf for certain arguments
near pi/2 arising from the use of an insufficiently accurate range
reduction. (To be clear, this is a quality-of-implementation issue
relating to the apparent intent of those particular cosf and tanf
implementations; 3ulp is within the general glibc accuracy goals, so
not inherently a bug.)
This patch fixes that error by making a wider range of cases use the
existing more accurate range reduction for arguments close to pi/2.
The wider range of values is still narrow enough for the "z -=
pio2_2;" in the more accurate case to be exact, as the code expects.
Tested for x86_64, x86 and mips64; no ulps updates needed (but at
least on mips64, the larger ulps were seen if the tests were added
without the substantive fix).
[BZ #21094]
* sysdeps/ieee754/flt-32/e_rem_pio2f.c (__ieee754_rem_pio2f): Use
24+24+24-bit pi for wider range of values around pi/2.
* math/auto-libm-test-in: Add more tests of cos and tan.
* math/auto-libm-test-out-cos: Regenerated.
* math/auto-libm-test-out-tan: Likewise.
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.
Joseph Myers