The value of PI is never exactly PI in any floating point representation,
and the value of PI/2 is never PI/2. It is wrong to expect cos(M_PI_2l)
to return 0, instead it will return an answer that is non-zero because
M_PI_2l doesn't round to exactly PI/2 in the type used.
That is to say that the correct answer is to do the following:
* Take PI or PI/2.
* Round to the floating point representation.
* Take the rounded value and compute an infinite precision cos or sin.
* Use the rounded result of the infinite precision cos or sin as the
answer to the test.
I used printf to do the type rounding, and Wolfram's Alpha to do the
infinite precision cos calculations.
The following changes bring x86-64 and x86 to 1/2 ulp for two tests.
It shows that the x86 cos implementation is quite good, and that
our test are flawed.
Unfortunately given that the rounding errors are type dependent we
need to fix this for each type. No regressions on x86-64 or x86.
---
2013-04-11 Carlos O'Donell <carlos@redhat.com>
* math/libm-test.inc (cos_test): Fix PI/2 test.
(sincos_test): Likewise.
* sysdeps/x86_64/fpu/libm-test-ulps: Regenerate.
* sysdeps/i386/fpu/libm-test-ulps: Regenerate.
The wiki "Regeneration" page has this to say about update ULPs.
"The libm-test-ulps files are semiautomatically updated. To
update an ulps baseline, run each of the failing tests (test-float,
test-double, etc.) with -u; this will generate a file called ULPs;
concatenate each of those files with the existing libm-test-ulps
file, after removing any entries for particularly huge numbers of
ulps that you do not want to mark as expected. Then run
gen-libm-test.pl -n -u FILE where FILE is the concatenated file
produced in the previous step. This generates a file called
NewUlps which is the new sorted version of libm-test-ulps."
The same information is listed in math/README.libm-test, and is a
lot of manual work that you often want to run over-and-over again
while working on a particular test.
The `regen-ulps' convenience target does this automatically for
developers.
We strictly assume the source tree is readonly and add a
new --output-dir option to libm-test.inc to allow for writing
out ULPs to $(objpfx).
When run the new target does the following:
* Starts with the baseline ULPs file.
* Runs each of the libm math tests with -u.
* Adds new changes seen with -u to the baseline.
* Sorts and prepares the test output with gen-libm-test.pl.
* Leaves math/NewUlps in your build tree to copy to your source
tree, cleanup, and checkin.
The math test documentation in math/README.libm-test is updated
document the new Makefile target.
---
2013-04-06 Carlos O'Donell <carlos@redhat.com>
* Makefile.in (regen-ulps): New target.
* math/Makefile [ifneq (no,$(PERL)]: Declare regen-ulps with .PHONY.
[ifneq (no,$(PERL)] (run-regen-ulps): New variable.
[ifneq (no,$(PERL)] (regen-ulps): New target.
[ifeq (no,$(PERL)] (regen-ulps): New target.
* math/libm-test.inc (ulps_file_name): Define.
(output_dir): New variable.
(options): Add "output-dir" option.
(parse_opt): Handle 'o' case.
(main): If output_dir is non-NULL use it as a prefix
otherwise use "".
* math/README.libm-test: Update `How can I generate "libm-test-ulps"?'
The patch increase the high value to check if expl overflows. Current
high mark value is not really correct, the algorithm accepts high values.
It also adds a correct wrapper function to check for overflow and underflow.
With help from Joseph Myers.
* sysdeps/ieee754/ldbl-128/s_atanl.c (__atanl): Handle tiny and
very large arguments properly.
* math/libm-test.inc (atan_test): New tests.
(atan2_test): New tests.
* sysdeps/sparc/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Update.
With help from Joseph Myers.
* sysdeps/ieee754/flt-32/e_j0f.c (__ieee754_y0f): Adjust tinyness
cutoff to 2**-13.
* sysdeps/ieee754/flt-32/e_j1f.c (__ieee754_y1f): Adjust tinyness
cutoff to 2**-25.
* sysdeps/ieee754/ldbl-128/e_j0l.c (U0): New constant.
( __ieee754_y0l): Avoid arithmetic underflow when 'x' is very
small.
* sysdeps/ieee754/ldbl-128/e_j1l.c (__ieee754_y1l): Likewise.
* math/libm-test.inc (y0_test): New tests.
(y1_test): New tests.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Update.
* sysdeps/sparc/fpu/libm-test-ulps: Update.
* sysdeps/i386/i686/fpu/multiarch/Makefile (sysdep_routines):
Add s_sinf-sse2, s_conf-sse2.
* sysdeps/i386/i686/fpu/multiarch/s_sinf-sse2.S: New file.
* sysdeps/i386/i686/fpu/multiarch/s_cosf-sse2.S: New file.
* sysdeps/i386/i686/fpu/multiarch/s_sinf.c: New file.
* sysdeps/i386/i686/fpu/multiarch/s_cosf.c: New file.
* sysdeps/ieee754/flt-32/s_sinf.c (SINF, SINF_FUNC): Add macros
for using routine as __sinf_ia32.
Use macro for function declaration and weak_alias.
* sysdeps/ieee754/flt-32/s_cosf.c (COSF, COSF_FUNC): Add macros
for using routine as __cosf_ia32.
Use macro for function declaration and weak_alias.
* sysdeps/i386/i686/fpu/multiarch/e_expf-sse2.S: Fix Copyright.
* sysdeps/i386/i686/fpu/multiarch/e_expf.c: Fix Copyright.
* sysdeps/x86_64/fpu/s_sinf.S: New file.
* sysdeps/x86_64/fpu/s_cosf.S: New file.
* sysdeps/x86_64/fpu/libm-test-ulps: Update.
* math/libm-test.inc (cos_test): Add more test cases.
(sin_test): Likewise.
(sincos_test): Likewise.
