http://sourceware.org/ml/libc-alpha/2013-08/msg00084.html
Another batch of ieee854 macros and union replacement. These four
files also have bugs fixed with this patch. The fact that the two
doubles in an IBM long double may have different signs means that
negation and absolute value operations can't just twiddle one sign bit
as you can with ieee864 style extended double. fmodl, remainderl,
erfl and erfcl all had errors of this type. erfl also returned +1 for
large magnitude negative input where it should return -1. The hypotl
error is innocuous since the value adjusted twice is only used as a
flag. The e_hypotl.c tests for large "a" and small "b" are mutually
exclusive because we've already exited when x/y > 2**120. That allows
some further small simplifications.
[BZ #15734], [BZ #15735]
* sysdeps/ieee754/ldbl-128ibm/e_fmodl.c (__ieee754_fmodl): Rewrite
all uses of ieee875 long double macros and unions. Simplify test
for 0.0L. Correct |x|<|y| and |x|=|y| test. Use
ldbl_extract_mantissa value for ix,iy exponents. Properly
normalize after ldbl_extract_mantissa, and don't add hidden bit
already handled. Don't treat low word of ieee854 mantissa like
low word of IBM long double and mask off bit when testing for
zero.
* sysdeps/ieee754/ldbl-128ibm/e_hypotl.c (__ieee754_hypotl): Rewrite
all uses of ieee875 long double macros and unions. Simplify tests
for 0.0L and inf. Correct double adjustment of k. Delete dead code
adjusting ha,hb. Simplify code setting kld. Delete two600 and
two1022, instead use their values. Recognise that tests for large
"a" and small "b" are mutually exclusive. Rename vars. Comment.
* sysdeps/ieee754/ldbl-128ibm/e_remainderl.c (__ieee754_remainderl):
Rewrite all uses of ieee875 long double macros and unions. Simplify
test for 0.0L and nan. Correct negation.
* sysdeps/ieee754/ldbl-128ibm/s_erfl.c (__erfl): Rewrite all uses of
ieee875 long double macros and unions. Correct output for large
magnitude x. Correct absolute value calculation.
(__erfcl): Likewise.
* math/libm-test.inc: Add tests for errors discovered in IBM long
double versions of fmodl, remainderl, erfl and erfcl.
In 128-bit IBM long double the precision of the type
decreases as you approach subnormal numbers, equaling
that of a double for subnormal numbers. Therefore
adjust the computation in ulp to use 2^(MIN_EXP - MANT_DIG)
which is correct for FP_SUBNORMAL for all types.
The current value used for ulp near zero is wrong,
and this commit fixes it such that ulp(0) is the smallest
subnormal value nearest to zero, which makes the most
sense for testing values near zero. Note that this is not
what Java does; they use the nearest normal value, which
is less accurate than what we want for glibc. Note that
there is no correct implementation of ulp since there
is no strict mathmatical definition that is accepted by
all groups using IEEE 754.
Previously with the large ulp values near zero there
were tests that previously passed, but were in fact
billions of ulp away from the precise answer. With this
commit we now need to disable one of the cpow tests which
is revealed to be inaccurate (bug 14473).
---
2013-05-24 Carlos O'Donell <carlos@redhat.com>
* math/libm-test.inc (MAX_EXP): Define.
(ULPDIFF): Define.
(ulp): New function.
(check_float_internal): Use ULPDIFF.
(cpow_test): Disable failing test.
(check_ulp): Test ulp() implemetnation.
(main): Call check_ulp before starting tests.
Use the most accurate hex literals possible for the answers to the
cos and sincos tests that vary according to the error in the rounding
of PI/2.
---
2013-04-24 Carlos O'Donell <carlos@redhat.com>
* math/libm-test.inc (cos_test): Use accurate hex constants.
(sincost_test): Likewise.
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"?'
Joseph Myers