Commit Graph

196 Commits

Author SHA1 Message Date
Joseph Myers
e02920bc02 Improve tgamma accuracy (bug 18613).
In non-default rounding modes, tgamma can be slightly less accurate
than permitted by glibc's accuracy goals.

Part of the problem is error accumulation, addressed in this patch by
setting round-to-nearest for internal computations.  However, there
was also a bug in the code dealing with computing pow (x + n, x + n)
where x + n is not exactly representable, providing another source of
error even in round-to-nearest mode; it was necessary to address both
bugs to get errors for all testcases within glibc's accuracy goals.
Given this second fix, accuracy in round-to-nearest mode is also
improved (hence regeneration of ulps for tgamma should be from scratch
- truncate libm-test-ulps or at least remove existing tgamma entries -
so that the expected ulps can be reduced).

Some additional complications also arose.  Certain tgamma tests should
strictly, according to IEEE semantics, overflow or not depending on
the rounding mode; this is beyond the scope of glibc's accuracy goals
for any function without exactly-determined results, but
gen-auto-libm-tests doesn't handle being lax there as it does for
underflow.  (libm-test.inc also doesn't handle being lax about whether
the result in cases very close to the overflow threshold is infinity
or a finite value close to overflow, but that doesn't cause problems
in this case though I've seen it cause problems with random test
generation for some functions.)  Thus, spurious-overflow markings,
with a comment, are added to auto-libm-test-in (no bug in Bugzilla
because the issue is with the testsuite, not a user-visible bug in
glibc).  And on x86, after the patch I saw ERANGE issues as previously
reported by Carlos (see my commentary in
<https://sourceware.org/ml/libc-alpha/2015-01/msg00485.html>), which
needed addressing by ensuring excess range and precision were
eliminated at various points if FLT_EVAL_METHOD != 0.

I also noticed and fixed a cosmetic issue where 1.0f was used in long
double functions and should have been 1.0L.

This completes the move of all functions to testing in all rounding
modes with ALL_RM_TEST, so gen-libm-have-vector-test.sh is updated to
remove the workaround for some functions not using ALL_RM_TEST.

Tested for x86_64, x86, mips64 and powerpc.

	[BZ #18613]
	* sysdeps/ieee754/dbl-64/e_gamma_r.c (gamma_positive): Take log of
	X_ADJ not X when adjusting exponent.
	(__ieee754_gamma_r): Do intermediate computations in
	round-to-nearest then adjust overflowing and underflowing results
	as needed.
	* sysdeps/ieee754/flt-32/e_gammaf_r.c (gammaf_positive): Take log
	of X_ADJ not X when adjusting exponent.
	(__ieee754_gammaf_r): Do intermediate computations in
	round-to-nearest then adjust overflowing and underflowing results
	as needed.
	* sysdeps/ieee754/ldbl-128/e_gammal_r.c (gammal_positive): Take
	log of X_ADJ not X when adjusting exponent.
	(__ieee754_gammal_r): Do intermediate computations in
	round-to-nearest then adjust overflowing and underflowing results
	as needed.  Use 1.0L not 1.0f as numerator of division.
	* sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c (gammal_positive): Take
	log of X_ADJ not X when adjusting exponent.
	(__ieee754_gammal_r): Do intermediate computations in
	round-to-nearest then adjust overflowing and underflowing results
	as needed.  Use 1.0L not 1.0f as numerator of division.
	* sysdeps/ieee754/ldbl-96/e_gammal_r.c (gammal_positive): Take log
	of X_ADJ not X when adjusting exponent.
	(__ieee754_gammal_r): Do intermediate computations in
	round-to-nearest then adjust overflowing and underflowing results
	as needed.  Use 1.0L not 1.0f as numerator of division.
	* math/libm-test.inc (tgamma_test_data): Remove one test.  Moved
	to auto-libm-test-in.
	(tgamma_test): Use ALL_RM_TEST.
	* math/auto-libm-test-in: Add one test of tgamma.  Mark some other
	tests of tgamma with spurious-overflow.
	* math/auto-libm-test-out: Regenerated.
	* math/gen-libm-have-vector-test.sh: Do not check for START.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-06-29 23:29:35 +00:00
Joseph Myers
a8e2112ae3 Use round-to-nearest internally in jn, test with ALL_RM_TEST (bug 18602).
Some existing jn tests, if run in non-default rounding modes, produce
errors above those accepted in glibc, which causes problems for moving
tests of jn to use ALL_RM_TEST.  This patch makes jn set rounding
to-nearest internally, as was done for yn some time ago, then computes
the appropriate underflowing value for results that underflowed to
zero in to-nearest, and moves the tests to ALL_RM_TEST.  It does
nothing about the general inaccuracy of Bessel function
implementations in glibc, though it should make jn more accurate on
average in non-default rounding modes through reduced error
accumulation.  The recomputation of results that underflowed to zero
should as a side-effect fix some cases of bug 16559, where jn just
used an exact zero, but that is *not* the goal of this patch and other
cases of that bug remain unfixed.

(Most of the changes in the patch are reindentation to add new scopes
for SET_RESTORE_ROUND*.)

Tested for x86_64, x86, powerpc and mips64.

	[BZ #16559]
	[BZ #18602]
	* sysdeps/ieee754/dbl-64/e_jn.c (__ieee754_jn): Set
	round-to-nearest internally then recompute results that
	underflowed to zero in the original rounding mode.
	* sysdeps/ieee754/flt-32/e_jnf.c (__ieee754_jnf): Likewise.
	* sysdeps/ieee754/ldbl-128/e_jnl.c (__ieee754_jnl): Likewise.
	* sysdeps/ieee754/ldbl-128ibm/e_jnl.c (__ieee754_jnl): Likewise.
	* sysdeps/ieee754/ldbl-96/e_jnl.c (__ieee754_jnl): Likewise
	* math/libm-test.inc (jn_test): Use ALL_RM_TEST.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-06-25 21:46:02 +00:00
Joseph Myers
a67894c505 Fix cexp, ccos, ccosh, csin, csinh spurious underflows (bug 18594).
cexp, ccos, ccosh, csin and csinh have spurious underflows in cases
where they compute sin of the smallest normal, that produces an
underflow exception (depending on which sin implementation is in use)
but the final result does not underflow.  ctan and ctanh may also have
such underflows, or they may be latent (the issue there is that
e.g. ctan (DBL_MIN) should, rounded upwards, be the next double value
above DBL_MIN, which under glibc's accuracy goals may not have an
underflow exception, but the intermediate computation of sin (DBL_MIN)
would legitimately underflow on before-rounding architectures).

This patch fixes all those functions so they use plain comparisons (>
DBL_MIN etc.) instead of comparing the result of fpclassify with
FP_SUBNORMAL (in all these cases, we already know the number being
compared is finite).  Note that in the case of csin / csinf / csinl,
there is no need for fabs calls in the comparison because the real
part has already been reduced to its absolute value.

As the patch fixes the failures that previously obstructed moving
tests of cexp to use ALL_RM_TEST, those tests are moved to ALL_RM_TEST
by the patch (two functions remain yet to be converted).

Tested for x86_64 and x86 and ulps updated accordingly.

	[BZ #18594]
	* math/s_ccosh.c (__ccosh): Compare with least normal value
	instead of comparing class with FP_SUBNORMAL.
	* math/s_ccoshf.c (__ccoshf): Likewise.
	* math/s_ccoshl.c (__ccoshl): Likewise.
	* math/s_cexp.c (__cexp): Likewise.
	* math/s_cexpf.c (__cexpf): Likewise.
	* math/s_cexpl.c (__cexpl): Likewise.
	* math/s_csin.c (__csin): Likewise.
	* math/s_csinf.c (__csinf): Likewise.
	* math/s_csinh.c (__csinh): Likewise.
	* math/s_csinhf.c (__csinhf): Likewise.
	* math/s_csinhl.c (__csinhl): Likewise.
	* math/s_csinl.c (__csinl): Likewise.
	* math/s_ctan.c (__ctan): Likewise.
	* math/s_ctanf.c (__ctanf): Likewise.
	* math/s_ctanh.c (__ctanh): Likewise.
	* math/s_ctanhf.c (__ctanhf): Likewise.
	* math/s_ctanhl.c (__ctanhl): Likewise.
	* math/s_ctanl.c (__ctanl): Likewise.
	* math/auto-libm-test-in: Add more tests of ccos, ccosh, cexp,
	csin, csinh, ctan and ctanh.
	* math/auto-libm-test-out: Regenerated.
	* math/libm-test.inc (cexp_test): Use ALL_RM_TEST.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-06-24 21:04:51 +00:00
Joseph Myers
718d34a309 Fix csqrt spurious underflows (bug 18371).
The csqrt implementations in glibc can cause spurious underflows in
some cases as a side-effect of the scaling for large arguments (when
underflow is correct for the square root of the argument that was
scaled down to avoid overflow, but not for the original argument).
This patch arranges to avoid the underflowing intermediate computation
(eliminating a multiplication in 0.5 in the problem cases where a
subsequent scaling by 2 would follow).

Tested for x86_64 and x86 and ulps updated accordingly (only needed
for x86).

	[BZ #18371]
	* math/s_csqrt.c (__csqrt): Avoid multiplication by 0.5 where
	intermediate but not final result might underflow.
	* math/s_csqrtf.c (__csqrtf): Likewise.
	* math/s_csqrtl.c (__csqrtl): Likewise.
	* math/auto-libm-test-in: Add more tests of csqrt.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
2015-06-23 16:01:54 +00:00
Joseph Myers
14f36098f2 Add more tests of csqrt, lgamma, log10, sinh.
This patch adds more randomly-generated tests of various libm
functions that are observed to increase ulps on x86_64.

Tested for x86_64 and x86 and ulps updated accordingly.

	* math/auto-libm-test-in: Add more tests of csqrt, lgamma, log10
	and sinh.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-05-08 17:55:11 +00:00
Joseph Myers
471dffa12c Add more tests of acosh, atanh, cos, csqrt, erfc, sin, sincos.
This patch adds more randomly-generated tests of various libm
functions that are observed to increase ulps on x86_64.

Tested for x86_64 and x86 and ulps updated accordingly.

	* math/auto-libm-test-in: Add more tests of acosh, atanh, cos,
	csqrt, erfc, sin and sincos.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-05-06 17:30:18 +00:00
Joseph Myers
31450d9a87 Add further tests of libm functions.
This patch adds more randomly-generated tests of various libm
functions that are observed to increase ulps on x86_64.  (This process
must eventually converge, when my random test generation stops finding
inputs that increase the listed ulps, except maybe for any cases
uncovered where the errors exceed the maximum allowed 9ulp error and
so indicate actual libm bugs needing fixing.)

Tested for x86_64 and x86 and ulps updated accordingly.

	* math/auto-libm-test-in: Add more tests of acosh, atanh, clog,
	clog10, csqrt, erfc, exp2, expm1, log10, log2 and sinh.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-05-05 22:59:41 +00:00
Joseph Myers
305392eaca Add more tests of libm functions.
This patch adds more randomly-generated tests of various libm
functions that are observed to increase ulps on x86_64.

Tested for x86_64 and x86 and ulps updated accordingly.

	* math/auto-libm-test-in: Add more tests of atan, clog, clog10,
	cos, csqrt, erf, erfc, exp2, lgamma, log1p, sin, sincos, tanh and
	tgamma.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-05-02 21:06:33 +00:00
Joseph Myers
51e15247c3 Add more tests of tgamma.
This patch adds some randomly-generated tests of tgamma that are
observed to increase ulps on x86_64.

Tested for x86_64 and x86 and ulps updated accordingly.

	* math/auto-libm-test-in: Add more tests of tgamma.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-05-01 23:15:07 +00:00
Joseph Myers
5ffb9a53d7 Add more tests of tanh.
This patch adds some randomly-generated tests of tanh that are
observed to increase ulps on x86_64.

Tested for x86_64 and x86 and ulps updated accordingly.

	* math/auto-libm-test-in: Add more tests of tanh.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-05-01 23:06:44 +00:00
Joseph Myers
0957e15d0a Add more tests of tan.
This patch adds some randomly-generated tests of tan that are observed
to increase ulps on x86_64.

Tested for x86_64 and x86 and ulps updated accordingly.

	* math/auto-libm-test-in: Add more tests of tan.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-05-01 22:54:39 +00:00
Joseph Myers
827bb5859c Add more tests of cos, sin, sincos.
This patch adds some randomly-generated tests of cos, sin and sincos
that are observed to increase ulps on x86_64.

Tested for x86_64 and x86 and ulps updated accordingly.

	* math/auto-libm-test-in: Add more tests of cos, sin and sincos.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-05-01 22:41:00 +00:00
Joseph Myers
038e4be99c Add more tests of lgamma.
This patch adds some randomly-generated tests of lgamma that are
observed to increase ulps on x86_64.

Tested for x86_64 and x86 and ulps updated accordingly.

	* math/auto-libm-test-in: Add more tests of lgamma.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-05-01 22:17:19 +00:00
Joseph Myers
a0d31f36aa Add more tests of log, log10, log1p, log2.
This patch adds some randomly-generated tests of log, log10, log1p and
log2 that are observed to increase ulps on x86_64.

Tested for x86_64 and x86 and ulps updated accordingly.

	* math/auto-libm-test-in: Add more tests of log, log10, log2 and
	log1p.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-05-01 21:08:37 +00:00
Joseph Myers
e1483b365d Add more tests of exp, exp10, exp2, expm1.
This patch adds some randomly-generated tests of exp, exp10, exp2 and
expm1 that are observed to increase ulps on x86_64.

Tested for x86_64 and x86 and ulps updated accordingly.

	* math/auto-libm-test-in: Add more tests of exp, exp10, exp2 and
	expm1.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-05-01 20:33:04 +00:00
Joseph Myers
c5a3a509df Add more tests of erf, erfc.
This patch adds some randomly-generated tests of erf and erfc that are
observed to increase ulps on x86_64.

Tested for x86_64 and x86 and ulps updated accordingly.

	* math/auto-libm-test-in: Add more tests of erf and erfc.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-05-01 17:49:44 +00:00
Joseph Myers
9862ab1f67 Add more tests of csqrt.
This patch adds some randomly-generated tests of csqrt that are
observed to increase ulps on x86_64.

Tested for x86_64 and x86 and ulps updated accordingly.

	* math/auto-libm-test-in: Add more tests of csqrt.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-04-30 22:51:29 +00:00
Joseph Myers
094fca83ee Add further tests of cosh and sinh.
This patch adds some further randomly-generated tests of cosh and sinh
that are observed to increase ulps on x86_64.

Tested for x86_64 and x86 and ulps updated accordingly.

	* math/auto-libm-test-in: Add more tests of cosh and sinh.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-04-30 22:32:08 +00:00
Joseph Myers
b3c66c534f Add more tests of clog and clog10.
This patch adds some randomly-generated tests of clog and clog10 that
are observed to increase ulps on x86_64.

Tested for x86_64 and x86 and ulps updated accordingly.

	* math/auto-libm-test-in: Add more tests of clog and clog10.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-04-09 22:14:34 +00:00
Joseph Myers
787d22bce6 Add more tests of atanh.
This patch adds some randomly-generated tests of atanh that are
observed to increase ulps on x86_64.

Tested for x86_64 and x86 and ulps updated accordingly.

	* math/auto-libm-test-in: Add more tests of atanh.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-04-08 21:13:35 +00:00
Joseph Myers
024bcc5106 Add more tests of atan.
This patch adds some randomly-generated tests of atan that are
observed to increase ulps on x86_64.

Tested for x86_64 and x86 and ulps updated accordingly.

	* math/auto-libm-test-in: Add more tests of atan.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-04-08 21:00:03 +00:00
Joseph Myers
80352c01c1 Add more tests of cabs.
This patch adds some randomly-generated tests of cabs that are
observed to increase ulps on x86_64.

Tested for x86_64 and x86 and ulps updated accordingly.

	* math/auto-libm-test-in: Add more tests of cabs.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-04-08 17:46:07 +00:00
Joseph Myers
8431838dde Fix dbl-64 atan2 in non-default rounding modes (bug 18210, bug 18211).
The dbl-64 implementation of atan2 does computations that expect to
run in round-to-nearest mode, and in other modes the errors can
accumulate to more than the maximum accepted 9ulp.  This patch makes
it use FE_TONEAREST internally, similar to other functions with such
issues.  Tests that previously produced large errors are added for
atan2 and the closely related carg, clog and clog10 functions.

Tested for x86_64 and x86 and ulps updated accordingly.

	[BZ #18210]
	[BZ #18211]
	* sysdeps/ieee754/dbl-64/e_atan2.c: Include <fenv.h>.
	(__ieee754_atan2): Set FE_TONEAREST mode for internal
	computations.
	* math/auto-libm-test-in: Add more tests of atan2, carg, clog and
	clog10.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-04-08 17:32:17 +00:00
Joseph Myers
efd5b641dd Add more tests of acosh, asinh and atanh.
This patch adds some randomly-generated tests of acosh, asinh and
atanh that are observed to increase ulps on x86_64.

Tested for x86_64 and x86 and ulps updated accordingly.

	* math/auto-libm-test-in: Add more tests of acosh, asinh and
	atanh.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-03-25 22:21:20 +00:00
Joseph Myers
e9b1015112 Add another test of asin.
This patch adds a randomly-generated test of asin that is observed to
increase ulps on x86_64.

Tested for x86_64 and x86 and ulps updated accordingly.

	* math/auto-libm-test-in: Add another test of asin.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-03-25 21:57:04 +00:00
Joseph Myers
38755f1421 Add more tests of asin.
This patch adds some randomly-generated tests of asin that are
observed to increase ulps on x86_64.

Tested for x86_64 and x86 and ulps updated accordingly.

	* math/auto-libm-test-in: Add more tests of asin.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-03-25 17:53:58 +00:00
Joseph Myers
8d6439712d Add more tests of acos.
This patch adds some randomly-generated tests of acos that are
observed to increase ulps on x86_64.

Tested for x86_64 and x86 and ulps updated accordingly.

	* math/auto-libm-test-in: Add more tests of acos.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-03-25 00:30:10 +00:00
Joseph Myers
bc899ea090 Add more tests of expm1.
This patch adds some randomly-generated tests of expm1 that are
observed to increase ulps on x86_64.

Tested for x86_64 and x86 and ulps updated accordingly.

	* math/auto-libm-test-in: Add more tests of expm1.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-03-25 00:05:13 +00:00
Joseph Myers
239ed6f309 Add more tests of cosh, sinh.
This patch adds some randomly-generated tests of cosh and sinh that
are observed to increase ulps on x86_64.

Tested for x86_64 and x86 and ulps updated accordingly.

	* math/auto-libm-test-in: Add more tests of cosh and sinh.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-03-24 23:48:04 +00:00
Joseph Myers
a737e8263a Regenerate x86_64, x86 ulps from scratch.
The x86_64 and x86 libm-test-ulps files hadn't been regenerated from
scratch for some time, as evidenced by the presence of entries for
*_tonearest functions (those tests duplicated the
default-rounding-mode tests, and such duplicates are no longer run).
The aarch64, alpha, hppa, ia64, m68k, microblaze, powerpc, s390, sh,
sparc, tile files similarly could do with from-scratch regeneration as
evidenced by the presence of such entries.  (Truncate the existing
file then run "make regen-ulps" and move the resulting file into
place.)

This patch regenerates the x86_64 and x86 files from scratch.  It's
likely some of the reduced / removed ulps will need restoring because
they appear on processors or compiler versions other than the one I
tested on, but in such cases I'd like to first see if I can generate
new tests that show such ulps on the Intel processor I'm testing on,
to reduce the effects from different people using different processors
and compilers to regenerate the ulps.

	* sysdeps/i386/fpu/libm-test-ulps: Regenerated.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-03-24 23:30:19 +00:00
Joseph Myers
7c84a5042f Add more tests of log2.
In testing for x86_64 on an AMD processor, I observed libm test
failures of the form:

testing long double (without inline functions)
Failure: Test: log2_downward (0x2.b7e151628aed4p+0)
Result:
 is:          1.44269504088896356633e+00   0xb.8aa3b295c17f67600000p-3
 should be:   1.44269504088896356622e+00   0xb.8aa3b295c17f67500000p-3
 difference:  1.08420217248550443400e-19   0x8.00000000000000000000p-66
 ulp       :  1.0000
 max.ulp   :  0.0000
Maximal error of `log2_downward'
 is      : 1 ulp
 accepted: 0 ulp

These issues arise because the maximum ulps when regenerating on one
processor are not the same as on another processor, so regeneration on
several processors may be needed when updating libm-test-ulps to avoid
failures for some users testing glibc - but such regeneration on
multiple processors is inconvenient.  Causes can be: on x86 and, for
x86_64, for long double, variation in results of x87 instructions for
transcendental operations between processors; on x86, variation in
compiler excess precision between compiler versions and
configurations; on any processor where the compiler may contract
expressions using fused multiply-add, variation in what contraction
occurs.

Although it's hard to be sure libm-test-ulps covers all ulps that may
be seen in any configuration for the given architecture, in practice
it helps simply to add wider test coverage to make it more likely
that, when testing on one processor, the ulps seen are the biggest
that can be seen for that function on that processor, and hopefully
they are also the biggest that can be seen for that function in other
configurations for that architecture.  Thus, this patch adds some
tests of log2 that increase the ulps I see on x86_64 on an Intel
processor, so that hopefully future from-scratch regenerations on that
processor will produce ulps big enough not to have errors from testing
on AMD processors.  These tests were found by randomly generating
inputs and seeing what produced ulps larger than those currently in
libm-test-ulps.  Of course such increases also improve the accuracy of
the empirical table of known ulps generated from libm-test-ulps files
that goes in the manual.

Tested for x86_64 and x86 and ulps updated accordingly.

	* math/auto-libm-test-in: Add more tests of log2.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-03-24 23:06:28 +00:00
Joseph Myers
2ca725c594 Fix ldbl-96, ldbl-128ibm atanhl inaccuracy (bug 18046, bug 18047).
The threshold in ldbl-96 atanhl for when to return the argument,
0x1p-28, is a bit too big, and that in ldbl-128ibm atanhl is much too
big (the relevant condition being x^3/3 being < 0.5ulp of x),
resulting in errors a bit above the limits of those considered
acceptable in glibc in the ldbl-96 case, and in large errors in the
ldbl-128ibm case.  This patch changes those implementations to use
more appropriate thresholds and adds tests around the thresholds for
various formats.

Tested for x86_64, x86 and powerpc.  x86_64 and x86 ulps updated
accordingly.

	[BZ #18046]
	[BZ #18047]
	* sysdeps/ieee754/ldbl-128ibm/e_atanhl.c (__ieee754_atanhl): Use
	0x1p-56L as threshold for just returning the argument.
	* sysdeps/ieee754/ldbl-96/e_atanhl.c (__ieee754_atanhl): Use
	0x1p-32L as threshold for just returning the argument.
	* math/auto-libm-test-in: Add more tests of atanh.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulp: Likewise.
2015-02-27 17:48:37 +00:00
Joseph Myers
137cef7d43 Fix ldbl-128ibm asinhl inaccuracy (bug 18020).
The ldbl-128ibm implementation of asinhl uses cut-offs of 0x1p28 and
0x1p-29 to determine when to use simpler formulas that avoid possible
overflow / underflow.  Both those cut-offs are inappropriate for this
format, resulting in large errors.  This patch changes the code to use
more appropriate cut-offs of 0x1p56 and 0x1p-56, adding tests around
the cut-offs for various floating-point formats.

Tested for powerpc.  Also tested for x86_64 and x86 and updated ulps.

	[BZ #18020]
	* sysdeps/ieee754/ldbl-128ibm/s_asinhl.c (__asinhl): Use 2**56 and
	2**-56 not 2**28 and 2**-29 as thresholds for simpler formulas.
	* math/auto-libm-test-in: Add more tests of asinh.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-02-25 11:13:41 +00:00
Joseph Myers
440169d681 Fix ldbl-128ibm acoshl inaccuracy (bug 18019).
The ldbl-128ibm implementation of acoshl uses a cut-off of 0x1p28 to
determine when to use log(x) + log(2) as a formula.  That cut-off is
too small for this format, resulting in large errors.  This patch
changes it to a more appropriate cut-off of 0x1p56, adding tests
around the cut-offs for various floating-point formats.

Tested for powerpc.  Also tested for x86_64 and x86 and updated ulps.

	[BZ #18019]
	* sysdeps/ieee754/ldbl-128ibm/e_acoshl.c (__ieee754_acoshl): Use
	2**56 not 2**28 as threshold for log (2x) formula.
	* math/auto-libm-test-in: Add more tests of acosh.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-02-25 00:01:15 +00:00
Joseph Myers
4629c866ad Fix atan / atan2 missing underflows (bug 15319).
This patch fixes bug 15319, missing underflows from atan / atan2 when
the result of atan is very close to its small argument (or that of
atan2 is very close to the ratio of its arguments, which may be an
exact division).

The usual approach of doing an underflowing computation if the
computed result is subnormal is followed.  For 32-bit x86, there are
extra complications: the inline __ieee754_atan2 in bits/mathinline.h
needs to be disabled for float and double because other libm functions
using it generally rely on getting proper underflow exceptions from
it, while the out-of-line functions have to remove excess range and
precision from the underflowing result so as to return an exact 0 in
the case where errno should be set for underflow to 0.  (The failures
I saw without that are similar to those Carlos reported for other
functions, where I haven't seen a response to
<https://sourceware.org/ml/libc-alpha/2015-01/msg00485.html>
confirming if my diagnosis is correct.  Arguably all libm functions
with float and double returns should remove excess range and
precision, but that's a separate matter.)

The x86_64 long double case reported in a comment in bug 15319 is not
a bug (it's an argument of LDBL_MIN, and x86_64 is an after-rounding
architecture so the correct IEEE result is not to raise underflow in
the given rounding mode, in addition to treating the result as an
exact LDBL_MIN being within the newly clarified documentation of
accuracy goals).  I'm presuming that the fpatan instruction can be
trusted to raise appropriate exceptions when the (long double) result
underflows (after rounding) and so no changes are needed for x86 /
x86_64 long double functions here; empirically this is the case for
the cases covered in the testsuite, on my system.

Tested for x86_64, x86, powerpc and mips64.  Only 32-bit x86 needs
ulps updates (for the changes to inlines meaning some functions no
longer get excess precision from their __ieee754_atan2* calls).

	[BZ #15319]
	* sysdeps/i386/fpu/e_atan2.S (dbl_min): New object.
	(MO): New macro.
	(__ieee754_atan2): For results with small absolute value, force
	underflow exception and remove excess range and precision from
	return value.
	* sysdeps/i386/fpu/e_atan2f.S (flt_min): New object.
	(MO): New macro.
	(__ieee754_atan2f): For results with small absolute value, force
	underflow exception and remove excess range and precision from
	return value.
	* sysdeps/i386/fpu/s_atan.S (dbl_min): New object.
	(MO): New macro.
	(__atan): For results with small absolute value, force underflow
	exception and remove excess range and precision from return value.
	* sysdeps/i386/fpu/s_atanf.S (flt_min): New object.
	(MO): New macro.
	(__atanf): For results with small absolute value, force underflow
	exception and remove excess range and precision from return value.
	* sysdeps/ieee754/dbl-64/e_atan2.c: Include <float.h> and
	<math.h>.
	(__ieee754_atan2): Force underflow exception for results with
	small absolute value.
	* sysdeps/ieee754/dbl-64/s_atan.c: Include <float.h> and
	<math_private.h>.
	(atan): Force underflow exception for results with small absolute
	value.
	* sysdeps/ieee754/flt-32/s_atanf.c: Include <float.h>.
	(__atanf): Force underflow exception for results with small
	absolute value.
	* sysdeps/ieee754/ldbl-128/s_atanl.c: Include <float.h> and
	<math.h>.
	(__atanl): Force underflow exception for results with small
	absolute value.
	* sysdeps/ieee754/ldbl-128ibm/s_atanl.c: Include <float.h>.
	(__atanl): Force underflow exception for results with small
	absolute value.
	* sysdeps/x86/fpu/bits/mathinline.h
	[!__SSE2_MATH__ && !__x86_64__ && __LIBC_INTERNAL_MATH_INLINES]
	(__ieee754_atan2): Only define inline for long double.
	* sysdeps/x86_64/fpu/multiarch/e_atan2.c
	[HAVE_FMA4_SUPPORT || HAVE_AVX_SUPPORT]: Include <math.h>.
	* math/auto-libm-test-in: Do not mark underflow exceptions as
	possibly missing for bug 15319.  Add more tests of atan2.
	* math/auto-libm-test-out: Regenerated.
	* math/libm-test.inc (casin_test_data): Do not mark underflow
	exceptions as possibly missing for bug 15319.
	(casinh_test_data): Likewise.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
2015-02-18 21:10:49 +00:00
Allan McRae
529bf51595 Update x86 ULPs
Using gcc-4.9, i7-2620M, i686 Linux.
2014-08-27 13:36:02 +10:00
Andreas Schwab
c213442ddd Update i386 libm test ULPs 2014-07-09 10:53:46 +02:00
Joseph Myers
be25493251 Fix yn overflow handling in non-default rounding modes (bug 16561, bug 16562).
This patch fixes bugs 16561 and 16562, bad results of yn in overflow
cases in non-default rounding modes, both because an intermediate
overflow in the recurrence does not get detected if the result is not
an infinity and because an overflowing result may occur in the wrong
sign.  The fix is to set FE_TONEAREST mode internally for the parts of
the function where such overflows can occur (which includes the call
to y1 - where yn is used to compute a Bessel function of order -1,
negating the result of y1 isn't correct for overflowing results in
directed rounding modes) and then compute an overflowing value in the
original rounding mode if the to-nearest result was an infinity.

Tested x86_64 and x86 and ulps updated accordingly.  Also tested for
mips64 and powerpc32 to test the ldbl-128 and ldbl-128ibm changes.

(The tests for these bugs were added in my previous y1 patch, so the
only thing this patch has to do with the testsuite is enable yn
testing in all rounding modes.)

	[BZ #16561]
	[BZ #16562]
	* sysdeps/ieee754/dbl-64/e_jn.c: Include <float.h>.
	(__ieee754_yn): Set FE_TONEAREST mode internally and then
	recompute overflowing results in original rounding mode.
	* sysdeps/ieee754/flt-32/e_jnf.c: Include <float.h>.
	(__ieee754_ynf): Set FE_TONEAREST mode internally and then
	recompute overflowing results in original rounding mode.
	* sysdeps/ieee754/ldbl-128/e_jnl.c: Include <float.h>.
	(__ieee754_ynl): Set FE_TONEAREST mode internally and then
	recompute overflowing results in original rounding mode.
	* sysdeps/ieee754/ldbl-128ibm/e_jnl.c: Include <float.h>.
	(__ieee754_ynl): Set FE_TONEAREST mode internally and then
	recompute overflowing results in original rounding mode.
	* sysdeps/ieee754/ldbl-96/e_jnl.c: Include <float.h>.
	(__ieee754_ynl): Set FE_TONEAREST mode internally and then
	recompute overflowing results in original rounding mode.
	* sysdeps/i386/fpu/fenv_private.h [!__SSE2_MATH__]
	(libc_feholdsetround_ctx): New macro.
	* math/libm-test.inc (yn_test): Use ALL_RM_TEST.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps : Likewise.
2014-06-27 14:52:13 +00:00
Joseph Myers
4648909d56 Fix cosh spurious underflows from expm1 (bug 16354), inaccurate results near 0 (bug 17061).
This patch fixes bug 16354, spurious underflows from cosh when a tiny
argument is passed to expm1 and expm1 correctly underflows although
the final result of cosh should be 1.  As noted in that bug, some
cases are latent because of expm1 implementations not raising
underflow (bug 16353), but all the implementations are fixed
similarly.  They already contained checks for tiny arguments, but the
checks were too late to avoid underflow from expm1 (although they
would avoid underflow from subsequent squaring of the result of
expm1); they are moved before the expm1 calls.

The thresholds used for considering arguments tiny are not
particularly consistent in how they relate to the precision of the
floating-point format in question.  They are, however, all sufficient
to ensure that the round-to-nearest result of cosh is indeed 1 below
the threshold (although sometimes they are smaller than necessary).
But the previous logic did not return 1, but the previously computed 1
+ expm1(abs(x)) value.  And the thresholds in the ldbl-128 and
ldbl-128ibm code (0x1p-71L - I suspect 0x3f8b was intended in the code
instead of 0x3fb8 - and (roughly) 0x1p-55L) are not sufficient for
that value to be 1.  So by moving the test for tiny arguments, and
consequently returning 1 directly now the expm1 value hasn't been
computed by that point, this patch also fixes bug 17061, the (large
number of ulps) inaccuracy for small arguments in those
implementations.  Tests for that bug are duly added.

Tested x86_64 and x86 and ulps updated accordingly.  Also tested for
mips64 and powerpc32 to validate the ldbl-128 and ldbl-128ibm changes.

	[BZ #16354]
	[BZ #17061]
	* sysdeps/ieee754/dbl-64/e_cosh.c (__ieee754_cosh): Check for
	small arguments before calling __expm1.
	* sysdeps/ieee754/flt-32/e_coshf.c (__ieee754_coshf): Check for
	small arguments before calling __expm1f.
	* sysdeps/ieee754/ldbl-128/e_coshl.c (__ieee754_coshl): Check for
	small arguments before calling __expm1l.
	* sysdeps/ieee754/ldbl-128ibm/e_coshl.c (__ieee754_coshl):
	Likewise.
	* sysdeps/ieee754/ldbl-96/e_coshl.c (__ieee754_coshl): Likewise.
	* math/auto-libm-test-in: Add more cosh tests.  Do not allow
	spurious underflow for some cosh tests.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
2014-06-23 20:20:10 +00:00
Joseph Myers
863893ec95 Test cpow in all rounding modes.
This patch enables testing of cpow in all rounding modes using
ALL_RM_TEST.  There were two reasons this was previously deferred:

* MPC has complicated rounding-mode-dependent rules for the signs of
  exact zero real or imaginary parts in the result of mpc_pow.  Annex
  G does not impose any such requirements and I don't think glibc
  should try to implement any particular logic here.  This patch adds
  support for gen-auto-libm-tests passing the IGNORE_ZERO_INF_SIGN
  flag to libm-test.inc.

* Error accumulations in some tests in non-default rounding modes
  exceed the maximum error permitted in libm-test.inc.  This patch
  marks the problem tests with xfail-rounding.  (It might be possible
  to reduce the accumulations a bit by using round-to-nearest when
  cpow calls clog, but I don't think there's much point; the
  implementation approach for cpow is fundamentally deficient, as
  discussed in the existing bug for cpow inaccuracy which can
  reasonably be considered to cover these less-inaccurate cases as
  well.  It's possible that the test "cpow 2 0 10 0" will also need
  xfail-rounding on some platforms.)

Tested x86_64 and x86 and ulps updated accordingly.

	* math/gen-auto-libm-tests.c: Document use of
	ignore-zero-inf-sign.
	(input_flag_type): Add value flag_ignore_zero_inf_sign.
	(input_flags): Add ignore-zero-inf-sign.
	(output_for_one_input_case): Handle flag_ignore_zero_inf_sign.
	* math/gen-libm-test.pl (generate_testfile): Handle
	ignore-zero-inf-sign.
	* math/auto-libm-test-in: Mark some cpow tests with
	ignore-zero-inf-sign and some with xfail-rounding.
	* math/auto-libm-test-out: Regenerated.
	* math/libm-test.inc (cpow_test): Use ALL_RM_TEST.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2014-06-23 20:15:14 +00:00
Joseph Myers
4da6db5188 Fix pow overflow in non-default rounding modes (bug 16315).
This patch fixes bug 16315, bad pow handling of overflow/underflow in
non-default rounding modes.  Tests of pow are duly converted to
ALL_RM_TEST to run all tests in all rounding modes.

There are two main issues here.  First, various implementations
compute a negative result by negating a positive result, but this
yields inappropriate overflow / underflow values for directed
rounding, so either overflow / underflow results need recomputing in
the correct sign, or the relevant overflowing / underflowing operation
needs to be made to have a result of the correct sign.  Second, the
dbl-64 implementation sets FE_TONEAREST internally; in the overflow /
underflow case, the result needs recomputing in the original rounding
mode.

Tested x86_64 and x86 and ulps updated accordingly.

	[BZ #16315]
	* sysdeps/i386/fpu/e_pow.S (__ieee754_pow): Ensure possibly
	overflowing or underflowing operations take place with sign of
	result.
	* sysdeps/i386/fpu/e_powf.S (__ieee754_powf): Likewise.
	* sysdeps/i386/fpu/e_powl.S (__ieee754_powl): Likewise.
	* sysdeps/ieee754/dbl-64/e_pow.c: Include <math.h>.
	(__ieee754_pow): Recompute overflowing and underflowing results in
	original rounding mode.
	* sysdeps/x86/fpu/powl_helper.c: Include <stdbool.h>.
	(__powl_helper): Allow negative argument X and scale negated value
	as needed.  Avoid passing value outside [-1, 1] to f2xm1.
	* sysdeps/x86_64/fpu/e_powl.S (__ieee754_powl): Ensure possibly
	overflowing or underflowing operations take place with sign of
	result.
	* sysdeps/x86_64/fpu/multiarch/e_pow.c [HAVE_FMA4_SUPPORT]:
	Include <math.h>.
	* math/auto-libm-test-in: Add more tests of pow.
	* math/auto-libm-test-out: Regenerated.
	* math/libm-test.inc (pow_test): Use ALL_RM_TEST.
	(pow_tonearest_test_data): Remove.
	(pow_test_tonearest): Likewise.
	(pow_towardzero_test_data): Likewise.
	(pow_test_towardzero): Likewise.
	(pow_downward_test_data): Likewise.
	(pow_test_downward): Likewise.
	(pow_upward_test_data): Likewise.
	(pow_test_upward): Likewise.
	(main): Don't call removed functions.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2014-06-23 20:12:33 +00:00
Joseph Myers
f8ba1b5654 Fix log2 (1) in round-downward mode (bug 17042).
As with other issues of this kind, bug 17042 is log2 (1) wrongly
returning -0 instead of +0 in round-downward mode because of
implementations effectively in terms of log1p (x - 1).  This patch
fixes the issue in the same way used for log and log10.

Tested x86_64 and x86 and ulps updated accordingly.  Also tested for
mips64 to confirm a fix was needed for ldbl-128 and to validate that
fix (also applied to ldbl-128ibm since that version of log2l is
essentially the same as the ldbl-128 one).

	[BZ #17042]
	* sysdeps/i386/fpu/e_log2.S (__ieee754_log2): Take absolete value
	when x - 1 is zero.
	* sysdeps/i386/fpu/e_log2f.S (__ieee754_log2f): Likewise.
	* sysdeps/i386/fpu/e_log2l.S (__ieee754_log2l): Likewise.
	* sysdeps/ieee754/ldbl-128/e_log2l.c (__ieee754_log2l): Return
	0.0L for an argument of 1.0L.
	* sysdeps/ieee754/ldbl-128ibm/e_log2l.c (__ieee754_log2l):
	Likewise.
	* sysdeps/x86_64/fpu/e_log2l.S (__ieee754_log2l): Take absolute
	value when x - 1 is zero.
	* math/libm-test.inc (log2_test): Use ALL_RM_TEST.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2014-06-10 12:07:15 +00:00
Joseph Myers
b72592e75f Fix log10 (1) in round-downward mode (bug 16977).
As with various other issues of this kind, bug 16977 is log10 (1)
wrongly returning -0 rather than +0 in round-downward mode because of
an implementation effectively in terms of log1p (x - 1).  This patch
fixes the issue in the same way used for log.

Tested x86_64 and x86 and ulps updated accordingly.  Also tested for
mips64 to confirm a fix was needed for ldbl-128 and to validate that
fix (also applied to ldbl-128ibm since that version of logl is
essentially the same as the ldbl-128 one).

	[BZ #16977]
	* sysdeps/i386/fpu/e_log10.S (__ieee754_log10): Take absolute
	value when x - 1 is zero.
	* sysdeps/i386/fpu/e_log10f.S (__ieee754_log10f): Likewise.
	* sysdeps/i386/fpu/e_log10l.S (__ieee754_log10l): Likewise.
	* sysdeps/ieee754/ldbl-128/e_log10l.c (__ieee754_log10l): Return
	0.0L for an argument of 1.0L.
	* sysdeps/ieee754/ldbl-128ibm/e_log10l.c (__ieee754_log10l):
	Likewise.
	* sysdeps/x86_64/fpu/e_log10l.S (__ieee754_log10l): Take absolute
	value when x - 1 is zero.
	* math/libm-test.inc (log10_test): Use ALL_RM_TEST.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2014-05-23 12:07:50 +00:00
Joseph Myers
01dbacd22a Fix cacos (+Inf + finite*i) in round-downward mode (bug 16928).
According to C99/C11 Annex G, cacos applied to a value with real part
+Inf and finite imaginary part should produce a result with real part
+0.  glibc wrongly produces a result with real part -0 in FE_DOWNWARD
mode.  This patch fixes this by checking for zero results in the
relevant case of non-finite arguments (where there should never be a
result with -0 real part), and converts the tests of cacos to
ALL_RM_TEST.

Tested x86_64 and x86 and ulps updated accordingly.

	[BZ #16928]
	* math/s_cacos.c (__cacos): Ensure zero real part of result from
	non-finite arguments is +0.
	* math/s_cacosf.c (__cacosf): Likewise.
	* math/s_cacosl.c (__cacosl): Likewise.
	* math/libm-test.inc (cacos_test): Use ALL_RM_TEST.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2014-05-14 12:37:24 +00:00
Joseph Myers
913d03c864 Fix acosh (1) in round-downward mode (bug 16927).
According to C99 and C11 Annex F, acosh (1) should be +0 in all
rounding modes.  However, some implementations in glibc wrongly return
-0 in round-downward mode (which is what you get if you end up
computing log1p (-0), via 1 - 1 being -0 in round-downward mode).
This patch fixes the problem implementations, by correcting the test
for an exact 1 value in the ldbl-96 implementation to allow for the
explicit high bit of the mantissa, and by inserting fabs instructions
in the i386 implementations; tests of acosh are duly converted to
ALL_RM_TEST.  I believe all the other sysdeps/ieee754 implementations
are already OK (I haven't checked the ia64 versions, but if buggy then
that will be obvious from the results of test runs after this patch is
in).

Tested x86_64 and x86 and ulps updated accordingly.

	[BZ #16927]
	* sysdeps/i386/fpu/e_acosh.S (__ieee754_acosh): Use fabs on x-1
	value.
	* sysdeps/i386/fpu/e_acoshf.S (__ieee754_acoshf): Likewise.
	* sysdeps/i386/fpu/e_acoshl.S (__ieee754_acoshl): Likewise.
	* sysdeps/ieee754/ldbl-96/e_acoshl.c (__ieee754_acoshl): Correct
	for explicit high bit of mantissa when testing for argument equal
	to 1.
	* math/libm-test.inc (acosh_test): Use ALL_RM_TEST.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2014-05-14 12:35:40 +00:00
Joseph Myers
a84e78c8b3 Fix catan, catanh, __ieee754_logf in round-downward mode (bug 16799, bug 16800).
This patch fixes incorrect results from catan and catanh of certain
special inputs in round-downward mode (bug 16799), and incorrect
results of __ieee754_logf (+/-0) in round-downward mode (bug 16800)
that show up through catan/catanh when tested in all rounding modes,
but not directly in the testing for logf because the bug gets hidden
by the wrappers.

Both bugs involve a zero that should be +0 being -0 instead: one
computed as (1-x)*(1+x) in the catan/catanh case, and one as (x-x) in
the logf case.  The fixes ensure positive zero is used.  Testing of
catan and catanh in all rounding modes is duly enabled.

I expect there are various other bugs in special cases in __ieee754_*
functions that are normally hidden by the wrappers but would show up
for testing with -lieee (or in future with -fno-math-errno if we
replace -lieee and _LIB_VERSION with compile-time redirection to new
*_noerrno symbol names).

Tested x86_64 and x86 and ulps updated accordingly.

	[BZ #16799]
	[BZ #16800]
	* math/s_catan.c (__catan): Avoid passing -0 denominator to atan2
	with 0 numerator.
	* math/s_catanf.c (__catanf): Likewise.
	* math/s_catanh.c (__catanh): Likewise.
	* math/s_catanhf.c (__catanhf): Likewise.
	* math/s_catanhl.c (__catanhl): Likewise.
	* math/s_catanl.c (__catanl): Likewise.
	* sysdeps/ieee754/flt-32/e_logf.c (__ieee754_logf): Always divide
	by positive zero when computing -Inf result.
	* math/libm-test.inc (catan_test): Use ALL_RM_TEST.
	(catanh_test): Likewise.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2014-04-02 17:41:02 +00:00
Joseph Myers
6f05bafeba Fix clog / clog10 sign of zero result in round-downward mode (bug 16789).
This patch fixes bug 16789, incorrect sign of (real part) zero result
from clog and clog10 in round-downward mode, arising from that real
part being computed as 0 - 0.  To ensure that an underflow exception
occurred, the code used an underflowing value (the next term in the
series for log1p) in arithmetic computing the real part of the result,
yielding the problematic 0 - 0 computation in some cases even when the
mathematical result would be small but positive.  The patch changes
this code to use the math_force_eval approach to ensuring that an
underflowing computation actually occurs.  Tests of clog and clog10
are enabled in all rounding modes.

Tested x86_64 and x86 and ulps updated accordingly.

	[BZ #16789]
	* math/s_clog.c (__clog): Use math_force_eval to ensure underflow
	instead of using underflowing value in computing result.
	* math/s_clog10.c (__clog10): Likewise.
	* math/s_clog10f.c (__clog10f): Likewise.
	* math/s_clog10l.c (__clog10l): Likewise.
	* math/s_clogf.c (__clogf): Likewise.
	* math/s_clogl.c (__clogl): Likewise.
	* math/libm-test.inc (clog_test): Use ALL_RM_TEST.
	(clog10_test): Likewise.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2014-04-02 13:10:19 +00:00
Joseph Myers
046651c168 Relax gen-auto-libm-tests may-underflow rules, test log1p in all rounding modes.
gen-auto-libm-tests presently allows but does not require underflow
exceptions for results with magnitude in the range (greatest
subnormal, least normal].

In some cases, the magnitude of the exact result is very slightly
above the least normal, but rounding in the implementation results in
it effectively computing an infinite-precision result that is slightly
below the least normal, so raising an underflow exception.  This is in
accordance with the documented accuracy goals, but results in
testsuite failures.

This patch changes the logic to allow underflows when the mathematical
result is up to 0.5ulp above the least normal (so in any case where
the round-to-nearest result is the least normal).  Ideally underflows
in all these cases would be accepted only when an underflow with the
actual result is consistent with the rounding mode (in FE_TOWARDZERO
mode, a return value of the least normal implies that the
infinite-precision result did not underflow so there should be no
underflow exception, for example), so as to match the documented goals
more precisely - whereas at present the tests for exceptions are
completely independent of the tests of the returned values.  (The same
applies to overflow exceptions as well - they too should be checked
for consistency with the result, as in FE_TOWARDZERO mode a result
1ulp below the largest finite value should be inconsistent with an
overflow exception and cause a failure with overflow rather than
simply being considered a 1ulp error when overflow is expected.)  But
the present patch at least deals with the cases causing spurious
failures so that (a) certain existing tests no longer need to be
marked as having spurious exceptions (such markings in
auto-libm-test-in end up applying to more cases than just those they
are needed for) and (b) log1p can be tested in all rounding modes
without introducing more such failures.  This patch duly moves tests
of log1p to ALL_RM_TEST.

Tested x86_64 and x86 and ulps updated accordingly.

	[BZ #16357]
	[BZ #16599]
	* math/gen-auto-libm-tests.c (fp_format_desc): Add field
	min_plus_half.
	(fp_formats): Update initializers.
	(init_fp_formats): Initialize new field.
	(output_for_one_input_case): Allow underflow for results up to
	min_plus_half.
	* math/libm-test.inc (log1p_test): Use ALL_RM_TEST.
	* math/auto-libm-test-in: Don't mark some underflows from asin and
	atanh as spurious.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2014-03-25 12:26:06 +00:00
Joseph Myers
b376a11a19 Fix dbl-64 exp overflow/underflow in non-default rounding modes (bug 16284).
The dbl-64 version of exp needs round-to-nearest mode for its internal
computations, but that has the consequence of inappropriate
overflowing and underflowing results in other rounding modes.  This
patch fixes this by recomputing the relevant results in cases where
the round-to-nearest result overflows to infinity or underflows to
zero (most of the diffs are actually just consequent reindentation).
Tests are enabled in all rounding modes for complex functions using
exp - but not for cexp because it turns out there are bugs causing
spurious underflows for cexp for some tests, which will need to be
fixed separately (I suspect ccos ccosh csin csinh ctan ctanh have
similar bugs, just not shown by the present set of test inputs).

Tested x86_64 and x86 and ulps updated accordingly.

	[BZ #16284]
	* sysdeps/ieee754/dbl-64/e_exp.c (__ieee754_exp): Use original
	rounding mode to recompute results that overflow to infinity or
	underflow to zero.
	* math/auto-libm-test-in: Don't mark tests as expected to fail for
	bug 16284.
	* math/auto-libm-test-out: Regenerated.
	* math/libm-test.inc (ccos_test): Use ALL_RM_TEST.
	(ccosh_test): Likewise.
	(csin_test_data): Use plus_oflow.
	(csin_test): Use ALL_RM_TEST.
	(csinh_test_data): Use plus_oflow.
	(csinh_test): Use ALL_RM_TEST.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2014-03-24 12:18:45 +00:00
Joseph Myers
f7be737659 Fix log (1) in round-downward mode (bug 16731).
According to ISO C Annex F, log (1) should be +0 in all rounding
modes, but some implementations in glibc wrongly return -0 in
round-downward mode (mapping to log1p (x - 1) is problematic because 1
- 1 is -0 in round-downward mode, and log1p (-0) is -0).  This patch
fixes this.  (It helps with some implementations of other functions
such as acosh, log2 and log10 that call out to log, but not enough to
enable all-rounding-modes testing for those functions without further
fixes to other implementations of them.)

Tested x86_64 and x86 and ulps updated accordingly, and did spot tests
for mips64 for the ldbl-128 fix, and i586 for the sysdeps/i386/fpu
implementations shadowed by those in sysdeps/i386/i686/fpu.

	[BZ #16731]
	* sysdeps/i386/fpu/e_log.S (__ieee754_log): Take absolute value
	when x - 1 is zero.
	* sysdeps/i386/fpu/e_logf.S (__ieee754_logf): Likewise.
	* sysdeps/i386/fpu/e_logl.S (__ieee754_logl): Likewise.
	* sysdeps/i386/i686/fpu/e_logl.S (__ieee754_logl): Likewise.
	* sysdeps/ieee754/dbl-64/e_log.c (__ieee754_log): Return +0 when
	argument is 1.
	* sysdeps/ieee754/ldbl-128/e_logl.c (__ieee754_logl): Likewise.
	* sysdeps/x86_64/fpu/e_logl.S: Take absolute value when x - 1 is
	zero.
	* math/libm-test.inc (log_test): Use ALL_RM_TEST.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2014-03-21 18:13:58 +00:00