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4648909d56
glibc/sysdeps/i386/fpu
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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
..
doasin.c
e_acos.S Fix x86 acos near 1 (bug 13942). 2012-04-30 18:56:39 +00:00
e_acosf.S Fix acos (-1) in round-downwards mode on x86 (bug 14034). 2012-04-30 09:38:06 +00:00
e_acosh.S Fix acosh (1) in round-downward mode (bug 16927). 2014-05-14 12:35:40 +00:00
e_acoshf.S Fix acosh (1) in round-downward mode (bug 16927). 2014-05-14 12:35:40 +00:00
e_acoshl.S Fix acosh (1) in round-downward mode (bug 16927). 2014-05-14 12:35:40 +00:00
e_acosl.c Fix x86 acos near 1 (bug 13942). 2012-04-30 18:56:39 +00:00
e_asin.S Fix x86 acos near 1 (bug 13942). 2012-04-30 18:56:39 +00:00
e_asinf.S
e_atan2.S
e_atan2f.S
e_atan2l.c
e_atanh.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
e_atanhf.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
e_atanhl.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
e_exp2.S
e_exp2f.S
e_exp2l.S
e_exp10.S
e_exp10f.S
e_exp10l.S Fix exp10 inaccuracy and exceptions (bugs 13884, 13914). 2012-05-06 18:23:44 +00:00
e_exp.S Optimize exp 2011-10-15 20:22:59 -04:00
e_expf.S Optimize exp 2011-10-15 20:22:59 -04:00
e_expl.S Fix x86/x86_64 expl/exp10l spurious underflows (bug 16348). 2014-03-27 18:41:14 +00:00
e_fmod.S
e_fmodf.S
e_fmodl.c
e_hypot.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
e_hypotf.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
e_ilogb.S Remove useless __ilogb*_finite aliases 2012-04-18 00:40:13 +02:00
e_ilogbf.S Remove useless __ilogb*_finite aliases 2012-04-18 00:40:13 +02:00
e_ilogbl.S Remove useless __ilogb*_finite aliases 2012-04-18 00:40:13 +02:00
e_log2.S Fix log2 (1) in round-downward mode (bug 17042). 2014-06-10 12:07:15 +00:00
e_log2f.S Fix log2 (1) in round-downward mode (bug 17042). 2014-06-10 12:07:15 +00:00
e_log2l.S Fix log2 (1) in round-downward mode (bug 17042). 2014-06-10 12:07:15 +00:00
e_log10.S Fix log10 (1) in round-downward mode (bug 16977). 2014-05-23 12:07:50 +00:00
e_log10f.S Fix log10 (1) in round-downward mode (bug 16977). 2014-05-23 12:07:50 +00:00
e_log10l.S Fix log10 (1) in round-downward mode (bug 16977). 2014-05-23 12:07:50 +00:00
e_log.S Fix log (1) in round-downward mode (bug 16731). 2014-03-21 18:13:58 +00:00
e_logf.S Fix log (1) in round-downward mode (bug 16731). 2014-03-21 18:13:58 +00:00
e_logl.S Fix __ieee754_logl (-LDBL_MAX) in FE_DOWNWARD mode (bug 17022). 2014-06-18 12:32:01 +00:00
e_pow.S Fix pow overflow in non-default rounding modes (bug 16315). 2014-06-23 20:12:33 +00:00
e_powf.S Fix pow overflow in non-default rounding modes (bug 16315). 2014-06-23 20:12:33 +00:00
e_powl.S Fix pow overflow in non-default rounding modes (bug 16315). 2014-06-23 20:12:33 +00:00
e_rem_pio2.c
e_remainder.S
e_remainderf.S
e_remainderl.S
e_scalb.S Get rid of ASM_TYPE_DIRECTIVE{,_PREFIX}. 2012-08-02 21:04:29 +02:00
e_scalbf.S Get rid of ASM_TYPE_DIRECTIVE{,_PREFIX}. 2012-08-02 21:04:29 +02:00
e_scalbl.S Get rid of ASM_TYPE_DIRECTIVE{,_PREFIX}. 2012-08-02 21:04:29 +02:00
e_sqrt.S Fix x86 sqrt rounding (bug 14032). 2013-11-29 16:31:16 +00:00
e_sqrtf.S
e_sqrtl.c
fclrexcpt.c Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
fedisblxcpt.c Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
feenablxcpt.c Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
fegetenv.c Include SSE state in i386 fenv_t (bug 16064). 2014-05-09 16:59:56 +00:00
fegetexcept.c Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
fegetround.c Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
feholdexcpt.c Include SSE state in i386 fenv_t (bug 16064). 2014-05-09 16:59:56 +00:00
fenv_private.h Set/restore rounding mode only when needed 2013-06-12 10:36:48 +05:30
fesetenv.c Include SSE state in i386 fenv_t (bug 16064). 2014-05-09 16:59:56 +00:00
fesetround.c Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
feupdateenv.c Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
fgetexcptflg.c Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
fraiseexcpt.c Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
fsetexcptflg.c Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
ftestexcept.c Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
halfulp.c
Implies Use x86_64 fpu/bits/fenv.h for i386 and x86_64 2012-06-06 10:13:19 -07:00
k_rem_pio2l.c
libm-test-ulps Fix cosh spurious underflows from expm1 (bug 16354), inaccurate results near 0 (bug 17061). 2014-06-23 20:20:10 +00:00
math_private.h Optimize private 387 fenv access; share code between i386 and x86_64. 2012-03-19 06:51:39 -07:00
math-tests.h Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
mpatan2.c
mpatan.c
mpexp.c
mplog.c
mpsqrt.c
s_asinh.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
s_asinhf.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
s_asinhl.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
s_atan.S
s_atanf.S
s_atanl.c
s_cbrt.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
s_cbrtf.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
s_cbrtl.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
s_ceil.S Add CFI to x86 ceil / floor / trunc (bug 16681). 2014-06-16 22:54:46 +00:00
s_ceilf.S Add CFI to x86 ceil / floor / trunc (bug 16681). 2014-06-16 22:54:46 +00:00
s_ceill.S Add CFI to x86 ceil / floor / trunc (bug 16681). 2014-06-16 22:54:46 +00:00
s_copysign.S
s_copysignf.S
s_copysignl.S
s_expm1.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
s_expm1f.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
s_expm1l.S Fix x86/x86_64 expm1l inaccuracy and exceptions (bugs 13885, 13923). 2012-05-07 19:13:08 +00:00
s_fabs.S
s_fabsf.S
s_fabsl.S
s_fdim.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
s_fdimf.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
s_fdiml.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
s_finite.S
s_finitef.S
s_finitel.S
s_floor.S Add CFI to x86 ceil / floor / trunc (bug 16681). 2014-06-16 22:54:46 +00:00
s_floorf.S Add CFI to x86 ceil / floor / trunc (bug 16681). 2014-06-16 22:54:46 +00:00
s_floorl.S Add CFI to x86 ceil / floor / trunc (bug 16681). 2014-06-16 22:54:46 +00:00
s_fmax.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
s_fmaxf.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
s_fmaxl.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
s_fmin.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
s_fminf.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
s_fminl.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
s_fpclassifyl.c Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
s_frexp.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
s_frexpf.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
s_frexpl.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
s_isinfl.c Use <> for math.h and math_private.h everywhere. 2012-03-09 16:09:10 -08:00
s_isnanl.c Use <> for math.h and math_private.h everywhere. 2012-03-09 16:09:10 -08:00
s_llrint.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
s_llrintf.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
s_llrintl.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
s_log1p.S Remove __ELF__ conditionals 2012-02-07 00:41:11 +01:00
s_log1pf.S Remove __ELF__ conditionals 2012-02-07 00:41:11 +01:00
s_log1pl.S Fix log1pl (LDBL_MAX) in FE_UPWARD mode (bug 16564). 2014-05-14 12:38:56 +00:00
s_logb.S
s_logbf.S
s_logbl.c
s_lrint.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
s_lrintf.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
s_lrintl.S Update copyright notices with scripts/update-copyrights 2014-01-01 22:00:23 +10:00
s_nearbyint.S
s_nearbyintf.S
s_nearbyintl.S
s_nextafterl.c Fix nextafter overflow in non-default rounding modes (bug 16677). 2014-03-11 22:24:00 +00:00
s_nexttoward.c Fix nexttoward bugs (bugs 2550, 2570). 2012-05-01 15:37:43 +00:00
s_nexttowardf.c Fix nexttoward bugs (bugs 2550, 2570). 2012-05-01 15:37:43 +00:00
s_remquo.S Remove remaining bounded-pointers support from i386 .S files. 2013-02-21 22:21:52 +00:00
s_remquof.S Remove remaining bounded-pointers support from i386 .S files. 2013-02-21 22:21:52 +00:00
s_remquol.S Remove remaining bounded-pointers support from i386 .S files. 2013-02-21 22:21:52 +00:00
s_rint.S
s_rintf.S
s_rintl.c
s_scalbln.c
s_scalblnf.c
s_scalblnl.c
s_scalbn.S [BZ #6803] Set errno for scalbln, scalbn 2014-06-20 07:48:20 +05:30
s_scalbnf.S [BZ #6803] Set errno for scalbln, scalbn 2014-06-20 07:48:20 +05:30
s_scalbnl.S [BZ #6803] Set errno for scalbln, scalbn 2014-06-20 07:48:20 +05:30
s_significand.S
s_significandf.S
s_significandl.c
s_trunc.S Add CFI to x86 ceil / floor / trunc (bug 16681). 2014-06-16 22:54:46 +00:00
s_truncf.S Add CFI to x86 ceil / floor / trunc (bug 16681). 2014-06-16 22:54:46 +00:00
s_truncl.S Add CFI to x86 ceil / floor / trunc (bug 16681). 2014-06-16 22:54:46 +00:00
slowexp.c
slowpow.c
t_exp.c
Versions
w_sqrt.c Fix x86 sqrt rounding (bug 14032). 2013-11-29 16:31:16 +00:00