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a5721ebc68
glibc/sysdeps/ieee754/dbl-64
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Joseph Myers a5721ebc68 Fix clog, clog10 inaccuracy (bug 19016). 
For arguments with X^2 + Y^2 close to 1, clog and clog10 avoid large
errors from log(hypot) by computing X^2 + Y^2 - 1 in a way that avoids
cancellation error and then using log1p.

However, the thresholds for using that approach still result in log
being used on argument as large as sqrt(13/16) > 0.9, leading to
significant errors, in some cases above the 9ulp maximum allowed in
glibc libm.  This patch arranges for the approach using log1p to be
used in any cases where |X|, |Y| < 1 and X^2 + Y^2 >= 0.5 (with the
existing allowance for cases where one of X and Y is very small),
adjusting the __x2y2m1 functions to work with the wider range of
inputs.  This way, log only gets used on arguments below sqrt(1/2) (or
substantially above 1), where the error involved is much less.

Tested for x86_64, x86, mips64 and powerpc.  For the ulps regeneration
I removed the existing clog and clog10 ulps before regenerating to
allow any reduced ulps to appear.  Tests added include those found by
random test generation to produce large ulps either before or after
the patch, and some found by trying inputs close to the (0.75, 0.5)
threshold where the potential errors from using log are largest.

	[BZ #19016]
	* sysdeps/generic/math_private.h (__x2y2m1f): Update comment to
	allow more cases with X^2 + Y^2 >= 0.5.
	* sysdeps/ieee754/dbl-64/x2y2m1.c (__x2y2m1): Likewise.  Add -1 as
	normal element in sum instead of special-casing based on values of
	arguments.
	* sysdeps/ieee754/dbl-64/x2y2m1f.c (__x2y2m1f): Update comment.
	* sysdeps/ieee754/ldbl-128/x2y2m1l.c (__x2y2m1l): Likewise.  Add
	-1 as normal element in sum instead of special-casing based on
	values of arguments.
	* sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c (__x2y2m1l): Likewise.
	* sysdeps/ieee754/ldbl-96/x2y2m1.c [FLT_EVAL_METHOD != 0]
	(__x2y2m1): Update comment.
	* sysdeps/ieee754/ldbl-96/x2y2m1l.c (__x2y2m1l): Likewise.  Add -1
	as normal element in sum instead of special-casing based on values
	of arguments.
	* math/s_clog.c (__clog): Handle more cases using log1p without
	hypot.
	* 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/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.
2015-09-28 22:11:22 +00:00
..
wordsize-64 Since we now inline isinf, isnan and isfinite in math.h, replace uses of __isinf_ns(l/f) 2015-09-18 20:51:52 +01:00
asincos.tbl Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
atnat2.h Fix several build failures with GCC6 due to unused static variables. 2015-09-18 20:42:54 +01:00
atnat.h Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
branred.c Remove various ABS macros and replace uses with fabs (or in one case abs) 2015-05-15 11:04:40 +00:00
branred.h Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
dbl2mpn.c Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
dla.h Remove various ABS macros and replace uses with fabs (or in one case abs) 2015-05-15 11:04:40 +00:00
doasin.c Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
doasin.h Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
dosincos.c Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
dosincos.h Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
e_acos.c
e_acosh.c Format floating routines. 2013-10-17 16:03:24 +02:00
e_asin.c Refactor code forcing underflow exceptions. 2015-09-23 22:42:30 +00:00
e_atan2.c Fix dbl-64 atan2 in non-default rounding modes (bug 18210, bug 18211). 2015-04-08 17:32:17 +00:00
e_atanh.c Refactor code forcing underflow exceptions. 2015-09-23 22:42:30 +00:00
e_cosh.c Avoid excess range overflowing results from cosh, sinh, lgamma (bug 18980). 2015-09-18 20:00:48 +00:00
e_exp2.c Refactor code forcing underflow exceptions. 2015-09-23 22:42:30 +00:00
e_exp10.c This patch renames all uses of __isinf*, __isnan*, __finite* and __signbit* to use standard C99 macros. This has no effect on generated code. 2015-06-03 15:41:36 +01:00
e_exp.c Refactor code forcing underflow exceptions. 2015-09-23 22:42:30 +00:00
e_fmod.c Use glibc_likely instead __builtin_expect. 2014-02-10 15:07:12 +01:00
e_gamma_r.c Refactor code forcing underflow exceptions. 2015-09-23 22:42:30 +00:00
e_hypot.c Fix hypot missing underflows (bug 18803). 2015-09-24 23:43:57 +00:00
e_ilogb.c Format floating routines. 2013-10-17 16:03:24 +02:00
e_j0.c Avoid uninitialized warnings in Bessel functions. 2015-02-26 21:49:19 +00:00
e_j1.c Refactor code forcing underflow exceptions. 2015-09-23 22:42:30 +00:00
e_jn.c Refactor code forcing underflow exceptions. 2015-09-23 22:42:30 +00:00
e_lgamma_r.c Avoid excess range overflowing results from cosh, sinh, lgamma (bug 18980). 2015-09-18 20:00:48 +00:00
e_log2.c Use glibc_likely instead __builtin_expect. 2014-02-10 15:07:12 +01:00
e_log10.c Use glibc_likely instead __builtin_expect. 2014-02-10 15:07:12 +01:00
e_log.c Remove various ABS macros and replace uses with fabs (or in one case abs) 2015-05-15 11:04:40 +00:00
e_pow.c Fix pow missing underflows (bug 18825). 2015-09-25 22:29:10 +00:00
e_rem_pio2.c Format floating routines. 2013-10-17 16:03:24 +02:00
e_remainder.c Remove various ABS macros and replace uses with fabs (or in one case abs) 2015-05-15 11:04:40 +00:00
e_sinh.c Refactor code forcing underflow exceptions. 2015-09-23 22:42:30 +00:00
e_sqrt.c Fix libm fegetround namespace (bug 17748). 2015-01-02 20:44:42 +00:00
gamma_product.c Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
gamma_productf.c Use math_narrow_eval more consistently. 2015-09-23 18:14:57 +00:00
halfulp.c Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
k_cos.c
k_rem_pio2.c Use math_narrow_eval more consistently. 2015-09-23 18:14:57 +00:00
k_sin.c
k_tan.c Replace sysdeps/ieee754/dbl-64/k_tan.c with empty file 2012-02-26 16:10:46 +01:00
lgamma_neg.c Use math_narrow_eval more consistently. 2015-09-23 18:14:57 +00:00
lgamma_product.c Fix lgamma (negative) inaccuracy (bug 2542, bug 2543, bug 2558). 2015-09-10 22:27:58 +00:00
Makefile powerpc: Fix incorrect results for pow when using FMA 2015-03-10 09:38:54 -04:00
MathLib.h Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
mpa-arch.h Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
mpa.c Fix sysdeps/ieee754/dbl-64/mpa.c for -Wuninitialized. 2015-05-21 23:05:45 +00:00
mpa.h Remove various ABS macros and replace uses with fabs (or in one case abs) 2015-05-15 11:04:40 +00:00
mpatan2.c Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
mpatan.c Remove various ABS macros and replace uses with fabs (or in one case abs) 2015-05-15 11:04:40 +00:00
mpatan.h Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
mpexp.c Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
mplog.c Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
mpn2dbl.c Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
mpsqrt.c Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
mpsqrt.h Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
mptan.c Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
mydefs.h Remove various ABS macros and replace uses with fabs (or in one case abs) 2015-05-15 11:04:40 +00:00
powtwo.tbl Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
root.tbl Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
s_asinh.c Refactor code forcing underflow exceptions. 2015-09-23 22:42:30 +00:00
s_atan.c Refactor code forcing underflow exceptions. 2015-09-23 22:42:30 +00:00
s_cbrt.c Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
s_ceil.c Format floating routines. 2013-10-17 16:03:24 +02:00
s_copysign.c Format floating routines. 2013-10-17 16:03:24 +02:00
s_cos.c
s_erf.c Refactor code forcing underflow exceptions. 2015-09-23 22:42:30 +00:00
s_expm1.c Refactor code forcing underflow exceptions. 2015-09-23 22:42:30 +00:00
s_fabs.c 2015-05-28 Wilco Dijkstra <wdijkstr@arm.com> 2015-05-28 11:42:55 +01:00
s_finite.c Reduce number of constants in __finite* (bug 15384). 2015-09-17 16:47:14 +00:00
s_floor.c Format floating routines. 2013-10-17 16:03:24 +02:00
s_fma.c Refactor code forcing underflow exceptions. 2015-09-23 22:42:30 +00:00
s_fmaf.c Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
s_fpclassify.c Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
s_frexp.c Format floating routines. 2013-10-17 16:03:24 +02:00
s_isinf.c Format floating routines. 2013-10-17 16:03:24 +02:00
s_isnan.c Format floating routines. 2013-10-17 16:03:24 +02:00
s_issignaling.c Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
s_llrint.c Use math_narrow_eval more consistently. 2015-09-23 18:14:57 +00:00
s_llround.c Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
s_log1p.c Refactor code forcing underflow exceptions. 2015-09-23 22:42:30 +00:00
s_logb.c Use glibc_likely instead __builtin_expect. 2014-02-10 15:07:12 +01:00
s_lrint.c Use math_narrow_eval more consistently. 2015-09-23 18:14:57 +00:00
s_lround.c Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
s_modf.c Use glibc_likely instead __builtin_expect. 2014-02-10 15:07:12 +01:00
s_nearbyint.c Format floating routines. 2013-10-17 16:03:24 +02:00
s_nexttoward.c
s_remquo.c Fix sign of remquo zero remainder in round-downward mode (bug 17987). 2015-02-17 00:41:50 +00:00
s_rint.c Format floating routines. 2013-10-17 16:03:24 +02:00
s_round.c Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
s_scalbln.c [BZ #6803] Set errno for scalbln, scalbn 2014-06-20 07:48:20 +05:30
s_scalbn.c Make scalbn set errno (bug 6803). 2015-09-16 21:11:00 +00:00
s_signbit.c Use the GCC builtin functions for the non-inlined signbit implementations. 2015-09-18 16:39:08 +01:00
s_sin.c Refactor code forcing underflow exceptions. 2015-09-23 22:42:30 +00:00
s_sincos.c Since we now inline isinf, isnan and isfinite in math.h, replace uses of __isinf_ns(l/f) 2015-09-18 20:51:52 +01:00
s_tan.c Refactor code forcing underflow exceptions. 2015-09-23 22:42:30 +00:00
s_tanh.c Refactor code forcing underflow exceptions. 2015-09-23 22:42:30 +00:00
s_trunc.c Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
sincos32.c Remove various ABS macros and replace uses with fabs (or in one case abs) 2015-05-15 11:04:40 +00:00
sincos32.h Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
sincostab.c Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
slowexp.c Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
slowpow.c Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
t_exp2.h
t_exp.c Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
uasncs.h Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
uatan.tbl Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
uexp.h Fix several build failures with GCC6 due to unused static variables. 2015-09-18 20:42:54 +01:00
uexp.tbl Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
ulog.h Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
ulog.tbl Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
upow.h Fix several build failures with GCC6 due to unused static variables. 2015-09-18 20:42:54 +01:00
upow.tbl Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
urem.h Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
uroot.h Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
usncs.h Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
utan.h Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
utan.tbl Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
w_exp.c This patch renames all uses of __isinf*, __isnan*, __finite* and __signbit* to use standard C99 macros. This has no effect on generated code. 2015-06-03 15:41:36 +01:00
x2y2m1.c Fix clog, clog10 inaccuracy (bug 19016). 2015-09-28 22:11:22 +00:00
x2y2m1f.c Fix clog, clog10 inaccuracy (bug 19016). 2015-09-28 22:11:22 +00:00