glibc/sysdeps/ieee754/flt-32/s_erff.c

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/* s_erff.c -- float version of s_erf.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: s_erff.c,v 1.4 1995/05/10 20:47:07 jtc Exp $";
#endif
#include <errno.h>
#include <float.h>
#include <math.h>
#include <math_private.h>
Work around powerpc32 integer 0 converting to -0 (bug 887, bug 19049, bug 19050). On powerpc32 hard-float, older processors (ones where fcfid is not available for 32-bit code), GCC generates conversions from integers to floating point that wrongly convert integer 0 to -0 instead of +0 in FE_DOWNWARD mode. This in turn results in logb and a few other functions wrongly returning -0 when they should return +0. This patch works around this issue in glibc as I proposed in <https://sourceware.org/ml/libc-alpha/2015-09/msg00728.html>, so that the affected functions can be correct and the affected tests pass in the absence of a GCC fix for this longstanding issue (GCC bug 67771 - if fixed, of course we can put in GCC version conditionals, and eventually phase out the workarounds). A new macro FIX_INT_FP_CONVERT_ZERO is added in a new sysdeps header fix-int-fp-convert-zero.h, and the powerpc32/fpu version of that header defines the macro based on the results of a configure test for whether such conversions use the fcfid instruction. Tested for x86_64 (that installed stripped shared libraries are unchanged by the patch) and powerpc (that HAVE_PPC_FCFID comes out to 0 as expected and that the relevant tests are fixed). Also tested a build with GCC configured for -mcpu=power4 and verified that HAVE_PPC_FCFID comes out to 1 in that case. There are still some other issues to fix to get test-float and test-double passing cleanly for older powerpc32 processors (apart from the need for an ulps regeneration for powerpc). (test-ldouble will be harder to get passing cleanly, but with a combination of selected fixes to ldbl-128ibm code that don't involve significant performance issues, allowing spurious underflow and inexact exceptions for that format, and lots of XFAILing for the default case of unpatched libgcc, it should be doable.) [BZ #887] [BZ #19049] [BZ #19050] * sysdeps/generic/fix-int-fp-convert-zero.h: New file. * sysdeps/ieee754/dbl-64/e_log10.c: Include <fix-int-fp-convert-zero.h>. (__ieee754_log10): Adjust signs as needed if FIX_INT_FP_CONVERT_ZERO. * sysdeps/ieee754/dbl-64/e_log2.c: Include <fix-int-fp-convert-zero.h>. (__ieee754_log2): Adjust signs as needed if FIX_INT_FP_CONVERT_ZERO. * sysdeps/ieee754/dbl-64/s_erf.c: Include <fix-int-fp-convert-zero.h>. (__erfc): Adjust signs as needed if FIX_INT_FP_CONVERT_ZERO. * sysdeps/ieee754/dbl-64/s_logb.c: Include <fix-int-fp-convert-zero.h>. (__logb): Adjust signs as needed if FIX_INT_FP_CONVERT_ZERO. * sysdeps/ieee754/flt-32/e_log10f.c: Include <fix-int-fp-convert-zero.h>. (__ieee754_log10f): Adjust signs as needed if FIX_INT_FP_CONVERT_ZERO. * sysdeps/ieee754/flt-32/e_log2f.c: Include <fix-int-fp-convert-zero.h>. (__ieee754_log2f): Adjust signs as needed if FIX_INT_FP_CONVERT_ZERO. * sysdeps/ieee754/flt-32/s_erff.c: Include <fix-int-fp-convert-zero.h>. (__erfcf): Adjust signs as needed if FIX_INT_FP_CONVERT_ZERO. * sysdeps/ieee754/flt-32/s_logbf.c: Include <fix-int-fp-convert-zero.h>. (__logbf): Adjust signs as needed if FIX_INT_FP_CONVERT_ZERO. * sysdeps/ieee754/ldbl-128ibm/s_erfl.c: Include <fix-int-fp-convert-zero.h>. (__erfcl): Adjust signs as needed if FIX_INT_FP_CONVERT_ZERO. * sysdeps/ieee754/ldbl-128ibm/s_logbl.c: Include <fix-int-fp-convert-zero.h>. (__logbl): Adjust signs as needed if FIX_INT_FP_CONVERT_ZERO. * sysdeps/powerpc/powerpc32/fpu/configure.ac: New file. * sysdeps/powerpc/powerpc32/fpu/configure: New generated file. * sysdeps/powerpc/powerpc32/fpu/fix-int-fp-convert-zero.h: New file. * config.h.in [_LIBC] (HAVE_PPC_FCFID): New macro.
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#include <fix-int-fp-convert-zero.h>
static const float
tiny = 1e-30,
half= 5.0000000000e-01, /* 0x3F000000 */
one = 1.0000000000e+00, /* 0x3F800000 */
two = 2.0000000000e+00, /* 0x40000000 */
/* c = (subfloat)0.84506291151 */
erx = 8.4506291151e-01, /* 0x3f58560b */
/*
* Coefficients for approximation to erf on [0,0.84375]
*/
efx = 1.2837916613e-01, /* 0x3e0375d4 */
pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
pp1 = -3.2504209876e-01, /* 0xbea66beb */
pp2 = -2.8481749818e-02, /* 0xbce9528f */
pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
qq2 = 6.5022252500e-02, /* 0x3d852a63 */
qq3 = 5.0813062117e-03, /* 0x3ba68116 */
qq4 = 1.3249473704e-04, /* 0x390aee49 */
qq5 = -3.9602282413e-06, /* 0xb684e21a */
/*
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* Coefficients for approximation to erf in [0.84375,1.25]
*/
pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
pa1 = 4.1485610604e-01, /* 0x3ed46805 */
pa2 = -3.7220788002e-01, /* 0xbebe9208 */
pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
qa4 = 1.2617121637e-01, /* 0x3e013307 */
qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
/*
* Coefficients for approximation to erfc in [1.25,1/0.35]
*/
ra0 = -9.8649440333e-03, /* 0xbc21a093 */
ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
ra2 = -1.0558626175e+01, /* 0xc128f022 */
ra3 = -6.2375331879e+01, /* 0xc2798057 */
ra4 = -1.6239666748e+02, /* 0xc322658c */
ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
ra6 = -8.1287437439e+01, /* 0xc2a2932b */
ra7 = -9.8143291473e+00, /* 0xc11d077e */
sa1 = 1.9651271820e+01, /* 0x419d35ce */
sa2 = 1.3765776062e+02, /* 0x4309a863 */
sa3 = 4.3456588745e+02, /* 0x43d9486f */
sa4 = 6.4538726807e+02, /* 0x442158c9 */
sa5 = 4.2900814819e+02, /* 0x43d6810b */
sa6 = 1.0863500214e+02, /* 0x42d9451f */
sa7 = 6.5702495575e+00, /* 0x40d23f7c */
sa8 = -6.0424413532e-02, /* 0xbd777f97 */
/*
* Coefficients for approximation to erfc in [1/.35,28]
*/
rb0 = -9.8649431020e-03, /* 0xbc21a092 */
rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
rb2 = -1.7757955551e+01, /* 0xc18e104b */
rb3 = -1.6063638306e+02, /* 0xc320a2ea */
rb4 = -6.3756646729e+02, /* 0xc41f6441 */
rb5 = -1.0250950928e+03, /* 0xc480230b */
rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
sb1 = 3.0338060379e+01, /* 0x41f2b459 */
sb2 = 3.2579251099e+02, /* 0x43a2e571 */
sb3 = 1.5367296143e+03, /* 0x44c01759 */
sb4 = 3.1998581543e+03, /* 0x4547fdbb */
sb5 = 2.5530502930e+03, /* 0x451f90ce */
sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
sb7 = -2.2440952301e+01; /* 0xc1b38712 */
float __erff(float x)
{
int32_t hx,ix,i;
float R,S,P,Q,s,y,z,r;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>=0x7f800000) { /* erf(nan)=nan */
i = ((u_int32_t)hx>>31)<<1;
return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */
}
if(ix < 0x3f580000) { /* |x|<0.84375 */
if(ix < 0x31800000) { /* |x|<2**-28 */
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if (ix < 0x04000000)
Fix erf underflow handling near 0 (bug 16516). Bug 16516 reports spurious underflows from erf (for all floating-point types), when the result is close to underflowing but does not actually underflow. erf (x) is about (2/sqrt(pi))*x for x close to 0, so there are subnormal arguments for which it does not underflow. The various implementations do (x + efx*x) (for efx = 2/sqrt(pi) - 1), for greater accuracy than if just using a single multiplication by an approximation to 2/sqrt(pi) (effectively, this way there are a few more bits in the approximation to 2/sqrt(pi)). This can introduce underflows when efx*x underflows even though the final result does not, so a scaled calculation with 8*efx is done in these cases - but 8 is not a big enough scale factor to avoid all such underflows. 16 is (any underflows with a scale factor of 16 would only occur when the final result underflows), so this patch changes the code to use that factor. Rather than recomputing all the values of the efx8 variable, it is removed, leaving it to the compiler's constant folding to compute 16*efx. As such scaling can also lose underflows when the final scaling down happens to be exact, appropriate checks are added to ensure underflow exceptions occur when required in such cases. Tested x86_64 and x86; no ulps updates needed. Also spot-checked for powerpc32 and mips64 to verify the changes to the ldbl-128ibm and ldbl-128 implementations. [BZ #16516] * sysdeps/ieee754/dbl-64/s_erf.c (efx8): Remove variable. (__erf): Scale by 16 instead of 8 in potentially underflowing case. Ensure exception if result actually underflows. * sysdeps/ieee754/flt-32/s_erff.c (efx8): Remove variable. (__erff): Scale by 16 instead of 8 in potentially underflowing case. Ensure exception if result actually underflows. * sysdeps/ieee754/ldbl-128/s_erfl.c: Include <float.h>. (efx8): Remove variable. (__erfl): Scale by 16 instead of 8 in potentially underflowing case. Ensure exception if result actually underflows. * sysdeps/ieee754/ldbl-128ibm/s_erfl.c: Include <float.h>. (efx8): Remove variable. (__erfl): Scale by 16 instead of 8 in potentially underflowing case. Ensure exception if result actually underflows. * sysdeps/ieee754/ldbl-96/s_erfl.c: Include <float.h>. (efx8): Remove variable. (__erfl): Scale by 16 instead of 8 in potentially underflowing case. Ensure exception if result actually underflows. * math/auto-libm-test-in: Add more tests of erf. * math/auto-libm-test-out: Regenerated.
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{
/* Avoid spurious underflow. */
float ret = 0.0625f * (16.0f * x + (16.0f * efx) * x);
Refactor code forcing underflow exceptions. Various floating-point functions have code to force underflow exceptions if a tiny result was computed in a way that might not have resulted in such exceptions even though the result is inexact. This typically uses math_force_eval to ensure that the underflowing expression is evaluated, but sometimes uses volatile. This patch refactors such code to use three new macros math_check_force_underflow, math_check_force_underflow_nonneg and math_check_force_underflow_complex (which in turn use math_force_eval). In the limited number of cases not suited to a simple conversion to these macros, existing uses of volatile are changed to use math_force_eval instead. The converted code does not always execute exactly the same sequence of operations as the original code, but the overall effects should be the same. Tested for x86_64, x86, mips64 and powerpc. * sysdeps/generic/math_private.h (fabs_tg): New macro. (min_of_type): Likewise. (math_check_force_underflow): Likewise. (math_check_force_underflow_nonneg): Likewise. (math_check_force_underflow_complex): Likewise. * math/e_exp2l.c (__ieee754_exp2l): Use math_check_force_underflow_nonneg. * math/k_casinh.c (__kernel_casinh): Likewise. * math/k_casinhf.c (__kernel_casinhf): Likewise. * math/k_casinhl.c (__kernel_casinhl): Likewise. * math/s_catan.c (__catan): Use math_check_force_underflow_complex. * 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. * math/s_ccosh.c (__ccosh): Likewise. * 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_clog.c (__clog): Use math_check_force_underflow_nonneg. * 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/s_csin.c (__csin): Use math_check_force_underflow_complex. * 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_csqrt.c (__csqrt): Use math_check_force_underflow. * math/s_csqrtf.c (__csqrtf): Likewise. * math/s_csqrtl.c (__csqrtl): Likewise. * math/s_ctan.c (__ctan): Use math_check_force_underflow_complex. * 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. * stdlib/strtod_l.c (round_and_return): Use math_force_eval instead of volatile. * sysdeps/ieee754/dbl-64/e_asin.c (__ieee754_asin): Use math_check_force_underflow. * sysdeps/ieee754/dbl-64/e_atanh.c (__ieee754_atanh): Likewise. * sysdeps/ieee754/dbl-64/e_exp.c (__ieee754_exp): Do not use volatile when forcing underflow. * sysdeps/ieee754/dbl-64/e_exp2.c (__ieee754_exp2): Use math_check_force_underflow_nonneg. * sysdeps/ieee754/dbl-64/e_gamma_r.c (__ieee754_gamma_r): Likewise. * sysdeps/ieee754/dbl-64/e_j1.c (__ieee754_j1): Use math_check_force_underflow. * sysdeps/ieee754/dbl-64/e_jn.c (__ieee754_jn): Likewise. * sysdeps/ieee754/dbl-64/e_sinh.c (__ieee754_sinh): Likewise. * sysdeps/ieee754/dbl-64/s_asinh.c (__asinh): Likewise. * sysdeps/ieee754/dbl-64/s_atan.c (atan): Use math_check_force_underflow_nonneg. * sysdeps/ieee754/dbl-64/s_erf.c (__erf): Use math_check_force_underflow. * sysdeps/ieee754/dbl-64/s_expm1.c (__expm1): Likewise. * sysdeps/ieee754/dbl-64/s_fma.c (__fma): Use math_force_eval instead of volatile. * sysdeps/ieee754/dbl-64/s_log1p.c (__log1p): Use math_check_force_underflow. * sysdeps/ieee754/dbl-64/s_sin.c (__sin): Likewise. * sysdeps/ieee754/dbl-64/s_tan.c (tan): Use math_check_force_underflow_nonneg. * sysdeps/ieee754/dbl-64/s_tanh.c (__tanh): Use math_check_force_underflow. * sysdeps/ieee754/flt-32/e_asinf.c (__ieee754_asinf): Likewise. * sysdeps/ieee754/flt-32/e_atanhf.c (__ieee754_atanhf): Likewise. * sysdeps/ieee754/flt-32/e_exp2f.c (__ieee754_exp2f): Use math_check_force_underflow_nonneg. * sysdeps/ieee754/flt-32/e_gammaf_r.c (__ieee754_gammaf_r): Likewise. * sysdeps/ieee754/flt-32/e_j1f.c (__ieee754_j1f): Use math_check_force_underflow. * sysdeps/ieee754/flt-32/e_jnf.c (__ieee754_jnf): Likewise. * sysdeps/ieee754/flt-32/e_sinhf.c (__ieee754_sinhf): Likewise. * sysdeps/ieee754/flt-32/k_sinf.c (__kernel_sinf): Likewise. * sysdeps/ieee754/flt-32/k_tanf.c (__kernel_tanf): Likewise. * sysdeps/ieee754/flt-32/s_asinhf.c (__asinhf): Likewise. * sysdeps/ieee754/flt-32/s_atanf.c (__atanf): Likewise. * sysdeps/ieee754/flt-32/s_erff.c (__erff): Likewise. * sysdeps/ieee754/flt-32/s_expm1f.c (__expm1f): Likewise. * sysdeps/ieee754/flt-32/s_log1pf.c (__log1pf): Likewise. * sysdeps/ieee754/flt-32/s_tanhf.c (__tanhf): Likewise. * sysdeps/ieee754/ldbl-128/e_asinl.c (__ieee754_asinl): Likewise. * sysdeps/ieee754/ldbl-128/e_atanhl.c (__ieee754_atanhl): Likewise. * sysdeps/ieee754/ldbl-128/e_expl.c (__ieee754_expl): Use math_check_force_underflow_nonneg. * sysdeps/ieee754/ldbl-128/e_gammal_r.c (__ieee754_gammal_r): Likewise. * sysdeps/ieee754/ldbl-128/e_j1l.c (__ieee754_j1l): Use math_check_force_underflow. * sysdeps/ieee754/ldbl-128/e_jnl.c (__ieee754_jnl): Likewise. * sysdeps/ieee754/ldbl-128/e_sinhl.c (__ieee754_sinhl): Likewise. * sysdeps/ieee754/ldbl-128/k_sincosl.c (__kernel_sincosl): Likewise. * sysdeps/ieee754/ldbl-128/k_sinl.c (__kernel_sinl): Likewise. * sysdeps/ieee754/ldbl-128/k_tanl.c (__kernel_tanl): Likewise. * sysdeps/ieee754/ldbl-128/s_asinhl.c (__asinhl): Likewise. * sysdeps/ieee754/ldbl-128/s_atanl.c (__atanl): Likewise. * sysdeps/ieee754/ldbl-128/s_erfl.c (__erfl): Likewise. * sysdeps/ieee754/ldbl-128/s_expm1l.c (__expm1l): Likewise. * sysdeps/ieee754/ldbl-128/s_fmal.c (__fmal): Use math_force_eval instead of volatile. * sysdeps/ieee754/ldbl-128/s_log1pl.c (__log1pl): Use math_check_force_underflow. * sysdeps/ieee754/ldbl-128/s_tanhl.c (__tanhl): Likewise. * sysdeps/ieee754/ldbl-128ibm/e_asinl.c (__ieee754_asinl): Use math_check_force_underflow. * sysdeps/ieee754/ldbl-128ibm/e_atanhl.c (__ieee754_atanhl): Likewise. * sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c (__ieee754_gammal_r): Use math_check_force_underflow_nonneg. * sysdeps/ieee754/ldbl-128ibm/e_jnl.c (__ieee754_jnl): Use math_check_force_underflow. * sysdeps/ieee754/ldbl-128ibm/e_sinhl.c (__ieee754_sinhl): Likewise. * sysdeps/ieee754/ldbl-128ibm/k_sincosl.c (__kernel_sincosl): Likewise. * sysdeps/ieee754/ldbl-128ibm/k_sinl.c (__kernel_sinl): Likewise. * sysdeps/ieee754/ldbl-128ibm/k_tanl.c (__kernel_tanl): Likewise. * sysdeps/ieee754/ldbl-128ibm/s_asinhl.c (__asinhl): Likewise. * sysdeps/ieee754/ldbl-128ibm/s_atanl.c (__atanl): Likewise. * sysdeps/ieee754/ldbl-128ibm/s_erfl.c (__erfl): Likewise. * sysdeps/ieee754/ldbl-128ibm/s_tanhl.c (__tanhl): Likewise. * sysdeps/ieee754/ldbl-96/e_asinl.c (__ieee754_asinl): Likewise. * sysdeps/ieee754/ldbl-96/e_atanhl.c (__ieee754_atanhl): Likewise. * sysdeps/ieee754/ldbl-96/e_gammal_r.c (__ieee754_gammal_r): Use math_check_force_underflow_nonneg. * sysdeps/ieee754/ldbl-96/e_j1l.c (__ieee754_j1l): Use math_check_force_underflow. * sysdeps/ieee754/ldbl-96/e_jnl.c (__ieee754_jnl): Likewise. * sysdeps/ieee754/ldbl-96/e_sinhl.c (__ieee754_sinhl): Likewise. * sysdeps/ieee754/ldbl-96/k_sinl.c (__kernel_sinl): Likewise. * sysdeps/ieee754/ldbl-96/k_tanl.c (__kernel_tanl): Use math_check_force_underflow_nonneg. * sysdeps/ieee754/ldbl-96/s_asinhl.c (__asinhl): Use math_check_force_underflow. * sysdeps/ieee754/ldbl-96/s_erfl.c (__erfl): Likewise. * sysdeps/ieee754/ldbl-96/s_fmal.c (__fmal): Use math_force_eval instead of volatile. * sysdeps/ieee754/ldbl-96/s_tanhl.c (__tanhl): Use math_check_force_underflow.
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math_check_force_underflow (ret);
Fix erf underflow handling near 0 (bug 16516). Bug 16516 reports spurious underflows from erf (for all floating-point types), when the result is close to underflowing but does not actually underflow. erf (x) is about (2/sqrt(pi))*x for x close to 0, so there are subnormal arguments for which it does not underflow. The various implementations do (x + efx*x) (for efx = 2/sqrt(pi) - 1), for greater accuracy than if just using a single multiplication by an approximation to 2/sqrt(pi) (effectively, this way there are a few more bits in the approximation to 2/sqrt(pi)). This can introduce underflows when efx*x underflows even though the final result does not, so a scaled calculation with 8*efx is done in these cases - but 8 is not a big enough scale factor to avoid all such underflows. 16 is (any underflows with a scale factor of 16 would only occur when the final result underflows), so this patch changes the code to use that factor. Rather than recomputing all the values of the efx8 variable, it is removed, leaving it to the compiler's constant folding to compute 16*efx. As such scaling can also lose underflows when the final scaling down happens to be exact, appropriate checks are added to ensure underflow exceptions occur when required in such cases. Tested x86_64 and x86; no ulps updates needed. Also spot-checked for powerpc32 and mips64 to verify the changes to the ldbl-128ibm and ldbl-128 implementations. [BZ #16516] * sysdeps/ieee754/dbl-64/s_erf.c (efx8): Remove variable. (__erf): Scale by 16 instead of 8 in potentially underflowing case. Ensure exception if result actually underflows. * sysdeps/ieee754/flt-32/s_erff.c (efx8): Remove variable. (__erff): Scale by 16 instead of 8 in potentially underflowing case. Ensure exception if result actually underflows. * sysdeps/ieee754/ldbl-128/s_erfl.c: Include <float.h>. (efx8): Remove variable. (__erfl): Scale by 16 instead of 8 in potentially underflowing case. Ensure exception if result actually underflows. * sysdeps/ieee754/ldbl-128ibm/s_erfl.c: Include <float.h>. (efx8): Remove variable. (__erfl): Scale by 16 instead of 8 in potentially underflowing case. Ensure exception if result actually underflows. * sysdeps/ieee754/ldbl-96/s_erfl.c: Include <float.h>. (efx8): Remove variable. (__erfl): Scale by 16 instead of 8 in potentially underflowing case. Ensure exception if result actually underflows. * math/auto-libm-test-in: Add more tests of erf. * math/auto-libm-test-out: Regenerated.
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return ret;
}
return x + efx*x;
}
z = x*x;
r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
y = r/s;
return x + x*y;
}
if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
s = fabsf(x)-one;
P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
if(hx>=0) return erx + P/Q; else return -erx - P/Q;
}
if (ix >= 0x40c00000) { /* inf>|x|>=6 */
if(hx>=0) return one-tiny; else return tiny-one;
}
x = fabsf(x);
s = one/(x*x);
if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */
R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
ra5+s*(ra6+s*ra7))))));
S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
sa5+s*(sa6+s*(sa7+s*sa8)))))));
} else { /* |x| >= 1/0.35 */
R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
rb5+s*rb6)))));
S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
sb5+s*(sb6+s*sb7))))));
}
GET_FLOAT_WORD(ix,x);
SET_FLOAT_WORD(z,ix&0xfffff000);
r = __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S);
if(hx>=0) return one-r/x; else return r/x-one;
}
weak_alias (__erff, erff)
float __erfcf(float x)
{
int32_t hx,ix;
float R,S,P,Q,s,y,z,r;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>=0x7f800000) { /* erfc(nan)=nan */
/* erfc(+-inf)=0,2 */
Work around powerpc32 integer 0 converting to -0 (bug 887, bug 19049, bug 19050). On powerpc32 hard-float, older processors (ones where fcfid is not available for 32-bit code), GCC generates conversions from integers to floating point that wrongly convert integer 0 to -0 instead of +0 in FE_DOWNWARD mode. This in turn results in logb and a few other functions wrongly returning -0 when they should return +0. This patch works around this issue in glibc as I proposed in <https://sourceware.org/ml/libc-alpha/2015-09/msg00728.html>, so that the affected functions can be correct and the affected tests pass in the absence of a GCC fix for this longstanding issue (GCC bug 67771 - if fixed, of course we can put in GCC version conditionals, and eventually phase out the workarounds). A new macro FIX_INT_FP_CONVERT_ZERO is added in a new sysdeps header fix-int-fp-convert-zero.h, and the powerpc32/fpu version of that header defines the macro based on the results of a configure test for whether such conversions use the fcfid instruction. Tested for x86_64 (that installed stripped shared libraries are unchanged by the patch) and powerpc (that HAVE_PPC_FCFID comes out to 0 as expected and that the relevant tests are fixed). Also tested a build with GCC configured for -mcpu=power4 and verified that HAVE_PPC_FCFID comes out to 1 in that case. There are still some other issues to fix to get test-float and test-double passing cleanly for older powerpc32 processors (apart from the need for an ulps regeneration for powerpc). (test-ldouble will be harder to get passing cleanly, but with a combination of selected fixes to ldbl-128ibm code that don't involve significant performance issues, allowing spurious underflow and inexact exceptions for that format, and lots of XFAILing for the default case of unpatched libgcc, it should be doable.) [BZ #887] [BZ #19049] [BZ #19050] * sysdeps/generic/fix-int-fp-convert-zero.h: New file. * sysdeps/ieee754/dbl-64/e_log10.c: Include <fix-int-fp-convert-zero.h>. (__ieee754_log10): Adjust signs as needed if FIX_INT_FP_CONVERT_ZERO. * sysdeps/ieee754/dbl-64/e_log2.c: Include <fix-int-fp-convert-zero.h>. (__ieee754_log2): Adjust signs as needed if FIX_INT_FP_CONVERT_ZERO. * sysdeps/ieee754/dbl-64/s_erf.c: Include <fix-int-fp-convert-zero.h>. (__erfc): Adjust signs as needed if FIX_INT_FP_CONVERT_ZERO. * sysdeps/ieee754/dbl-64/s_logb.c: Include <fix-int-fp-convert-zero.h>. (__logb): Adjust signs as needed if FIX_INT_FP_CONVERT_ZERO. * sysdeps/ieee754/flt-32/e_log10f.c: Include <fix-int-fp-convert-zero.h>. (__ieee754_log10f): Adjust signs as needed if FIX_INT_FP_CONVERT_ZERO. * sysdeps/ieee754/flt-32/e_log2f.c: Include <fix-int-fp-convert-zero.h>. (__ieee754_log2f): Adjust signs as needed if FIX_INT_FP_CONVERT_ZERO. * sysdeps/ieee754/flt-32/s_erff.c: Include <fix-int-fp-convert-zero.h>. (__erfcf): Adjust signs as needed if FIX_INT_FP_CONVERT_ZERO. * sysdeps/ieee754/flt-32/s_logbf.c: Include <fix-int-fp-convert-zero.h>. (__logbf): Adjust signs as needed if FIX_INT_FP_CONVERT_ZERO. * sysdeps/ieee754/ldbl-128ibm/s_erfl.c: Include <fix-int-fp-convert-zero.h>. (__erfcl): Adjust signs as needed if FIX_INT_FP_CONVERT_ZERO. * sysdeps/ieee754/ldbl-128ibm/s_logbl.c: Include <fix-int-fp-convert-zero.h>. (__logbl): Adjust signs as needed if FIX_INT_FP_CONVERT_ZERO. * sysdeps/powerpc/powerpc32/fpu/configure.ac: New file. * sysdeps/powerpc/powerpc32/fpu/configure: New generated file. * sysdeps/powerpc/powerpc32/fpu/fix-int-fp-convert-zero.h: New file. * config.h.in [_LIBC] (HAVE_PPC_FCFID): New macro.
2015-10-05 17:46:50 +00:00
float ret = (float)(((u_int32_t)hx>>31)<<1)+one/x;
if (FIX_INT_FP_CONVERT_ZERO && ret == 0.0f)
return 0.0f;
return ret;
}
if(ix < 0x3f580000) { /* |x|<0.84375 */
if(ix < 0x32800000) /* |x|<2**-26 */
return one-x;
z = x*x;
r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
y = r/s;
if(hx < 0x3e800000) { /* x<1/4 */
return one-(x+x*y);
} else {
r = x*y;
r += (x-half);
return half - r ;
}
}
if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
s = fabsf(x)-one;
P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
if(hx>=0) {
2013-06-05 20:44:03 +00:00
z = one-erx; return z - P/Q;
} else {
z = erx+P/Q; return one+z;
}
}
if (ix < 0x41e00000) { /* |x|<28 */
x = fabsf(x);
s = one/(x*x);
if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/
R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
ra5+s*(ra6+s*ra7))))));
S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
sa5+s*(sa6+s*(sa7+s*sa8)))))));
} else { /* |x| >= 1/.35 ~ 2.857143 */
if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */
R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
rb5+s*rb6)))));
S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
sb5+s*(sb6+s*sb7))))));
}
GET_FLOAT_WORD(ix,x);
2012-03-01 21:15:38 +00:00
SET_FLOAT_WORD(z,ix&0xffffe000);
r = __ieee754_expf(-z*z-(float)0.5625)*
__ieee754_expf((z-x)*(z+x)+R/S);
if(hx>0) {
Use math_narrow_eval more consistently. Where glibc code needs to avoid excess range and precision in floating-point arithmetic, code variously uses either asms or volatile to force the results of that arithmetic to memory; mostly this is conditional on FLT_EVAL_METHOD, but in the case of lrint / llrint functions some use of volatile is unconditional (and is present unnecessarily in versions for long double). This patch make such code use the recently-added math_narrow_eval macro consistently, removing the unnecessary uses of volatile in long double lrint / llrint implementations completely. Tested for x86_64, x86, mips64 and powerpc. * math/s_nexttowardf.c (__nexttowardf): Use math_narrow_eval. * stdlib/strtod_l.c: Include <math_private.h>. (overflow_value): Use math_narrow_eval. (underflow_value): Likewise. * sysdeps/i386/fpu/s_nexttoward.c (__nexttoward): Likewise. * sysdeps/i386/fpu/s_nexttowardf.c (__nexttowardf): Likewise. * sysdeps/ieee754/dbl-64/e_gamma_r.c (gamma_positive): Likewise. (__ieee754_gamma_r): Likewise. * sysdeps/ieee754/dbl-64/gamma_productf.c (__gamma_productf): Likewise. * sysdeps/ieee754/dbl-64/k_rem_pio2.c (__kernel_rem_pio2): Likewise. * sysdeps/ieee754/dbl-64/lgamma_neg.c (__lgamma_neg): Likewise. * sysdeps/ieee754/dbl-64/s_erf.c (__erfc): Likewise. * sysdeps/ieee754/dbl-64/s_llrint.c (__llrint): Likewise. * sysdeps/ieee754/dbl-64/s_lrint.c (__lrint): Likewise. * sysdeps/ieee754/flt-32/e_gammaf_r.c (gammaf_positive): Likewise. (__ieee754_gammaf_r): Likewise. * sysdeps/ieee754/flt-32/k_rem_pio2f.c (__kernel_rem_pio2f): Likewise. * sysdeps/ieee754/flt-32/lgamma_negf.c (__lgamma_negf): Likewise. * sysdeps/ieee754/flt-32/s_erff.c (__erfcf): Likewise. * sysdeps/ieee754/flt-32/s_llrintf.c (__llrintf): Likewise. * sysdeps/ieee754/flt-32/s_lrintf.c (__lrintf): Likewise. * sysdeps/ieee754/ldbl-128/s_llrintl.c (__llrintl): Do not use volatile. * sysdeps/ieee754/ldbl-128/s_lrintl.c (__lrintl): Likewise. * sysdeps/ieee754/ldbl-128/s_nexttoward.c (__nexttoward): Use math_narrow_eval. * sysdeps/ieee754/ldbl-128ibm/s_nexttoward.c (__nexttoward): Likewise. * sysdeps/ieee754/ldbl-128ibm/s_nexttowardf.c (__nexttowardf): Likewise. * sysdeps/ieee754/ldbl-96/gamma_product.c (__gamma_product): Likewise. * sysdeps/ieee754/ldbl-96/s_llrintl.c (__llrintl): Do not use volatile. * sysdeps/ieee754/ldbl-96/s_lrintl.c (__lrintl): Likewise. * sysdeps/ieee754/ldbl-96/s_nexttoward.c (__nexttoward): Use math_narrow_eval. * sysdeps/ieee754/ldbl-96/s_nexttowardf.c (__nexttowardf): Likewise. * sysdeps/ieee754/ldbl-opt/s_nexttowardfd.c (__nldbl_nexttowardf): Likewise.
2015-09-23 18:14:57 +00:00
float ret = math_narrow_eval (r/x);
if (ret == 0)
__set_errno (ERANGE);
return ret;
} else
return two-r/x;
} else {
if(hx>0) {
__set_errno (ERANGE);
return tiny*tiny;
} else
return two-tiny;
}
}
weak_alias (__erfcf, erfcf)