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bc3753638a
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.
429 lines
14 KiB
C
429 lines
14 KiB
C
/* @(#)s_erf.c 5.1 93/09/24 */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25,
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for performance improvement on pipelined processors.
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*/
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#if defined(LIBM_SCCS) && !defined(lint)
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static char rcsid[] = "$NetBSD: s_erf.c,v 1.8 1995/05/10 20:47:05 jtc Exp $";
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#endif
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/* double erf(double x)
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* double erfc(double x)
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* x
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* 2 |\
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* erf(x) = --------- | exp(-t*t)dt
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* sqrt(pi) \|
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* 0
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*
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* erfc(x) = 1-erf(x)
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* Note that
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* erf(-x) = -erf(x)
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* erfc(-x) = 2 - erfc(x)
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*
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* Method:
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* 1. For |x| in [0, 0.84375]
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* erf(x) = x + x*R(x^2)
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* erfc(x) = 1 - erf(x) if x in [-.84375,0.25]
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* = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375]
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* where R = P/Q where P is an odd poly of degree 8 and
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* Q is an odd poly of degree 10.
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* -57.90
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* | R - (erf(x)-x)/x | <= 2
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*
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*
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* Remark. The formula is derived by noting
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* erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....)
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* and that
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* 2/sqrt(pi) = 1.128379167095512573896158903121545171688
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* is close to one. The interval is chosen because the fix
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* point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is
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* near 0.6174), and by some experiment, 0.84375 is chosen to
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* guarantee the error is less than one ulp for erf.
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*
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* 2. For |x| in [0.84375,1.25], let s = |x| - 1, and
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* c = 0.84506291151 rounded to single (24 bits)
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* erf(x) = sign(x) * (c + P1(s)/Q1(s))
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* erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0
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* 1+(c+P1(s)/Q1(s)) if x < 0
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* |P1/Q1 - (erf(|x|)-c)| <= 2**-59.06
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* Remark: here we use the taylor series expansion at x=1.
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* erf(1+s) = erf(1) + s*Poly(s)
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* = 0.845.. + P1(s)/Q1(s)
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* That is, we use rational approximation to approximate
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* erf(1+s) - (c = (single)0.84506291151)
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* Note that |P1/Q1|< 0.078 for x in [0.84375,1.25]
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* where
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* P1(s) = degree 6 poly in s
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* Q1(s) = degree 6 poly in s
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*
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* 3. For x in [1.25,1/0.35(~2.857143)],
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* erfc(x) = (1/x)*exp(-x*x-0.5625+R1/S1)
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* erf(x) = 1 - erfc(x)
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* where
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* R1(z) = degree 7 poly in z, (z=1/x^2)
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* S1(z) = degree 8 poly in z
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*
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* 4. For x in [1/0.35,28]
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* erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0
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* = 2.0 - (1/x)*exp(-x*x-0.5625+R2/S2) if -6<x<0
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* = 2.0 - tiny (if x <= -6)
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* erf(x) = sign(x)*(1.0 - erfc(x)) if x < 6, else
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* erf(x) = sign(x)*(1.0 - tiny)
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* where
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* R2(z) = degree 6 poly in z, (z=1/x^2)
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* S2(z) = degree 7 poly in z
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*
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* Note1:
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* To compute exp(-x*x-0.5625+R/S), let s be a single
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* precision number and s := x; then
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* -x*x = -s*s + (s-x)*(s+x)
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* exp(-x*x-0.5626+R/S) =
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* exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S);
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* Note2:
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* Here 4 and 5 make use of the asymptotic series
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* exp(-x*x)
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* erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) )
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* x*sqrt(pi)
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* We use rational approximation to approximate
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* g(s)=f(1/x^2) = log(erfc(x)*x) - x*x + 0.5625
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* Here is the error bound for R1/S1 and R2/S2
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* |R1/S1 - f(x)| < 2**(-62.57)
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* |R2/S2 - f(x)| < 2**(-61.52)
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*
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* 5. For inf > x >= 28
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* erf(x) = sign(x) *(1 - tiny) (raise inexact)
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* erfc(x) = tiny*tiny (raise underflow) if x > 0
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* = 2 - tiny if x<0
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*
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* 7. Special case:
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* erf(0) = 0, erf(inf) = 1, erf(-inf) = -1,
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* erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2,
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* erfc/erf(NaN) is NaN
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*/
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#include <errno.h>
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#include <float.h>
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#include <math.h>
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#include <math_private.h>
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#include <fix-int-fp-convert-zero.h>
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static const double
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tiny = 1e-300,
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half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
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one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
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two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */
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/* c = (float)0.84506291151 */
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erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */
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/*
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* Coefficients for approximation to erf on [0,0.84375]
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*/
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efx = 1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */
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pp[] = { 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */
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-3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */
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-2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */
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-5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */
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-2.37630166566501626084e-05 }, /* 0xBEF8EAD6, 0x120016AC */
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qq[] = { 0.0, 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */
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6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */
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5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */
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1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */
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-3.96022827877536812320e-06 }, /* 0xBED09C43, 0x42A26120 */
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/*
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* Coefficients for approximation to erf in [0.84375,1.25]
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*/
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pa[] = { -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */
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4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */
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-3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */
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3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */
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-1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */
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3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */
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-2.16637559486879084300e-03 }, /* 0xBF61BF38, 0x0A96073F */
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qa[] = { 0.0, 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */
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5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */
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7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */
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1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */
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1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */
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1.19844998467991074170e-02 }, /* 0x3F888B54, 0x5735151D */
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/*
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* Coefficients for approximation to erfc in [1.25,1/0.35]
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*/
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ra[] = { -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */
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-6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */
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-1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */
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-6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */
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-1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */
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-1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */
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-8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */
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-9.81432934416914548592e+00 }, /* 0xC023A0EF, 0xC69AC25C */
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sa[] = { 0.0, 1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */
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1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */
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4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */
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6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */
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4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */
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1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */
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6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */
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-6.04244152148580987438e-02 }, /* 0xBFAEEFF2, 0xEE749A62 */
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/*
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* Coefficients for approximation to erfc in [1/.35,28]
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*/
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rb[] = { -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */
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-7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */
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-1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */
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-1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */
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-6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */
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-1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */
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-4.83519191608651397019e+02 }, /* 0xC07E384E, 0x9BDC383F */
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sb[] = { 0.0, 3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */
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3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */
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1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */
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3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */
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2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */
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4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */
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-2.24409524465858183362e+01 }; /* 0xC03670E2, 0x42712D62 */
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double
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__erf (double x)
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{
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int32_t hx, ix, i;
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double R, S, P, Q, s, y, z, r;
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GET_HIGH_WORD (hx, x);
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ix = hx & 0x7fffffff;
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if (ix >= 0x7ff00000) /* erf(nan)=nan */
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{
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i = ((u_int32_t) hx >> 31) << 1;
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return (double) (1 - i) + one / x; /* erf(+-inf)=+-1 */
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}
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if (ix < 0x3feb0000) /* |x|<0.84375 */
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{
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double r1, r2, s1, s2, s3, z2, z4;
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if (ix < 0x3e300000) /* |x|<2**-28 */
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{
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if (ix < 0x00800000)
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{
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/* Avoid spurious underflow. */
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double ret = 0.0625 * (16.0 * x + (16.0 * efx) * x);
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math_check_force_underflow (ret);
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return ret;
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}
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return x + efx * x;
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}
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z = x * x;
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r1 = pp[0] + z * pp[1]; z2 = z * z;
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r2 = pp[2] + z * pp[3]; z4 = z2 * z2;
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s1 = one + z * qq[1];
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s2 = qq[2] + z * qq[3];
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s3 = qq[4] + z * qq[5];
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r = r1 + z2 * r2 + z4 * pp[4];
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s = s1 + z2 * s2 + z4 * s3;
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y = r / s;
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return x + x * y;
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}
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if (ix < 0x3ff40000) /* 0.84375 <= |x| < 1.25 */
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{
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double s2, s4, s6, P1, P2, P3, P4, Q1, Q2, Q3, Q4;
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s = fabs (x) - one;
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P1 = pa[0] + s * pa[1]; s2 = s * s;
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Q1 = one + s * qa[1]; s4 = s2 * s2;
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P2 = pa[2] + s * pa[3]; s6 = s4 * s2;
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Q2 = qa[2] + s * qa[3];
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P3 = pa[4] + s * pa[5];
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Q3 = qa[4] + s * qa[5];
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P4 = pa[6];
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Q4 = qa[6];
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P = P1 + s2 * P2 + s4 * P3 + s6 * P4;
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Q = Q1 + s2 * Q2 + s4 * Q3 + s6 * Q4;
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if (hx >= 0)
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return erx + P / Q;
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else
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return -erx - P / Q;
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}
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if (ix >= 0x40180000) /* inf>|x|>=6 */
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{
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if (hx >= 0)
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return one - tiny;
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else
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return tiny - one;
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}
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x = fabs (x);
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s = one / (x * x);
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if (ix < 0x4006DB6E) /* |x| < 1/0.35 */
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{
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double R1, R2, R3, R4, S1, S2, S3, S4, s2, s4, s6, s8;
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R1 = ra[0] + s * ra[1]; s2 = s * s;
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S1 = one + s * sa[1]; s4 = s2 * s2;
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R2 = ra[2] + s * ra[3]; s6 = s4 * s2;
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S2 = sa[2] + s * sa[3]; s8 = s4 * s4;
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R3 = ra[4] + s * ra[5];
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S3 = sa[4] + s * sa[5];
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R4 = ra[6] + s * ra[7];
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S4 = sa[6] + s * sa[7];
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R = R1 + s2 * R2 + s4 * R3 + s6 * R4;
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S = S1 + s2 * S2 + s4 * S3 + s6 * S4 + s8 * sa[8];
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}
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else /* |x| >= 1/0.35 */
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{
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double R1, R2, R3, S1, S2, S3, S4, s2, s4, s6;
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R1 = rb[0] + s * rb[1]; s2 = s * s;
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S1 = one + s * sb[1]; s4 = s2 * s2;
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R2 = rb[2] + s * rb[3]; s6 = s4 * s2;
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S2 = sb[2] + s * sb[3];
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R3 = rb[4] + s * rb[5];
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S3 = sb[4] + s * sb[5];
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S4 = sb[6] + s * sb[7];
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R = R1 + s2 * R2 + s4 * R3 + s6 * rb[6];
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S = S1 + s2 * S2 + s4 * S3 + s6 * S4;
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}
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z = x;
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SET_LOW_WORD (z, 0);
|
|
r = __ieee754_exp (-z * z - 0.5625) *
|
|
__ieee754_exp ((z - x) * (z + x) + R / S);
|
|
if (hx >= 0)
|
|
return one - r / x;
|
|
else
|
|
return r / x - one;
|
|
}
|
|
weak_alias (__erf, erf)
|
|
#ifdef NO_LONG_DOUBLE
|
|
strong_alias (__erf, __erfl)
|
|
weak_alias (__erf, erfl)
|
|
#endif
|
|
|
|
double
|
|
__erfc (double x)
|
|
{
|
|
int32_t hx, ix;
|
|
double R, S, P, Q, s, y, z, r;
|
|
GET_HIGH_WORD (hx, x);
|
|
ix = hx & 0x7fffffff;
|
|
if (ix >= 0x7ff00000) /* erfc(nan)=nan */
|
|
{ /* erfc(+-inf)=0,2 */
|
|
double ret = (double) (((u_int32_t) hx >> 31) << 1) + one / x;
|
|
if (FIX_INT_FP_CONVERT_ZERO && ret == 0.0)
|
|
return 0.0;
|
|
return ret;
|
|
}
|
|
|
|
if (ix < 0x3feb0000) /* |x|<0.84375 */
|
|
{
|
|
double r1, r2, s1, s2, s3, z2, z4;
|
|
if (ix < 0x3c700000) /* |x|<2**-56 */
|
|
return one - x;
|
|
z = x * x;
|
|
r1 = pp[0] + z * pp[1]; z2 = z * z;
|
|
r2 = pp[2] + z * pp[3]; z4 = z2 * z2;
|
|
s1 = one + z * qq[1];
|
|
s2 = qq[2] + z * qq[3];
|
|
s3 = qq[4] + z * qq[5];
|
|
r = r1 + z2 * r2 + z4 * pp[4];
|
|
s = s1 + z2 * s2 + z4 * s3;
|
|
y = r / s;
|
|
if (hx < 0x3fd00000) /* x<1/4 */
|
|
{
|
|
return one - (x + x * y);
|
|
}
|
|
else
|
|
{
|
|
r = x * y;
|
|
r += (x - half);
|
|
return half - r;
|
|
}
|
|
}
|
|
if (ix < 0x3ff40000) /* 0.84375 <= |x| < 1.25 */
|
|
{
|
|
double s2, s4, s6, P1, P2, P3, P4, Q1, Q2, Q3, Q4;
|
|
s = fabs (x) - one;
|
|
P1 = pa[0] + s * pa[1]; s2 = s * s;
|
|
Q1 = one + s * qa[1]; s4 = s2 * s2;
|
|
P2 = pa[2] + s * pa[3]; s6 = s4 * s2;
|
|
Q2 = qa[2] + s * qa[3];
|
|
P3 = pa[4] + s * pa[5];
|
|
Q3 = qa[4] + s * qa[5];
|
|
P4 = pa[6];
|
|
Q4 = qa[6];
|
|
P = P1 + s2 * P2 + s4 * P3 + s6 * P4;
|
|
Q = Q1 + s2 * Q2 + s4 * Q3 + s6 * Q4;
|
|
if (hx >= 0)
|
|
{
|
|
z = one - erx; return z - P / Q;
|
|
}
|
|
else
|
|
{
|
|
z = erx + P / Q; return one + z;
|
|
}
|
|
}
|
|
if (ix < 0x403c0000) /* |x|<28 */
|
|
{
|
|
x = fabs (x);
|
|
s = one / (x * x);
|
|
if (ix < 0x4006DB6D) /* |x| < 1/.35 ~ 2.857143*/
|
|
{
|
|
double R1, R2, R3, R4, S1, S2, S3, S4, s2, s4, s6, s8;
|
|
R1 = ra[0] + s * ra[1]; s2 = s * s;
|
|
S1 = one + s * sa[1]; s4 = s2 * s2;
|
|
R2 = ra[2] + s * ra[3]; s6 = s4 * s2;
|
|
S2 = sa[2] + s * sa[3]; s8 = s4 * s4;
|
|
R3 = ra[4] + s * ra[5];
|
|
S3 = sa[4] + s * sa[5];
|
|
R4 = ra[6] + s * ra[7];
|
|
S4 = sa[6] + s * sa[7];
|
|
R = R1 + s2 * R2 + s4 * R3 + s6 * R4;
|
|
S = S1 + s2 * S2 + s4 * S3 + s6 * S4 + s8 * sa[8];
|
|
}
|
|
else /* |x| >= 1/.35 ~ 2.857143 */
|
|
{
|
|
double R1, R2, R3, S1, S2, S3, S4, s2, s4, s6;
|
|
if (hx < 0 && ix >= 0x40180000)
|
|
return two - tiny; /* x < -6 */
|
|
R1 = rb[0] + s * rb[1]; s2 = s * s;
|
|
S1 = one + s * sb[1]; s4 = s2 * s2;
|
|
R2 = rb[2] + s * rb[3]; s6 = s4 * s2;
|
|
S2 = sb[2] + s * sb[3];
|
|
R3 = rb[4] + s * rb[5];
|
|
S3 = sb[4] + s * sb[5];
|
|
S4 = sb[6] + s * sb[7];
|
|
R = R1 + s2 * R2 + s4 * R3 + s6 * rb[6];
|
|
S = S1 + s2 * S2 + s4 * S3 + s6 * S4;
|
|
}
|
|
z = x;
|
|
SET_LOW_WORD (z, 0);
|
|
r = __ieee754_exp (-z * z - 0.5625) *
|
|
__ieee754_exp ((z - x) * (z + x) + R / S);
|
|
if (hx > 0)
|
|
{
|
|
double 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 (__erfc, erfc)
|
|
#ifdef NO_LONG_DOUBLE
|
|
strong_alias (__erfc, __erfcl)
|
|
weak_alias (__erfc, erfcl)
|
|
#endif
|