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authormatz <matz@b2dd03c8-39d4-4d8f-98ff-823fe69b080e>2005-07-06 09:47:08 +0000
committermatz <matz@b2dd03c8-39d4-4d8f-98ff-823fe69b080e>2005-07-06 09:47:08 +0000
commit7b7c03717949dbe5c41631bbf02652b251d02636 (patch)
treed1a1f3477269afcf2712463ea131713c75bf44e1 /missing/erf.c
parent2e0680f22100e8fc46c8efb43ff1a1b875a9e306 (diff)
* object.c (rb_obj_pattern_match): now returns nil.
[ruby-core:05391] * sample/svr.rb: service can be stopped by ill-behaved client; use tsvr.rb instead. * missing/erf.c: original erf.c by prof. Okumura is confirmed to be public domain. reverted BSD implementation. git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@8732 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
Diffstat (limited to 'missing/erf.c')
-rw-r--r--missing/erf.c557
1 files changed, 74 insertions, 483 deletions
diff --git a/missing/erf.c b/missing/erf.c
index c0ab65f..d9e7469 100644
--- a/missing/erf.c
+++ b/missing/erf.c
@@ -1,501 +1,92 @@
-/*-
- * Copyright (c) 1992, 1993
- * The Regents of the University of California. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- * 3. Neither the name of the University nor the names of its contributors
- * may be used to endorse or promote products derived from this software
- * without specific prior written permission.
- *
- * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-#ifndef lint
-static char sccsid[] = "@(#)erf.c 8.1 (Berkeley) 6/4/93";
-#endif /* not lint */
+/* erf.c - public domain implementation of error function erf(3m)
+reference - Haruhiko Okumura: C-gengo niyoru saishin algorithm jiten
+ (New Algorithm handbook in C language) (Gijyutsu hyouron
+ sha, Tokyo, 1991) p.227 [in Japanese] */
#include <stdio.h>
-#include "config.h"
-#include "defines.h"
-
-#if defined(vax)||defined(tahoe)
+#include <math.h>
-/* Deal with different ways to concatenate in cpp */
-# ifdef __STDC__
-# define cat3(a,b,c) a ## b ## c
-# else
-# define cat3(a,b,c) a/**/b/**/c
+#ifdef _WIN32
+# include <float.h>
+# if !defined __MINGW32__ || defined __NO_ISOCEXT
+# ifndef isnan
+# define isnan(x) _isnan(x)
# endif
-
-/* Deal with vax/tahoe byte order issues */
-# ifdef vax
-# define cat3t(a,b,c) cat3(a,b,c)
-# else
-# define cat3t(a,b,c) cat3(a,c,b)
+# ifndef isinf
+# define isinf(x) (!_finite(x) && !_isnan(x))
# endif
+# ifndef finite
+# define finite(x) _finite(x)
+# endif
+# endif
+#endif
-# define vccast(name) (*(const double *)(cat3(name,,x)))
-
- /*
- * Define a constant to high precision on a Vax or Tahoe.
- *
- * Args are the name to define, the decimal floating point value,
- * four 16-bit chunks of the float value in hex
- * (because the vax and tahoe differ in float format!), the power
- * of 2 of the hex-float exponent, and the hex-float mantissa.
- * Most of these arguments are not used at compile time; they are
- * used in a post-check to make sure the constants were compiled
- * correctly.
- *
- * People who want to use the constant will have to do their own
- * #define foo vccast(foo)
- * since CPP cannot do this for them from inside another macro (sigh).
- * We define "vccast" if this needs doing.
- */
-# define vc(name, value, x1,x2,x3,x4, bexp, xval) \
- const static long cat3(name,,x)[] = {cat3t(0x,x1,x2), cat3t(0x,x3,x4)};
-
-# define ic(name, value, bexp, xval) ;
-
-#else /* vax or tahoe */
-
- /* Hooray, we have an IEEE machine */
-# undef vccast
-# define vc(name, value, x1,x2,x3,x4, bexp, xval) ;
-
-# define ic(name, value, bexp, xval) \
- const static double name = value;
-
-#endif /* defined(vax)||defined(tahoe) */
-
-const static double ln2hi = 6.9314718055829871446E-1;
-const static double ln2lo = 1.6465949582897081279E-12;
-const static double lnhuge = 9.4961163736712506989E1;
-const static double lntiny = -9.5654310917272452386E1;
-const static double invln2 = 1.4426950408889634148E0;
-const static double ep1 = 1.6666666666666601904E-1;
-const static double ep2 = -2.7777777777015593384E-3;
-const static double ep3 = 6.6137563214379343612E-5;
-const static double ep4 = -1.6533902205465251539E-6;
-const static double ep5 = 4.1381367970572384604E-8;
+static double q_gamma(double, double, double);
-/* returns exp(r = x + c) for |c| < |x| with no overlap. */
-double __exp__D(x, c)
-double x, c;
+/* Incomplete gamma function
+ 1 / Gamma(a) * Int_0^x exp(-t) t^(a-1) dt */
+static double p_gamma(a, x, loggamma_a)
+ double a, x, loggamma_a;
{
- double z,hi,lo, t;
- int k;
-
-#if !defined(vax)&&!defined(tahoe)
- if (x!=x) return(x); /* x is NaN */
-#endif /* !defined(vax)&&!defined(tahoe) */
- if ( x <= lnhuge ) {
- if ( x >= lntiny ) {
-
- /* argument reduction : x --> x - k*ln2 */
- z = invln2*x;
- k = z + copysign(.5, x);
-
- /* express (x+c)-k*ln2 as hi-lo and let x=hi-lo rounded */
-
- hi=(x-k*ln2hi); /* Exact. */
- x= hi - (lo = k*ln2lo-c);
- /* return 2^k*[1+x+x*c/(2+c)] */
- z=x*x;
- c= x - z*(ep1+z*(ep2+z*(ep3+z*(ep4+z*ep5))));
- c = (x*c)/(2.0-c);
-
- return scalb(1.+(hi-(lo - c)), k);
- }
- /* end of x > lntiny */
-
- else
- /* exp(-big#) underflows to zero */
- if(finite(x)) return(scalb(1.0,-5000));
-
- /* exp(-INF) is zero */
- else return(0.0);
- }
- /* end of x < lnhuge */
-
- else
- /* exp(INF) is INF, exp(+big#) overflows to INF */
- return( finite(x) ? scalb(1.0,5000) : x);
+ int k;
+ double result, term, previous;
+
+ if (x >= 1 + a) return 1 - q_gamma(a, x, loggamma_a);
+ if (x == 0) return 0;
+ result = term = exp(a * log(x) - x - loggamma_a) / a;
+ for (k = 1; k < 1000; k++) {
+ term *= x / (a + k);
+ previous = result; result += term;
+ if (result == previous) return result;
+ }
+ fprintf(stderr, "erf.c:%d:p_gamma() could not converge.", __LINE__);
+ return result;
}
-/* Modified Nov 30, 1992 P. McILROY:
- * Replaced expansions for x >= 1.25 (error 1.7ulp vs ~6ulp)
- * Replaced even+odd with direct calculation for x < .84375,
- * to avoid destructive cancellation.
- *
- * Performance of erfc(x):
- * In 300000 trials in the range [.83, .84375] the
- * maximum observed error was 3.6ulp.
- *
- * In [.84735,1.25] the maximum observed error was <2.5ulp in
- * 100000 runs in the range [1.2, 1.25].
- *
- * In [1.25,26] (Not including subnormal results)
- * the error is < 1.7ulp.
- */
-
-/* double erf(double x)
- * double erfc(double x)
- * x
- * 2 |\
- * erf(x) = --------- | exp(-t*t)dt
- * sqrt(pi) \|
- * 0
- *
- * erfc(x) = 1-erf(x)
- *
- * Method:
- * 1. Reduce x to |x| by erf(-x) = -erf(x)
- * 2. For x in [0, 0.84375]
- * erf(x) = x + x*P(x^2)
- * erfc(x) = 1 - erf(x) if x<=0.25
- * = 0.5 + ((0.5-x)-x*P) if x in [0.25,0.84375]
- * where
- * 2 2 4 20
- * P = P(x ) = (p0 + p1 * x + p2 * x + ... + p10 * x )
- * is an approximation to (erf(x)-x)/x with precision
- *
- * -56.45
- * | P - (erf(x)-x)/x | <= 2
- *
- *
- * Remark. The formula is derived by noting
- * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....)
- * and that
- * 2/sqrt(pi) = 1.128379167095512573896158903121545171688
- * is close to one. The interval is chosen because the fixed
- * point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is
- * near 0.6174), and by some experiment, 0.84375 is chosen to
- * guarantee the error is less than one ulp for erf.
- *
- * 3. For x in [0.84375,1.25], let s = x - 1, and
- * c = 0.84506291151 rounded to single (24 bits)
- * erf(x) = c + P1(s)/Q1(s)
- * erfc(x) = (1-c) - P1(s)/Q1(s)
- * |P1/Q1 - (erf(x)-c)| <= 2**-59.06
- * Remark: here we use the taylor series expansion at x=1.
- * erf(1+s) = erf(1) + s*Poly(s)
- * = 0.845.. + P1(s)/Q1(s)
- * That is, we use rational approximation to approximate
- * erf(1+s) - (c = (single)0.84506291151)
- * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25]
- * where
- * P1(s) = degree 6 poly in s
- * Q1(s) = degree 6 poly in s
- *
- * 4. For x in [1.25, 2]; [2, 4]
- * erf(x) = 1.0 - tiny
- * erfc(x) = (1/x)exp(-x*x-(.5*log(pi) -.5z + R(z)/S(z))
- *
- * Where z = 1/(x*x), R is degree 9, and S is degree 3;
- *
- * 5. For x in [4,28]
- * erf(x) = 1.0 - tiny
- * erfc(x) = (1/x)exp(-x*x-(.5*log(pi)+eps + zP(z))
- *
- * Where P is degree 14 polynomial in 1/(x*x).
- *
- * Notes:
- * Here 4 and 5 make use of the asymptotic series
- * exp(-x*x)
- * erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) );
- * x*sqrt(pi)
- *
- * where for z = 1/(x*x)
- * P(z) ~ z/2*(-1 + z*3/2*(1 + z*5/2*(-1 + z*7/2*(1 +...))))
- *
- * Thus we use rational approximation to approximate
- * erfc*x*exp(x*x) ~ 1/sqrt(pi);
- *
- * The error bound for the target function, G(z) for
- * the interval
- * [4, 28]:
- * |eps + 1/(z)P(z) - G(z)| < 2**(-56.61)
- * for [2, 4]:
- * |R(z)/S(z) - G(z)| < 2**(-58.24)
- * for [1.25, 2]:
- * |R(z)/S(z) - G(z)| < 2**(-58.12)
- *
- * 6. For inf > x >= 28
- * erf(x) = 1 - tiny (raise inexact)
- * erfc(x) = tiny*tiny (raise underflow)
- *
- * 7. Special cases:
- * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1,
- * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2,
- * erfc/erf(NaN) is NaN
- */
-
-#if defined(vax) || defined(tahoe)
-#define _IEEE 0
-#define TRUNC(x) (double) (float) (x)
-#else
-#define _IEEE 1
-#define TRUNC(x) *(((int *) &x) + 1) &= 0xf8000000
-#define infnan(x) 0.0
-#endif
-
-#ifdef _IEEE_LIBM
-/*
- * redefining "___function" to "function" in _IEEE_LIBM mode
- */
-#include "ieee_libm.h"
-#endif
+/* Incomplete gamma function
+ 1 / Gamma(a) * Int_x^inf exp(-t) t^(a-1) dt */
+static double q_gamma(a, x, loggamma_a)
+ double a, x, loggamma_a;
+{
+ int k;
+ double result, w, temp, previous;
+ double la = 1, lb = 1 + x - a; /* Laguerre polynomial */
+
+ if (x < 1 + a) return 1 - p_gamma(a, x, loggamma_a);
+ w = exp(a * log(x) - x - loggamma_a);
+ result = w / lb;
+ for (k = 2; k < 1000; k++) {
+ temp = ((k - 1 - a) * (lb - la) + (k + x) * lb) / k;
+ la = lb; lb = temp;
+ w *= (k - 1 - a) / k;
+ temp = w / (la * lb);
+ previous = result; result += temp;
+ if (result == previous) return result;
+ }
+ fprintf(stderr, "erf.c:%d:q_gamma() could not converge.", __LINE__);
+ return result;
+}
-const static double
-tiny = 1e-300,
-half = 0.5,
-one = 1.0,
-two = 2.0,
-c = 8.45062911510467529297e-01, /* (float)0.84506291151 */
-/*
- * Coefficients for approximation to erf in [0,0.84375]
- */
-p0t8 = 1.02703333676410051049867154944018394163280,
-p0 = 1.283791670955125638123339436800229927041e-0001,
-p1 = -3.761263890318340796574473028946097022260e-0001,
-p2 = 1.128379167093567004871858633779992337238e-0001,
-p3 = -2.686617064084433642889526516177508374437e-0002,
-p4 = 5.223977576966219409445780927846432273191e-0003,
-p5 = -8.548323822001639515038738961618255438422e-0004,
-p6 = 1.205520092530505090384383082516403772317e-0004,
-p7 = -1.492214100762529635365672665955239554276e-0005,
-p8 = 1.640186161764254363152286358441771740838e-0006,
-p9 = -1.571599331700515057841960987689515895479e-0007,
-p10= 1.073087585213621540635426191486561494058e-0008;
-/*
- * Coefficients for approximation to erf in [0.84375,1.25]
- */
-static double
-pa0 = -2.362118560752659485957248365514511540287e-0003,
-pa1 = 4.148561186837483359654781492060070469522e-0001,
-pa2 = -3.722078760357013107593507594535478633044e-0001,
-pa3 = 3.183466199011617316853636418691420262160e-0001,
-pa4 = -1.108946942823966771253985510891237782544e-0001,
-pa5 = 3.547830432561823343969797140537411825179e-0002,
-pa6 = -2.166375594868790886906539848893221184820e-0003,
-qa1 = 1.064208804008442270765369280952419863524e-0001,
-qa2 = 5.403979177021710663441167681878575087235e-0001,
-qa3 = 7.182865441419627066207655332170665812023e-0002,
-qa4 = 1.261712198087616469108438860983447773726e-0001,
-qa5 = 1.363708391202905087876983523620537833157e-0002,
-qa6 = 1.198449984679910764099772682882189711364e-0002;
-/*
- * log(sqrt(pi)) for large x expansions.
- * The tail (lsqrtPI_lo) is included in the rational
- * approximations.
-*/
-static double
- lsqrtPI_hi = .5723649429247000819387380943226;
-/*
- * lsqrtPI_lo = .000000000000000005132975581353913;
- *
- * Coefficients for approximation to erfc in [2, 4]
-*/
-static double
-rb0 = -1.5306508387410807582e-010, /* includes lsqrtPI_lo */
-rb1 = 2.15592846101742183841910806188e-008,
-rb2 = 6.24998557732436510470108714799e-001,
-rb3 = 8.24849222231141787631258921465e+000,
-rb4 = 2.63974967372233173534823436057e+001,
-rb5 = 9.86383092541570505318304640241e+000,
-rb6 = -7.28024154841991322228977878694e+000,
-rb7 = 5.96303287280680116566600190708e+000,
-rb8 = -4.40070358507372993983608466806e+000,
-rb9 = 2.39923700182518073731330332521e+000,
-rb10 = -6.89257464785841156285073338950e-001,
-sb1 = 1.56641558965626774835300238919e+001,
-sb2 = 7.20522741000949622502957936376e+001,
-sb3 = 9.60121069770492994166488642804e+001;
-/*
- * Coefficients for approximation to erfc in [1.25, 2]
-*/
-static double
-rc0 = -2.47925334685189288817e-007, /* includes lsqrtPI_lo */
-rc1 = 1.28735722546372485255126993930e-005,
-rc2 = 6.24664954087883916855616917019e-001,
-rc3 = 4.69798884785807402408863708843e+000,
-rc4 = 7.61618295853929705430118701770e+000,
-rc5 = 9.15640208659364240872946538730e-001,
-rc6 = -3.59753040425048631334448145935e-001,
-rc7 = 1.42862267989304403403849619281e-001,
-rc8 = -4.74392758811439801958087514322e-002,
-rc9 = 1.09964787987580810135757047874e-002,
-rc10 = -1.28856240494889325194638463046e-003,
-sc1 = 9.97395106984001955652274773456e+000,
-sc2 = 2.80952153365721279953959310660e+001,
-sc3 = 2.19826478142545234106819407316e+001;
-/*
- * Coefficients for approximation to erfc in [4,28]
- */
-static double
-rd0 = -2.1491361969012978677e-016, /* includes lsqrtPI_lo */
-rd1 = -4.99999999999640086151350330820e-001,
-rd2 = 6.24999999772906433825880867516e-001,
-rd3 = -1.54166659428052432723177389562e+000,
-rd4 = 5.51561147405411844601985649206e+000,
-rd5 = -2.55046307982949826964613748714e+001,
-rd6 = 1.43631424382843846387913799845e+002,
-rd7 = -9.45789244999420134263345971704e+002,
-rd8 = 6.94834146607051206956384703517e+003,
-rd9 = -5.27176414235983393155038356781e+004,
-rd10 = 3.68530281128672766499221324921e+005,
-rd11 = -2.06466642800404317677021026611e+006,
-rd12 = 7.78293889471135381609201431274e+006,
-rd13 = -1.42821001129434127360582351685e+007;
+#define LOG_PI_OVER_2 0.572364942924700087071713675675 /* log_e(PI)/2 */
double erf(x)
- double x;
+ double x;
{
- double R,S,P,Q,ax,s,y,z,r,fabs(),exp();
- if(!finite(x)) { /* erf(nan)=nan */
- if (isnan(x))
- return(x);
- return (x > 0 ? one : -one); /* erf(+/-inf)= +/-1 */
- }
- if ((ax = x) < 0)
- ax = - ax;
- if (ax < .84375) {
- if (ax < 3.7e-09) {
- if (ax < 1.0e-308)
- return 0.125*(8.0*x+p0t8*x); /*avoid underflow */
- return x + p0*x;
- }
- y = x*x;
- r = y*(p1+y*(p2+y*(p3+y*(p4+y*(p5+
- y*(p6+y*(p7+y*(p8+y*(p9+y*p10)))))))));
- return x + x*(p0+r);
- }
- if (ax < 1.25) { /* 0.84375 <= |x| < 1.25 */
- s = fabs(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 (x>=0)
- return (c + P/Q);
- else
- return (-c - P/Q);
- }
- if (ax >= 6.0) { /* inf>|x|>=6 */
- if (x >= 0.0)
- return (one-tiny);
- else
- return (tiny-one);
- }
- /* 1.25 <= |x| < 6 */
- z = -ax*ax;
- s = -one/z;
- if (ax < 2.0) {
- R = rc0+s*(rc1+s*(rc2+s*(rc3+s*(rc4+s*(rc5+
- s*(rc6+s*(rc7+s*(rc8+s*(rc9+s*rc10)))))))));
- S = one+s*(sc1+s*(sc2+s*sc3));
- } else {
- R = rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(rb5+
- s*(rb6+s*(rb7+s*(rb8+s*(rb9+s*rb10)))))))));
- S = one+s*(sb1+s*(sb2+s*sb3));
- }
- y = (R/S -.5*s) - lsqrtPI_hi;
- z += y;
- z = exp(z)/ax;
- if (x >= 0)
- return (one-z);
- else
- return (z-one);
+ if (!finite(x)) {
+ if (isnan(x)) return x; /* erf(NaN) = NaN */
+ return (x>0 ? 1.0 : -1.0); /* erf(+-inf) = +-1.0 */
+ }
+ if (x >= 0) return p_gamma(0.5, x * x, LOG_PI_OVER_2);
+ else return - p_gamma(0.5, x * x, LOG_PI_OVER_2);
}
-double erfc(x)
- double x;
+double erfc(x)
+ double x;
{
- double R,S,P,Q,s,ax,y,z,r,fabs();
- if (!finite(x)) {
- if (isnan(x)) /* erfc(NaN) = NaN */
- return(x);
- else if (x > 0) /* erfc(+-inf)=0,2 */
- return 0.0;
- else
- return 2.0;
- }
- if ((ax = x) < 0)
- ax = -ax;
- if (ax < .84375) { /* |x|<0.84375 */
- if (ax < 1.38777878078144568e-17) /* |x|<2**-56 */
- return one-x;
- y = x*x;
- r = y*(p1+y*(p2+y*(p3+y*(p4+y*(p5+
- y*(p6+y*(p7+y*(p8+y*(p9+y*p10)))))))));
- if (ax < .0625) { /* |x|<2**-4 */
- return (one-(x+x*(p0+r)));
- } else {
- r = x*(p0+r);
- r += (x-half);
- return (half - r);
- }
- }
- if (ax < 1.25) { /* 0.84375 <= |x| < 1.25 */
- s = ax-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 (x>=0) {
- z = one-c; return z - P/Q;
- } else {
- z = c+P/Q; return one+z;
- }
- }
- if (ax >= 28) /* Out of range */
- if (x>0)
- return (tiny*tiny);
- else
- return (two-tiny);
- z = ax;
- TRUNC(z);
- y = z - ax; y *= (ax+z);
- z *= -z; /* Here z + y = -x^2 */
- s = one/(-z-y); /* 1/(x*x) */
- if (ax >= 4) { /* 6 <= ax */
- R = s*(rd1+s*(rd2+s*(rd3+s*(rd4+s*(rd5+
- s*(rd6+s*(rd7+s*(rd8+s*(rd9+s*(rd10
- +s*(rd11+s*(rd12+s*rd13))))))))))));
- y += rd0;
- } else if (ax >= 2) {
- R = rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(rb5+
- s*(rb6+s*(rb7+s*(rb8+s*(rb9+s*rb10)))))))));
- S = one+s*(sb1+s*(sb2+s*sb3));
- y += R/S;
- R = -.5*s;
- } else {
- R = rc0+s*(rc1+s*(rc2+s*(rc3+s*(rc4+s*(rc5+
- s*(rc6+s*(rc7+s*(rc8+s*(rc9+s*rc10)))))))));
- S = one+s*(sc1+s*(sc2+s*sc3));
- y += R/S;
- R = -.5*s;
- }
- /* return exp(-x^2 - lsqrtPI_hi + R + y)/x; */
- s = ((R + y) - lsqrtPI_hi) + z;
- y = (((z-s) - lsqrtPI_hi) + R) + y;
- r = __exp__D(s, y)/x;
- if (x>0)
- return r;
- else
- return two-r;
+ if (!finite(x)) {
+ if (isnan(x)) return x; /* erfc(NaN) = NaN */
+ return (x>0 ? 0.0 : 2.0); /* erfc(+-inf) = 0.0, 2.0 */
+ }
+ if (x >= 0) return q_gamma(0.5, x * x, LOG_PI_OVER_2);
+ else return 1 + p_gamma(0.5, x * x, LOG_PI_OVER_2);
}