* 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

1 files changed, 74 insertions, 483 deletions

diff --git a/missing/erf.c b/missing/erf.c
index c0ab65f881..d9e7469024 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);
 }