lib/msun/src/s_erff.c

   1 /* s_erff.c -- float version of s_erf.c.
   2  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
   3  */
   4
   5 /*
   6  * ====================================================
   7  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   8  *
   9  * Developed at SunPro, a Sun Microsystems, Inc. business.
  10  * Permission to use, copy, modify, and distribute this
  11  * software is freely granted, provided that this notice
  12  * is preserved.
  13  * ====================================================
  14  */
  15
  16 #include <sys/cdefs.h>
  17 #include "math.h"
  18 #include "math_private.h"
  19
  20 /* XXX Prevent compilers from erroneously constant folding: */
  21 static const volatile float tiny = 1e-30;
  22
  23 static const float
  24 half= 0.5,
  25 one = 1,
  26 two = 2,
  27 erx = 8.42697144e-01,                   /* 0x3f57bb00 */
  28 /*
  29  * In the domain [0, 2**-14], only the first term in the power series
  30  * expansion of erf(x) is used.  The magnitude of the first neglected
  31  * terms is less than 2**-42.
  32  */
  33 efx = 1.28379166e-01, /* 0x3e0375d4 */
  34 efx8= 1.02703333e+00, /* 0x3f8375d4 */
  35 /*
  36  * Domain [0, 0.84375], range ~[-5.4419e-10, 5.5179e-10]:
  37  * |(erf(x) - x)/x - pp(x)/qq(x)| < 2**-31
  38  */
  39 pp0  =  1.28379166e-01, /* 0x3e0375d4 */
  40 pp1  = -3.36030394e-01, /* 0xbeac0c2d */
  41 pp2  = -1.86261395e-03, /* 0xbaf422f4 */
  42 qq1  =  3.12324315e-01, /* 0x3e9fe8f9 */
  43 qq2  =  2.16070414e-02, /* 0x3cb10140 */
  44 qq3  = -1.98859372e-03, /* 0xbb025311 */
  45 /*
  46  * Domain [0.84375, 1.25], range ~[-1.023e-9, 1.023e-9]:
  47  * |(erf(x) - erx) - pa(x)/qa(x)| < 2**-31
  48  */
  49 pa0  =  3.65041046e-06, /* 0x3674f993 */
  50 pa1  =  4.15109307e-01, /* 0x3ed48935 */
  51 pa2  = -2.09395722e-01, /* 0xbe566bd5 */
  52 pa3  =  8.67677554e-02, /* 0x3db1b34b */
  53 qa1  =  4.95560974e-01, /* 0x3efdba2b */
  54 qa2  =  3.71248513e-01, /* 0x3ebe1449 */
  55 qa3  =  3.92478965e-02, /* 0x3d20c267 */
  56 /*
  57  * Domain [1.25,1/0.35], range ~[-4.821e-9, 4.927e-9]:
  58  * |log(x*erfc(x)) + x**2 + 0.5625 - ra(x)/sa(x)| < 2**-28
  59  */
  60 ra0  = -9.88156721e-03, /* 0xbc21e64c */
  61 ra1  = -5.43658376e-01, /* 0xbf0b2d32 */
  62 ra2  = -1.66828310e+00, /* 0xbfd58a4d */
  63 ra3  = -6.91554189e-01, /* 0xbf3109b2 */
  64 sa1  =  4.48581553e+00, /* 0x408f8bcd */
  65 sa2  =  4.10799170e+00, /* 0x408374ab */
  66 sa3  =  5.53855181e-01, /* 0x3f0dc974 */
  67 /*
  68  * Domain [2.85715, 11], range ~[-1.484e-9, 1.505e-9]:
  69  * |log(x*erfc(x)) + x**2 + 0.5625 - rb(x)/sb(x)| < 2**-30
  70  */
  71 rb0  = -9.86496918e-03, /* 0xbc21a0ae */
  72 rb1  = -5.48049808e-01, /* 0xbf0c4cfe */
  73 rb2  = -1.84115684e+00, /* 0xbfebab07 */
  74 sb1  =  4.87132740e+00, /* 0x409be1ea */
  75 sb2  =  3.04982710e+00, /* 0x4043305e */
  76 sb3  = -7.61900663e-01; /* 0xbf430bec */
  77
  78 float
  79 erff(float x)
  80 {
  81         int32_t hx,ix,i;
  82         float R,S,P,Q,s,y,z,r;
  83         GET_FLOAT_WORD(hx,x);
  84         ix = hx&0x7fffffff;
  85         if(ix>=0x7f800000) {            /* erff(nan)=nan */
  86             i = ((u_int32_t)hx>>31)<<1;
  87             return (float)(1-i)+one/x;  /* erff(+-inf)=+-1 */
  88         }
  89
  90         if(ix < 0x3f580000) {           /* |x|<0.84375 */
  91             if(ix < 0x38800000) {       /* |x|<2**-14 */
  92                 if (ix < 0x04000000)    /* |x|<0x1p-119 */
  93                     return (8*x+efx8*x)/8;      /* avoid spurious underflow */
  94                 return x + efx*x;
  95             }
  96             z = x*x;
  97             r = pp0+z*(pp1+z*pp2);
  98             s = one+z*(qq1+z*(qq2+z*qq3));
  99             y = r/s;
 100             return x + x*y;
 101         }
 102         if(ix < 0x3fa00000) {           /* 0.84375 <= |x| < 1.25 */
 103             s = fabsf(x)-one;
 104             P = pa0+s*(pa1+s*(pa2+s*pa3));
 105             Q = one+s*(qa1+s*(qa2+s*qa3));
 106             if(hx>=0) return erx + P/Q; else return -erx - P/Q;
 107         }
 108         if (ix >= 0x40800000) {         /* inf>|x|>=4 */
 109             if(hx>=0) return one-tiny; else return tiny-one;
 110         }
 111         x = fabsf(x);
 112         s = one/(x*x);
 113         if(ix< 0x4036db8c) {    /* |x| < 2.85715 ~ 1/0.35 */
 114             R=ra0+s*(ra1+s*(ra2+s*ra3));
 115             S=one+s*(sa1+s*(sa2+s*sa3));
 116         } else {        /* |x| >= 2.85715 ~ 1/0.35 */
 117             R=rb0+s*(rb1+s*rb2);
 118             S=one+s*(sb1+s*(sb2+s*sb3));
 119         }
 120         SET_FLOAT_WORD(z,hx&0xffffe000);
 121         r  = expf(-z*z-0.5625F)*expf((z-x)*(z+x)+R/S);
 122         if(hx>=0) return one-r/x; else return  r/x-one;
 123 }
 124
 125 float
 126 erfcf(float x)
 127 {
 128         int32_t hx,ix;
 129         float R,S,P,Q,s,y,z,r;
 130         GET_FLOAT_WORD(hx,x);
 131         ix = hx&0x7fffffff;
 132         if(ix>=0x7f800000) {                    /* erfcf(nan)=nan */
 133                                                 /* erfcf(+-inf)=0,2 */
 134             return (float)(((u_int32_t)hx>>31)<<1)+one/x;
 135         }
 136
 137         if(ix < 0x3f580000) {           /* |x|<0.84375 */
 138             if(ix < 0x33800000)         /* |x|<2**-24 */
 139                 return one-x;
 140             z = x*x;
 141             r = pp0+z*(pp1+z*pp2);
 142             s = one+z*(qq1+z*(qq2+z*qq3));
 143             y = r/s;
 144             if(hx < 0x3e800000) {       /* x<1/4 */
 145                 return one-(x+x*y);
 146             } else {
 147                 r = x*y;
 148                 r += (x-half);
 149                 return half - r ;
 150             }
 151         }
 152         if(ix < 0x3fa00000) {           /* 0.84375 <= |x| < 1.25 */
 153             s = fabsf(x)-one;
 154             P = pa0+s*(pa1+s*(pa2+s*pa3));
 155             Q = one+s*(qa1+s*(qa2+s*qa3));
 156             if(hx>=0) {
 157                 z  = one-erx; return z - P/Q;
 158             } else {
 159                 z = erx+P/Q; return one+z;
 160             }
 161         }
 162         if (ix < 0x41300000) {          /* |x|<11 */
 163             x = fabsf(x);
 164             s = one/(x*x);
 165             if(ix< 0x4036db8c) {        /* |x| < 2.85715 ~ 1/.35 */
 166                 R=ra0+s*(ra1+s*(ra2+s*ra3));
 167                 S=one+s*(sa1+s*(sa2+s*sa3));
 168             } else {                    /* |x| >= 2.85715 ~ 1/.35 */
 169                 if(hx<0&&ix>=0x40a00000) return two-tiny;/* x < -5 */
 170                 R=rb0+s*(rb1+s*rb2);
 171                 S=one+s*(sb1+s*(sb2+s*sb3));
 172             }
 173             SET_FLOAT_WORD(z,hx&0xffffe000);
 174             r  = expf(-z*z-0.5625F)*expf((z-x)*(z+x)+R/S);
 175             if(hx>0) return r/x; else return two-r/x;
 176         } else {
 177             if(hx>0) return tiny*tiny; else return two-tiny;
 178         }
 179 }