lib/libm/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  * $NetBSD: s_erff.c,v 1.7 2002/05/26 22:01:55 wiz Exp $
  16  * $DragonFly: src/lib/libm/src/s_erff.c,v 1.1 2005/07/26 21:15:20 joerg Exp $
  17  */
  18
  19 #include <math.h>
  20 #include "math_private.h"
  21
  22 static const float
  23 tiny        = 1e-30,
  24 half=  5.0000000000e-01, /* 0x3F000000 */
  25 one =  1.0000000000e+00, /* 0x3F800000 */
  26 two =  2.0000000000e+00, /* 0x40000000 */
  27         /* c = (subfloat)0.84506291151 */
  28 erx =  8.4506291151e-01, /* 0x3f58560b */
  29 /*
  30  * Coefficients for approximation to  erf on [0,0.84375]
  31  */
  32 efx =  1.2837916613e-01, /* 0x3e0375d4 */
  33 efx8=  1.0270333290e+00, /* 0x3f8375d4 */
  34 pp0  =  1.2837916613e-01, /* 0x3e0375d4 */
  35 pp1  = -3.2504209876e-01, /* 0xbea66beb */
  36 pp2  = -2.8481749818e-02, /* 0xbce9528f */
  37 pp3  = -5.7702702470e-03, /* 0xbbbd1489 */
  38 pp4  = -2.3763017452e-05, /* 0xb7c756b1 */
  39 qq1  =  3.9791721106e-01, /* 0x3ecbbbce */
  40 qq2  =  6.5022252500e-02, /* 0x3d852a63 */
  41 qq3  =  5.0813062117e-03, /* 0x3ba68116 */
  42 qq4  =  1.3249473704e-04, /* 0x390aee49 */
  43 qq5  = -3.9602282413e-06, /* 0xb684e21a */
  44 /*
  45  * Coefficients for approximation to  erf  in [0.84375,1.25]
  46  */
  47 pa0  = -2.3621185683e-03, /* 0xbb1acdc6 */
  48 pa1  =  4.1485610604e-01, /* 0x3ed46805 */
  49 pa2  = -3.7220788002e-01, /* 0xbebe9208 */
  50 pa3  =  3.1834661961e-01, /* 0x3ea2fe54 */
  51 pa4  = -1.1089469492e-01, /* 0xbde31cc2 */
  52 pa5  =  3.5478305072e-02, /* 0x3d1151b3 */
  53 pa6  = -2.1663755178e-03, /* 0xbb0df9c0 */
  54 qa1  =  1.0642088205e-01, /* 0x3dd9f331 */
  55 qa2  =  5.4039794207e-01, /* 0x3f0a5785 */
  56 qa3  =  7.1828655899e-02, /* 0x3d931ae7 */
  57 qa4  =  1.2617121637e-01, /* 0x3e013307 */
  58 qa5  =  1.3637083583e-02, /* 0x3c5f6e13 */
  59 qa6  =  1.1984500103e-02, /* 0x3c445aa3 */
  60 /*
  61  * Coefficients for approximation to  erfc in [1.25,1/0.35]
  62  */
  63 ra0  = -9.8649440333e-03, /* 0xbc21a093 */
  64 ra1  = -6.9385856390e-01, /* 0xbf31a0b7 */
  65 ra2  = -1.0558626175e+01, /* 0xc128f022 */
  66 ra3  = -6.2375331879e+01, /* 0xc2798057 */
  67 ra4  = -1.6239666748e+02, /* 0xc322658c */
  68 ra5  = -1.8460508728e+02, /* 0xc3389ae7 */
  69 ra6  = -8.1287437439e+01, /* 0xc2a2932b */
  70 ra7  = -9.8143291473e+00, /* 0xc11d077e */
  71 sa1  =  1.9651271820e+01, /* 0x419d35ce */
  72 sa2  =  1.3765776062e+02, /* 0x4309a863 */
  73 sa3  =  4.3456588745e+02, /* 0x43d9486f */
  74 sa4  =  6.4538726807e+02, /* 0x442158c9 */
  75 sa5  =  4.2900814819e+02, /* 0x43d6810b */
  76 sa6  =  1.0863500214e+02, /* 0x42d9451f */
  77 sa7  =  6.5702495575e+00, /* 0x40d23f7c */
  78 sa8  = -6.0424413532e-02, /* 0xbd777f97 */
  79 /*
  80  * Coefficients for approximation to  erfc in [1/.35,28]
  81  */
  82 rb0  = -9.8649431020e-03, /* 0xbc21a092 */
  83 rb1  = -7.9928326607e-01, /* 0xbf4c9dd4 */
  84 rb2  = -1.7757955551e+01, /* 0xc18e104b */
  85 rb3  = -1.6063638306e+02, /* 0xc320a2ea */
  86 rb4  = -6.3756646729e+02, /* 0xc41f6441 */
  87 rb5  = -1.0250950928e+03, /* 0xc480230b */
  88 rb6  = -4.8351919556e+02, /* 0xc3f1c275 */
  89 sb1  =  3.0338060379e+01, /* 0x41f2b459 */
  90 sb2  =  3.2579251099e+02, /* 0x43a2e571 */
  91 sb3  =  1.5367296143e+03, /* 0x44c01759 */
  92 sb4  =  3.1998581543e+03, /* 0x4547fdbb */
  93 sb5  =  2.5530502930e+03, /* 0x451f90ce */
  94 sb6  =  4.7452853394e+02, /* 0x43ed43a7 */
  95 sb7  = -2.2440952301e+01; /* 0xc1b38712 */
  96
  97 float
  98 erff(float x)
  99 {
 100         int32_t hx,ix,i;
 101         float R,S,P,Q,s,y,z,r;
 102         GET_FLOAT_WORD(hx,x);
 103         ix = hx&0x7fffffff;
 104         if(ix>=0x7f800000) {            /* erf(nan)=nan */
 105             i = ((u_int32_t)hx>>31)<<1;
 106             return (float)(1-i)+one/x;  /* erf(+-inf)=+-1 */
 107         }
 108
 109         if(ix < 0x3f580000) {           /* |x|<0.84375 */
 110             if(ix < 0x31800000) {       /* |x|<2**-28 */
 111                 if (ix < 0x04000000)
 112                     /*avoid underflow */
 113                     return (float)0.125*((float)8.0*x+efx8*x);
 114                 return x + efx*x;
 115             }
 116             z = x*x;
 117             r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
 118             s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
 119             y = r/s;
 120             return x + x*y;
 121         }
 122         if(ix < 0x3fa00000) {           /* 0.84375 <= |x| < 1.25 */
 123             s = fabsf(x)-one;
 124             P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
 125             Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
 126             if(hx>=0) return erx + P/Q; else return -erx - P/Q;
 127         }
 128         if (ix >= 0x40c00000) {         /* inf>|x|>=6 */
 129             if(hx>=0) return one-tiny; else return tiny-one;
 130         }
 131         x = fabsf(x);
 132         s = one/(x*x);
 133         if(ix< 0x4036DB6E) {    /* |x| < 1/0.35 */
 134             R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
 135                                 ra5+s*(ra6+s*ra7))))));
 136             S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
 137                                 sa5+s*(sa6+s*(sa7+s*sa8)))))));
 138         } else {        /* |x| >= 1/0.35 */
 139             R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
 140                                 rb5+s*rb6)))));
 141             S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
 142                                 sb5+s*(sb6+s*sb7))))));
 143         }
 144         GET_FLOAT_WORD(ix,x);
 145         SET_FLOAT_WORD(z,ix&0xfffff000);
 146         r  =  expf(-z*z-(float)0.5625)*expf((z-x)*(z+x)+R/S);
 147         if(hx>=0) return one-r/x; else return  r/x-one;
 148 }
 149
 150 float
 151 erfcf(float x)
 152 {
 153         int32_t hx,ix;
 154         float R,S,P,Q,s,y,z,r;
 155         GET_FLOAT_WORD(hx,x);
 156         ix = hx&0x7fffffff;
 157         if(ix>=0x7f800000) {                    /* erfc(nan)=nan */
 158                                                 /* erfc(+-inf)=0,2 */
 159             return (float)(((u_int32_t)hx>>31)<<1)+one/x;
 160         }
 161
 162         if(ix < 0x3f580000) {           /* |x|<0.84375 */
 163             if(ix < 0x23800000)         /* |x|<2**-56 */
 164                 return one-x;
 165             z = x*x;
 166             r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
 167             s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
 168             y = r/s;
 169             if(hx < 0x3e800000) {       /* x<1/4 */
 170                 return one-(x+x*y);
 171             } else {
 172                 r = x*y;
 173                 r += (x-half);
 174                 return half - r ;
 175             }
 176         }
 177         if(ix < 0x3fa00000) {           /* 0.84375 <= |x| < 1.25 */
 178             s = fabsf(x)-one;
 179             P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
 180             Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
 181             if(hx>=0) {
 182                 z  = one-erx; return z - P/Q;
 183             } else {
 184                 z = erx+P/Q; return one+z;
 185             }
 186         }
 187         if (ix < 0x41e00000) {          /* |x|<28 */
 188             x = fabsf(x);
 189             s = one/(x*x);
 190             if(ix< 0x4036DB6D) {        /* |x| < 1/.35 ~ 2.857143*/
 191                 R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
 192                                 ra5+s*(ra6+s*ra7))))));
 193                 S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
 194                                 sa5+s*(sa6+s*(sa7+s*sa8)))))));
 195             } else {                    /* |x| >= 1/.35 ~ 2.857143 */
 196                 if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */
 197                 R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
 198                                 rb5+s*rb6)))));
 199                 S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
 200                                 sb5+s*(sb6+s*sb7))))));
 201             }
 202             GET_FLOAT_WORD(ix,x);
 203             SET_FLOAT_WORD(z,ix&0xfffff000);
 204             r  =  expf(-z*z-(float)0.5625)*
 205                         expf((z-x)*(z+x)+R/S);
 206             if(hx>0) return r/x; else return two-r/x;
 207         } else {
 208             if(hx>0) return tiny*tiny; else return two-tiny;
 209         }
 210 }