nsz Git - libm/blob - src/math/erff.c

   1 /* origin: FreeBSD /usr/src/lib/msun/src/s_erff.c */
   2 /*
   3  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
   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 "libm.h"
  17
  18 static const float
  19 tiny = 1e-30,
  20 half =  5.0000000000e-01, /* 0x3F000000 */
  21 one  =  1.0000000000e+00, /* 0x3F800000 */
  22 two  =  2.0000000000e+00, /* 0x40000000 */
  23 /* c = (subfloat)0.84506291151 */
  24 erx  =  8.4506291151e-01, /* 0x3f58560b */
  25 /*
  26  * Coefficients for approximation to  erf on [0,0.84375]
  27  */
  28 efx  =  1.2837916613e-01, /* 0x3e0375d4 */
  29 efx8 =  1.0270333290e+00, /* 0x3f8375d4 */
  30 pp0  =  1.2837916613e-01, /* 0x3e0375d4 */
  31 pp1  = -3.2504209876e-01, /* 0xbea66beb */
  32 pp2  = -2.8481749818e-02, /* 0xbce9528f */
  33 pp3  = -5.7702702470e-03, /* 0xbbbd1489 */
  34 pp4  = -2.3763017452e-05, /* 0xb7c756b1 */
  35 qq1  =  3.9791721106e-01, /* 0x3ecbbbce */
  36 qq2  =  6.5022252500e-02, /* 0x3d852a63 */
  37 qq3  =  5.0813062117e-03, /* 0x3ba68116 */
  38 qq4  =  1.3249473704e-04, /* 0x390aee49 */
  39 qq5  = -3.9602282413e-06, /* 0xb684e21a */
  40 /*
  41  * Coefficients for approximation to  erf  in [0.84375,1.25]
  42  */
  43 pa0  = -2.3621185683e-03, /* 0xbb1acdc6 */
  44 pa1  =  4.1485610604e-01, /* 0x3ed46805 */
  45 pa2  = -3.7220788002e-01, /* 0xbebe9208 */
  46 pa3  =  3.1834661961e-01, /* 0x3ea2fe54 */
  47 pa4  = -1.1089469492e-01, /* 0xbde31cc2 */
  48 pa5  =  3.5478305072e-02, /* 0x3d1151b3 */
  49 pa6  = -2.1663755178e-03, /* 0xbb0df9c0 */
  50 qa1  =  1.0642088205e-01, /* 0x3dd9f331 */
  51 qa2  =  5.4039794207e-01, /* 0x3f0a5785 */
  52 qa3  =  7.1828655899e-02, /* 0x3d931ae7 */
  53 qa4  =  1.2617121637e-01, /* 0x3e013307 */
  54 qa5  =  1.3637083583e-02, /* 0x3c5f6e13 */
  55 qa6  =  1.1984500103e-02, /* 0x3c445aa3 */
  56 /*
  57  * Coefficients for approximation to  erfc in [1.25,1/0.35]
  58  */
  59 ra0  = -9.8649440333e-03, /* 0xbc21a093 */
  60 ra1  = -6.9385856390e-01, /* 0xbf31a0b7 */
  61 ra2  = -1.0558626175e+01, /* 0xc128f022 */
  62 ra3  = -6.2375331879e+01, /* 0xc2798057 */
  63 ra4  = -1.6239666748e+02, /* 0xc322658c */
  64 ra5  = -1.8460508728e+02, /* 0xc3389ae7 */
  65 ra6  = -8.1287437439e+01, /* 0xc2a2932b */
  66 ra7  = -9.8143291473e+00, /* 0xc11d077e */
  67 sa1  =  1.9651271820e+01, /* 0x419d35ce */
  68 sa2  =  1.3765776062e+02, /* 0x4309a863 */
  69 sa3  =  4.3456588745e+02, /* 0x43d9486f */
  70 sa4  =  6.4538726807e+02, /* 0x442158c9 */
  71 sa5  =  4.2900814819e+02, /* 0x43d6810b */
  72 sa6  =  1.0863500214e+02, /* 0x42d9451f */
  73 sa7  =  6.5702495575e+00, /* 0x40d23f7c */
  74 sa8  = -6.0424413532e-02, /* 0xbd777f97 */
  75 /*
  76  * Coefficients for approximation to  erfc in [1/.35,28]
  77  */
  78 rb0  = -9.8649431020e-03, /* 0xbc21a092 */
  79 rb1  = -7.9928326607e-01, /* 0xbf4c9dd4 */
  80 rb2  = -1.7757955551e+01, /* 0xc18e104b */
  81 rb3  = -1.6063638306e+02, /* 0xc320a2ea */
  82 rb4  = -6.3756646729e+02, /* 0xc41f6441 */
  83 rb5  = -1.0250950928e+03, /* 0xc480230b */
  84 rb6  = -4.8351919556e+02, /* 0xc3f1c275 */
  85 sb1  =  3.0338060379e+01, /* 0x41f2b459 */
  86 sb2  =  3.2579251099e+02, /* 0x43a2e571 */
  87 sb3  =  1.5367296143e+03, /* 0x44c01759 */
  88 sb4  =  3.1998581543e+03, /* 0x4547fdbb */
  89 sb5  =  2.5530502930e+03, /* 0x451f90ce */
  90 sb6  =  4.7452853394e+02, /* 0x43ed43a7 */
  91 sb7  = -2.2440952301e+01; /* 0xc1b38712 */
  92
  93 float erff(float x)
  94 {
  95         int32_t hx,ix,i;
  96         float R,S,P,Q,s,y,z,r;
  97
  98         GET_FLOAT_WORD(hx, x);
  99         ix = hx & 0x7fffffff;
 100         if (ix >= 0x7f800000) {
 101                 /* erf(nan)=nan, erf(+-inf)=+-1 */
 102                 i = ((uint32_t)hx>>31)<<1;
 103                 return (float)(1-i)+one/x;
 104         }
 105         if (ix < 0x3f580000) {  /* |x| < 0.84375 */
 106                 if (ix < 0x31800000) {  /* |x| < 2**-28 */
 107                         if (ix < 0x04000000)
 108                                 /*avoid underflow */
 109                                 return (float)0.125*((float)8.0*x+efx8*x);
 110                         return x + efx*x;
 111                 }
 112                 z = x*x;
 113                 r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
 114                 s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
 115                 y = r/s;
 116                 return x + x*y;
 117         }
 118         if (ix < 0x3fa00000) {  /* 0.84375 <= |x| < 1.25 */
 119                 s = fabsf(x)-one;
 120                 P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
 121                 Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
 122                 if (hx >= 0)
 123                         return erx + P/Q;
 124                 return -erx - P/Q;
 125         }
 126         if (ix >= 0x40c00000) {  /* inf > |x| >= 6 */
 127                 if (hx >= 0)
 128                         return one - tiny;
 129                 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)
 148                 return one - r/x;
 149         return  r/x - one;
 150 }
 151
 152 float erfcf(float x)
 153 {
 154         int32_t hx,ix;
 155         float R,S,P,Q,s,y,z,r;
 156
 157         GET_FLOAT_WORD(hx, x);
 158         ix = hx & 0x7fffffff;
 159         if (ix >= 0x7f800000) {
 160                 /* erfc(nan)=nan, erfc(+-inf)=0,2 */
 161                 return (float)(((uint32_t)hx>>31)<<1) + one/x;
 162         }
 163
 164         if (ix < 0x3f580000) {  /* |x| < 0.84375 */
 165                 if (ix < 0x23800000)  /* |x| < 2**-56 */
 166                         return one - x;
 167                 z = x*x;
 168                 r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
 169                 s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
 170                 y = r/s;
 171                 if (hx < 0x3e800000) {  /* x<1/4 */
 172                         return one - (x+x*y);
 173                 } else {
 174                         r = x*y;
 175                         r += (x-half);
 176                         return half - r ;
 177                 }
 178         }
 179         if (ix < 0x3fa00000) {  /* 0.84375 <= |x| < 1.25 */
 180                 s = fabsf(x)-one;
 181                 P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
 182                 Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
 183                 if(hx >= 0) {
 184                         z = one - erx;
 185                         return z - P/Q;
 186                 } else {
 187                         z = erx + P/Q;
 188                         return one + z;
 189                 }
 190         }
 191         if (ix < 0x41e00000) {  /* |x| < 28 */
 192                 x = fabsf(x);
 193                 s = one/(x*x);
 194                 if (ix < 0x4036DB6D) {  /* |x| < 1/.35 ~ 2.857143*/
 195                         R = ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
 196                              ra5+s*(ra6+s*ra7))))));
 197                         S = one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
 198                              sa5+s*(sa6+s*(sa7+s*sa8)))))));
 199                 } else {                /* |x| >= 1/.35 ~ 2.857143 */
 200                         if (hx < 0 && ix >= 0x40c00000) /* x < -6 */
 201                                 return two-tiny;
 202                         R = rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
 203                              rb5+s*rb6)))));
 204                         S = one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
 205                              sb5+s*(sb6+s*sb7))))));
 206                 }
 207                 GET_FLOAT_WORD(ix, x);
 208                 SET_FLOAT_WORD(z, ix&0xfffff000);
 209                 r = expf(-z*z - (float)0.5625) * expf((z-x)*(z+x) + R/S);
 210                 if (hx > 0)
 211                         return r/x;
 212                 return two - r/x;
 213         }
 214         if (hx > 0)
 215                 return tiny*tiny;
 216         return two - tiny;
 217 }