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
  16 #ifndef lint
  17 static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_erff.c,v 1.7 2002/05/28 18:15:04 alfred Exp $";
  18 #endif
  19
  20 #include "math.h"
  21 #include "math_private.h"
  22
  23 static const float
  24 tiny        = 1e-30,
  25 half=  5.0000000000e-01, /* 0x3F000000 */
  26 one =  1.0000000000e+00, /* 0x3F800000 */
  27 two =  2.0000000000e+00, /* 0x40000000 */
  28         /* c = (subfloat)0.84506291151 */
  29 erx =  8.4506291151e-01, /* 0x3f58560b */
  30 /*
  31  * Coefficients for approximation to  erf on [0,0.84375]
  32  */
  33 efx =  1.2837916613e-01, /* 0x3e0375d4 */
  34 efx8=  1.0270333290e+00, /* 0x3f8375d4 */
  35 pp0  =  1.2837916613e-01, /* 0x3e0375d4 */
  36 pp1  = -3.2504209876e-01, /* 0xbea66beb */
  37 pp2  = -2.8481749818e-02, /* 0xbce9528f */
  38 pp3  = -5.7702702470e-03, /* 0xbbbd1489 */
  39 pp4  = -2.3763017452e-05, /* 0xb7c756b1 */
  40 qq1  =  3.9791721106e-01, /* 0x3ecbbbce */
  41 qq2  =  6.5022252500e-02, /* 0x3d852a63 */
  42 qq3  =  5.0813062117e-03, /* 0x3ba68116 */
  43 qq4  =  1.3249473704e-04, /* 0x390aee49 */
  44 qq5  = -3.9602282413e-06, /* 0xb684e21a */
  45 /*
  46  * Coefficients for approximation to  erf  in [0.84375,1.25]
  47  */
  48 pa0  = -2.3621185683e-03, /* 0xbb1acdc6 */
  49 pa1  =  4.1485610604e-01, /* 0x3ed46805 */
  50 pa2  = -3.7220788002e-01, /* 0xbebe9208 */
  51 pa3  =  3.1834661961e-01, /* 0x3ea2fe54 */
  52 pa4  = -1.1089469492e-01, /* 0xbde31cc2 */
  53 pa5  =  3.5478305072e-02, /* 0x3d1151b3 */
  54 pa6  = -2.1663755178e-03, /* 0xbb0df9c0 */
  55 qa1  =  1.0642088205e-01, /* 0x3dd9f331 */
  56 qa2  =  5.4039794207e-01, /* 0x3f0a5785 */
  57 qa3  =  7.1828655899e-02, /* 0x3d931ae7 */
  58 qa4  =  1.2617121637e-01, /* 0x3e013307 */
  59 qa5  =  1.3637083583e-02, /* 0x3c5f6e13 */
  60 qa6  =  1.1984500103e-02, /* 0x3c445aa3 */
  61 /*
  62  * Coefficients for approximation to  erfc in [1.25,1/0.35]
  63  */
  64 ra0  = -9.8649440333e-03, /* 0xbc21a093 */
  65 ra1  = -6.9385856390e-01, /* 0xbf31a0b7 */
  66 ra2  = -1.0558626175e+01, /* 0xc128f022 */
  67 ra3  = -6.2375331879e+01, /* 0xc2798057 */
  68 ra4  = -1.6239666748e+02, /* 0xc322658c */
  69 ra5  = -1.8460508728e+02, /* 0xc3389ae7 */
  70 ra6  = -8.1287437439e+01, /* 0xc2a2932b */
  71 ra7  = -9.8143291473e+00, /* 0xc11d077e */
  72 sa1  =  1.9651271820e+01, /* 0x419d35ce */
  73 sa2  =  1.3765776062e+02, /* 0x4309a863 */
  74 sa3  =  4.3456588745e+02, /* 0x43d9486f */
  75 sa4  =  6.4538726807e+02, /* 0x442158c9 */
  76 sa5  =  4.2900814819e+02, /* 0x43d6810b */
  77 sa6  =  1.0863500214e+02, /* 0x42d9451f */
  78 sa7  =  6.5702495575e+00, /* 0x40d23f7c */
  79 sa8  = -6.0424413532e-02, /* 0xbd777f97 */
  80 /*
  81  * Coefficients for approximation to  erfc in [1/.35,28]
  82  */
  83 rb0  = -9.8649431020e-03, /* 0xbc21a092 */
  84 rb1  = -7.9928326607e-01, /* 0xbf4c9dd4 */
  85 rb2  = -1.7757955551e+01, /* 0xc18e104b */
  86 rb3  = -1.6063638306e+02, /* 0xc320a2ea */
  87 rb4  = -6.3756646729e+02, /* 0xc41f6441 */
  88 rb5  = -1.0250950928e+03, /* 0xc480230b */
  89 rb6  = -4.8351919556e+02, /* 0xc3f1c275 */
  90 sb1  =  3.0338060379e+01, /* 0x41f2b459 */
  91 sb2  =  3.2579251099e+02, /* 0x43a2e571 */
  92 sb3  =  1.5367296143e+03, /* 0x44c01759 */
  93 sb4  =  3.1998581543e+03, /* 0x4547fdbb */
  94 sb5  =  2.5530502930e+03, /* 0x451f90ce */
  95 sb6  =  4.7452853394e+02, /* 0x43ed43a7 */
  96 sb7  = -2.2440952301e+01; /* 0xc1b38712 */
  97
  98 float
  99 erff(float x)
 100 {
 101         int32_t hx,ix,i;
 102         float R,S,P,Q,s,y,z,r;
 103         GET_FLOAT_WORD(hx,x);
 104         ix = hx&0x7fffffff;
 105         if(ix>=0x7f800000) {            /* erf(nan)=nan */
 106             i = ((u_int32_t)hx>>31)<<1;
 107             return (float)(1-i)+one/x;  /* erf(+-inf)=+-1 */
 108         }
 109
 110         if(ix < 0x3f580000) {           /* |x|<0.84375 */
 111             if(ix < 0x31800000) {       /* |x|<2**-28 */
 112                 if (ix < 0x04000000)
 113                     /*avoid underflow */
 114                     return (float)0.125*((float)8.0*x+efx8*x);
 115                 return x + efx*x;
 116             }
 117             z = x*x;
 118             r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
 119             s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
 120             y = r/s;
 121             return x + x*y;
 122         }
 123         if(ix < 0x3fa00000) {           /* 0.84375 <= |x| < 1.25 */
 124             s = fabsf(x)-one;
 125             P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
 126             Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
 127             if(hx>=0) return erx + P/Q; else return -erx - P/Q;
 128         }
 129         if (ix >= 0x40c00000) {         /* inf>|x|>=6 */
 130             if(hx>=0) return one-tiny; else return tiny-one;
 131         }
 132         x = fabsf(x);
 133         s = one/(x*x);
 134         if(ix< 0x4036DB6E) {    /* |x| < 1/0.35 */
 135             R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
 136                                 ra5+s*(ra6+s*ra7))))));
 137             S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
 138                                 sa5+s*(sa6+s*(sa7+s*sa8)))))));
 139         } else {        /* |x| >= 1/0.35 */
 140             R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
 141                                 rb5+s*rb6)))));
 142             S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
 143                                 sb5+s*(sb6+s*sb7))))));
 144         }
 145         GET_FLOAT_WORD(ix,x);
 146         SET_FLOAT_WORD(z,ix&0xfffff000);
 147         r  =  __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S);
 148         if(hx>=0) return one-r/x; else return  r/x-one;
 149 }
 150
 151 float
 152 erfcf(float x)
 153 {
 154         int32_t hx,ix;
 155         float R,S,P,Q,s,y,z,r;
 156         GET_FLOAT_WORD(hx,x);
 157         ix = hx&0x7fffffff;
 158         if(ix>=0x7f800000) {                    /* erfc(nan)=nan */
 159                                                 /* erfc(+-inf)=0,2 */
 160             return (float)(((u_int32_t)hx>>31)<<1)+one/x;
 161         }
 162
 163         if(ix < 0x3f580000) {           /* |x|<0.84375 */
 164             if(ix < 0x23800000)         /* |x|<2**-56 */
 165                 return one-x;
 166             z = x*x;
 167             r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
 168             s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
 169             y = r/s;
 170             if(hx < 0x3e800000) {       /* x<1/4 */
 171                 return one-(x+x*y);
 172             } else {
 173                 r = x*y;
 174                 r += (x-half);
 175                 return half - r ;
 176             }
 177         }
 178         if(ix < 0x3fa00000) {           /* 0.84375 <= |x| < 1.25 */
 179             s = fabsf(x)-one;
 180             P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
 181             Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
 182             if(hx>=0) {
 183                 z  = one-erx; return z - P/Q;
 184             } else {
 185                 z = erx+P/Q; return one+z;
 186             }
 187         }
 188         if (ix < 0x41e00000) {          /* |x|<28 */
 189             x = fabsf(x);
 190             s = one/(x*x);
 191             if(ix< 0x4036DB6D) {        /* |x| < 1/.35 ~ 2.857143*/
 192                 R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
 193                                 ra5+s*(ra6+s*ra7))))));
 194                 S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
 195                                 sa5+s*(sa6+s*(sa7+s*sa8)))))));
 196             } else {                    /* |x| >= 1/.35 ~ 2.857143 */
 197                 if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */
 198                 R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
 199                                 rb5+s*rb6)))));
 200                 S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
 201                                 sb5+s*(sb6+s*sb7))))));
 202             }
 203             GET_FLOAT_WORD(ix,x);
 204             SET_FLOAT_WORD(z,ix&0xfffff000);
 205             r  =  __ieee754_expf(-z*z-(float)0.5625)*
 206                         __ieee754_expf((z-x)*(z+x)+R/S);
 207             if(hx>0) return r/x; else return two-r/x;
 208         } else {
 209             if(hx>0) return tiny*tiny; else return two-tiny;
 210         }
 211 }