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