toolchain/gcc/newlib/libm/math/sf_erf.c

   1 /* sf_erf.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 "fdlibm.h"
  17
  18 #ifdef __v810__
  19 #define const
  20 #endif
  21
  22 #ifdef __STDC__
  23 static const float
  24 #else
  25 static float
  26 #endif
  27 tiny        = 1e-30,
  28 half=  5.0000000000e-01, /* 0x3F000000 */
  29 one =  1.0000000000e+00, /* 0x3F800000 */
  30 two =  2.0000000000e+00, /* 0x40000000 */
  31         /* c = (subfloat)0.84506291151 */
  32 erx =  8.4506291151e-01, /* 0x3f58560b */
  33 /*
  34  * Coefficients for approximation to  erf on [0,0.84375]
  35  */
  36 efx =  1.2837916613e-01, /* 0x3e0375d4 */
  37 efx8=  1.0270333290e+00, /* 0x3f8375d4 */
  38 pp0  =  1.2837916613e-01, /* 0x3e0375d4 */
  39 pp1  = -3.2504209876e-01, /* 0xbea66beb */
  40 pp2  = -2.8481749818e-02, /* 0xbce9528f */
  41 pp3  = -5.7702702470e-03, /* 0xbbbd1489 */
  42 pp4  = -2.3763017452e-05, /* 0xb7c756b1 */
  43 qq1  =  3.9791721106e-01, /* 0x3ecbbbce */
  44 qq2  =  6.5022252500e-02, /* 0x3d852a63 */
  45 qq3  =  5.0813062117e-03, /* 0x3ba68116 */
  46 qq4  =  1.3249473704e-04, /* 0x390aee49 */
  47 qq5  = -3.9602282413e-06, /* 0xb684e21a */
  48 /*
  49  * Coefficients for approximation to  erf  in [0.84375,1.25]
  50  */
  51 pa0  = -2.3621185683e-03, /* 0xbb1acdc6 */
  52 pa1  =  4.1485610604e-01, /* 0x3ed46805 */
  53 pa2  = -3.7220788002e-01, /* 0xbebe9208 */
  54 pa3  =  3.1834661961e-01, /* 0x3ea2fe54 */
  55 pa4  = -1.1089469492e-01, /* 0xbde31cc2 */
  56 pa5  =  3.5478305072e-02, /* 0x3d1151b3 */
  57 pa6  = -2.1663755178e-03, /* 0xbb0df9c0 */
  58 qa1  =  1.0642088205e-01, /* 0x3dd9f331 */
  59 qa2  =  5.4039794207e-01, /* 0x3f0a5785 */
  60 qa3  =  7.1828655899e-02, /* 0x3d931ae7 */
  61 qa4  =  1.2617121637e-01, /* 0x3e013307 */
  62 qa5  =  1.3637083583e-02, /* 0x3c5f6e13 */
  63 qa6  =  1.1984500103e-02, /* 0x3c445aa3 */
  64 /*
  65  * Coefficients for approximation to  erfc in [1.25,1/0.35]
  66  */
  67 ra0  = -9.8649440333e-03, /* 0xbc21a093 */
  68 ra1  = -6.9385856390e-01, /* 0xbf31a0b7 */
  69 ra2  = -1.0558626175e+01, /* 0xc128f022 */
  70 ra3  = -6.2375331879e+01, /* 0xc2798057 */
  71 ra4  = -1.6239666748e+02, /* 0xc322658c */
  72 ra5  = -1.8460508728e+02, /* 0xc3389ae7 */
  73 ra6  = -8.1287437439e+01, /* 0xc2a2932b */
  74 ra7  = -9.8143291473e+00, /* 0xc11d077e */
  75 sa1  =  1.9651271820e+01, /* 0x419d35ce */
  76 sa2  =  1.3765776062e+02, /* 0x4309a863 */
  77 sa3  =  4.3456588745e+02, /* 0x43d9486f */
  78 sa4  =  6.4538726807e+02, /* 0x442158c9 */
  79 sa5  =  4.2900814819e+02, /* 0x43d6810b */
  80 sa6  =  1.0863500214e+02, /* 0x42d9451f */
  81 sa7  =  6.5702495575e+00, /* 0x40d23f7c */
  82 sa8  = -6.0424413532e-02, /* 0xbd777f97 */
  83 /*
  84  * Coefficients for approximation to  erfc in [1/.35,28]
  85  */
  86 rb0  = -9.8649431020e-03, /* 0xbc21a092 */
  87 rb1  = -7.9928326607e-01, /* 0xbf4c9dd4 */
  88 rb2  = -1.7757955551e+01, /* 0xc18e104b */
  89 rb3  = -1.6063638306e+02, /* 0xc320a2ea */
  90 rb4  = -6.3756646729e+02, /* 0xc41f6441 */
  91 rb5  = -1.0250950928e+03, /* 0xc480230b */
  92 rb6  = -4.8351919556e+02, /* 0xc3f1c275 */
  93 sb1  =  3.0338060379e+01, /* 0x41f2b459 */
  94 sb2  =  3.2579251099e+02, /* 0x43a2e571 */
  95 sb3  =  1.5367296143e+03, /* 0x44c01759 */
  96 sb4  =  3.1998581543e+03, /* 0x4547fdbb */
  97 sb5  =  2.5530502930e+03, /* 0x451f90ce */
  98 sb6  =  4.7452853394e+02, /* 0x43ed43a7 */
  99 sb7  = -2.2440952301e+01; /* 0xc1b38712 */
 100
 101 #ifdef __STDC__
 102         float erff(float x)
 103 #else
 104         float erff(x)
 105         float x;
 106 #endif
 107 {
 108         __int32_t hx,ix,i;
 109         float R,S,P,Q,s,y,z,r;
 110         GET_FLOAT_WORD(hx,x);
 111         ix = hx&0x7fffffff;
 112         if(!FLT_UWORD_IS_FINITE(ix)) {          /* erf(nan)=nan */
 113             i = ((__uint32_t)hx>>31)<<1;
 114             return (float)(1-i)+one/x;  /* erf(+-inf)=+-1 */
 115         }
 116
 117         if(ix < 0x3f580000) {           /* |x|<0.84375 */
 118             if(ix < 0x31800000) {       /* |x|<2**-28 */
 119                 if (ix < 0x04000000)
 120                     /*avoid underflow */
 121                     return (float)0.125*((float)8.0*x+efx8*x);
 122                 return x + efx*x;
 123             }
 124             z = x*x;
 125             r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
 126             s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
 127             y = r/s;
 128             return x + x*y;
 129         }
 130         if(ix < 0x3fa00000) {           /* 0.84375 <= |x| < 1.25 */
 131             s = fabsf(x)-one;
 132             P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
 133             Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
 134             if(hx>=0) return erx + P/Q; else return -erx - P/Q;
 135         }
 136         if (ix >= 0x40c00000) {         /* inf>|x|>=6 */
 137             if(hx>=0) return one-tiny; else return tiny-one;
 138         }
 139         x = fabsf(x);
 140         s = one/(x*x);
 141         if(ix< 0x4036DB6E) {    /* |x| < 1/0.35 */
 142             R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
 143                                 ra5+s*(ra6+s*ra7))))));
 144             S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
 145                                 sa5+s*(sa6+s*(sa7+s*sa8)))))));
 146         } else {        /* |x| >= 1/0.35 */
 147             R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
 148                                 rb5+s*rb6)))));
 149             S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
 150                                 sb5+s*(sb6+s*sb7))))));
 151         }
 152         GET_FLOAT_WORD(ix,x);
 153         SET_FLOAT_WORD(z,ix&0xfffff000);
 154         r  =  __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S);
 155         if(hx>=0) return one-r/x; else return  r/x-one;
 156 }
 157
 158 #ifdef __STDC__
 159         float erfcf(float x)
 160 #else
 161         float erfcf(x)
 162         float x;
 163 #endif
 164 {
 165         __int32_t hx,ix;
 166         float R,S,P,Q,s,y,z,r;
 167         GET_FLOAT_WORD(hx,x);
 168         ix = hx&0x7fffffff;
 169         if(!FLT_UWORD_IS_FINITE(ix)) {                  /* erfc(nan)=nan */
 170                                                 /* erfc(+-inf)=0,2 */
 171             return (float)(((__uint32_t)hx>>31)<<1)+one/x;
 172         }
 173
 174         if(ix < 0x3f580000) {           /* |x|<0.84375 */
 175             if(ix < 0x23800000)         /* |x|<2**-56 */
 176                 return one-x;
 177             z = x*x;
 178             r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
 179             s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
 180             y = r/s;
 181             if(hx < 0x3e800000) {       /* x<1/4 */
 182                 return one-(x+x*y);
 183             } else {
 184                 r = x*y;
 185                 r += (x-half);
 186                 return half - r ;
 187             }
 188         }
 189         if(ix < 0x3fa00000) {           /* 0.84375 <= |x| < 1.25 */
 190             s = fabsf(x)-one;
 191             P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
 192             Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
 193             if(hx>=0) {
 194                 z  = one-erx; return z - P/Q;
 195             } else {
 196                 z = erx+P/Q; return one+z;
 197             }
 198         }
 199         if (ix < 0x41e00000) {          /* |x|<28 */
 200             x = fabsf(x);
 201             s = one/(x*x);
 202             if(ix< 0x4036DB6D) {        /* |x| < 1/.35 ~ 2.857143*/
 203                 R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
 204                                 ra5+s*(ra6+s*ra7))))));
 205                 S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
 206                                 sa5+s*(sa6+s*(sa7+s*sa8)))))));
 207             } else {                    /* |x| >= 1/.35 ~ 2.857143 */
 208                 if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */
 209                 R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
 210                                 rb5+s*rb6)))));
 211                 S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
 212                                 sb5+s*(sb6+s*sb7))))));
 213             }
 214             GET_FLOAT_WORD(ix,x);
 215             SET_FLOAT_WORD(z,ix&0xfffff000);
 216             r  =  __ieee754_expf(-z*z-(float)0.5625)*
 217                         __ieee754_expf((z-x)*(z+x)+R/S);
 218             if(hx>0) return r/x; else return two-r/x;
 219         } else {
 220             if(hx>0) return tiny*tiny; else return two-tiny;
 221         }
 222 }
 223
 224 #ifdef _DOUBLE_IS_32BITS
 225
 226 #ifdef __STDC__
 227         double erf(double x)
 228 #else
 229         double erf(x)
 230         double x;
 231 #endif
 232 {
 233         return (double) erff((float) x);
 234 }
 235
 236 #ifdef __STDC__
 237         double erfc(double x)
 238 #else
 239         double erfc(x)
 240         double x;
 241 #endif
 242 {
 243         return (double) erfcf((float) x);
 244 }
 245
 246 #endif /* defined(_DOUBLE_IS_32BITS) */