gonzui

    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: }