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sf_erf.c

/* sf_erf.c -- float version of s_erf.c.
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */

/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 */

/*
#include "fdlibm.h"
*/
#include <math.h>
#include <stdint.h>
#include <errno.h>

#define __ieee754_expf expf

00025 typedef union
{
  float value;
  uint32_t word;
} ieee_float_shape_type;

/* Get a 32 bit int from a float.  */

static inline int
__get_float_word(float d)
{
  ieee_float_shape_type u;
  u.value = d;
  return u.word;
}

/* Set a float from a 32 bit int.  */

#define SET_FLOAT_WORD(d,i)               \
do {                                \
  ieee_float_shape_type sf_u;             \
  sf_u.word = (i);                        \
  (d) = sf_u.value;                       \
} while (0)

static inline void __trunc_float_word(float * x)
{
  ieee_float_shape_type u;
  u.value = * x;
  u.word &= 0xfffff000;
}

#ifdef __v810__
#define const
#endif

static const float
  tiny= 1e-30,
  half=  5.0000000000e-01, /* 0x3F000000 */
  one =  1.0000000000e+00, /* 0x3F800000 */
  two =  2.0000000000e+00, /* 0x40000000 */
      /* c = (subfloat)0.84506291151 */
  erx =  8.4506291151e-01, /* 0x3f58560b */
  /*
   * Coefficients for approximation to  erf on [0,0.84375]
   */
  efx =  1.2837916613e-01, /* 0x3e0375d4 */
  efx8=  1.0270333290e+00, /* 0x3f8375d4 */
  pp0 =  1.2837916613e-01, /* 0x3e0375d4 */
  pp1 = -3.2504209876e-01, /* 0xbea66beb */
  pp2 = -2.8481749818e-02, /* 0xbce9528f */
  pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
  pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
  qq1 =  3.9791721106e-01, /* 0x3ecbbbce */
  qq2 =  6.5022252500e-02, /* 0x3d852a63 */
  qq3 =  5.0813062117e-03, /* 0x3ba68116 */
  qq4 =  1.3249473704e-04, /* 0x390aee49 */
  qq5 = -3.9602282413e-06, /* 0xb684e21a */
  /*
   * Coefficients for approximation to  erf  in [0.84375,1.25] 
   */
  pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
  pa1 =  4.1485610604e-01, /* 0x3ed46805 */
  pa2 = -3.7220788002e-01, /* 0xbebe9208 */
  pa3 =  3.1834661961e-01, /* 0x3ea2fe54 */
  pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
  pa5 =  3.5478305072e-02, /* 0x3d1151b3 */
  pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
  qa1 =  1.0642088205e-01, /* 0x3dd9f331 */
  qa2 =  5.4039794207e-01, /* 0x3f0a5785 */
  qa3 =  7.1828655899e-02, /* 0x3d931ae7 */
  qa4 =  1.2617121637e-01, /* 0x3e013307 */
  qa5 =  1.3637083583e-02, /* 0x3c5f6e13 */
  qa6 =  1.1984500103e-02, /* 0x3c445aa3 */
  /*
   * Coefficients for approximation to  erfc in [1.25,1/0.35]
   */
  ra0 = -9.8649440333e-03, /* 0xbc21a093 */
  ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
  ra2 = -1.0558626175e+01, /* 0xc128f022 */
  ra3 = -6.2375331879e+01, /* 0xc2798057 */
  ra4 = -1.6239666748e+02, /* 0xc322658c */
  ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
  ra6 = -8.1287437439e+01, /* 0xc2a2932b */
  ra7 = -9.8143291473e+00, /* 0xc11d077e */
  sa1 =  1.9651271820e+01, /* 0x419d35ce */
  sa2 =  1.3765776062e+02, /* 0x4309a863 */
  sa3 =  4.3456588745e+02, /* 0x43d9486f */
  sa4 =  6.4538726807e+02, /* 0x442158c9 */
  sa5 =  4.2900814819e+02, /* 0x43d6810b */
  sa6 =  1.0863500214e+02, /* 0x42d9451f */
  sa7 =  6.5702495575e+00, /* 0x40d23f7c */
  sa8 = -6.0424413532e-02, /* 0xbd777f97 */
  /*
   * Coefficients for approximation to  erfc in [1/.35,28]
   */
  rb0 = -9.8649431020e-03, /* 0xbc21a092 */
  rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
  rb2 = -1.7757955551e+01, /* 0xc18e104b */
  rb3 = -1.6063638306e+02, /* 0xc320a2ea */
  rb4 = -6.3756646729e+02, /* 0xc41f6441 */
  rb5 = -1.0250950928e+03, /* 0xc480230b */
  rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
  sb1 =  3.0338060379e+01, /* 0x41f2b459 */
  sb2 =  3.2579251099e+02, /* 0x43a2e571 */
  sb3 =  1.5367296143e+03, /* 0x44c01759 */
  sb4 =  3.1998581543e+03, /* 0x4547fdbb */
  sb5 =  2.5530502930e+03, /* 0x451f90ce */
  sb6 =  4.7452853394e+02, /* 0x43ed43a7 */
  sb7 = -2.2440952301e+01; /* 0xc1b38712 */

float erff(float x)
{
      int32_t hx, ix, i;
      float R, S, P, Q, s, y, z, r;
      hx = __get_float_word(x);
      ix = hx & 0x7fffffff;
      if (!(ix<0x7f800000L)) {      /* erf(nan)=nan */
          i = ((uint32_t)hx>>31)<<1;
          return (float)(1-i)+one/x;      /* erf(+-inf)=+-1 */
      }

      if (ix < 0x3f580000) {        /* |x|<0.84375 */
          if (ix < 0x31800000) {    /* |x|<2**-28 */
            if (ix < 0x04000000)
                /*avoid underflow */
                return (float)0.125*((float)8.0*x+efx8*x);
            return x + efx*x;
          }
          z = x*x;
          r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
          s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
          y = r/s;
          return x + x*y;
      }
      if (ix < 0x3fa00000) {        /* 0.84375 <= |x| < 1.25 */
          s = fabsf(x)-one;
          P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
          Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
          if (hx >= 0)
            return erx + P/Q;
          else
            return -erx - P/Q;
      }
      if (ix >= 0x40c00000) {       /* inf>|x|>=6 */
          if (hx >= 0)
            return one-tiny;
          else
            return tiny-one;
      }
      x = fabsf(x);
      s = one/(x*x);
      if (ix< 0x4036DB6E) {   /* |x| < 1/0.35 */
          R = ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
                        ra5+s*(ra6+s*ra7))))));
          S = one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
                        sa5+s*(sa6+s*(sa7+s*sa8)))))));
      } else {    /* |x| >= 1/0.35 */
          R = rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
                        rb5+s*rb6)))));
          S = one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
                        sb5+s*(sb6+s*sb7))))));
      }

      z = x;
      __trunc_float_word (&z);
      r = __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S);
      if (hx >= 0)
        return one-r/x;
      else
        return  r/x-one;
}

float erfcf(float x)
{
      int32_t hx, ix;
      float R, S, P, Q, s, y, z, r;
      hx = __get_float_word(x);
      ix = hx & 0x7fffffff;
      if (!(ix < 0x7f800000L)) {          /* erfc(nan)=nan */
                                    /* erfc(+-inf)=0,2 */
          return (float)(((uint32_t)hx>>31)<<1)+one/x;
      }

      if (ix < 0x3f580000) {        /* |x|<0.84375 */
          if (ix < 0x23800000)      /* |x|<2**-56 */
            return one-x;
          z = x*x;
          r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
          s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
          y = r/s;
          if (hx < 0x3e800000) {    /* x<1/4 */
            return one-(x+x*y);
          } else {
            r = x*y;
            r += (x-half);
            return half - r ;
          }
      }
      if (ix < 0x3fa00000) {        /* 0.84375 <= |x| < 1.25 */
          s = fabsf(x)-one;
          P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
          Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
          if (hx >= 0) {
              z  = one-erx; return z - P/Q; 
          } else {
            z = erx+P/Q; return one+z;
          }
      }

      if (ix < 0x41e00000) {        /* |x|<28 */
          x = fabsf(x);
          s = one/(x*x);
          if (ix< 0x4036DB6D) {     /* |x| < 1/.35 ~ 2.857143*/
              R = ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
                        ra5+s*(ra6+s*ra7))))));
              S = one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
                        sa5+s*(sa6+s*(sa7+s*sa8)))))));
          } else {                  /* |x| >= 1/.35 ~ 2.857143 */
            if (hx < 0 && ix >= 0x40c00000)
              return two-tiny;/* x < -6 */
            R = rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
                        rb5+s*rb6)))));
            S = one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
                        sb5+s*(sb6+s*sb7))))));
          }

          z = x;
          __trunc_float_word (&z);
          r = __ieee754_expf(-z*z-(float)0.5625)*
                  __ieee754_expf((z-x)*(z+x)+R/S);
          if (hx > 0)
            return r/x;
          else
            return two-r/x;
      } else {
          /* set range error */
            errno = ERANGE;
          if (hx > 0)
            return tiny*tiny;
          else
            return two-tiny;
      }
}

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