/* 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

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;
	}
}