/* s_erff.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 <sys/cdefs.h>
__FBSDID("$FreeBSD$");
#include "math.h"
#include "math_private.h"
static const float
tiny = 1e-30,
half= 5.0000000000e-01, /* 0x3F000000 */
one = 1.0000000000e+00, /* 0x3F800000 */
two = 2.0000000000e+00, /* 0x40000000 */
/*
* Coefficients for approximation to erf on [0,0.84375]
*/
efx = 1.2837916613e-01, /* 0x3e0375d4 */
efx8= 1.0270333290e+00, /* 0x3f8375d4 */
/*
* Domain [0, 0.84375], range ~[-5.4446e-10,5.5197e-10]:
* |(erf(x) - x)/x - p(x)/q(x)| < 2**-31.
*/
pp0 = 1.28379166e-01F, /* 0x1.06eba8p-3 */
pp1 = -3.36030394e-01F, /* -0x1.58185ap-2 */
pp2 = -1.86260219e-03F, /* -0x1.e8451ep-10 */
qq1 = 3.12324286e-01F, /* 0x1.3fd1f0p-2 */
qq2 = 2.16070302e-02F, /* 0x1.620274p-6 */
qq3 = -1.98859419e-03F, /* -0x1.04a626p-9 */
/*
* Domain [0.84375, 1.25], range ~[-1.953e-11,1.940e-11]:
* |(erf(x) - erx) - p(x)/q(x)| < 2**-36.
*/
erx = 8.42697144e-01F, /* 0x1.af7600p-1. erf(1) rounded to 16 bits. */
pa0 = 3.64939137e-06F, /* 0x1.e9d022p-19 */
pa1 = 4.15109694e-01F, /* 0x1.a91284p-2 */
pa2 = -1.65179938e-01F, /* -0x1.5249dcp-3 */
pa3 = 1.10914491e-01F, /* 0x1.c64e46p-4 */
qa1 = 6.02074385e-01F, /* 0x1.344318p-1 */
qa2 = 5.35934687e-01F, /* 0x1.126608p-1 */
qa3 = 1.68576106e-01F, /* 0x1.593e6ep-3 */
qa4 = 5.62181212e-02F, /* 0x1.cc89f2p-5 */
/*
* Domain [1.25,1/0.35], range ~[-7.043e-10,7.457e-10]:
* |log(x*erfc(x)) + x**2 + 0.5625 - r(x)/s(x)| < 2**-30
*/
ra0 = -9.87132732e-03F, /* -0x1.4376b2p-7 */
ra1 = -5.53605914e-01F, /* -0x1.1b723cp-1 */
ra2 = -2.17589188e+00F, /* -0x1.1683a0p+1 */
ra3 = -1.43268085e+00F, /* -0x1.6ec42cp+0 */
sa1 = 5.45995426e+00F, /* 0x1.5d6fe4p+2 */
sa2 = 6.69798088e+00F, /* 0x1.acabb8p+2 */
sa3 = 1.43113089e+00F, /* 0x1.6e5e98p+0 */
sa4 = -5.77397496e-02F, /* -0x1.d90108p-5 */
/*
* Domain [1/0.35, 11], range ~[-2.264e-13,2.336e-13]:
* |log(x*erfc(x)) + x**2 + 0.5625 - r(x)/s(x)| < 2**-42
*/
rb0 = -9.86494310e-03F, /* -0x1.434124p-7 */
rb1 = -6.25171244e-01F, /* -0x1.401672p-1 */
rb2 = -6.16498327e+00F, /* -0x1.8a8f16p+2 */
rb3 = -1.66696873e+01F, /* -0x1.0ab70ap+4 */
rb4 = -9.53764343e+00F, /* -0x1.313460p+3 */
sb1 = 1.26884899e+01F, /* 0x1.96081cp+3 */
sb2 = 4.51839523e+01F, /* 0x1.6978bcp+5 */
sb3 = 4.72810211e+01F, /* 0x1.7a3f88p+5 */
sb4 = 8.93033314e+00F; /* 0x1.1dc54ap+3 */
float
erff(float x)
{
int32_t hx,ix,i;
float R,S,P,Q,s,y,z,r;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>=0x7f800000) { /* erf(nan)=nan */
i = ((u_int32_t)hx>>31)<<1;
return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */
}
if(ix < 0x3f580000) { /* |x|<0.84375 */
if(ix < 0x38800000) { /* |x|<2**-14 */
if (ix < 0x04000000) /* |x|<0x1p-119 */
return (8*x+efx8*x)/8; /* avoid spurious underflow */
return x + efx*x;
}
z = x*x;
r = pp0+z*(pp1+z*pp2);
s = one+z*(qq1+z*(qq2+z*qq3));
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));
Q = one+s*(qa1+s*(qa2+s*(qa3+s*qa4)));
if(hx>=0) return erx + P/Q; else return -erx - P/Q;
}
if (ix >= 0x40800000) { /* inf>|x|>=4 */
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=one+s*(sa1+s*(sa2+s*(sa3+s*sa4)));
} else { /* |x| >= 1/0.35 */
R=rb0+s*(rb1+s*(rb2+s*(rb3+s*rb4)));
S=one+s*(sb1+s*(sb2+s*(sb3+s*sb4)));
}
SET_FLOAT_WORD(z,hx&0xffffe000);
r = expf(-z*z-0.5625F)*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;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>=0x7f800000) { /* erfc(nan)=nan */
/* erfc(+-inf)=0,2 */
return (float)(((u_int32_t)hx>>31)<<1)+one/x;
}
if(ix < 0x3f580000) { /* |x|<0.84375 */
if(ix < 0x33800000) /* |x|<2**-24 */
return one-x;
z = x*x;
r = pp0+z*(pp1+z*pp2);
s = one+z*(qq1+z*(qq2+z*qq3));
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));
Q = one+s*(qa1+s*(qa2+s*(qa3+s*qa4)));
if(hx>=0) {
z = one-erx; return z - P/Q;
} else {
z = erx+P/Q; return one+z;
}
}
if (ix < 0x41300000) { /* |x|<11 */
x = fabsf(x);
s = one/(x*x);
if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/
R=ra0+s*(ra1+s*(ra2+s*ra3));
S=one+s*(sa1+s*(sa2+s*(sa3+s*sa4)));
} else { /* |x| >= 1/.35 ~ 2.857143 */
if(hx<0&&ix>=0x40a00000) return two-tiny;/* x < -5 */
R=rb0+s*(rb1+s*(rb2+s*(rb3+s*rb4)));
S=one+s*(sb1+s*(sb2+s*(sb3+s*sb4)));
}
SET_FLOAT_WORD(z,hx&0xffffe000);
r = expf(-z*z-0.5625F)*expf((z-x)*(z+x)+R/S);
if(hx>0) return r/x; else return two-r/x;
} else {
if(hx>0) return tiny*tiny; else return two-tiny;
}
}