| /* 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; |
| } |
| } |