12116Sjkh/* s_erff.c -- float version of s_erf.c. 22116Sjkh * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 32116Sjkh */ 42116Sjkh 52116Sjkh/* 62116Sjkh * ==================================================== 72116Sjkh * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 82116Sjkh * 92116Sjkh * Developed at SunPro, a Sun Microsystems, Inc. business. 102116Sjkh * Permission to use, copy, modify, and distribute this 118870Srgrimes * software is freely granted, provided that this notice 122116Sjkh * is preserved. 132116Sjkh * ==================================================== 142116Sjkh */ 152116Sjkh 16176451Sdas#include <sys/cdefs.h> 17176451Sdas__FBSDID("$FreeBSD$"); 182116Sjkh 192116Sjkh#include "math.h" 202116Sjkh#include "math_private.h" 212116Sjkh 222116Sjkhstatic const float 232116Sjkhtiny = 1e-30, 242116Sjkhhalf= 5.0000000000e-01, /* 0x3F000000 */ 252116Sjkhone = 1.0000000000e+00, /* 0x3F800000 */ 262116Sjkhtwo = 2.0000000000e+00, /* 0x40000000 */ 272116Sjkh/* 28254969Skargl * Coefficients for approximation to erf on [0,0.84375] 292116Sjkh */ 302116Sjkhefx = 1.2837916613e-01, /* 0x3e0375d4 */ 312116Sjkhefx8= 1.0270333290e+00, /* 0x3f8375d4 */ 322116Sjkh/* 33254969Skargl * Domain [0, 0.84375], range ~[-5.4446e-10,5.5197e-10]: 34254969Skargl * |(erf(x) - x)/x - p(x)/q(x)| < 2**-31. 352116Sjkh */ 36254969Skarglpp0 = 1.28379166e-01F, /* 0x1.06eba8p-3 */ 37254969Skarglpp1 = -3.36030394e-01F, /* -0x1.58185ap-2 */ 38254969Skarglpp2 = -1.86260219e-03F, /* -0x1.e8451ep-10 */ 39254969Skarglqq1 = 3.12324286e-01F, /* 0x1.3fd1f0p-2 */ 40254969Skarglqq2 = 2.16070302e-02F, /* 0x1.620274p-6 */ 41254969Skarglqq3 = -1.98859419e-03F, /* -0x1.04a626p-9 */ 422116Sjkh/* 43254969Skargl * Domain [0.84375, 1.25], range ~[-1.953e-11,1.940e-11]: 44254969Skargl * |(erf(x) - erx) - p(x)/q(x)| < 2**-36. 452116Sjkh */ 46254969Skarglerx = 8.42697144e-01F, /* 0x1.af7600p-1. erf(1) rounded to 16 bits. */ 47254969Skarglpa0 = 3.64939137e-06F, /* 0x1.e9d022p-19 */ 48254969Skarglpa1 = 4.15109694e-01F, /* 0x1.a91284p-2 */ 49254969Skarglpa2 = -1.65179938e-01F, /* -0x1.5249dcp-3 */ 50254969Skarglpa3 = 1.10914491e-01F, /* 0x1.c64e46p-4 */ 51254969Skarglqa1 = 6.02074385e-01F, /* 0x1.344318p-1 */ 52254969Skarglqa2 = 5.35934687e-01F, /* 0x1.126608p-1 */ 53254969Skarglqa3 = 1.68576106e-01F, /* 0x1.593e6ep-3 */ 54254969Skarglqa4 = 5.62181212e-02F, /* 0x1.cc89f2p-5 */ 552116Sjkh/* 56254969Skargl * Domain [1.25,1/0.35], range ~[-7.043e-10,7.457e-10]: 57254969Skargl * |log(x*erfc(x)) + x**2 + 0.5625 - r(x)/s(x)| < 2**-30 582116Sjkh */ 59254969Skarglra0 = -9.87132732e-03F, /* -0x1.4376b2p-7 */ 60254969Skarglra1 = -5.53605914e-01F, /* -0x1.1b723cp-1 */ 61254969Skarglra2 = -2.17589188e+00F, /* -0x1.1683a0p+1 */ 62254969Skarglra3 = -1.43268085e+00F, /* -0x1.6ec42cp+0 */ 63254969Skarglsa1 = 5.45995426e+00F, /* 0x1.5d6fe4p+2 */ 64254969Skarglsa2 = 6.69798088e+00F, /* 0x1.acabb8p+2 */ 65254969Skarglsa3 = 1.43113089e+00F, /* 0x1.6e5e98p+0 */ 66254969Skarglsa4 = -5.77397496e-02F, /* -0x1.d90108p-5 */ 67254969Skargl/* 68254969Skargl * Domain [1/0.35, 11], range ~[-2.264e-13,2.336e-13]: 69254969Skargl * |log(x*erfc(x)) + x**2 + 0.5625 - r(x)/s(x)| < 2**-42 70254969Skargl */ 71254969Skarglrb0 = -9.86494310e-03F, /* -0x1.434124p-7 */ 72254969Skarglrb1 = -6.25171244e-01F, /* -0x1.401672p-1 */ 73254969Skarglrb2 = -6.16498327e+00F, /* -0x1.8a8f16p+2 */ 74254969Skarglrb3 = -1.66696873e+01F, /* -0x1.0ab70ap+4 */ 75254969Skarglrb4 = -9.53764343e+00F, /* -0x1.313460p+3 */ 76254969Skarglsb1 = 1.26884899e+01F, /* 0x1.96081cp+3 */ 77254969Skarglsb2 = 4.51839523e+01F, /* 0x1.6978bcp+5 */ 78254969Skarglsb3 = 4.72810211e+01F, /* 0x1.7a3f88p+5 */ 79254969Skarglsb4 = 8.93033314e+00F; /* 0x1.1dc54ap+3 */ 802116Sjkh 8197413Salfredfloat 8297413Salfrederff(float x) 832116Sjkh{ 842116Sjkh int32_t hx,ix,i; 852116Sjkh float R,S,P,Q,s,y,z,r; 862116Sjkh GET_FLOAT_WORD(hx,x); 872116Sjkh ix = hx&0x7fffffff; 882116Sjkh if(ix>=0x7f800000) { /* erf(nan)=nan */ 892116Sjkh i = ((u_int32_t)hx>>31)<<1; 902116Sjkh return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */ 912116Sjkh } 922116Sjkh 932116Sjkh if(ix < 0x3f580000) { /* |x|<0.84375 */ 94254969Skargl if(ix < 0x38800000) { /* |x|<2**-14 */ 95254969Skargl if (ix < 0x04000000) /* |x|<0x1p-119 */ 96254969Skargl return (8*x+efx8*x)/8; /* avoid spurious underflow */ 972116Sjkh return x + efx*x; 982116Sjkh } 992116Sjkh z = x*x; 100254969Skargl r = pp0+z*(pp1+z*pp2); 101254969Skargl s = one+z*(qq1+z*(qq2+z*qq3)); 1022116Sjkh y = r/s; 1032116Sjkh return x + x*y; 1042116Sjkh } 1052116Sjkh if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ 1062116Sjkh s = fabsf(x)-one; 107254969Skargl P = pa0+s*(pa1+s*(pa2+s*pa3)); 108254969Skargl Q = one+s*(qa1+s*(qa2+s*(qa3+s*qa4))); 1092116Sjkh if(hx>=0) return erx + P/Q; else return -erx - P/Q; 1102116Sjkh } 111254969Skargl if (ix >= 0x40800000) { /* inf>|x|>=4 */ 1122116Sjkh if(hx>=0) return one-tiny; else return tiny-one; 1132116Sjkh } 1142116Sjkh x = fabsf(x); 1152116Sjkh s = one/(x*x); 1162116Sjkh if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */ 117254969Skargl R=ra0+s*(ra1+s*(ra2+s*ra3)); 118254969Skargl S=one+s*(sa1+s*(sa2+s*(sa3+s*sa4))); 1192116Sjkh } else { /* |x| >= 1/0.35 */ 120254969Skargl R=rb0+s*(rb1+s*(rb2+s*(rb3+s*rb4))); 121254969Skargl S=one+s*(sb1+s*(sb2+s*(sb3+s*sb4))); 1222116Sjkh } 123254969Skargl SET_FLOAT_WORD(z,hx&0xffffe000); 124254969Skargl r = expf(-z*z-0.5625F)*expf((z-x)*(z+x)+R/S); 1252116Sjkh if(hx>=0) return one-r/x; else return r/x-one; 1262116Sjkh} 1272116Sjkh 12897413Salfredfloat 12997413Salfrederfcf(float x) 1302116Sjkh{ 1312116Sjkh int32_t hx,ix; 1322116Sjkh float R,S,P,Q,s,y,z,r; 1332116Sjkh GET_FLOAT_WORD(hx,x); 1342116Sjkh ix = hx&0x7fffffff; 1352116Sjkh if(ix>=0x7f800000) { /* erfc(nan)=nan */ 1362116Sjkh /* erfc(+-inf)=0,2 */ 1372116Sjkh return (float)(((u_int32_t)hx>>31)<<1)+one/x; 1382116Sjkh } 1392116Sjkh 1402116Sjkh if(ix < 0x3f580000) { /* |x|<0.84375 */ 141254969Skargl if(ix < 0x33800000) /* |x|<2**-24 */ 1422116Sjkh return one-x; 1432116Sjkh z = x*x; 144254969Skargl r = pp0+z*(pp1+z*pp2); 145254969Skargl s = one+z*(qq1+z*(qq2+z*qq3)); 1462116Sjkh y = r/s; 1472116Sjkh if(hx < 0x3e800000) { /* x<1/4 */ 1482116Sjkh return one-(x+x*y); 1492116Sjkh } else { 1502116Sjkh r = x*y; 1512116Sjkh r += (x-half); 1522116Sjkh return half - r ; 1532116Sjkh } 1542116Sjkh } 1552116Sjkh if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ 1562116Sjkh s = fabsf(x)-one; 157254969Skargl P = pa0+s*(pa1+s*(pa2+s*pa3)); 158254969Skargl Q = one+s*(qa1+s*(qa2+s*(qa3+s*qa4))); 1592116Sjkh if(hx>=0) { 1608870Srgrimes z = one-erx; return z - P/Q; 1612116Sjkh } else { 1622116Sjkh z = erx+P/Q; return one+z; 1632116Sjkh } 1642116Sjkh } 165254969Skargl if (ix < 0x41300000) { /* |x|<11 */ 1662116Sjkh x = fabsf(x); 1672116Sjkh s = one/(x*x); 1682116Sjkh if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/ 169254969Skargl R=ra0+s*(ra1+s*(ra2+s*ra3)); 170254969Skargl S=one+s*(sa1+s*(sa2+s*(sa3+s*sa4))); 1712116Sjkh } else { /* |x| >= 1/.35 ~ 2.857143 */ 172254969Skargl if(hx<0&&ix>=0x40a00000) return two-tiny;/* x < -5 */ 173254969Skargl R=rb0+s*(rb1+s*(rb2+s*(rb3+s*rb4))); 174254969Skargl S=one+s*(sb1+s*(sb2+s*(sb3+s*sb4))); 1752116Sjkh } 176254969Skargl SET_FLOAT_WORD(z,hx&0xffffe000); 177254969Skargl r = expf(-z*z-0.5625F)*expf((z-x)*(z+x)+R/S); 1782116Sjkh if(hx>0) return r/x; else return two-r/x; 1792116Sjkh } else { 1802116Sjkh if(hx>0) return tiny*tiny; else return two-tiny; 1812116Sjkh } 1822116Sjkh} 183