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 /* c = (subfloat)0.84506291151 */ 282116Sjkherx = 8.4506291151e-01, /* 0x3f58560b */ 292116Sjkh/* 302116Sjkh * Coefficients for approximation to erf on [0,0.84375] 312116Sjkh */ 322116Sjkhefx = 1.2837916613e-01, /* 0x3e0375d4 */ 332116Sjkhefx8= 1.0270333290e+00, /* 0x3f8375d4 */ 342116Sjkhpp0 = 1.2837916613e-01, /* 0x3e0375d4 */ 352116Sjkhpp1 = -3.2504209876e-01, /* 0xbea66beb */ 362116Sjkhpp2 = -2.8481749818e-02, /* 0xbce9528f */ 372116Sjkhpp3 = -5.7702702470e-03, /* 0xbbbd1489 */ 382116Sjkhpp4 = -2.3763017452e-05, /* 0xb7c756b1 */ 392116Sjkhqq1 = 3.9791721106e-01, /* 0x3ecbbbce */ 402116Sjkhqq2 = 6.5022252500e-02, /* 0x3d852a63 */ 412116Sjkhqq3 = 5.0813062117e-03, /* 0x3ba68116 */ 422116Sjkhqq4 = 1.3249473704e-04, /* 0x390aee49 */ 432116Sjkhqq5 = -3.9602282413e-06, /* 0xb684e21a */ 442116Sjkh/* 458870Srgrimes * Coefficients for approximation to erf in [0.84375,1.25] 462116Sjkh */ 472116Sjkhpa0 = -2.3621185683e-03, /* 0xbb1acdc6 */ 482116Sjkhpa1 = 4.1485610604e-01, /* 0x3ed46805 */ 492116Sjkhpa2 = -3.7220788002e-01, /* 0xbebe9208 */ 502116Sjkhpa3 = 3.1834661961e-01, /* 0x3ea2fe54 */ 512116Sjkhpa4 = -1.1089469492e-01, /* 0xbde31cc2 */ 522116Sjkhpa5 = 3.5478305072e-02, /* 0x3d1151b3 */ 532116Sjkhpa6 = -2.1663755178e-03, /* 0xbb0df9c0 */ 542116Sjkhqa1 = 1.0642088205e-01, /* 0x3dd9f331 */ 552116Sjkhqa2 = 5.4039794207e-01, /* 0x3f0a5785 */ 562116Sjkhqa3 = 7.1828655899e-02, /* 0x3d931ae7 */ 572116Sjkhqa4 = 1.2617121637e-01, /* 0x3e013307 */ 582116Sjkhqa5 = 1.3637083583e-02, /* 0x3c5f6e13 */ 592116Sjkhqa6 = 1.1984500103e-02, /* 0x3c445aa3 */ 602116Sjkh/* 612116Sjkh * Coefficients for approximation to erfc in [1.25,1/0.35] 622116Sjkh */ 632116Sjkhra0 = -9.8649440333e-03, /* 0xbc21a093 */ 642116Sjkhra1 = -6.9385856390e-01, /* 0xbf31a0b7 */ 652116Sjkhra2 = -1.0558626175e+01, /* 0xc128f022 */ 662116Sjkhra3 = -6.2375331879e+01, /* 0xc2798057 */ 672116Sjkhra4 = -1.6239666748e+02, /* 0xc322658c */ 682116Sjkhra5 = -1.8460508728e+02, /* 0xc3389ae7 */ 692116Sjkhra6 = -8.1287437439e+01, /* 0xc2a2932b */ 702116Sjkhra7 = -9.8143291473e+00, /* 0xc11d077e */ 712116Sjkhsa1 = 1.9651271820e+01, /* 0x419d35ce */ 722116Sjkhsa2 = 1.3765776062e+02, /* 0x4309a863 */ 732116Sjkhsa3 = 4.3456588745e+02, /* 0x43d9486f */ 742116Sjkhsa4 = 6.4538726807e+02, /* 0x442158c9 */ 752116Sjkhsa5 = 4.2900814819e+02, /* 0x43d6810b */ 762116Sjkhsa6 = 1.0863500214e+02, /* 0x42d9451f */ 772116Sjkhsa7 = 6.5702495575e+00, /* 0x40d23f7c */ 782116Sjkhsa8 = -6.0424413532e-02, /* 0xbd777f97 */ 792116Sjkh/* 802116Sjkh * Coefficients for approximation to erfc in [1/.35,28] 812116Sjkh */ 822116Sjkhrb0 = -9.8649431020e-03, /* 0xbc21a092 */ 832116Sjkhrb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */ 842116Sjkhrb2 = -1.7757955551e+01, /* 0xc18e104b */ 852116Sjkhrb3 = -1.6063638306e+02, /* 0xc320a2ea */ 862116Sjkhrb4 = -6.3756646729e+02, /* 0xc41f6441 */ 872116Sjkhrb5 = -1.0250950928e+03, /* 0xc480230b */ 882116Sjkhrb6 = -4.8351919556e+02, /* 0xc3f1c275 */ 892116Sjkhsb1 = 3.0338060379e+01, /* 0x41f2b459 */ 902116Sjkhsb2 = 3.2579251099e+02, /* 0x43a2e571 */ 912116Sjkhsb3 = 1.5367296143e+03, /* 0x44c01759 */ 922116Sjkhsb4 = 3.1998581543e+03, /* 0x4547fdbb */ 932116Sjkhsb5 = 2.5530502930e+03, /* 0x451f90ce */ 942116Sjkhsb6 = 4.7452853394e+02, /* 0x43ed43a7 */ 952116Sjkhsb7 = -2.2440952301e+01; /* 0xc1b38712 */ 962116Sjkh 9797413Salfredfloat 9897413Salfrederff(float x) 992116Sjkh{ 1002116Sjkh int32_t hx,ix,i; 1012116Sjkh float R,S,P,Q,s,y,z,r; 1022116Sjkh GET_FLOAT_WORD(hx,x); 1032116Sjkh ix = hx&0x7fffffff; 1042116Sjkh if(ix>=0x7f800000) { /* erf(nan)=nan */ 1052116Sjkh i = ((u_int32_t)hx>>31)<<1; 1062116Sjkh return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */ 1072116Sjkh } 1082116Sjkh 1092116Sjkh if(ix < 0x3f580000) { /* |x|<0.84375 */ 1102116Sjkh if(ix < 0x31800000) { /* |x|<2**-28 */ 1118870Srgrimes if (ix < 0x04000000) 1122116Sjkh /*avoid underflow */ 1132116Sjkh return (float)0.125*((float)8.0*x+efx8*x); 1142116Sjkh return x + efx*x; 1152116Sjkh } 1162116Sjkh z = x*x; 1172116Sjkh r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); 1182116Sjkh s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); 1192116Sjkh y = r/s; 1202116Sjkh return x + x*y; 1212116Sjkh } 1222116Sjkh if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ 1232116Sjkh s = fabsf(x)-one; 1242116Sjkh P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); 1252116Sjkh Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); 1262116Sjkh if(hx>=0) return erx + P/Q; else return -erx - P/Q; 1272116Sjkh } 1282116Sjkh if (ix >= 0x40c00000) { /* inf>|x|>=6 */ 1292116Sjkh if(hx>=0) return one-tiny; else return tiny-one; 1302116Sjkh } 1312116Sjkh x = fabsf(x); 1322116Sjkh s = one/(x*x); 1332116Sjkh if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */ 1342116Sjkh R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( 1352116Sjkh ra5+s*(ra6+s*ra7)))))); 1362116Sjkh S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( 1372116Sjkh sa5+s*(sa6+s*(sa7+s*sa8))))))); 1382116Sjkh } else { /* |x| >= 1/0.35 */ 1392116Sjkh R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( 1402116Sjkh rb5+s*rb6))))); 1412116Sjkh S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( 1422116Sjkh sb5+s*(sb6+s*sb7)))))); 1432116Sjkh } 1442116Sjkh GET_FLOAT_WORD(ix,x); 1452116Sjkh SET_FLOAT_WORD(z,ix&0xfffff000); 1462116Sjkh r = __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S); 1472116Sjkh if(hx>=0) return one-r/x; else return r/x-one; 1482116Sjkh} 1492116Sjkh 15097413Salfredfloat 15197413Salfrederfcf(float x) 1522116Sjkh{ 1532116Sjkh int32_t hx,ix; 1542116Sjkh float R,S,P,Q,s,y,z,r; 1552116Sjkh GET_FLOAT_WORD(hx,x); 1562116Sjkh ix = hx&0x7fffffff; 1572116Sjkh if(ix>=0x7f800000) { /* erfc(nan)=nan */ 1582116Sjkh /* erfc(+-inf)=0,2 */ 1592116Sjkh return (float)(((u_int32_t)hx>>31)<<1)+one/x; 1602116Sjkh } 1612116Sjkh 1622116Sjkh if(ix < 0x3f580000) { /* |x|<0.84375 */ 1632116Sjkh if(ix < 0x23800000) /* |x|<2**-56 */ 1642116Sjkh return one-x; 1652116Sjkh z = x*x; 1662116Sjkh r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); 1672116Sjkh s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); 1682116Sjkh y = r/s; 1692116Sjkh if(hx < 0x3e800000) { /* x<1/4 */ 1702116Sjkh return one-(x+x*y); 1712116Sjkh } else { 1722116Sjkh r = x*y; 1732116Sjkh r += (x-half); 1742116Sjkh return half - r ; 1752116Sjkh } 1762116Sjkh } 1772116Sjkh if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ 1782116Sjkh s = fabsf(x)-one; 1792116Sjkh P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); 1802116Sjkh Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); 1812116Sjkh if(hx>=0) { 1828870Srgrimes z = one-erx; return z - P/Q; 1832116Sjkh } else { 1842116Sjkh z = erx+P/Q; return one+z; 1852116Sjkh } 1862116Sjkh } 1872116Sjkh if (ix < 0x41e00000) { /* |x|<28 */ 1882116Sjkh x = fabsf(x); 1892116Sjkh s = one/(x*x); 1902116Sjkh if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/ 1912116Sjkh R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( 1922116Sjkh ra5+s*(ra6+s*ra7)))))); 1932116Sjkh S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( 1942116Sjkh sa5+s*(sa6+s*(sa7+s*sa8))))))); 1952116Sjkh } else { /* |x| >= 1/.35 ~ 2.857143 */ 1962116Sjkh if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */ 1972116Sjkh R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( 1982116Sjkh rb5+s*rb6))))); 1992116Sjkh S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( 2002116Sjkh sb5+s*(sb6+s*sb7)))))); 2012116Sjkh } 2022116Sjkh GET_FLOAT_WORD(ix,x); 2032116Sjkh SET_FLOAT_WORD(z,ix&0xfffff000); 2042116Sjkh r = __ieee754_expf(-z*z-(float)0.5625)* 2052116Sjkh __ieee754_expf((z-x)*(z+x)+R/S); 2062116Sjkh if(hx>0) return r/x; else return two-r/x; 2072116Sjkh } else { 2082116Sjkh if(hx>0) return tiny*tiny; else return two-tiny; 2092116Sjkh } 2102116Sjkh} 211