/* 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. * ==================================================== */ #if defined(LIBM_SCCS) && !defined(lint) static char rcsid[] = "$NetBSD: s_erff.c,v 1.4 1995/05/10 20:47:07 jtc Exp $"; #endif #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 */ /* 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; 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 < 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)))))); } GET_FLOAT_WORD(ix,x); SET_FLOAT_WORD(z,ix&0xfffff000); 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; } weak_alias (__erff, erff) 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 < 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)))))); } GET_FLOAT_WORD(ix,x); SET_FLOAT_WORD(z,ix&0xfffff000); 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 { if(hx>0) return tiny*tiny; else return two-tiny; } } weak_alias (__erfcf, erfcf)