| /* 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. |
| * ==================================================== |
| */ |
| |
| #ifndef lint |
| static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_erff.c,v 1.7 2002/05/28 18:15:04 alfred 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; |
| } |
| |
| 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; |
| } |
| } |
