| /* 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" |
| |
| /* XXX Prevent compilers from erroneously constant folding: */ |
| static const volatile float tiny = 1e-30; |
| |
| static const float |
| half= 0.5, |
| one = 1, |
| two = 2, |
| erx = 8.42697144e-01, /* 0x3f57bb00 */ |
| /* |
| * In the domain [0, 2**-14], only the first term in the power series |
| * expansion of erf(x) is used. The magnitude of the first neglected |
| * terms is less than 2**-42. |
| */ |
| efx = 1.28379166e-01, /* 0x3e0375d4 */ |
| efx8= 1.02703333e+00, /* 0x3f8375d4 */ |
| /* |
| * Domain [0, 0.84375], range ~[-5.4419e-10, 5.5179e-10]: |
| * |(erf(x) - x)/x - pp(x)/qq(x)| < 2**-31 |
| */ |
| pp0 = 1.28379166e-01, /* 0x3e0375d4 */ |
| pp1 = -3.36030394e-01, /* 0xbeac0c2d */ |
| pp2 = -1.86261395e-03, /* 0xbaf422f4 */ |
| qq1 = 3.12324315e-01, /* 0x3e9fe8f9 */ |
| qq2 = 2.16070414e-02, /* 0x3cb10140 */ |
| qq3 = -1.98859372e-03, /* 0xbb025311 */ |
| /* |
| * Domain [0.84375, 1.25], range ~[-1.023e-9, 1.023e-9]: |
| * |(erf(x) - erx) - pa(x)/qa(x)| < 2**-31 |
| */ |
| pa0 = 3.65041046e-06, /* 0x3674f993 */ |
| pa1 = 4.15109307e-01, /* 0x3ed48935 */ |
| pa2 = -2.09395722e-01, /* 0xbe566bd5 */ |
| pa3 = 8.67677554e-02, /* 0x3db1b34b */ |
| qa1 = 4.95560974e-01, /* 0x3efdba2b */ |
| qa2 = 3.71248513e-01, /* 0x3ebe1449 */ |
| qa3 = 3.92478965e-02, /* 0x3d20c267 */ |
| /* |
| * Domain [1.25,1/0.35], range ~[-4.821e-9, 4.927e-9]: |
| * |log(x*erfc(x)) + x**2 + 0.5625 - ra(x)/sa(x)| < 2**-28 |
| */ |
| ra0 = -9.88156721e-03, /* 0xbc21e64c */ |
| ra1 = -5.43658376e-01, /* 0xbf0b2d32 */ |
| ra2 = -1.66828310e+00, /* 0xbfd58a4d */ |
| ra3 = -6.91554189e-01, /* 0xbf3109b2 */ |
| sa1 = 4.48581553e+00, /* 0x408f8bcd */ |
| sa2 = 4.10799170e+00, /* 0x408374ab */ |
| sa3 = 5.53855181e-01, /* 0x3f0dc974 */ |
| /* |
| * Domain [2.85715, 11], range ~[-1.484e-9, 1.505e-9]: |
| * |log(x*erfc(x)) + x**2 + 0.5625 - rb(x)/sb(x)| < 2**-30 |
| */ |
| rb0 = -9.86496918e-03, /* 0xbc21a0ae */ |
| rb1 = -5.48049808e-01, /* 0xbf0c4cfe */ |
| rb2 = -1.84115684e+00, /* 0xbfebab07 */ |
| sb1 = 4.87132740e+00, /* 0x409be1ea */ |
| sb2 = 3.04982710e+00, /* 0x4043305e */ |
| sb3 = -7.61900663e-01; /* 0xbf430bec */ |
| |
| 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) { /* erff(nan)=nan */ |
| i = ((u_int32_t)hx>>31)<<1; |
| return (float)(1-i)+one/x; /* erff(+-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)); |
| 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< 0x4036db8c) { /* |x| < 2.85715 ~ 1/0.35 */ |
| R=ra0+s*(ra1+s*(ra2+s*ra3)); |
| S=one+s*(sa1+s*(sa2+s*sa3)); |
| } else { /* |x| >= 2.85715 ~ 1/0.35 */ |
| R=rb0+s*(rb1+s*rb2); |
| S=one+s*(sb1+s*(sb2+s*sb3)); |
| } |
| 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) { /* erfcf(nan)=nan */ |
| /* erfcf(+-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)); |
| 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< 0x4036db8c) { /* |x| < 2.85715 ~ 1/.35 */ |
| R=ra0+s*(ra1+s*(ra2+s*ra3)); |
| S=one+s*(sa1+s*(sa2+s*sa3)); |
| } else { /* |x| >= 2.85715 ~ 1/.35 */ |
| if(hx<0&&ix>=0x40a00000) return two-tiny;/* x < -5 */ |
| R=rb0+s*(rb1+s*rb2); |
| S=one+s*(sb1+s*(sb2+s*sb3)); |
| } |
| 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; |
| } |
| } |