diff --git a/liba/Makefile b/liba/Makefile index e3659c1a2..676fa88d0 100644 --- a/liba/Makefile +++ b/liba/Makefile @@ -57,6 +57,7 @@ liba_src += $(addprefix liba/src/external/openbsd/, \ s_copysignf.c \ s_cosf.c \ s_erf.c \ + s_erff.c \ s_expm1f.o\ s_fabsf.c \ s_fmaxf.c \ diff --git a/liba/src/external/openbsd/s_erff.c b/liba/src/external/openbsd/s_erff.c new file mode 100644 index 000000000..d2d6b7b5d --- /dev/null +++ b/liba/src/external/openbsd/s_erff.c @@ -0,0 +1,185 @@ +/* s_erff.c -- float version of s_erf.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + * Taken from openlibm at 5b0e7e981321687ac0abe711fdeb30adcd9da932 and + * modified for Numworks Epsilon by Neven Sajko + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +//__FBSDID("$FreeBSD: src/lib/msun/src/s_erff.c,v 1.8 2008/02/22 02:30:35 das Exp $"); + +#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 */ +/* + * Coefficients for approximation to erf on [0,0.84375] + */ +efx = 1.2837916613e-01, /* 0x3e0375d4 */ +efx8= 1.0270333290e+00, /* 0x3f8375d4 */ +/* + * Domain [0, 0.84375], range ~[-5.4446e-10,5.5197e-10]: + * |(erf(x) - x)/x - p(x)/q(x)| < 2**-31. + */ +pp0 = 1.28379166e-01F, /* 0x1.06eba8p-3 */ +pp1 = -3.36030394e-01F, /* -0x1.58185ap-2 */ +pp2 = -1.86260219e-03F, /* -0x1.e8451ep-10 */ +qq1 = 3.12324286e-01F, /* 0x1.3fd1f0p-2 */ +qq2 = 2.16070302e-02F, /* 0x1.620274p-6 */ +qq3 = -1.98859419e-03F, /* -0x1.04a626p-9 */ +/* + * Domain [0.84375, 1.25], range ~[-1.953e-11,1.940e-11]: + * |(erf(x) - erx) - p(x)/q(x)| < 2**-36. + */ +erx = 8.42697144e-01F, /* 0x1.af7600p-1. erf(1) rounded to 16 bits. */ +pa0 = 3.64939137e-06F, /* 0x1.e9d022p-19 */ +pa1 = 4.15109694e-01F, /* 0x1.a91284p-2 */ +pa2 = -1.65179938e-01F, /* -0x1.5249dcp-3 */ +pa3 = 1.10914491e-01F, /* 0x1.c64e46p-4 */ +qa1 = 6.02074385e-01F, /* 0x1.344318p-1 */ +qa2 = 5.35934687e-01F, /* 0x1.126608p-1 */ +qa3 = 1.68576106e-01F, /* 0x1.593e6ep-3 */ +qa4 = 5.62181212e-02F, /* 0x1.cc89f2p-5 */ +/* + * Domain [1.25,1/0.35], range ~[-7.043e-10,7.457e-10]: + * |log(x*erfc(x)) + x**2 + 0.5625 - r(x)/s(x)| < 2**-30 + */ +ra0 = -9.87132732e-03F, /* -0x1.4376b2p-7 */ +ra1 = -5.53605914e-01F, /* -0x1.1b723cp-1 */ +ra2 = -2.17589188e+00F, /* -0x1.1683a0p+1 */ +ra3 = -1.43268085e+00F, /* -0x1.6ec42cp+0 */ +sa1 = 5.45995426e+00F, /* 0x1.5d6fe4p+2 */ +sa2 = 6.69798088e+00F, /* 0x1.acabb8p+2 */ +sa3 = 1.43113089e+00F, /* 0x1.6e5e98p+0 */ +sa4 = -5.77397496e-02F, /* -0x1.d90108p-5 */ +/* + * Domain [1/0.35, 11], range ~[-2.264e-13,2.336e-13]: + * |log(x*erfc(x)) + x**2 + 0.5625 - r(x)/s(x)| < 2**-42 + */ +rb0 = -9.86494310e-03F, /* -0x1.434124p-7 */ +rb1 = -6.25171244e-01F, /* -0x1.401672p-1 */ +rb2 = -6.16498327e+00F, /* -0x1.8a8f16p+2 */ +rb3 = -1.66696873e+01F, /* -0x1.0ab70ap+4 */ +rb4 = -9.53764343e+00F, /* -0x1.313460p+3 */ +sb1 = 1.26884899e+01F, /* 0x1.96081cp+3 */ +sb2 = 4.51839523e+01F, /* 0x1.6978bcp+5 */ +sb3 = 4.72810211e+01F, /* 0x1.7a3f88p+5 */ +sb4 = 8.93033314e+00F; /* 0x1.1dc54ap+3 */ + + +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 < 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+s*qa4))); + 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< 0x4036DB6E) { /* |x| < 1/0.35 */ + R=ra0+s*(ra1+s*(ra2+s*ra3)); + S=one+s*(sa1+s*(sa2+s*(sa3+s*sa4))); + } else { /* |x| >= 1/0.35 */ + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*rb4))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*sb4))); + } + 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) { /* 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 < 0x33800000) /* |x|<2**-56 */ + 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+s*qa4))); + if(hx>=0) { + z = one-erx; return z - P/Q; + } else { + z = erx+P/Q; return one+z; + } + } + if (ix < 0x41300000) { /* |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=one+s*(sa1+s*(sa2+s*(sa3+s*sa4))); + } else { /* |x| >= 1/.35 ~ 2.857143 */ + if(hx<0&&ix>=0x40a00000) return two-tiny;/* x < -5 */ + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*rb4))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*sb4))); + } + 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; + } +} diff --git a/libaxx/include/cmath b/libaxx/include/cmath index 5bcfbfa7b..9fdad6b7a 100644 --- a/libaxx/include/cmath +++ b/libaxx/include/cmath @@ -114,6 +114,8 @@ inline constexpr float ceil(float x) { return __builtin_ceilf(x); } inline constexpr float copysign(float x, float y) { return __builtin_copysignf(x, y); } inline constexpr float cos(float x) { return __builtin_cosf(x); } inline constexpr float cosh(float x) { return __builtin_coshf(x); } +inline constexpr float erf(float x) { return __builtin_erff(x); } +inline constexpr float erfc(float x) { return __builtin_erfcf(x); } inline constexpr float exp(float x) { return __builtin_expf(x); } inline constexpr float expm1(float x) { return __builtin_expm1f(x); } inline constexpr float fabs(float x) { return __builtin_fabsf(x); }