From 482ccd2f7497a79ca83e998f54e823e7cedaaa6e Mon Sep 17 00:00:00 2001 From: Szabolcs Nagy Date: Tue, 11 Dec 2012 23:06:20 +0100 Subject: math: rewrite inverse hyperbolic functions to be simpler/smaller modifications: * avoid unsigned->signed integer conversion * do not handle special cases when they work correctly anyway * more strict threshold values (0x1p26 instead of 0x1p28 etc) * smaller code, cleaner branching logic * same precision as the old code: acosh(x) has up to 2ulp error in [1,1.125] asinh(x) has up to 1.6ulp error in [0.125,0.5], [-0.5,-0.125] atanh(x) has up to 1.7ulp error in [0.125,0.5], [-0.5,-0.125] --- src/math/atanh.c | 67 +++++++++++++------------------------------------------- 1 file changed, 15 insertions(+), 52 deletions(-) (limited to 'src/math/atanh.c') diff --git a/src/math/atanh.c b/src/math/atanh.c index dbe241d1..84a84c69 100644 --- a/src/math/atanh.c +++ b/src/math/atanh.c @@ -1,58 +1,21 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_atanh.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - * - */ -/* atanh(x) - * Method : - * 1.Reduced x to positive by atanh(-x) = -atanh(x) - * 2.For x>=0.5 - * 1 2x x - * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) - * 2 1 - x 1 - x - * - * For x<0.5 - * atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) - * - * Special cases: - * atanh(x) is NaN if |x| > 1 with signal; - * atanh(NaN) is that NaN with no signal; - * atanh(+-1) is +-INF with signal. - * - */ - #include "libm.h" -static const double huge = 1e300; - +/* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */ double atanh(double x) { - double t; - int32_t hx,ix; - uint32_t lx; + union {double f; uint64_t i;} u = {.f = x}; + unsigned e = u.i >> 52 & 0x7ff; + unsigned s = u.i >> 63; + + /* |x| */ + u.i &= (uint64_t)-1/2; + x = u.f; - EXTRACT_WORDS(hx, lx, x); - ix = hx & 0x7fffffff; - if ((ix | ((lx|-lx)>>31)) > 0x3ff00000) /* |x| > 1 */ - return (x-x)/(x-x); - if (ix == 0x3ff00000) - return x/0.0; - if (ix < 0x3e300000 && (huge+x) > 0.0) /* x < 2**-28 */ - return x; - SET_HIGH_WORD(x, ix); - if (ix < 0x3fe00000) { /* x < 0.5 */ - t = x+x; - t = 0.5*log1p(t + t*x/(1.0-x)); - } else - t = 0.5*log1p((x+x)/(1.0-x)); - if (hx >= 0) - return t; - return -t; + if (e < 0x3ff - 1) { + /* |x| < 0.5, up to 1.7ulp error */ + x = 0.5*log1p(2*x + 2*x*x/(1-x)); + } else { + x = 0.5*log1p(2*x/(1-x)); + } + return s ? -x : x; } -- cgit 1.4.1