/* @(#)e_atanh.c 5.1 93/09/24 */ /* * ==================================================== * 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. * ==================================================== */ /* atanhl(x) * Method : * 1.Reduced x to positive by atanh(-x) = -atanh(x) * 2.For x>=0.5 * 1 2x x * atanhl(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) * 2 1 - x 1 - x * * For x<0.5 * atanhl(x) = 0.5*log1pl(2x+2x*x/(1-x)) * * Special cases: * atanhl(x) is NaN if |x| > 1 with signal; * atanhl(NaN) is that NaN with no signal; * atanhl(+-1) is +-INF with signal. * */ #include #include "math_private.h" static const long double one = 1.0L, huge = 1e4900L; static const long double zero = 0.0L; long double atanhl(long double x) { long double t; u_int32_t jx, ix; ieee_quad_shape_type u; u.value = x; jx = u.parts32.mswhi; ix = jx & 0x7fffffff; u.parts32.mswhi = ix; if (ix >= 0x3fff0000) /* |x| >= 1.0 or infinity or NaN */ { if (u.value == one) return x/zero; else return (x-x)/(x-x); } if(ix<0x3fc60000 && (huge+x)>zero) return x; /* x < 2^-57 */ if(ix<0x3ffe0000) { /* x < 0.5 */ t = u.value+u.value; t = 0.5*log1pl(t+t*u.value/(one-u.value)); } else t = 0.5*log1pl((u.value+u.value)/(one-u.value)); if(jx & 0x80000000) return -t; else return t; }