1/* s_atanhl.c -- long double version of s_atan.c. 2 * Conversion to long double by Ulrich Drepper, 3 * Cygnus Support, drepper@cygnus.com. 4 */ 5 6/* 7 * ==================================================== 8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 9 * 10 * Developed at SunPro, a Sun Microsystems, Inc. business. 11 * Permission to use, copy, modify, and distribute this 12 * software is freely granted, provided that this notice 13 * is preserved. 14 * ==================================================== 15 */ 16 17/* atanhq(x) 18 * Method : 19 * 1.Reduced x to positive by atanh(-x) = -atanh(x) 20 * 2.For x>=0.5 21 * 1 2x x 22 * atanhl(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) 23 * 2 1 - x 1 - x 24 * 25 * For x<0.5 26 * atanhl(x) = 0.5*log1pq(2x+2x*x/(1-x)) 27 * 28 * Special cases: 29 * atanhl(x) is NaN if |x| > 1 with signal; 30 * atanhl(NaN) is that NaN with no signal; 31 * atanhl(+-1) is +-INF with signal. 32 * 33 */ 34 35#include "quadmath-imp.h" 36 37static const __float128 one = 1, huge = 1e4900Q; 38 39static const __float128 zero = 0; 40 41__float128 42atanhq(__float128 x) 43{ 44 __float128 t; 45 uint32_t jx, ix; 46 ieee854_float128 u; 47 48 u.value = x; 49 jx = u.words32.w0; 50 ix = jx & 0x7fffffff; 51 u.words32.w0 = ix; 52 if (ix >= 0x3fff0000) /* |x| >= 1.0 or infinity or NaN */ 53 { 54 if (u.value == one) 55 return x/zero; 56 else 57 return (x-x)/(x-x); 58 } 59 if(ix<0x3fc60000 && (huge+x)>zero) /* x < 2^-57 */ 60 { 61 math_check_force_underflow (x); 62 return x; 63 } 64 65 if(ix<0x3ffe0000) { /* x < 0.5 */ 66 t = u.value+u.value; 67 t = 0.5*log1pq(t+t*u.value/(one-u.value)); 68 } else 69 t = 0.5*log1pq((u.value+u.value)/(one-u.value)); 70 if(jx & 0x80000000) return -t; else return t; 71} 72