1 /* @(#)e_atanh.c 5.1 93/09/24 */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunPro, a Sun Microsystems, Inc. business. 7 * Permission to use, copy, modify, and distribute this 8 * software is freely granted, provided that this notice 9 * is preserved. 10 * ==================================================== 11 */ 12 13 /* atanhl(x) 14 * Method : 15 * 1.Reduced x to positive by atanh(-x) = -atanh(x) 16 * 2.For x>=0.5 17 * 1 2x x 18 * atanhl(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) 19 * 2 1 - x 1 - x 20 * 21 * For x<0.5 22 * atanhl(x) = 0.5*log1pl(2x+2x*x/(1-x)) 23 * 24 * Special cases: 25 * atanhl(x) is NaN if |x| > 1 with signal; 26 * atanhl(NaN) is that NaN with no signal; 27 * atanhl(+-1) is +-INF with signal. 28 * 29 */ 30 31 #include <math.h> 32 33 #include "math_private.h" 34 35 static const long double one = 1.0L, huge = 1e4900L; 36 37 static const long double zero = 0.0L; 38 39 long double 40 atanhl(long double x) 41 { 42 long double t; 43 u_int32_t jx, ix; 44 ieee_quad_shape_type u; 45 46 u.value = x; 47 jx = u.parts32.mswhi; 48 ix = jx & 0x7fffffff; 49 u.parts32.mswhi = ix; 50 if (ix >= 0x3fff0000) /* |x| >= 1.0 or infinity or NaN */ 51 { 52 if (u.value == one) 53 return x/zero; 54 else 55 return (x-x)/(x-x); 56 } 57 if(ix<0x3fc60000 && (huge+x)>zero) return x; /* x < 2^-57 */ 58 59 if(ix<0x3ffe0000) { /* x < 0.5 */ 60 t = u.value+u.value; 61 t = 0.5*log1pl(t+t*u.value/(one-u.value)); 62 } else 63 t = 0.5*log1pl((u.value+u.value)/(one-u.value)); 64 if(jx & 0x80000000) return -t; else return t; 65 } 66