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 = 1.0, huge = 1e4900L; 36 37 static const long double zero = 0.0; 38 39 long double 40 atanhl(long double x) 41 { 42 long double t; 43 int32_t ix; 44 u_int32_t se,i0,i1; 45 GET_LDOUBLE_WORDS(se,i0,i1,x); 46 ix = se&0x7fff; 47 if ((ix+((((i0&0x7fffffff)|i1)|(-((i0&0x7fffffff)|i1)))>>31))>0x3fff) 48 /* |x|>1 */ 49 return (x-x)/(x-x); 50 if(ix==0x3fff) 51 return x/zero; 52 if(ix<0x3fe3&&(huge+x)>zero) return x; /* x<2**-28 */ 53 SET_LDOUBLE_EXP(x,ix); 54 if(ix<0x3ffe) { /* x < 0.5 */ 55 t = x+x; 56 t = 0.5*log1pl(t+t*x/(one-x)); 57 } else 58 t = 0.5*log1pl((x+x)/(one-x)); 59 if(se<=0x7fff) return t; else return -t; 60 } 61