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 /* atanh(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 * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) 19 * 2 1 - x 1 - x 20 * 21 * For x<0.5 22 * atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) 23 * 24 * Special cases: 25 * atanh(x) is NaN if |x| > 1 with signal; 26 * atanh(NaN) is that NaN with no signal; 27 * atanh(+-1) is +-INF with signal. 28 * 29 */ 30 31 #include <float.h> 32 #include <math.h> 33 34 #include "math_private.h" 35 36 static const double one = 1.0, huge = 1e300; 37 static const double zero = 0.0; 38 39 double 40 atanh(double x) 41 { 42 double t; 43 int32_t hx,ix; 44 u_int32_t lx; 45 EXTRACT_WORDS(hx,lx,x); 46 ix = hx&0x7fffffff; 47 if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */ 48 return (x-x)/(x-x); 49 if(ix==0x3ff00000) 50 return x/zero; 51 if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */ 52 SET_HIGH_WORD(x,ix); 53 if(ix<0x3fe00000) { /* x < 0.5 */ 54 t = x+x; 55 t = 0.5*log1p(t+t*x/(one-x)); 56 } else 57 t = 0.5*log1p((x+x)/(one-x)); 58 if(hx>=0) return t; else return -t; 59 } 60 61 #if LDBL_MANT_DIG == DBL_MANT_DIG 62 __strong_alias(atanhl, atanh); 63 #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ 64