1 2 /* @(#)e_atanh.c 1.3 95/01/18 */ 3 /* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunSoft, a Sun Microsystems, Inc. business. 8 * Permission to use, copy, modify, and distribute this 9 * software is freely granted, provided that this notice 10 * is preserved. 11 * ==================================================== 12 * 13 */ 14 15 #ifndef lint 16 static char rcsid[] = "$FreeBSD$"; 17 #endif 18 19 /* __ieee754_atanh(x) 20 * Method : 21 * 1.Reduced x to positive by atanh(-x) = -atanh(x) 22 * 2.For x>=0.5 23 * 1 2x x 24 * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) 25 * 2 1 - x 1 - x 26 * 27 * For x<0.5 28 * atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) 29 * 30 * Special cases: 31 * atanh(x) is NaN if |x| > 1 with signal; 32 * atanh(NaN) is that NaN with no signal; 33 * atanh(+-1) is +-INF with signal. 34 * 35 */ 36 37 #include "math.h" 38 #include "math_private.h" 39 40 static const double one = 1.0, huge = 1e300; 41 static const double zero = 0.0; 42 43 double 44 __ieee754_atanh(double x) 45 { 46 double t; 47 int32_t hx,ix; 48 u_int32_t lx; 49 EXTRACT_WORDS(hx,lx,x); 50 ix = hx&0x7fffffff; 51 if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */ 52 return (x-x)/(x-x); 53 if(ix==0x3ff00000) 54 return x/zero; 55 if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */ 56 SET_HIGH_WORD(x,ix); 57 if(ix<0x3fe00000) { /* x < 0.5 */ 58 t = x+x; 59 t = 0.5*log1p(t+t*x/(one-x)); 60 } else 61 t = 0.5*log1p((x+x)/(one-x)); 62 if(hx>=0) return t; else return -t; 63 } 64