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 #ifndef lint 14 static char rcsid[] = "$FreeBSD$"; 15 #endif 16 17 /* __ieee754_atanh(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 * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) 23 * 2 1 - x 1 - x 24 * 25 * For x<0.5 26 * atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) 27 * 28 * Special cases: 29 * atanh(x) is NaN if |x| > 1 with signal; 30 * atanh(NaN) is that NaN with no signal; 31 * atanh(+-1) is +-INF with signal. 32 * 33 */ 34 35 #include "math.h" 36 #include "math_private.h" 37 38 #ifdef __STDC__ 39 static const double one = 1.0, huge = 1e300; 40 #else 41 static double one = 1.0, huge = 1e300; 42 #endif 43 44 #ifdef __STDC__ 45 static const double zero = 0.0; 46 #else 47 static double zero = 0.0; 48 #endif 49 50 #ifdef __STDC__ 51 double __ieee754_atanh(double x) 52 #else 53 double __ieee754_atanh(x) 54 double x; 55 #endif 56 { 57 double t; 58 int32_t hx,ix; 59 u_int32_t lx; 60 EXTRACT_WORDS(hx,lx,x); 61 ix = hx&0x7fffffff; 62 if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */ 63 return (x-x)/(x-x); 64 if(ix==0x3ff00000) 65 return x/zero; 66 if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */ 67 SET_HIGH_WORD(x,ix); 68 if(ix<0x3fe00000) { /* x < 0.5 */ 69 t = x+x; 70 t = 0.5*log1p(t+t*x/(one-x)); 71 } else 72 t = 0.5*log1p((x+x)/(one-x)); 73 if(hx>=0) return t; else return -t; 74 } 75