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[] = "$Id: e_atanh.c,v 1.4 1994/03/03 17:04:09 jtc Exp $"; 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 <machine/endian.h> 37 38 #if BYTE_ORDER == LITTLE_ENDIAN 39 #define n0 1 40 #else 41 #define n0 0 42 #endif 43 44 #ifdef __STDC__ 45 static const double one = 1.0, huge = 1e300; 46 #else 47 static double one = 1.0, huge = 1e300; 48 #endif 49 50 static double zero = 0.0; 51 52 #ifdef __STDC__ 53 double __ieee754_atanh(double x) 54 #else 55 double __ieee754_atanh(x) 56 double x; 57 #endif 58 { 59 double t; 60 int hx,ix; 61 unsigned lx; 62 63 hx = *(n0+(int*)&x); /* high word */ 64 lx = *(1-n0+(int*)&x); /* low word */ 65 ix = hx&0x7fffffff; 66 if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */ 67 return (x-x)/(x-x); 68 if(ix==0x3ff00000) 69 return x/zero; 70 if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */ 71 *(n0+(int*)&x) = ix; /* x <- |x| */ 72 if(ix<0x3fe00000) { /* x < 0.5 */ 73 t = x+x; 74 t = 0.5*log1p(t+t*x/(one-x)); 75 } else 76 t = 0.5*log1p((x+x)/(one-x)); 77 if(hx>=0) return t; else return -t; 78 } 79