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 /* __ieee754_atanh(x) 16 * Method : 17 * 1.Reduced x to positive by atanh(-x) = -atanh(x) 18 * 2.For x>=0.5 19 * 1 2x x 20 * atanh(x) = --- * ieee_log(1 + -------) = 0.5 * ieee_log1p(2 * --------) 21 * 2 1 - x 1 - x 22 * 23 * For x<0.5 24 * atanh(x) = 0.5*ieee_log1p(2x+2x*x/(1-x)) 25 * 26 * Special cases: 27 * atanh(x) is NaN if |x| > 1 with signal; 28 * atanh(NaN) is that NaN with no signal; 29 * atanh(+-1) is +-INF with signal. 30 * 31 */ 32 33 #include "fdlibm.h" 34 35 #ifdef __STDC__ 36 static const double one = 1.0, huge = 1e300; 37 #else 38 static double one = 1.0, huge = 1e300; 39 #endif 40 41 static double zero = 0.0; 42 43 #ifdef __STDC__ __ieee754_atanh(double x)44 double __ieee754_atanh(double x) 45 #else 46 double __ieee754_atanh(x) 47 double x; 48 #endif 49 { 50 double t; 51 int hx,ix; 52 unsigned lx; 53 hx = __HI(x); /* high word */ 54 lx = __LO(x); /* low word */ 55 ix = hx&0x7fffffff; 56 if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */ 57 return (x-x)/(x-x); 58 if(ix==0x3ff00000) 59 return x/zero; 60 if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */ 61 __HI(x) = ix; /* x <- |x| */ 62 if(ix<0x3fe00000) { /* x < 0.5 */ 63 t = x+x; 64 t = 0.5*ieee_log1p(t+t*x/(one-x)); 65 } else 66 t = 0.5*ieee_log1p((x+x)/(one-x)); 67 if(hx>=0) return t; else return -t; 68 } 69