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 #include <sys/cdefs.h> 16 __FBSDID("$FreeBSD$"); 17 18 /* atanh(x) 19 * Method : 20 * 1.Reduced x to positive by atanh(-x) = -atanh(x) 21 * 2.For x>=0.5 22 * 1 2x x 23 * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) 24 * 2 1 - x 1 - x 25 * 26 * For x<0.5 27 * atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) 28 * 29 * Special cases: 30 * atanh(x) is NaN if |x| > 1 with signal; 31 * atanh(NaN) is that NaN with no signal; 32 * atanh(+-1) is +-INF with signal. 33 * 34 */ 35 36 #include <float.h> 37 38 #include "math.h" 39 #include "math_private.h" 40 41 static const double one = 1.0, huge = 1e300; 42 static const double zero = 0.0; 43 44 double 45 atanh(double x) 46 { 47 double t; 48 int32_t hx,ix; 49 u_int32_t lx; 50 EXTRACT_WORDS(hx,lx,x); 51 ix = hx&0x7fffffff; 52 if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */ 53 return (x-x)/(x-x); 54 if(ix==0x3ff00000) 55 return x/zero; 56 if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */ 57 SET_HIGH_WORD(x,ix); 58 if(ix<0x3fe00000) { /* x < 0.5 */ 59 t = x+x; 60 t = 0.5*log1p(t+t*x/(one-x)); 61 } else 62 t = 0.5*log1p((x+x)/(one-x)); 63 if(hx>=0) return t; else return -t; 64 } 65 66 #if LDBL_MANT_DIG == 53 67 __weak_reference(atanh, atanhl); 68 #endif 69