1 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunSoft, 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 14 /* atanh(x) 15 * Method : 16 * 1.Reduced x to positive by atanh(-x) = -atanh(x) 17 * 2.For x>=0.5 18 * 1 2x x 19 * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) 20 * 2 1 - x 1 - x 21 * 22 * For x<0.5 23 * atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) 24 * 25 * Special cases: 26 * atanh(x) is NaN if |x| > 1 with signal; 27 * atanh(NaN) is that NaN with no signal; 28 * atanh(+-1) is +-INF with signal. 29 * 30 */ 31 32 #include <float.h> 33 34 #include "math.h" 35 #include "math_private.h" 36 37 static const double one = 1.0, huge = 1e300; 38 static const double zero = 0.0; 39 40 double 41 atanh(double x) 42 { 43 double t; 44 int32_t hx,ix; 45 u_int32_t lx; 46 EXTRACT_WORDS(hx,lx,x); 47 ix = hx&0x7fffffff; 48 if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */ 49 return (x-x)/(x-x); 50 if(ix==0x3ff00000) 51 return x/zero; 52 if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */ 53 SET_HIGH_WORD(x,ix); 54 if(ix<0x3fe00000) { /* x < 0.5 */ 55 t = x+x; 56 t = 0.5*log1p(t+t*x/(one-x)); 57 } else 58 t = 0.5*log1p((x+x)/(one-x)); 59 if(hx>=0) return t; else return -t; 60 } 61 62 #if LDBL_MANT_DIG == 53 63 __weak_reference(atanh, atanhl); 64 #endif 65