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       ---
       e_atanh.c (1657B)
       ---
            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: src/lib/msun/src/e_atanh.c,v 1.6 2002/05/28 17:03:12 alfred 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 "math_private.h"
           37 
           38 static const double one = 1.0, huge = 1e300;
           39 static const double zero = 0.0;
           40 
           41 double
           42 __ieee754_atanh(double x)
           43 {
           44         double t;
           45         int32_t hx,ix;
           46         u_int32_t lx;
           47         EXTRACT_WORDS(hx,lx,x);
           48         ix = hx&0x7fffffff;
           49         if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
           50             return (x-x)/(x-x);
           51         if(ix==0x3ff00000)
           52             return x/zero;
           53         if(ix<0x3e300000&&(huge+x)>zero) return x;        /* x<2**-28 */
           54         SET_HIGH_WORD(x,ix);
           55         if(ix<0x3fe00000) {                /* x < 0.5 */
           56             t = x+x;
           57             t = 0.5*log1p(t+t*x/(one-x));
           58         } else
           59             t = 0.5*log1p((x+x)/(one-x));
           60         if(hx>=0) return t; else return -t;
           61 }