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