1 
2 /* @(#)e_atanh.c 5.1 93/09/24 */
3 /*
4  * ====================================================
5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6  *
7  * Developed at SunPro, 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) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
21  *                  2             1 - x                      1 - x
22  *
23  * 	For x<0.5
24  *	atanh(x) = 0.5*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 #ifndef _DOUBLE_IS_32BITS
36 
37 #ifdef __STDC__
38 static const double one = 1.0, huge = 1e300;
39 #else
40 static double one = 1.0, huge = 1e300;
41 #endif
42 
43 #ifdef __STDC__
44 static const double zero = 0.0;
45 #else
46 static double zero = 0.0;
47 #endif
48 
49 #ifdef __STDC__
__ieee754_atanh(double x)50 	double __ieee754_atanh(double x)
51 #else
52 	double __ieee754_atanh(x)
53 	double x;
54 #endif
55 {
56 	double t;
57 	__int32_t hx,ix;
58 	__uint32_t lx;
59 	EXTRACT_WORDS(hx,lx,x);
60 	ix = hx&0x7fffffff;
61 	if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
62 	    return (x-x)/(x-x);
63 	if(ix==0x3ff00000)
64 	    return x/zero;
65 	if(ix<0x3e300000&&(huge+x)>zero) return x;	/* x<2**-28 */
66 	SET_HIGH_WORD(x,ix);
67 	if(ix<0x3fe00000) {		/* x < 0.5 */
68 	    t = x+x;
69 	    t = 0.5*log1p(t+t*x/(one-x));
70 	} else
71 	    t = 0.5*log1p((x+x)/(one-x));
72 	if(hx>=0) return t; else return -t;
73 }
74 
75 #endif /* defined(_DOUBLE_IS_32BITS) */
76