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/* __ieee754_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
41static const double one = 1.0, huge = 1e300;
42static const double zero = 0.0;
43
44double
45__ieee754_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