CommitLineData
6ff43c94
PA
1
2/* @(#)e_atanh.c 1.3 95/01/18 */
a8a6a916 3/* \$FreeBSD: head/lib/msun/src/e_atanh.c 251599 2013-06-10 06:04:58Z das \$ */
b34b60bc
JS
4/*
5 * ====================================================
7 *
6ff43c94 8 * Developed at SunSoft, a Sun Microsystems, Inc. business.
b34b60bc 9 * Permission to use, copy, modify, and distribute this
6ff43c94 10 * software is freely granted, provided that this notice
b34b60bc
JS
11 * is preserved.
12 * ====================================================
13 *
b34b60bc
JS
14 */
15
6ff43c94 16/* __ieee754_atanh(x)
b34b60bc
JS
17 * Method :
18 * 1.Reduced x to positive by atanh(-x) = -atanh(x)
19 * 2.For x>=0.5
20 * 1 2x x
21 * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
22 * 2 1 - x 1 - x
6ff43c94 23 *
b34b60bc
JS
24 * For x<0.5
25 * atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
26 *
27 * Special cases:
28 * atanh(x) is NaN if |x| > 1 with signal;
29 * atanh(NaN) is that NaN with no signal;
30 * atanh(+-1) is +-INF with signal.
31 *
32 */
33
a8a6a916
JM
34#include <float.h>
35
6ff43c94 36#include "math.h"
b34b60bc
JS
37#include "math_private.h"
38
39static const double one = 1.0, huge = 1e300;
b34b60bc
JS
40static const double zero = 0.0;
41
42double
6ff43c94 43__ieee754_atanh(double x)
b34b60bc
JS
44{
45 double t;
46 int32_t hx,ix;
47 u_int32_t lx;
48 EXTRACT_WORDS(hx,lx,x);
49 ix = hx&0x7fffffff;
50 if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
51 return (x-x)/(x-x);
6ff43c94 52 if(ix==0x3ff00000)
b34b60bc
JS
53 return x/zero;
54 if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */
55 SET_HIGH_WORD(x,ix);
56 if(ix<0x3fe00000) { /* x < 0.5 */
57 t = x+x;
58 t = 0.5*log1p(t+t*x/(one-x));
6ff43c94 59 } else
b34b60bc
JS
60 t = 0.5*log1p((x+x)/(one-x));
61 if(hx>=0) return t; else return -t;
62}
a8a6a916
JM
63
64#if LDBL_MANT_DIG == 53
65__weak_reference(atanh, atanhl);
66#endif