source: trunk/sys/libm/e_atanh.c @ 1

Last change on this file since 1 was 1, checked in by alain, 5 years ago

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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 <libm/fdlibm.h>
34
35#ifdef __STDC__
36static const double one = 1.0, huge = 1e300;
37#else
38static double one = 1.0, huge = 1e300;
39#endif
40
41static double zero = 0.0;
42
43#ifdef __STDC__
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,n0,ix;
52        unsigned lx;
53        n0 = ((*(int*)&one)>>29)^1;
54        hx = *(n0+(int*)&x);            /* high word */
55        lx = *(1-n0+(int*)&x);          /* low word */
56        ix = hx&0x7fffffff;
57        if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
58            return (x-x)/(x-x);
59        if(ix==0x3ff00000) 
60            return x/zero;
61        if(ix<0x3e300000&&(huge+x)>zero) return x;      /* x<2**-28 */
62        *(n0+(int*)&x) = ix;            /* x <- |x| */
63        if(ix<0x3fe00000) {             /* x < 0.5 */
64            t = x+x;
65            t = 0.5*log1p(t+t*x/(one-x));
66        } else 
67            t = 0.5*log1p((x+x)/(one-x));
68        if(hx>=0) return t; else return -t;
69}
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