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2/* @(#)e_atanh.c 1.3 95/01/18 */
3/* \$FreeBSD: head/lib/msun/src/e_atanh.c 176451 2008-02-22 02:30:36Z das \$ */
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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
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11 * is preserved.
12 * ====================================================
13 *
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14 */
15
6ff43c94 16/* __ieee754_atanh(x)
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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 *
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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
6ff43c94 34#include "math.h"
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35#include "math_private.h"
36
37static const double one = 1.0, huge = 1e300;
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38static const double zero = 0.0;
39
40double
6ff43c94 41__ieee754_atanh(double x)
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42{
43 double t;
44 int32_t hx,ix;
45 u_int32_t lx;
46 EXTRACT_WORDS(hx,lx,x);
47 ix = hx&0x7fffffff;
48 if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
49 return (x-x)/(x-x);
6ff43c94 50 if(ix==0x3ff00000)
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51 return x/zero;
52 if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */
53 SET_HIGH_WORD(x,ix);
54 if(ix<0x3fe00000) { /* x < 0.5 */
55 t = x+x;
56 t = 0.5*log1p(t+t*x/(one-x));
6ff43c94 57 } else
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58 t = 0.5*log1p((x+x)/(one-x));
59 if(hx>=0) return t; else return -t;
60}