1
2 /*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunSoft, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 *
12 */
13
14 /* atanh(x)
15 * Method :
16 * 1.Reduced x to positive by atanh(-x) = -atanh(x)
17 * 2.For x>=0.5
18 * 1 2x x
19 * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
20 * 2 1 - x 1 - x
21 *
22 * For x<0.5
23 * atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
24 *
25 * Special cases:
26 * atanh(x) is NaN if |x| > 1 with signal;
27 * atanh(NaN) is that NaN with no signal;
28 * atanh(+-1) is +-INF with signal.
29 *
30 */
31
32 #include <float.h>
33
34 #include "math.h"
35 #include "math_private.h"
36
37 static const double one = 1.0, huge = 1e300;
38 static const double zero = 0.0;
39
40 double
atanh(double x)41 atanh(double x)
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);
50 if(ix==0x3ff00000)
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));
57 } else
58 t = 0.5*log1p((x+x)/(one-x));
59 if(hx>=0) return t; else return -t;
60 }
61
62 #if LDBL_MANT_DIG == 53
63 __weak_reference(atanh, atanhl);
64 #endif
65