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 /* 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 "fdlibm.h"
34
35 #ifdef _NEED_FLOAT64
36
37 static const __float64 one = _F_64(1.0), huge = _F_64(1e300);
38
39 static const __float64 zero = _F_64(0.0);
40
41 __float64
atanh64(__float64 x)42 atanh64(__float64 x)
43 {
44 __float64 t;
45 __int32_t hx, ix;
46 __uint32_t lx;
47 EXTRACT_WORDS(hx, lx, x);
48 ix = hx & 0x7fffffff;
49 if ((ix | ((lx | (-lx)) >> 31)) > 0x3ff00000) /* |x|>1 */
50 return __math_invalid(x);
51 if (ix == 0x3ff00000)
52 return __math_divzero(x < 0);
53 if (ix < 0x3e300000 && (huge + x) > zero)
54 return x; /* x<2**-28 */
55 SET_HIGH_WORD(x, ix);
56 if (ix < 0x3fe00000) { /* x < 0.5 */
57 t = x + x;
58 t = _F_64(0.5) * log1p64(t + t * x / (one - x));
59 } else
60 t = _F_64(0.5) * log1p64((x + x) / (one - x));
61 if (hx >= 0)
62 return t;
63 else
64 return -t;
65 }
66
67 _MATH_ALIAS_d_d(atanh)
68
69 #endif /* _NEED_FLOAT64 */
70
