1 /* @(#)e_atanh.c 5.1 93/09/24 */
2 /*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, 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 /* __ieee754_atanh(x)
14 * Method :
15 * 1.Reduced x to positive by atanh(-x) = -atanh(x)
16 * 2.For x>=0.5
17 * 1 2x x
18 * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
19 * 2 1 - x 1 - x
20 *
21 * For x<0.5
22 * atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
23 *
24 * Special cases:
25 * atanh(x) is NaN if |x| > 1 with signal;
26 * atanh(NaN) is that NaN with no signal;
27 * atanh(+-1) is +-INF with signal.
28 *
29 */
30
31 #include <float.h>
32 #include <math.h>
33 #include <math_private.h>
34 #include <math-underflow.h>
35 #include <libm-alias-finite.h>
36
37 static const long double one = 1.0L, huge = 1e300L;
38
39 static const long double zero = 0.0L;
40
41 long double
__ieee754_atanhl(long double x)42 __ieee754_atanhl(long double x)
43 {
44 long double t;
45 int64_t hx,ix;
46 double xhi;
47
48 xhi = ldbl_high (x);
49 EXTRACT_WORDS64 (hx, xhi);
50 ix = hx&0x7fffffffffffffffLL;
51 if (ix >= 0x3ff0000000000000LL) { /* |x|>=1 */
52 if (ix > 0x3ff0000000000000LL)
53 return (x-x)/(x-x);
54 t = fabsl (x);
55 if (t > one)
56 return (x-x)/(x-x);
57 if (t == one)
58 return x/zero;
59 }
60 if(ix<0x3c70000000000000LL&&(huge+x)>zero) /* x<2**-56 */
61 {
62 math_check_force_underflow (x);
63 return x;
64 }
65 x = fabsl (x);
66 if(ix<0x3fe0000000000000LL) { /* x < 0.5 */
67 t = x+x;
68 t = 0.5*__log1pl(t+t*x/(one-x));
69 } else
70 t = 0.5*__log1pl((x+x)/(one-x));
71 if(hx>=0) return t; else return -t;
72 }
73 libm_alias_finite (__ieee754_atanhl, __atanhl)
74