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 |
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: 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: x); |
66 | if(ix<0x3fe0000000000000LL) { /* x < 0.5 */ |
67 | t = x+x; |
68 | t = 0.5*__log1pl(x: t+t*x/(one-x)); |
69 | } else |
70 | t = 0.5*__log1pl(x: (x+x)/(one-x)); |
71 | if(hx>=0) return t; else return -t; |
72 | } |
73 | libm_alias_finite (__ieee754_atanhl, __atanhl) |
74 | |