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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 | #if defined(LIBM_SCCS) && !defined(lint) | |
14 | static char rcsid[] = "$NetBSD: e_atanh.c,v 1.8 1995/05/10 20:44:55 jtc Exp $"; | |
15 | #endif | |
16 | ||
17 | /* __ieee754_atanh(x) | |
18 | * Method : | |
19 | * 1.Reduced x to positive by atanh(-x) = -atanh(x) | |
20 | * 2.For x>=0.5 | |
21 | * 1 2x x | |
22 | * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) | |
23 | * 2 1 - x 1 - x | |
24 | * | |
25 | * For x<0.5 | |
26 | * atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) | |
27 | * | |
28 | * Special cases: | |
29 | * atanh(x) is NaN if |x| > 1 with signal; | |
30 | * atanh(NaN) is that NaN with no signal; | |
31 | * atanh(+-1) is +-INF with signal. | |
32 | * | |
33 | */ | |
34 | ||
35 | #include "math.h" | |
36 | #include "math_private.h" | |
37 | ||
38 | #ifdef __STDC__ | |
39 | static const long double one = 1.0L, huge = 1e300L; | |
40 | #else | |
41 | static long double one = 1.0L, huge = 1e300L; | |
42 | #endif | |
43 | ||
44 | #ifdef __STDC__ | |
45 | static const long double zero = 0.0L; | |
46 | #else | |
47 | static long double zero = 0.0L; | |
48 | #endif | |
49 | ||
50 | #ifdef __STDC__ | |
51 | long double __ieee754_atanhl(long double x) | |
52 | #else | |
53 | long double __ieee754_atanhl(x) | |
54 | long double x; | |
55 | #endif | |
56 | { | |
57 | long double t; | |
58 | int64_t hx,ix; | |
59 | u_int64_t lx; | |
60 | GET_LDOUBLE_WORDS64(hx,lx,x); | |
61 | ix = hx&0x7fffffffffffffffLL; | |
62 | if (ix >= 0x3ff0000000000000LL) { /* |x|>=1 */ | |
63 | if (ix > 0x3ff0000000000000LL) | |
64 | return (x-x)/(x-x); | |
65 | t = fabsl (x); | |
66 | if (t > one) | |
67 | return (x-x)/(x-x); | |
68 | if (t == one) | |
69 | return x/zero; | |
70 | } | |
71 | if(ix<0x3e20000000000000LL&&(huge+x)>zero) return x; /* x<2**-29 */ | |
72 | x = fabsl (x); | |
73 | if(ix<0x3fe0000000000000LL) { /* x < 0.5 */ | |
74 | t = x+x; | |
75 | t = 0.5*__log1pl(t+t*x/(one-x)); | |
76 | } else | |
77 | t = 0.5*__log1pl((x+x)/(one-x)); | |
78 | if(hx>=0) return t; else return -t; | |
79 | } |