1 | /* s_asinhl.c -- long double version of s_asinh.c. |
2 | * Conversion to long double by Ulrich Drepper, |
3 | * Cygnus Support, drepper@cygnus.com. |
4 | */ |
5 | |
6 | /* |
7 | * ==================================================== |
8 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
9 | * |
10 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
11 | * Permission to use, copy, modify, and distribute this |
12 | * software is freely granted, provided that this notice |
13 | * is preserved. |
14 | * ==================================================== |
15 | */ |
16 | |
17 | #if defined(LIBM_SCCS) && !defined(lint) |
18 | static char rcsid[] = "$NetBSD: $" ; |
19 | #endif |
20 | |
21 | /* asinhl(x) |
22 | * Method : |
23 | * Based on |
24 | * asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ] |
25 | * we have |
26 | * asinhl(x) := x if 1+x*x=1, |
27 | * := signl(x)*(logl(x)+ln2)) for large |x|, else |
28 | * := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else |
29 | * := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2))) |
30 | */ |
31 | |
32 | #include <float.h> |
33 | #include <math.h> |
34 | #include <math_private.h> |
35 | #include <libm-alias-ldouble.h> |
36 | |
37 | static const _Float128 |
38 | one = 1, |
39 | ln2 = L(6.931471805599453094172321214581765681e-1), |
40 | huge = L(1.0e+4900); |
41 | |
42 | _Float128 |
43 | __asinhl (_Float128 x) |
44 | { |
45 | _Float128 t, w; |
46 | int32_t ix, sign; |
47 | ieee854_long_double_shape_type u; |
48 | |
49 | u.value = x; |
50 | sign = u.parts32.w0; |
51 | ix = sign & 0x7fffffff; |
52 | if (ix == 0x7fff0000) |
53 | return x + x; /* x is inf or NaN */ |
54 | if (ix < 0x3fc70000) |
55 | { /* |x| < 2^ -56 */ |
56 | math_check_force_underflow (x); |
57 | if (huge + x > one) |
58 | return x; /* return x inexact except 0 */ |
59 | } |
60 | u.parts32.w0 = ix; |
61 | if (ix > 0x40350000) |
62 | { /* |x| > 2 ^ 54 */ |
63 | w = __ieee754_logl (u.value) + ln2; |
64 | } |
65 | else if (ix >0x40000000) |
66 | { /* 2^ 54 > |x| > 2.0 */ |
67 | t = u.value; |
68 | w = __ieee754_logl (2.0 * t + one / (__ieee754_sqrtl (x * x + one) + t)); |
69 | } |
70 | else |
71 | { /* 2.0 > |x| > 2 ^ -56 */ |
72 | t = x * x; |
73 | w = __log1pl (u.value + t / (one + __ieee754_sqrtl (one + t))); |
74 | } |
75 | if (sign & 0x80000000) |
76 | return -w; |
77 | else |
78 | return w; |
79 | } |
80 | libm_alias_ldouble (__asinh, asinh) |
81 | |