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)
18static 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 <math-underflow.h>
36#include <libm-alias-ldouble.h>
37
38static const _Float128
39 one = 1,
40 ln2 = L(6.931471805599453094172321214581765681e-1),
41 huge = L(1.0e+4900);
42
43_Float128
44__asinhl (_Float128 x)
45{
46 _Float128 t, w;
47 int32_t ix, sign;
48 ieee854_long_double_shape_type u;
49
50 u.value = x;
51 sign = u.parts32.w0;
52 ix = sign & 0x7fffffff;
53 if (ix == 0x7fff0000)
54 return x + x; /* x is inf or NaN */
55 if (ix < 0x3fc70000)
56 { /* |x| < 2^ -56 */
57 math_check_force_underflow (x);
58 if (huge + x > one)
59 return x; /* return x inexact except 0 */
60 }
61 u.parts32.w0 = ix;
62 if (ix > 0x40350000)
63 { /* |x| > 2 ^ 54 */
64 w = __ieee754_logl (u.value) + ln2;
65 }
66 else if (ix >0x40000000)
67 { /* 2^ 54 > |x| > 2.0 */
68 t = u.value;
69 w = __ieee754_logl (2.0 * t + one / (sqrtl (x * x + one) + t));
70 }
71 else
72 { /* 2.0 > |x| > 2 ^ -56 */
73 t = x * x;
74 w = __log1pl (u.value + t / (one + sqrtl (one + t)));
75 }
76 if (sign & 0x80000000)
77 return -w;
78 else
79 return w;
80}
81libm_alias_ldouble (__asinh, asinh)
82