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 /* asinhq(x)
22 * Method :
23 * Based on
24 * asinhq(x) = signl(x) * logq [ |x| + sqrtq(x*x+1) ]
25 * we have
26 * asinhq(x) := x if 1+x*x=1,
27 * := signl(x)*(logq(x)+ln2)) for large |x|, else
28 * := signl(x)*logq(2|x|+1/(|x|+sqrtq(x*x+1))) if|x|>2, else
29 * := signl(x)*log1pq(|x| + x^2/(1 + sqrtq(1+x^2)))
30 */
31
32 #include "quadmath-imp.h"
33
34 static const __float128
35 one = 1,
36 ln2 = 6.931471805599453094172321214581765681e-1Q,
37 huge = 1.0e+4900Q;
38
39 __float128
asinhq(__float128 x)40 asinhq (__float128 x)
41 {
42 __float128 t, w;
43 int32_t ix, sign;
44 ieee854_float128 u;
45
46 u.value = x;
47 sign = u.words32.w0;
48 ix = sign & 0x7fffffff;
49 if (ix == 0x7fff0000)
50 return x + x; /* x is inf or NaN */
51 if (ix < 0x3fc70000)
52 { /* |x| < 2^ -56 */
53 math_check_force_underflow (x);
54 if (huge + x > one)
55 return x; /* return x inexact except 0 */
56 }
57 u.words32.w0 = ix;
58 if (ix > 0x40350000)
59 { /* |x| > 2 ^ 54 */
60 w = logq (u.value) + ln2;
61 }
62 else if (ix >0x40000000)
63 { /* 2^ 54 > |x| > 2.0 */
64 t = u.value;
65 w = logq (2.0 * t + one / (sqrtq (x * x + one) + t));
66 }
67 else
68 { /* 2.0 > |x| > 2 ^ -56 */
69 t = x * x;
70 w = log1pq (u.value + t / (one + sqrtq (one + t)));
71 }
72 if (sign & 0x80000000)
73 return -w;
74 else
75 return w;
76 }
77