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