1 /* @(#)s_asinh.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 /* asinhl(x)
14 * Method :
15 * Based on
16 * asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ]
17 * we have
18 * asinhl(x) := x if 1+x*x=1,
19 * := signl(x)*(logl(x)+ln2)) for large |x|, else
20 * := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else
21 * := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2)))
22 */
23
24
25
26 static const long double
27 one = 1.0L,
28 ln2 = 6.931471805599453094172321214581765681e-1L,
29 huge = 1.0e+4900L;
30
31 long double
asinhl(long double x)32 asinhl(long double x)
33 {
34 long double t, w;
35 int32_t ix, sign;
36 ieee_quad_shape_type u;
37
38 u.value = x;
39 sign = u.parts32.mswhi;
40 ix = sign & 0x7fffffff;
41 if (ix >= 0x7fff0000)
42 return x + x; /* x is inf or NaN */
43 if (ix < 0x3fc70000)
44 { /* |x| < 2^ -56 */
45 if (huge + x > one)
46 return x; /* return x inexact except 0 */
47 }
48 u.parts32.mswhi = ix;
49 if (ix > 0x40350000)
50 { /* |x| > 2 ^ 54 */
51 w = logl (u.value) + ln2;
52 }
53 else if (ix >0x40000000)
54 { /* 2^ 54 > |x| > 2.0 */
55 t = u.value;
56 w = logl (2.0L * t + one / (sqrtl (x * x + one) + t));
57 }
58 else
59 { /* 2.0 > |x| > 2 ^ -56 */
60 t = x * x;
61 w = log1pl (u.value + t / (one + sqrtl (one + t)));
62 }
63 if (sign & 0x80000000)
64 return -w;
65 else
66 return w;
67 }
68
