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/* asinh(x)
14 * Method :
15 * Based on
16 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
17 * we have
18 * asinh(x) := x if 1+x*x=1,
19 * := sign(x)*(log(x)+ln2)) for large |x|, else
20 * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
21 * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
22 */
23
24#include <float.h>
25#include <math.h>
26#include <math_private.h>
27#include <libm-alias-double.h>
28
29static const double
30 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
31 ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
32 huge = 1.00000000000000000000e+300;
33
34double
35__asinh (double x)
36{
37 double w;
38 int32_t hx, ix;
39 GET_HIGH_WORD (hx, x);
40 ix = hx & 0x7fffffff;
41 if (__glibc_unlikely (ix < 0x3e300000)) /* |x|<2**-28 */
42 {
43 math_check_force_underflow (x);
44 if (huge + x > one)
45 return x; /* return x inexact except 0 */
46 }
47 if (__glibc_unlikely (ix > 0x41b00000)) /* |x| > 2**28 */
48 {
49 if (ix >= 0x7ff00000)
50 return x + x; /* x is inf or NaN */
51 w = __ieee754_log (fabs (x)) + ln2;
52 }
53 else
54 {
55 double xa = fabs (x);
56 if (ix > 0x40000000) /* 2**28 > |x| > 2.0 */
57 {
58 w = __ieee754_log (2.0 * xa + one / (__ieee754_sqrt (xa * xa + one) +
59 xa));
60 }
61 else /* 2.0 > |x| > 2**-28 */
62 {
63 double t = xa * xa;
64 w = __log1p (xa + t / (one + __ieee754_sqrt (one + t)));
65 }
66 }
67 return __copysign (w, x);
68}
69libm_alias_double (__asinh, asinh)
70