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 <math-underflow.h>
28#include <libm-alias-double.h>
29
30static const double
31 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
32 ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
33 huge = 1.00000000000000000000e+300;
34
35double
36__asinh (double x)
37{
38 double w;
39 int32_t hx, ix;
40 GET_HIGH_WORD (hx, x);
41 ix = hx & 0x7fffffff;
42 if (__glibc_unlikely (ix < 0x3e300000)) /* |x|<2**-28 */
43 {
44 math_check_force_underflow (x);
45 if (huge + x > one)
46 return x; /* return x inexact except 0 */
47 }
48 if (__glibc_unlikely (ix > 0x41b00000)) /* |x| > 2**28 */
49 {
50 if (ix >= 0x7ff00000)
51 return x + x; /* x is inf or NaN */
52 w = __ieee754_log (fabs (x)) + ln2;
53 }
54 else
55 {
56 double xa = fabs (x);
57 if (ix > 0x40000000) /* 2**28 > |x| > 2.0 */
58 {
59 w = __ieee754_log (2.0 * xa + one / (sqrt (xa * xa + one) +
60 xa));
61 }
62 else /* 2.0 > |x| > 2**-28 */
63 {
64 double t = xa * xa;
65 w = __log1p (xa + t / (one + sqrt (one + t)));
66 }
67 }
68 return copysign (w, x);
69}
70libm_alias_double (__asinh, asinh)
71