1 /*
2 * CDDL HEADER START
3 *
4 * The contents of this file are subject to the terms of the
5 * Common Development and Distribution License (the "License").
6 * You may not use this file except in compliance with the License.
7 *
8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9 * or http://www.opensolaris.org/os/licensing.
10 * See the License for the specific language governing permissions
11 * and limitations under the License.
12 *
13 * When distributing Covered Code, include this CDDL HEADER in each
14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15 * If applicable, add the following below this CDDL HEADER, with the
16 * fields enclosed by brackets "[]" replaced with your own identifying
17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 *
19 * CDDL HEADER END
20 */
21
22 /*
23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
24 */
25 /*
26 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
27 * Use is subject to license terms.
28 */
29
30 #pragma weak __asinh = asinh
31
32 /* INDENT OFF */
33 /*
34 * asinh(x)
35 * Method :
36 * Based on
37 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
38 * we have
39 * asinh(x) := x if 1+x*x == 1,
40 * := sign(x)*(log(x)+ln2)) for large |x|, else
41 * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x| > 2, else
42 * := sign(x)*log1p(|x|+x^2/(1+sqrt(1+x^2)))
43 */
44 /* INDENT ON */
45
46 #include "libm_macros.h"
47 #include <math.h>
48
49 static const double xxx[] = {
50 /* one */ 1.00000000000000000000e+00, /* 3FF00000, 00000000 */
51 /* ln2 */ 6.93147180559945286227e-01, /* 3FE62E42, FEFA39EF */
52 /* huge */ 1.00000000000000000000e+300
53 };
54 #define one xxx[0]
55 #define ln2 xxx[1]
56 #define huge xxx[2]
57
58 double
asinh(double x)59 asinh(double x) {
60 double t, w;
61 int hx, ix;
62
63 hx = ((int *) &x)[HIWORD];
64 ix = hx & 0x7fffffff;
65 if (ix >= 0x7ff00000)
66 #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
67 return (ix >= 0x7ff80000 ? x : x + x);
68 /* assumes sparc-like QNaN */
69 #else
70 return (x + x); /* x is inf or NaN */
71 #endif
72 if (ix < 0x3e300000) { /* |x|<2**-28 */
73 if (huge + x > one)
74 return (x); /* return x inexact except 0 */
75 }
76 if (ix > 0x41b00000) { /* |x| > 2**28 */
77 w = log(fabs(x)) + ln2;
78 } else if (ix > 0x40000000) {
79 /* 2**28 > |x| > 2.0 */
80 t = fabs(x);
81 w = log(2.0 * t + one / (sqrt(x * x + one) + t));
82 } else {
83 /* 2.0 > |x| > 2**-28 */
84 t = x * x;
85 w = log1p(fabs(x) + t / (one + sqrt(one + t)));
86 }
87 return (hx > 0 ? w : -w);
88 }
89