xref: /illumos-gate/usr/src/lib/libm/common/C/asinh.c (revision ddc0e0b53c661f6e439e3b7072b3ef353eadb4af)
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