1 /* $NetBSD: n_asinh.c,v 1.7 2008/04/29 15:10:02 uwe Exp $ */
2 /*
3 * Copyright (c) 1985, 1993
4 * The Regents of the University of California. All rights reserved.
5 *
6 * Redistribution and use in source and binary forms, with or without
7 * modification, are permitted provided that the following conditions
8 * are met:
9 * 1. Redistributions of source code must retain the above copyright
10 * notice, this list of conditions and the following disclaimer.
11 * 2. Redistributions in binary form must reproduce the above copyright
12 * notice, this list of conditions and the following disclaimer in the
13 * documentation and/or other materials provided with the distribution.
14 * 3. Neither the name of the University nor the names of its contributors
15 * may be used to endorse or promote products derived from this software
16 * without specific prior written permission.
17 *
18 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
19 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
20 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
21 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
22 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
23 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
24 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
25 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
26 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
27 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
28 * SUCH DAMAGE.
29 */
30
31 #ifndef lint
32 #if 0
33 static char sccsid[] = "@(#)asinh.c 8.1 (Berkeley) 6/4/93";
34 #endif
35 #endif /* not lint */
36
37 /* ASINH(X)
38 * RETURN THE INVERSE HYPERBOLIC SINE OF X
39 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
40 * CODED IN C BY K.C. NG, 2/16/85;
41 * REVISED BY K.C. NG on 3/7/85, 3/24/85, 4/16/85.
42 *
43 * Required system supported functions :
44 * copysign(x,y)
45 * sqrt(x)
46 *
47 * Required kernel function:
48 * log1p(x) ...return log(1+x)
49 *
50 * Method :
51 * Based on
52 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
53 * we have
54 * asinh(x) := x if 1+x*x=1,
55 * := sign(x)*(log1p(x)+ln2)) if sqrt(1+x*x)=x, else
56 * := sign(x)*log1p(|x| + |x|/(1/|x| + sqrt(1+(1/|x|)^2)) )
57 *
58 * Accuracy:
59 * asinh(x) returns the exact inverse hyperbolic sine of x nearly rounded.
60 * In a test run with 52,000 random arguments on a VAX, the maximum
61 * observed error was 1.58 ulps (units in the last place).
62 *
63 * Constants:
64 * The hexadecimal values are the intended ones for the following constants.
65 * The decimal values may be used, provided that the compiler will convert
66 * from decimal to binary accurately enough to produce the hexadecimal values
67 * shown.
68 */
69 #define _LIBM_STATIC
70 #include "mathimpl.h"
71
72 vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000)
73 vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
74
75 ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000)
76 ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76)
77
78 #ifdef vccast
79 #define ln2hi vccast(ln2hi)
80 #define ln2lo vccast(ln2lo)
81 #endif
82
83 double
asinh(double x)84 asinh(double x)
85 {
86 double t,s;
87 static const double small=1.0E-10, /* fl(1+small*small) == 1 */
88 big =1.0E20, /* fl(1+big) == big */
89 one =1.0 ;
90
91 #if !defined(__vax__)&&!defined(tahoe)
92 if(x!=x) return(x); /* x is NaN */
93 #endif /* !defined(__vax__)&&!defined(tahoe) */
94 if((t=copysign(x,one))>small)
95 if(t<big) {
96 s=one/t; return(copysign(log1p(t+t/(s+sqrt(one+s*s))),x)); }
97 else /* if |x| > big */
98 {s=log1p(t)+ln2lo; return(copysign(s+ln2hi,x));}
99 else /* if |x| < small */
100 return(x);
101 }
102