1 /* $NetBSD: n_acosh.c,v 1.6 2003/08/07 16:44:50 agc 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[] = "@(#)acosh.c 8.1 (Berkeley) 6/4/93";
34 #endif
35 #endif /* not lint */
36
37 /* ACOSH(X)
38 * RETURN THE INVERSE HYPERBOLIC COSINE 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 3/6/85, 3/24/85, 4/16/85, 8/17/85.
42 *
43 * Required system supported functions :
44 * sqrt(x)
45 *
46 * Required kernel function:
47 * log1p(x) ...return log(1+x)
48 *
49 * Method :
50 * Based on
51 * acosh(x) = log [ x + sqrt(x*x-1) ]
52 * we have
53 * acosh(x) := log1p(x)+ln2, if (x > 1.0E20); else
54 * acosh(x) := log1p( sqrt(x-1) * (sqrt(x-1) + sqrt(x+1)) ) .
55 * These formulae avoid the over/underflow complication.
56 *
57 * Special cases:
58 * acosh(x) is NaN with signal if x<1.
59 * acosh(NaN) is NaN without signal.
60 *
61 * Accuracy:
62 * acosh(x) returns the exact inverse hyperbolic cosine of x nearly
63 * rounded. In a test run with 512,000 random arguments on a VAX, the
64 * maximum observed error was 3.30 ulps (units of the last place) at
65 * x=1.0070493753568216 .
66 *
67 * Constants:
68 * The hexadecimal values are the intended ones for the following constants.
69 * The decimal values may be used, provided that the compiler will convert
70 * from decimal to binary accurately enough to produce the hexadecimal values
71 * shown.
72 */
73
74 #define _LIBM_STATIC
75 #include "mathimpl.h"
76
77 vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000)
78 vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
79
80 ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000)
81 ic(ln2lo, 1.9082149292705877000E-10,-33, 1.A39EF35793C76)
82
83 #ifdef vccast
84 #define ln2hi vccast(ln2hi)
85 #define ln2lo vccast(ln2lo)
86 #endif
87
88 double
acosh(double x)89 acosh(double x)
90 {
91 double t,big=1.E20; /* big+1==big */
92
93 #if !defined(__vax__)&&!defined(tahoe)
94 if(x!=x) return(x); /* x is NaN */
95 #endif /* !defined(__vax__)&&!defined(tahoe) */
96
97 /* return log1p(x) + log(2) if x is large */
98 if(x>big) {t=log1p(x)+ln2lo; return(t+ln2hi);}
99
100 t=sqrt(x-1.0);
101 return(log1p(t*(t+sqrt(x+1.0))));
102 }
103