1 #include "FEATURE/uwin"
2
3 #if !_UWIN || _lib_acosh
4
_STUB_acosh()5 void _STUB_acosh(){}
6
7 #else
8
9 /*
10 * Copyright (c) 1985, 1993
11 * The Regents of the University of California. All rights reserved.
12 *
13 * Redistribution and use in source and binary forms, with or without
14 * modification, are permitted provided that the following conditions
15 * are met:
16 * 1. Redistributions of source code must retain the above copyright
17 * notice, this list of conditions and the following disclaimer.
18 * 2. Redistributions in binary form must reproduce the above copyright
19 * notice, this list of conditions and the following disclaimer in the
20 * documentation and/or other materials provided with the distribution.
21 * 3. Neither the name of the University nor the names of its contributors
22 * may be used to endorse or promote products derived from this software
23 * without specific prior written permission.
24 *
25 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
26 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
27 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
28 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
29 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
30 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
31 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
32 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
33 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
34 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
35 * SUCH DAMAGE.
36 */
37
38 #ifndef lint
39 static char sccsid[] = "@(#)acosh.c 8.1 (Berkeley) 6/4/93";
40 #endif /* not lint */
41
42 /* ACOSH(X)
43 * RETURN THE INVERSE HYPERBOLIC COSINE OF X
44 * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)
45 * CODED IN C BY K.C. NG, 2/16/85;
46 * REVISED BY K.C. NG on 3/6/85, 3/24/85, 4/16/85, 8/17/85.
47 *
48 * Required system supported functions :
49 * sqrt(x)
50 *
51 * Required kernel function:
52 * log1p(x) ...return log(1+x)
53 *
54 * Method :
55 * Based on
56 * acosh(x) = log [ x + sqrt(x*x-1) ]
57 * we have
58 * acosh(x) := log1p(x)+ln2, if (x > 1.0E20); else
59 * acosh(x) := log1p( sqrt(x-1) * (sqrt(x-1) + sqrt(x+1)) ) .
60 * These formulae avoid the over/underflow complication.
61 *
62 * Special cases:
63 * acosh(x) is NaN with signal if x<1.
64 * acosh(NaN) is NaN without signal.
65 *
66 * Accuracy:
67 * acosh(x) returns the exact inverse hyperbolic cosine of x nearly
68 * rounded. In a test run with 512,000 random arguments on a VAX, the
69 * maximum observed error was 3.30 ulps (units of the last place) at
70 * x=1.0070493753568216 .
71 *
72 * Constants:
73 * The hexadecimal values are the intended ones for the following constants.
74 * The decimal values may be used, provided that the compiler will convert
75 * from decimal to binary accurately enough to produce the hexadecimal values
76 * shown.
77 */
78
79 #include "mathimpl.h"
80
81 vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000)
82 vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
83
84 ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000)
85 ic(ln2lo, 1.9082149292705877000E-10,-33, 1.A39EF35793C76)
86
87 #ifdef vccast
88 #define ln2hi vccast(ln2hi)
89 #define ln2lo vccast(ln2lo)
90 #endif
91
92 extern double acosh(x)
93 double x;
94 {
95 double t,big=1.E20; /* big+1==big */
96
97 #if !defined(vax)&&!defined(tahoe)
98 if(x!=x) return(x); /* x is NaN */
99 #endif /* !defined(vax)&&!defined(tahoe) */
100
101 /* return log1p(x) + log(2) if x is large */
102 if(x>big) {t=log1p(x)+ln2lo; return(t+ln2hi);}
103
104 t=sqrt(x-1.0);
105 return(log1p(t*(t+sqrt(x+1.0))));
106 }
107
108 #endif
109