1*2fe8fb19SBen Gras /* $NetBSD: n_acosh.c,v 1.6 2003/08/07 16:44:50 agc Exp $ */
2*2fe8fb19SBen Gras /*
3*2fe8fb19SBen Gras * Copyright (c) 1985, 1993
4*2fe8fb19SBen Gras * The Regents of the University of California. All rights reserved.
5*2fe8fb19SBen Gras *
6*2fe8fb19SBen Gras * Redistribution and use in source and binary forms, with or without
7*2fe8fb19SBen Gras * modification, are permitted provided that the following conditions
8*2fe8fb19SBen Gras * are met:
9*2fe8fb19SBen Gras * 1. Redistributions of source code must retain the above copyright
10*2fe8fb19SBen Gras * notice, this list of conditions and the following disclaimer.
11*2fe8fb19SBen Gras * 2. Redistributions in binary form must reproduce the above copyright
12*2fe8fb19SBen Gras * notice, this list of conditions and the following disclaimer in the
13*2fe8fb19SBen Gras * documentation and/or other materials provided with the distribution.
14*2fe8fb19SBen Gras * 3. Neither the name of the University nor the names of its contributors
15*2fe8fb19SBen Gras * may be used to endorse or promote products derived from this software
16*2fe8fb19SBen Gras * without specific prior written permission.
17*2fe8fb19SBen Gras *
18*2fe8fb19SBen Gras * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
19*2fe8fb19SBen Gras * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
20*2fe8fb19SBen Gras * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
21*2fe8fb19SBen Gras * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
22*2fe8fb19SBen Gras * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
23*2fe8fb19SBen Gras * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
24*2fe8fb19SBen Gras * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
25*2fe8fb19SBen Gras * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
26*2fe8fb19SBen Gras * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
27*2fe8fb19SBen Gras * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
28*2fe8fb19SBen Gras * SUCH DAMAGE.
29*2fe8fb19SBen Gras */
30*2fe8fb19SBen Gras
31*2fe8fb19SBen Gras #ifndef lint
32*2fe8fb19SBen Gras #if 0
33*2fe8fb19SBen Gras static char sccsid[] = "@(#)acosh.c 8.1 (Berkeley) 6/4/93";
34*2fe8fb19SBen Gras #endif
35*2fe8fb19SBen Gras #endif /* not lint */
36*2fe8fb19SBen Gras
37*2fe8fb19SBen Gras /* ACOSH(X)
38*2fe8fb19SBen Gras * RETURN THE INVERSE HYPERBOLIC COSINE OF X
39*2fe8fb19SBen Gras * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)
40*2fe8fb19SBen Gras * CODED IN C BY K.C. NG, 2/16/85;
41*2fe8fb19SBen Gras * REVISED BY K.C. NG on 3/6/85, 3/24/85, 4/16/85, 8/17/85.
42*2fe8fb19SBen Gras *
43*2fe8fb19SBen Gras * Required system supported functions :
44*2fe8fb19SBen Gras * sqrt(x)
45*2fe8fb19SBen Gras *
46*2fe8fb19SBen Gras * Required kernel function:
47*2fe8fb19SBen Gras * log1p(x) ...return log(1+x)
48*2fe8fb19SBen Gras *
49*2fe8fb19SBen Gras * Method :
50*2fe8fb19SBen Gras * Based on
51*2fe8fb19SBen Gras * acosh(x) = log [ x + sqrt(x*x-1) ]
52*2fe8fb19SBen Gras * we have
53*2fe8fb19SBen Gras * acosh(x) := log1p(x)+ln2, if (x > 1.0E20); else
54*2fe8fb19SBen Gras * acosh(x) := log1p( sqrt(x-1) * (sqrt(x-1) + sqrt(x+1)) ) .
55*2fe8fb19SBen Gras * These formulae avoid the over/underflow complication.
56*2fe8fb19SBen Gras *
57*2fe8fb19SBen Gras * Special cases:
58*2fe8fb19SBen Gras * acosh(x) is NaN with signal if x<1.
59*2fe8fb19SBen Gras * acosh(NaN) is NaN without signal.
60*2fe8fb19SBen Gras *
61*2fe8fb19SBen Gras * Accuracy:
62*2fe8fb19SBen Gras * acosh(x) returns the exact inverse hyperbolic cosine of x nearly
63*2fe8fb19SBen Gras * rounded. In a test run with 512,000 random arguments on a VAX, the
64*2fe8fb19SBen Gras * maximum observed error was 3.30 ulps (units of the last place) at
65*2fe8fb19SBen Gras * x=1.0070493753568216 .
66*2fe8fb19SBen Gras *
67*2fe8fb19SBen Gras * Constants:
68*2fe8fb19SBen Gras * The hexadecimal values are the intended ones for the following constants.
69*2fe8fb19SBen Gras * The decimal values may be used, provided that the compiler will convert
70*2fe8fb19SBen Gras * from decimal to binary accurately enough to produce the hexadecimal values
71*2fe8fb19SBen Gras * shown.
72*2fe8fb19SBen Gras */
73*2fe8fb19SBen Gras
74*2fe8fb19SBen Gras #define _LIBM_STATIC
75*2fe8fb19SBen Gras #include "mathimpl.h"
76*2fe8fb19SBen Gras
77*2fe8fb19SBen Gras vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000)
78*2fe8fb19SBen Gras vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
79*2fe8fb19SBen Gras
80*2fe8fb19SBen Gras ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000)
81*2fe8fb19SBen Gras ic(ln2lo, 1.9082149292705877000E-10,-33, 1.A39EF35793C76)
82*2fe8fb19SBen Gras
83*2fe8fb19SBen Gras #ifdef vccast
84*2fe8fb19SBen Gras #define ln2hi vccast(ln2hi)
85*2fe8fb19SBen Gras #define ln2lo vccast(ln2lo)
86*2fe8fb19SBen Gras #endif
87*2fe8fb19SBen Gras
88*2fe8fb19SBen Gras double
acosh(double x)89*2fe8fb19SBen Gras acosh(double x)
90*2fe8fb19SBen Gras {
91*2fe8fb19SBen Gras double t,big=1.E20; /* big+1==big */
92*2fe8fb19SBen Gras
93*2fe8fb19SBen Gras #if !defined(__vax__)&&!defined(tahoe)
94*2fe8fb19SBen Gras if(x!=x) return(x); /* x is NaN */
95*2fe8fb19SBen Gras #endif /* !defined(__vax__)&&!defined(tahoe) */
96*2fe8fb19SBen Gras
97*2fe8fb19SBen Gras /* return log1p(x) + log(2) if x is large */
98*2fe8fb19SBen Gras if(x>big) {t=log1p(x)+ln2lo; return(t+ln2hi);}
99*2fe8fb19SBen Gras
100*2fe8fb19SBen Gras t=sqrt(x-1.0);
101*2fe8fb19SBen Gras return(log1p(t*(t+sqrt(x+1.0))));
102*2fe8fb19SBen Gras }
103