mirror of
https://git.FreeBSD.org/src.git
synced 2024-12-22 11:17:19 +00:00
103 lines
3.8 KiB
C
103 lines
3.8 KiB
C
/*
|
|
* Copyright (c) 1985, 1993
|
|
* The Regents of the University of California. All rights reserved.
|
|
*
|
|
* Redistribution and use in source and binary forms, with or without
|
|
* modification, are permitted provided that the following conditions
|
|
* are met:
|
|
* 1. Redistributions of source code must retain the above copyright
|
|
* notice, this list of conditions and the following disclaimer.
|
|
* 2. Redistributions in binary form must reproduce the above copyright
|
|
* notice, this list of conditions and the following disclaimer in the
|
|
* documentation and/or other materials provided with the distribution.
|
|
* 3. All advertising materials mentioning features or use of this software
|
|
* must display the following acknowledgement:
|
|
* This product includes software developed by the University of
|
|
* California, Berkeley and its contributors.
|
|
* 4. Neither the name of the University nor the names of its contributors
|
|
* may be used to endorse or promote products derived from this software
|
|
* without specific prior written permission.
|
|
*
|
|
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
|
|
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
|
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
|
* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
|
|
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
|
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
|
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
|
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
|
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
|
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
|
* SUCH DAMAGE.
|
|
*/
|
|
|
|
#ifndef lint
|
|
static char sccsid[] = "@(#)acosh.c 8.1 (Berkeley) 6/4/93";
|
|
#endif /* not lint */
|
|
|
|
/* ACOSH(X)
|
|
* RETURN THE INVERSE HYPERBOLIC COSINE OF X
|
|
* DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)
|
|
* CODED IN C BY K.C. NG, 2/16/85;
|
|
* REVISED BY K.C. NG on 3/6/85, 3/24/85, 4/16/85, 8/17/85.
|
|
*
|
|
* Required system supported functions :
|
|
* sqrt(x)
|
|
*
|
|
* Required kernel function:
|
|
* log1p(x) ...return log(1+x)
|
|
*
|
|
* Method :
|
|
* Based on
|
|
* acosh(x) = log [ x + sqrt(x*x-1) ]
|
|
* we have
|
|
* acosh(x) := log1p(x)+ln2, if (x > 1.0E20); else
|
|
* acosh(x) := log1p( sqrt(x-1) * (sqrt(x-1) + sqrt(x+1)) ) .
|
|
* These formulae avoid the over/underflow complication.
|
|
*
|
|
* Special cases:
|
|
* acosh(x) is NaN with signal if x<1.
|
|
* acosh(NaN) is NaN without signal.
|
|
*
|
|
* Accuracy:
|
|
* acosh(x) returns the exact inverse hyperbolic cosine of x nearly
|
|
* rounded. In a test run with 512,000 random arguments on a VAX, the
|
|
* maximum observed error was 3.30 ulps (units of the last place) at
|
|
* x=1.0070493753568216 .
|
|
*
|
|
* Constants:
|
|
* The hexadecimal values are the intended ones for the following constants.
|
|
* The decimal values may be used, provided that the compiler will convert
|
|
* from decimal to binary accurately enough to produce the hexadecimal values
|
|
* shown.
|
|
*/
|
|
|
|
#include "mathimpl.h"
|
|
|
|
vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000)
|
|
vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
|
|
|
|
ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000)
|
|
ic(ln2lo, 1.9082149292705877000E-10,-33, 1.A39EF35793C76)
|
|
|
|
#ifdef vccast
|
|
#define ln2hi vccast(ln2hi)
|
|
#define ln2lo vccast(ln2lo)
|
|
#endif
|
|
|
|
double acosh(x)
|
|
double x;
|
|
{
|
|
double t,big=1.E20; /* big+1==big */
|
|
|
|
#if !defined(vax)&&!defined(tahoe)
|
|
if(x!=x) return(x); /* x is NaN */
|
|
#endif /* !defined(vax)&&!defined(tahoe) */
|
|
|
|
/* return log1p(x) + log(2) if x is large */
|
|
if(x>big) {t=log1p(x)+ln2lo; return(t+ln2hi);}
|
|
|
|
t=sqrt(x-1.0);
|
|
return(log1p(t*(t+sqrt(x+1.0))));
|
|
}
|