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