134 lines
4.9 KiB
C
134 lines
4.9 KiB
C
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/*
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* Copyright (c) 1985 Regents of the University of California.
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* 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[] = "@(#)cosh.c 5.6 (Berkeley) 10/9/90";
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#endif /* not lint */
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/* COSH(X)
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* RETURN THE 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, 1/8/85;
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* REVISED BY K.C. NG on 2/8/85, 2/23/85, 3/7/85, 3/29/85, 4/16/85.
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*
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* Required system supported functions :
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* copysign(x,y)
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* scalb(x,N)
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*
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* Required kernel function:
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* exp(x)
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* exp__E(x,c) ...return exp(x+c)-1-x for |x|<0.3465
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*
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* Method :
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* 1. Replace x by |x|.
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* 2.
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* [ exp(x) - 1 ]^2
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* 0 <= x <= 0.3465 : cosh(x) := 1 + -------------------
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* 2*exp(x)
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*
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* exp(x) + 1/exp(x)
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* 0.3465 <= x <= 22 : cosh(x) := -------------------
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* 2
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* 22 <= x <= lnovfl : cosh(x) := exp(x)/2
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* lnovfl <= x <= lnovfl+log(2)
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* : cosh(x) := exp(x)/2 (avoid overflow)
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* log(2)+lnovfl < x < INF: overflow to INF
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*
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* Note: .3465 is a number near one half of ln2.
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*
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* Special cases:
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* cosh(x) is x if x is +INF, -INF, or NaN.
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* only cosh(0)=1 is exact for finite x.
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*
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* Accuracy:
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* cosh(x) returns the exact hyperbolic cosine of x nearly rounded.
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* In a test run with 768,000 random arguments on a VAX, the maximum
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* observed error was 1.23 ulps (units in the last place).
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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(mln2hi, 8.8029691931113054792E1 ,0f33,43b0,2bdb,c7e2, 7, .B00F33C7E22BDB)
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vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A)
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vc(lnovfl, 8.8029691931113053016E1 ,0f33,43b0,2bda,c7e2, 7, .B00F33C7E22BDA)
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ic(mln2hi, 7.0978271289338397310E2, 10, 1.62E42FEFA39EF)
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ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F)
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ic(lnovfl, 7.0978271289338397310E2, 9, 1.62E42FEFA39EF)
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#ifdef vccast
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#define mln2hi vccast(mln2hi)
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#define mln2lo vccast(mln2lo)
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#define lnovfl vccast(lnovfl)
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#endif
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#if defined(vax)||defined(tahoe)
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static max = 126 ;
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#else /* defined(vax)||defined(tahoe) */
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static max = 1023 ;
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#endif /* defined(vax)||defined(tahoe) */
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double cosh(x)
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double x;
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{
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static const double half=1.0/2.0,
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one=1.0, small=1.0E-18; /* fl(1+small)==1 */
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double t;
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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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if((x=copysign(x,one)) <= 22)
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if(x<0.3465)
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if(x<small) return(one+x);
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else {t=x+exp__E(x,0.0);x=t+t; return(one+t*t/(2.0+x)); }
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else /* for x lies in [0.3465,22] */
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{ t=exp(x); return((t+one/t)*half); }
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if( lnovfl <= x && x <= (lnovfl+0.7))
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/* for x lies in [lnovfl, lnovfl+ln2], decrease x by ln(2^(max+1))
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* and return 2^max*exp(x) to avoid unnecessary overflow
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*/
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return(scalb(exp((x-mln2hi)-mln2lo), max));
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else
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return(exp(x)*half); /* for large x, cosh(x)=exp(x)/2 */
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}
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