mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-26 23:10:06 +00:00
134 lines
4.9 KiB
C
134 lines
4.9 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[] = "@(#)cosh.c 8.1 (Berkeley) 6/4/93";
|
|
#endif /* not lint */
|
|
|
|
/* COSH(X)
|
|
* RETURN THE HYPERBOLIC COSINE OF X
|
|
* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
|
|
* CODED IN C BY K.C. NG, 1/8/85;
|
|
* REVISED BY K.C. NG on 2/8/85, 2/23/85, 3/7/85, 3/29/85, 4/16/85.
|
|
*
|
|
* Required system supported functions :
|
|
* copysign(x,y)
|
|
* scalb(x,N)
|
|
*
|
|
* Required kernel function:
|
|
* exp(x)
|
|
* exp__E(x,c) ...return exp(x+c)-1-x for |x|<0.3465
|
|
*
|
|
* Method :
|
|
* 1. Replace x by |x|.
|
|
* 2.
|
|
* [ exp(x) - 1 ]^2
|
|
* 0 <= x <= 0.3465 : cosh(x) := 1 + -------------------
|
|
* 2*exp(x)
|
|
*
|
|
* exp(x) + 1/exp(x)
|
|
* 0.3465 <= x <= 22 : cosh(x) := -------------------
|
|
* 2
|
|
* 22 <= x <= lnovfl : cosh(x) := exp(x)/2
|
|
* lnovfl <= x <= lnovfl+log(2)
|
|
* : cosh(x) := exp(x)/2 (avoid overflow)
|
|
* log(2)+lnovfl < x < INF: overflow to INF
|
|
*
|
|
* Note: .3465 is a number near one half of ln2.
|
|
*
|
|
* Special cases:
|
|
* cosh(x) is x if x is +INF, -INF, or NaN.
|
|
* only cosh(0)=1 is exact for finite x.
|
|
*
|
|
* Accuracy:
|
|
* cosh(x) returns the exact hyperbolic cosine of x nearly rounded.
|
|
* In a test run with 768,000 random arguments on a VAX, the maximum
|
|
* observed error was 1.23 ulps (units in the last place).
|
|
*
|
|
* 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(mln2hi, 8.8029691931113054792E1 ,0f33,43b0,2bdb,c7e2, 7, .B00F33C7E22BDB)
|
|
vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A)
|
|
vc(lnovfl, 8.8029691931113053016E1 ,0f33,43b0,2bda,c7e2, 7, .B00F33C7E22BDA)
|
|
|
|
ic(mln2hi, 7.0978271289338397310E2, 10, 1.62E42FEFA39EF)
|
|
ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F)
|
|
ic(lnovfl, 7.0978271289338397310E2, 9, 1.62E42FEFA39EF)
|
|
|
|
#ifdef vccast
|
|
#define mln2hi vccast(mln2hi)
|
|
#define mln2lo vccast(mln2lo)
|
|
#define lnovfl vccast(lnovfl)
|
|
#endif
|
|
|
|
#if defined(vax)||defined(tahoe)
|
|
static max = 126 ;
|
|
#else /* defined(vax)||defined(tahoe) */
|
|
static max = 1023 ;
|
|
#endif /* defined(vax)||defined(tahoe) */
|
|
|
|
double cosh(x)
|
|
double x;
|
|
{
|
|
static const double half=1.0/2.0,
|
|
one=1.0, small=1.0E-18; /* fl(1+small)==1 */
|
|
double t;
|
|
|
|
#if !defined(vax)&&!defined(tahoe)
|
|
if(x!=x) return(x); /* x is NaN */
|
|
#endif /* !defined(vax)&&!defined(tahoe) */
|
|
if((x=copysign(x,one)) <= 22)
|
|
if(x<0.3465)
|
|
if(x<small) return(one+x);
|
|
else {t=x+__exp__E(x,0.0);x=t+t; return(one+t*t/(2.0+x)); }
|
|
|
|
else /* for x lies in [0.3465,22] */
|
|
{ t=exp(x); return((t+one/t)*half); }
|
|
|
|
if( lnovfl <= x && x <= (lnovfl+0.7))
|
|
/* for x lies in [lnovfl, lnovfl+ln2], decrease x by ln(2^(max+1))
|
|
* and return 2^max*exp(x) to avoid unnecessary overflow
|
|
*/
|
|
return(scalb(exp((x-mln2hi)-mln2lo), max));
|
|
|
|
else
|
|
return(exp(x)*half); /* for large x, cosh(x)=exp(x)/2 */
|
|
}
|