mirror of
https://sourceware.org/git/glibc.git
synced 2024-12-01 17:30:07 +00:00
122 lines
4.5 KiB
C
122 lines
4.5 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[] = "@(#)sinh.c 8.1 (Berkeley) 6/4/93";
|
|
#endif /* not lint */
|
|
|
|
/* SINH(X)
|
|
* RETURN THE HYPERBOLIC SINE 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, 3/7/85, 3/24/85, 4/16/85.
|
|
*
|
|
* Required system supported functions :
|
|
* copysign(x,y)
|
|
* scalb(x,N)
|
|
*
|
|
* Required kernel functions:
|
|
* expm1(x) ...return exp(x)-1
|
|
*
|
|
* Method :
|
|
* 1. reduce x to non-negative by sinh(-x) = - sinh(x).
|
|
* 2.
|
|
*
|
|
* expm1(x) + expm1(x)/(expm1(x)+1)
|
|
* 0 <= x <= lnovfl : sinh(x) := --------------------------------
|
|
* 2
|
|
* lnovfl <= x <= lnovfl+ln2 : sinh(x) := expm1(x)/2 (avoid overflow)
|
|
* lnovfl+ln2 < x < INF : overflow to INF
|
|
*
|
|
*
|
|
* Special cases:
|
|
* sinh(x) is x if x is +INF, -INF, or NaN.
|
|
* only sinh(0)=0 is exact for finite argument.
|
|
*
|
|
* Accuracy:
|
|
* sinh(x) returns the exact hyperbolic sine of x nearly rounded. In
|
|
* a test run with 1,024,000 random arguments on a VAX, the maximum
|
|
* observed error was 1.93 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 sinh(x)
|
|
double x;
|
|
{
|
|
static const double one=1.0, half=1.0/2.0 ;
|
|
double t, sign;
|
|
#if !defined(vax)&&!defined(tahoe)
|
|
if(x!=x) return(x); /* x is NaN */
|
|
#endif /* !defined(vax)&&!defined(tahoe) */
|
|
sign=copysign(one,x);
|
|
x=copysign(x,one);
|
|
if(x<lnovfl)
|
|
{t=expm1(x); return(copysign((t+t/(one+t))*half,sign));}
|
|
|
|
else if(x <= lnovfl+0.7)
|
|
/* subtract x by ln(2^(max+1)) and return 2^max*exp(x)
|
|
to avoid unnecessary overflow */
|
|
return(copysign(scalb(one+expm1((x-mln2hi)-mln2lo),max),sign));
|
|
|
|
else /* sinh(+-INF) = +-INF, sinh(+-big no.) overflow to +-INF */
|
|
return( expm1(x)*sign );
|
|
}
|