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/* $OpenBSD: n_sinh.c,v 1.10 2009/10/27 23:59:29 deraadt Exp $ */
/* $NetBSD: n_sinh.c,v 1.1 1995/10/10 23:37:05 ragge Exp $ */
/*
* 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. 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.
*/
/* 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)
* scalbn(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 "math.h"
#include "mathimpl.h"
static const double mln2hi = 8.8029691931113054792E1;
static const double mln2lo = -4.9650192275318476525E-16;
static const double lnovfl = 8.8029691931113053016E1;
#if defined(__vax__)
static max = 126 ;
#else /* defined(__vax__) */
static max = 1023 ;
#endif /* defined(__vax__) */
double
sinh(double x)
{
static const double one=1.0, half=1.0/2.0 ;
double t, sign;
if (isnan(x))
return (x);
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(scalbn(one+expm1((x-mln2hi)-mln2lo),max),sign));
else /* sinh(+-INF) = +-INF, sinh(+-big no.) overflow to +-INF */
return( expm1(x)*sign );
}
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