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/* $OpenBSD: n_exp__E.c,v 1.12 2009/10/27 23:59:29 deraadt Exp $ */
/* $NetBSD: n_exp__E.c,v 1.1 1995/10/10 23:36:45 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.
*/
/* exp__E(x,c)
* ASSUMPTION: c << x SO THAT fl(x+c)=x.
* (c is the correction term for x)
* exp__E RETURNS
*
* / exp(x+c) - 1 - x , 1E-19 < |x| < .3465736
* exp__E(x,c) = |
* \ 0 , |x| < 1E-19.
*
* DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
* KERNEL FUNCTION OF EXP, EXPM1, POW FUNCTIONS
* CODED IN C BY K.C. NG, 1/31/85;
* REVISED BY K.C. NG on 3/16/85, 4/16/85.
*
* Required system supported function:
* copysign(x,y)
*
* Method:
* 1. Rational approximation. Let r=x+c.
* Based on
* 2 * sinh(r/2)
* exp(r) - 1 = ---------------------- ,
* cosh(r/2) - sinh(r/2)
* exp__E(r) is computed using
* x*x (x/2)*W - ( Q - ( 2*P + x*P ) )
* --- + (c + x*[---------------------------------- + c ])
* 2 1 - W
* where P := p1*x^2 + p2*x^4,
* Q := q1*x^2 + q2*x^4 (for 56 bits precision, add q3*x^6)
* W := x/2-(Q-x*P),
*
* (See the listing below for the values of p1,p2,q1,q2,q3. The poly-
* nomials P and Q may be regarded as the approximations to sinh
* and cosh :
* sinh(r/2) = r/2 + r * P , cosh(r/2) = 1 + Q . )
*
* The coefficients were obtained by a special Remes algorithm.
*
* Approximation error:
*
* | exp(x) - 1 | 2**(-57), (IEEE double)
* | ------------ - (exp__E(x,0)+x)/x | <=
* | x | 2**(-69). (VAX D)
*
* 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 p1 = 1.5150724356786683059E-2;
static const double p2 = 6.3112487873718332688E-5;
static const double q1 = 1.1363478204690669916E-1;
static const double q2 = 1.2624568129896839182E-3;
static const double q3 = 1.5021856115869022674E-6;
double
__exp__E(double x, double c)
{
static const double zero=0.0, one=1.0, half=1.0/2.0, small=1.0E-19;
double z,p,q,xp,xh,w;
if(copysign(x,one)>small) {
z = x*x ;
p = z*( p1 +z* p2 );
#if defined(__vax__)
q = z*( q1 +z*( q2 +z* q3 ));
#else /* defined(__vax__) */
q = z*( q1 +z* q2 );
#endif /* defined(__vax__) */
xp= x*p ;
xh= x*half ;
w = xh-(q-xp) ;
p = p+p;
c += x*((xh*w-(q-(p+xp)))/(one-w)+c);
return(z*half+c);
}
/* end of |x| > small */
else {
if(x != zero) {
if (one + small >= 1.0) /* raise the inexact flag */
return(copysign(zero,x));
}
else
return(copysign(zero,x));
}
/* NOTREACHED */
}
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