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/* $OpenBSD: n_exp.c,v 1.10 2009/10/27 23:59:29 deraadt 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(X)
* RETURN THE EXPONENTIAL OF X
* DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
* CODED IN C BY K.C. NG, 1/19/85;
* REVISED BY K.C. NG on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86.
*
* Required system supported functions:
* scalbn(x,n)
* copysign(x,y)
* finite(x)
*
* Method:
* 1. Argument Reduction: given the input x, find r and integer k such
* that
* x = k*ln2 + r, |r| <= 0.5*ln2 .
* r will be represented as r := z+c for better accuracy.
*
* 2. Compute exp(r) by
*
* exp(r) = 1 + r + r*R1/(2-R1),
* where
* R1 = x - x^2*(p1+x^2*(p2+x^2*(p3+x^2*(p4+p5*x^2)))).
*
* 3. exp(x) = 2^k * exp(r) .
*
* Special cases:
* exp(INF) is INF, exp(NaN) is NaN;
* exp(-INF)= 0;
* for finite argument, only exp(0)=1 is exact.
*
* Accuracy:
* exp(x) returns the exponential of x nearly rounded. In a test run
* with 1,156,000 random arguments on a VAX, the maximum observed
* error was 0.869 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 ln2hi = 6.9314718055829871446E-1;
static const double ln2lo = 1.6465949582897081279E-12;
static const double lnhuge = 9.4961163736712506989E1;
static const double lntiny = -9.5654310917272452386E1;
static const double invln2 = 1.4426950408889634148E0;
static const double p1 = 1.6666666666666602251E-1;
static const double p2 = -2.7777777777015591216E-3;
static const double p3 = 6.6137563214379341918E-5;
static const double p4 = -1.6533902205465250480E-6;
static const double p5 = 4.1381367970572387085E-8;
double
exp(double x)
{
double z, hi, lo, c;
int k;
if (isnan(x))
return (x);
if( x <= lnhuge ) {
if( x >= lntiny ) {
/* argument reduction : x --> x - k*ln2 */
k=invln2*x+copysign(0.5,x); /* k=NINT(x/ln2) */
/* express x-k*ln2 as hi-lo and let x=hi-lo rounded */
hi=x-k*ln2hi;
x=hi-(lo=k*ln2lo);
/* return 2^k*[1+x+x*c/(2+c)] */
z=x*x;
c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5))));
return scalbn(1.0+(hi-(lo-(x*c)/(2.0-c))),k);
}
/* end of x > lntiny */
else
/* exp(-big#) underflows to zero */
if(finite(x)) return(scalbn(1.0,-5000));
/* exp(-INF) is zero */
else return(0.0);
}
/* end of x < lnhuge */
else
/* exp(INF) is INF, exp(+big#) overflows to INF */
return( finite(x) ? scalbn(1.0,5000) : x);
}
/* returns exp(r = x + c) for |c| < |x| with no overlap. */
double
__exp__D(double x, double c)
{
double z, hi, lo;
int k;
if (isnan(x))
return (x);
if ( x <= lnhuge ) {
if ( x >= lntiny ) {
/* argument reduction : x --> x - k*ln2 */
z = invln2*x;
k = z + copysign(.5, x);
/* express (x+c)-k*ln2 as hi-lo and let x=hi-lo rounded */
hi=(x-k*ln2hi); /* Exact. */
x= hi - (lo = k*ln2lo-c);
/* return 2^k*[1+x+x*c/(2+c)] */
z=x*x;
c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5))));
c = (x*c)/(2.0-c);
return scalbn(1.+(hi-(lo - c)), k);
}
/* end of x > lntiny */
else
/* exp(-big#) underflows to zero */
if(finite(x)) return(scalbn(1.0,-5000));
/* exp(-INF) is zero */
else return(0.0);
}
/* end of x < lnhuge */
else
/* exp(INF) is INF, exp(+big#) overflows to INF */
return( finite(x) ? scalbn(1.0,5000) : x);
}
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