df57947f08
The Software Package Data Exchange (SPDX) group provides a specification to make it easier for automated tools to detect and summarize well known opensource licenses. We are gradually adopting the specification, noting that the tags are considered only advisory and do not, in any way, superceed or replace the license texts. Special thanks to Wind River for providing access to "The Duke of Highlander" tool: an older (2014) run over FreeBSD tree was useful as a starting point. Initially, only tag files that use BSD 4-Clause "Original" license. RelNotes: yes Differential Revision: https://reviews.freebsd.org/D13133
178 lines
5.2 KiB
C
178 lines
5.2 KiB
C
/*-
|
|
* SPDX-License-Identifier: BSD-4-Clause
|
|
*
|
|
* 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.
|
|
*/
|
|
|
|
/* @(#)exp.c 8.1 (Berkeley) 6/4/93 */
|
|
#include <sys/cdefs.h>
|
|
__FBSDID("$FreeBSD$");
|
|
|
|
|
|
/* 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:
|
|
* scalb(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).
|
|
*/
|
|
|
|
#include "mathimpl.h"
|
|
|
|
static const double p1 = 0x1.555555555553ep-3;
|
|
static const double p2 = -0x1.6c16c16bebd93p-9;
|
|
static const double p3 = 0x1.1566aaf25de2cp-14;
|
|
static const double p4 = -0x1.bbd41c5d26bf1p-20;
|
|
static const double p5 = 0x1.6376972bea4d0p-25;
|
|
static const double ln2hi = 0x1.62e42fee00000p-1;
|
|
static const double ln2lo = 0x1.a39ef35793c76p-33;
|
|
static const double lnhuge = 0x1.6602b15b7ecf2p9;
|
|
static const double lntiny = -0x1.77af8ebeae354p9;
|
|
static const double invln2 = 0x1.71547652b82fep0;
|
|
|
|
#if 0
|
|
double exp(x)
|
|
double x;
|
|
{
|
|
double z,hi,lo,c;
|
|
int k;
|
|
|
|
#if !defined(vax)&&!defined(tahoe)
|
|
if(x!=x) return(x); /* x is NaN */
|
|
#endif /* !defined(vax)&&!defined(tahoe) */
|
|
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 scalb(1.0+(hi-(lo-(x*c)/(2.0-c))),k);
|
|
|
|
}
|
|
/* end of x > lntiny */
|
|
|
|
else
|
|
/* exp(-big#) underflows to zero */
|
|
if(finite(x)) return(scalb(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) ? scalb(1.0,5000) : x);
|
|
}
|
|
#endif
|
|
|
|
/* returns exp(r = x + c) for |c| < |x| with no overlap. */
|
|
|
|
double __exp__D(x, c)
|
|
double x, c;
|
|
{
|
|
double z,hi,lo;
|
|
int k;
|
|
|
|
if (x != x) /* x is NaN */
|
|
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 scalb(1.+(hi-(lo - c)), k);
|
|
}
|
|
/* end of x > lntiny */
|
|
|
|
else
|
|
/* exp(-big#) underflows to zero */
|
|
if(finite(x)) return(scalb(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) ? scalb(1.0,5000) : x);
|
|
}
|