178 lines
5.2 KiB
C
178 lines
5.2 KiB
C
/*
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* Copyright (c) 1985, 1993
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* The Regents of the University of California. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. All advertising materials mentioning features or use of this software
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* must display the following acknowledgement:
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* This product includes software developed by the University of
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* California, Berkeley and its contributors.
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* 4. Neither the name of the University nor the names of its contributors
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* may be used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#ifndef lint
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static char sccsid[] = "@(#)exp.c 8.1 (Berkeley) 6/4/93";
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#endif /* not lint */
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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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/* EXP(X)
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* RETURN THE EXPONENTIAL OF X
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* DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
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* CODED IN C BY K.C. NG, 1/19/85;
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* REVISED BY K.C. NG on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86.
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*
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* Required system supported functions:
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* scalb(x,n)
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* copysign(x,y)
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* finite(x)
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*
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* Method:
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* 1. Argument Reduction: given the input x, find r and integer k such
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* that
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* x = k*ln2 + r, |r| <= 0.5*ln2 .
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* r will be represented as r := z+c for better accuracy.
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*
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* 2. Compute exp(r) by
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*
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* exp(r) = 1 + r + r*R1/(2-R1),
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* where
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* R1 = x - x^2*(p1+x^2*(p2+x^2*(p3+x^2*(p4+p5*x^2)))).
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*
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* 3. exp(x) = 2^k * exp(r) .
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*
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* Special cases:
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* exp(INF) is INF, exp(NaN) is NaN;
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* exp(-INF)= 0;
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* for finite argument, only exp(0)=1 is exact.
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*
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* Accuracy:
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* exp(x) returns the exponential of x nearly rounded. In a test run
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* with 1,156,000 random arguments on a VAX, the maximum observed
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* error was 0.869 ulps (units in the last place).
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*/
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#include "mathimpl.h"
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const static double p1 = 0x1.555555555553ep-3;
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const static double p2 = -0x1.6c16c16bebd93p-9;
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const static double p3 = 0x1.1566aaf25de2cp-14;
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const static double p4 = -0x1.bbd41c5d26bf1p-20;
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const static double p5 = 0x1.6376972bea4d0p-25;
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const static double ln2hi = 0x1.62e42fee00000p-1;
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const static double ln2lo = 0x1.a39ef35793c76p-33;
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const static double lnhuge = 0x1.6602b15b7ecf2p9;
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const static double lntiny = -0x1.77af8ebeae354p9;
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const static double invln2 = 0x1.71547652b82fep0;
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#if 0
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double exp(x)
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double x;
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{
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double z,hi,lo,c;
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int k;
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#if !defined(vax)&&!defined(tahoe)
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if(x!=x) return(x); /* x is NaN */
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#endif /* !defined(vax)&&!defined(tahoe) */
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if( x <= lnhuge ) {
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if( x >= lntiny ) {
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/* argument reduction : x --> x - k*ln2 */
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k=invln2*x+copysign(0.5,x); /* k=NINT(x/ln2) */
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/* express x-k*ln2 as hi-lo and let x=hi-lo rounded */
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hi=x-k*ln2hi;
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x=hi-(lo=k*ln2lo);
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/* return 2^k*[1+x+x*c/(2+c)] */
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z=x*x;
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c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5))));
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return scalb(1.0+(hi-(lo-(x*c)/(2.0-c))),k);
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}
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/* end of x > lntiny */
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else
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/* exp(-big#) underflows to zero */
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if(finite(x)) return(scalb(1.0,-5000));
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/* exp(-INF) is zero */
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else return(0.0);
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}
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/* end of x < lnhuge */
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else
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/* exp(INF) is INF, exp(+big#) overflows to INF */
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return( finite(x) ? scalb(1.0,5000) : x);
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}
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#endif
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/* returns exp(r = x + c) for |c| < |x| with no overlap. */
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double __exp__D(x, c)
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double x, c;
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{
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double z,hi,lo;
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int k;
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if (x != x) /* x is NaN */
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return(x);
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if ( x <= lnhuge ) {
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if ( x >= lntiny ) {
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/* argument reduction : x --> x - k*ln2 */
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z = invln2*x;
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k = z + copysign(.5, x);
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/* express (x+c)-k*ln2 as hi-lo and let x=hi-lo rounded */
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hi=(x-k*ln2hi); /* Exact. */
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x= hi - (lo = k*ln2lo-c);
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/* return 2^k*[1+x+x*c/(2+c)] */
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z=x*x;
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c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5))));
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c = (x*c)/(2.0-c);
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return scalb(1.+(hi-(lo - c)), k);
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}
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/* end of x > lntiny */
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else
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/* exp(-big#) underflows to zero */
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if(finite(x)) return(scalb(1.0,-5000));
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/* exp(-INF) is zero */
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else return(0.0);
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}
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/* end of x < lnhuge */
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else
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/* exp(INF) is INF, exp(+big#) overflows to INF */
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return( finite(x) ? scalb(1.0,5000) : x);
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}
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