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/* $OpenBSD: b_exp__D.c,v 1.6 2016/09/12 04:39:47 guenther Exp $ */ |
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/* |
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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. 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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/* 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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* isfinite(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 "math.h" |
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#include "math_private.h" |
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static const double p1 = 0x1.555555555553ep-3; |
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static const double p2 = -0x1.6c16c16bebd93p-9; |
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static const double p3 = 0x1.1566aaf25de2cp-14; |
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static const double p4 = -0x1.bbd41c5d26bf1p-20; |
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static const double p5 = 0x1.6376972bea4d0p-25; |
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static const double ln2hi = 0x1.62e42fee00000p-1; |
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static const double ln2lo = 0x1.a39ef35793c76p-33; |
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static const double lnhuge = 0x1.6602b15b7ecf2p9; |
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static const double lntiny = -0x1.77af8ebeae354p9; |
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static const double invln2 = 0x1.71547652b82fep0; |
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/* returns exp(r = x + c) for |c| < |x| with no overlap. */ |
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double |
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__exp__D(double x, double c) |
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{ |
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double z, hi, lo; |
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int k; |
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✗✓ |
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if (isnan(x)) /* x is NaN */ |
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return(x); |
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✓✗ |
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if ( x <= lnhuge ) { |
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✓✗ |
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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(isfinite(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( isfinite(x) ? scalb(1.0,5000) : x); |
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} |