GCC Code Coverage Report
Directory: ./ Exec Total Coverage
File: lib/libm/src/b_exp__D.c Lines: 12 16 75.0 %
Date: 2017-11-13 Branches: 3 10 30.0 %

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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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	if (isnan(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(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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}