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+/*
+ * 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.
+ */
+
+#ifndef lint
+static char sccsid[] = "@(#)exp.c	8.1 (Berkeley) 6/4/93";
+#endif /* not lint */
+
+/* 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).
+ *
+ * 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 "mathimpl.h"
+
+vc(ln2hi,  6.9314718055829871446E-1  ,7217,4031,0000,f7d0,   0, .B17217F7D00000)
+vc(ln2lo,  1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
+vc(lnhuge, 9.4961163736712506989E1   ,ec1d,43bd,9010,a73e,   7, .BDEC1DA73E9010)
+vc(lntiny,-9.5654310917272452386E1   ,4f01,c3bf,33af,d72e,   7,-.BF4F01D72E33AF)
+vc(invln2, 1.4426950408889634148E0   ,aa3b,40b8,17f1,295c,   1, .B8AA3B295C17F1)
+vc(p1,     1.6666666666666602251E-1  ,aaaa,3f2a,a9f1,aaaa,  -2, .AAAAAAAAAAA9F1)
+vc(p2,    -2.7777777777015591216E-3  ,0b60,bc36,ec94,b5f5,  -8,-.B60B60B5F5EC94)
+vc(p3,     6.6137563214379341918E-5  ,b355,398a,f15f,792e, -13, .8AB355792EF15F)
+vc(p4,    -1.6533902205465250480E-6  ,ea0e,b6dd,5f84,2e93, -19,-.DDEA0E2E935F84)
+vc(p5,     4.1381367970572387085E-8  ,bb4b,3431,2683,95f5, -24, .B1BB4B95F52683)
+
+#ifdef vccast
+#define    ln2hi    vccast(ln2hi)
+#define    ln2lo    vccast(ln2lo)
+#define   lnhuge    vccast(lnhuge)
+#define   lntiny    vccast(lntiny)
+#define   invln2    vccast(invln2)
+#define       p1    vccast(p1)
+#define       p2    vccast(p2)
+#define       p3    vccast(p3)
+#define       p4    vccast(p4)
+#define       p5    vccast(p5)
+#endif
+
+ic(p1,     1.6666666666666601904E-1,  -3,  1.555555555553E)
+ic(p2,    -2.7777777777015593384E-3,  -9, -1.6C16C16BEBD93)
+ic(p3,     6.6137563214379343612E-5, -14,  1.1566AAF25DE2C)
+ic(p4,    -1.6533902205465251539E-6, -20, -1.BBD41C5D26BF1)
+ic(p5,     4.1381367970572384604E-8, -25,  1.6376972BEA4D0)
+ic(ln2hi,  6.9314718036912381649E-1,  -1,  1.62E42FEE00000)
+ic(ln2lo,  1.9082149292705877000E-10,-33,  1.A39EF35793C76)
+ic(lnhuge, 7.1602103751842355450E2,    9,  1.6602B15B7ECF2)
+ic(lntiny,-7.5137154372698068983E2,    9, -1.77AF8EBEAE354)
+ic(invln2, 1.4426950408889633870E0,    0,  1.71547652B82FE)
+
+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);
+}
+
+/* returns exp(r = x + c) for |c| < |x| with no overlap.  */
+
+double __exp__D(x, c)
+double x, c;
+{
+	double  z,hi,lo, t;
+	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 */
+			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);
+}