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authorRoland McGrath <roland@gnu.org>1995-02-18 01:27:10 +0000
committerRoland McGrath <roland@gnu.org>1995-02-18 01:27:10 +0000
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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[] = "@(#)expm1.c 8.1 (Berkeley) 6/4/93";
+#endif /* not lint */
+
+/* EXPM1(X)
+ * RETURN THE EXPONENTIAL OF X MINUS ONE
+ * 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, 3/7/85, 3/21/85, 4/16/85.
+ *
+ * Required system supported functions:
+ * scalb(x,n)
+ * copysign(x,y)
+ * finite(x)
+ *
+ * Kernel function:
+ * exp__E(x,c)
+ *
+ * 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 EXPM1(r)=exp(r)-1 by
+ *
+ * EXPM1(r=z+c) := z + exp__E(z,c)
+ *
+ * 3. EXPM1(x) = 2^k * ( EXPM1(r) + 1-2^-k ).
+ *
+ * Remarks:
+ * 1. When k=1 and z < -0.25, we use the following formula for
+ * better accuracy:
+ * EXPM1(x) = 2 * ( (z+0.5) + exp__E(z,c) )
+ * 2. To avoid rounding error in 1-2^-k where k is large, we use
+ * EXPM1(x) = 2^k * { [z+(exp__E(z,c)-2^-k )] + 1 }
+ * when k>56.
+ *
+ * Special cases:
+ * EXPM1(INF) is INF, EXPM1(NaN) is NaN;
+ * EXPM1(-INF)= -1;
+ * for finite argument, only EXPM1(0)=0 is exact.
+ *
+ * Accuracy:
+ * EXPM1(x) returns the exact (exp(x)-1) nearly rounded. In a test run with
+ * 1,166,000 random arguments on a VAX, the maximum observed error was
+ * .872 ulps (units of 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(invln2, 1.4426950408889634148E0 ,aa3b,40b8,17f1,295c, 1, .B8AA3B295C17F1)
+
+ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000)
+ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76)
+ic(lnhuge, 7.1602103751842355450E2, 9, 1.6602B15B7ECF2)
+ic(invln2, 1.4426950408889633870E0, 0, 1.71547652B82FE)
+
+#ifdef vccast
+#define ln2hi vccast(ln2hi)
+#define ln2lo vccast(ln2lo)
+#define lnhuge vccast(lnhuge)
+#define invln2 vccast(invln2)
+#endif
+
+double expm1(x)
+double x;
+{
+ const static double one=1.0, half=1.0/2.0;
+ double z,hi,lo,c;
+ int k;
+#if defined(vax)||defined(tahoe)
+ static prec=56;
+#else /* defined(vax)||defined(tahoe) */
+ static prec=53;
+#endif /* defined(vax)||defined(tahoe) */
+
+#if !defined(vax)&&!defined(tahoe)
+ if(x!=x) return(x); /* x is NaN */
+#endif /* !defined(vax)&&!defined(tahoe) */
+
+ if( x <= lnhuge ) {
+ if( x >= -40.0 ) {
+
+ /* argument reduction : x - k*ln2 */
+ k= invln2 *x+copysign(0.5,x); /* k=NINT(x/ln2) */
+ hi=x-k*ln2hi ;
+ z=hi-(lo=k*ln2lo);
+ c=(hi-z)-lo;
+
+ if(k==0) return(z+__exp__E(z,c));
+ if(k==1)
+ if(z< -0.25)
+ {x=z+half;x +=__exp__E(z,c); return(x+x);}
+ else
+ {z+=__exp__E(z,c); x=half+z; return(x+x);}
+ /* end of k=1 */
+
+ else {
+ if(k<=prec)
+ { x=one-scalb(one,-k); z += __exp__E(z,c);}
+ else if(k<100)
+ { x = __exp__E(z,c)-scalb(one,-k); x+=z; z=one;}
+ else
+ { x = __exp__E(z,c)+z; z=one;}
+
+ return (scalb(x+z,k));
+ }
+ }
+ /* end of x > lnunfl */
+
+ else
+ /* expm1(-big#) rounded to -1 (inexact) */
+ if(finite(x))
+ { ln2hi+ln2lo; return(-one);}
+
+ /* expm1(-INF) is -1 */
+ else return(-one);
+ }
+ /* end of x < lnhuge */
+
+ else
+ /* expm1(INF) is INF, expm1(+big#) overflows to INF */
+ return( finite(x) ? scalb(one,5000) : x);
+}
+
+weak_alias (__expm1, expm1)