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168 lines
5.5 KiB
C
168 lines
5.5 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[] = "@(#)expm1.c 8.1 (Berkeley) 6/4/93";
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#endif /* not lint */
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/* EXPM1(X)
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* RETURN THE EXPONENTIAL OF X MINUS ONE
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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, 3/7/85, 3/21/85, 4/16/85.
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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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* Kernel function:
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* exp__E(x,c)
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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 EXPM1(r)=exp(r)-1 by
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*
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* EXPM1(r=z+c) := z + exp__E(z,c)
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*
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* 3. EXPM1(x) = 2^k * ( EXPM1(r) + 1-2^-k ).
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*
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* Remarks:
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* 1. When k=1 and z < -0.25, we use the following formula for
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* better accuracy:
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* EXPM1(x) = 2 * ( (z+0.5) + exp__E(z,c) )
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* 2. To avoid rounding error in 1-2^-k where k is large, we use
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* EXPM1(x) = 2^k * { [z+(exp__E(z,c)-2^-k )] + 1 }
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* when k>56.
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*
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* Special cases:
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* EXPM1(INF) is INF, EXPM1(NaN) is NaN;
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* EXPM1(-INF)= -1;
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* for finite argument, only EXPM1(0)=0 is exact.
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*
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* Accuracy:
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* EXPM1(x) returns the exact (exp(x)-1) nearly rounded. In a test run with
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* 1,166,000 random arguments on a VAX, the maximum observed error was
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* .872 ulps (units of the last place).
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*
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* Constants:
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* The hexadecimal values are the intended ones for the following constants.
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* The decimal values may be used, provided that the compiler will convert
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* from decimal to binary accurately enough to produce the hexadecimal values
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* shown.
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*/
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#include "mathimpl.h"
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vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000)
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vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
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vc(lnhuge, 9.4961163736712506989E1 ,ec1d,43bd,9010,a73e, 7, .BDEC1DA73E9010)
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vc(invln2, 1.4426950408889634148E0 ,aa3b,40b8,17f1,295c, 1, .B8AA3B295C17F1)
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ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000)
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ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76)
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ic(lnhuge, 7.1602103751842355450E2, 9, 1.6602B15B7ECF2)
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ic(invln2, 1.4426950408889633870E0, 0, 1.71547652B82FE)
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#ifdef vccast
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#define ln2hi vccast(ln2hi)
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#define ln2lo vccast(ln2lo)
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#define lnhuge vccast(lnhuge)
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#define invln2 vccast(invln2)
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#endif
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double expm1(x)
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double x;
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{
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const static double one=1.0, half=1.0/2.0;
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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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static prec=56;
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#else /* defined(vax)||defined(tahoe) */
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static prec=53;
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#endif /* defined(vax)||defined(tahoe) */
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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 >= -40.0 ) {
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/* argument reduction : x - k*ln2 */
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k= invln2 *x+copysign(0.5,x); /* k=NINT(x/ln2) */
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hi=x-k*ln2hi ;
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z=hi-(lo=k*ln2lo);
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c=(hi-z)-lo;
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if(k==0) return(z+__exp__E(z,c));
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if(k==1)
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if(z< -0.25)
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{x=z+half;x +=__exp__E(z,c); return(x+x);}
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else
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{z+=__exp__E(z,c); x=half+z; return(x+x);}
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/* end of k=1 */
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else {
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if(k<=prec)
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{ x=one-scalb(one,-k); z += __exp__E(z,c);}
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else if(k<100)
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{ x = __exp__E(z,c)-scalb(one,-k); x+=z; z=one;}
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else
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{ x = __exp__E(z,c)+z; z=one;}
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return (scalb(x+z,k));
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}
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}
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/* end of x > lnunfl */
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else
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/* expm1(-big#) rounded to -1 (inexact) */
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if(finite(x))
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{ ln2hi+ln2lo; return(-one);}
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/* expm1(-INF) is -1 */
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else return(-one);
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}
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/* end of x < lnhuge */
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else
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/* expm1(INF) is INF, expm1(+big#) overflows to INF */
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return( finite(x) ? scalb(one,5000) : x);
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}
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