Removed the last vestiges of libm. These have been repo-copied to
msun/bsdsrc. Everything except true gamma() and its support functions was superseded by msun long ago, at least on IEEE machines.
This commit is contained in:
Bruce Evans
parent
6720311838
commit
4bcae9ff30
@ -1,7 +0,0 @@
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$FreeBSD$
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The libm library has been superceded by the msun library. The
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source has not been delegated to the attic yet because there are
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still bits that need to be merged into msun.
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(end)
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@ -1,206 +0,0 @@
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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
|
||||
* 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
|
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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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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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#ifndef lint
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static char sccsid[] = "@(#)exp.c 8.1 (Berkeley) 6/4/93";
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#endif /* not lint */
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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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* finite(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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* 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(lntiny,-9.5654310917272452386E1 ,4f01,c3bf,33af,d72e, 7,-.BF4F01D72E33AF)
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vc(invln2, 1.4426950408889634148E0 ,aa3b,40b8,17f1,295c, 1, .B8AA3B295C17F1)
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vc(p1, 1.6666666666666602251E-1 ,aaaa,3f2a,a9f1,aaaa, -2, .AAAAAAAAAAA9F1)
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vc(p2, -2.7777777777015591216E-3 ,0b60,bc36,ec94,b5f5, -8,-.B60B60B5F5EC94)
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vc(p3, 6.6137563214379341918E-5 ,b355,398a,f15f,792e, -13, .8AB355792EF15F)
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vc(p4, -1.6533902205465250480E-6 ,ea0e,b6dd,5f84,2e93, -19,-.DDEA0E2E935F84)
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vc(p5, 4.1381367970572387085E-8 ,bb4b,3431,2683,95f5, -24, .B1BB4B95F52683)
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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 lntiny vccast(lntiny)
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#define invln2 vccast(invln2)
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#define p1 vccast(p1)
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#define p2 vccast(p2)
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#define p3 vccast(p3)
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#define p4 vccast(p4)
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#define p5 vccast(p5)
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#endif
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ic(p1, 1.6666666666666601904E-1, -3, 1.555555555553E)
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ic(p2, -2.7777777777015593384E-3, -9, -1.6C16C16BEBD93)
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ic(p3, 6.6137563214379343612E-5, -14, 1.1566AAF25DE2C)
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ic(p4, -1.6533902205465251539E-6, -20, -1.BBD41C5D26BF1)
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ic(p5, 4.1381367970572384604E-8, -25, 1.6376972BEA4D0)
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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(lntiny,-7.5137154372698068983E2, 9, -1.77AF8EBEAE354)
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ic(invln2, 1.4426950408889633870E0, 0, 1.71547652B82FE)
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double exp(x)
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double x;
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{
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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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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 >= lntiny ) {
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/* argument reduction : x --> x - k*ln2 */
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k=invln2*x+copysign(0.5,x); /* k=NINT(x/ln2) */
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/* express x-k*ln2 as hi-lo and let x=hi-lo rounded */
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hi=x-k*ln2hi;
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x=hi-(lo=k*ln2lo);
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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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return scalb(1.0+(hi-(lo-(x*c)/(2.0-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(finite(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( finite(x) ? scalb(1.0,5000) : x);
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}
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/* returns exp(r = x + c) for |c| < |x| with no overlap. */
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double __exp__D(x, c)
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double x, c;
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{
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double z,hi,lo, t;
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int k;
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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 >= 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(finite(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( finite(x) ? scalb(1.0,5000) : x);
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}
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@ -1,339 +0,0 @@
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/*-
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* Copyright (c) 1992, 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
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
* 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
|
||||
* 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
|
||||
* 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)
|
||||
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
||||
* 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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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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#ifndef lint
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static char sccsid[] = "@(#)gamma.c 8.1 (Berkeley) 6/4/93";
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#endif /* not lint */
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/*
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* This code by P. McIlroy, Oct 1992;
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*
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* The financial support of UUNET Communications Services is greatfully
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* acknowledged.
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*/
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#include <math.h>
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#include "mathimpl.h"
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#include <errno.h>
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/* METHOD:
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* x < 0: Use reflection formula, G(x) = pi/(sin(pi*x)*x*G(x))
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* At negative integers, return +Inf, and set errno.
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*
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* x < 6.5:
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* Use argument reduction G(x+1) = xG(x) to reach the
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* range [1.066124,2.066124]. Use a rational
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* approximation centered at the minimum (x0+1) to
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* ensure monotonicity.
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*
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* x >= 6.5: Use the asymptotic approximation (Stirling's formula)
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* adjusted for equal-ripples:
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*
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* log(G(x)) ~= (x-.5)*(log(x)-1) + .5(log(2*pi)-1) + 1/x*P(1/(x*x))
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*
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* Keep extra precision in multiplying (x-.5)(log(x)-1), to
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* avoid premature round-off.
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*
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* Special values:
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* non-positive integer: Set overflow trap; return +Inf;
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* x > 171.63: Set overflow trap; return +Inf;
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* NaN: Set invalid trap; return NaN
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*
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* Accuracy: Gamma(x) is accurate to within
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* x > 0: error provably < 0.9ulp.
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* Maximum observed in 1,000,000 trials was .87ulp.
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* x < 0:
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* Maximum observed error < 4ulp in 1,000,000 trials.
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*/
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static double neg_gam __P((double));
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static double small_gam __P((double));
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static double smaller_gam __P((double));
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static struct Double large_gam __P((double));
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static struct Double ratfun_gam __P((double, double));
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|
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/*
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* Rational approximation, A0 + x*x*P(x)/Q(x), on the interval
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* [1.066.., 2.066..] accurate to 4.25e-19.
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*/
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#define LEFT -.3955078125 /* left boundary for rat. approx */
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#define x0 .461632144968362356785 /* xmin - 1 */
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#define a0_hi 0.88560319441088874992
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#define a0_lo -.00000000000000004996427036469019695
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#define P0 6.21389571821820863029017800727e-01
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#define P1 2.65757198651533466104979197553e-01
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#define P2 5.53859446429917461063308081748e-03
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#define P3 1.38456698304096573887145282811e-03
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#define P4 2.40659950032711365819348969808e-03
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#define Q0 1.45019531250000000000000000000e+00
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#define Q1 1.06258521948016171343454061571e+00
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#define Q2 -2.07474561943859936441469926649e-01
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#define Q3 -1.46734131782005422506287573015e-01
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#define Q4 3.07878176156175520361557573779e-02
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#define Q5 5.12449347980666221336054633184e-03
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#define Q6 -1.76012741431666995019222898833e-03
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#define Q7 9.35021023573788935372153030556e-05
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#define Q8 6.13275507472443958924745652239e-06
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/*
|
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* Constants for large x approximation (x in [6, Inf])
|
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* (Accurate to 2.8*10^-19 absolute)
|
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*/
|
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#define lns2pi_hi 0.418945312500000
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#define lns2pi_lo -.000006779295327258219670263595
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#define Pa0 8.33333333333333148296162562474e-02
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#define Pa1 -2.77777777774548123579378966497e-03
|
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#define Pa2 7.93650778754435631476282786423e-04
|
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#define Pa3 -5.95235082566672847950717262222e-04
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#define Pa4 8.41428560346653702135821806252e-04
|
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#define Pa5 -1.89773526463879200348872089421e-03
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#define Pa6 5.69394463439411649408050664078e-03
|
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#define Pa7 -1.44705562421428915453880392761e-02
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|
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static const double zero = 0., one = 1.0, tiny = 1e-300;
|
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static int endian;
|
||||
/*
|
||||
* TRUNC sets trailing bits in a floating-point number to zero.
|
||||
* is a temporary variable.
|
||||
*/
|
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#if defined(vax) || defined(tahoe)
|
||||
#define _IEEE 0
|
||||
#define TRUNC(x) x = (double) (float) (x)
|
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#else
|
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#define _IEEE 1
|
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#define TRUNC(x) *(((int *) &x) + endian) &= 0xf8000000
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#define infnan(x) 0.0
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#endif
|
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|
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double
|
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gamma(x)
|
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double x;
|
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{
|
||||
struct Double u;
|
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endian = (*(int *) &one) ? 1 : 0;
|
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|
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if (x >= 6) {
|
||||
if(x > 171.63)
|
||||
return(one/zero);
|
||||
u = large_gam(x);
|
||||
return(__exp__D(u.a, u.b));
|
||||
} else if (x >= 1.0 + LEFT + x0)
|
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return (small_gam(x));
|
||||
else if (x > 1.e-17)
|
||||
return (smaller_gam(x));
|
||||
else if (x > -1.e-17) {
|
||||
if (x == 0.0)
|
||||
if (!_IEEE) return (infnan(ERANGE));
|
||||
else return (one/x);
|
||||
one+1e-20; /* Raise inexact flag. */
|
||||
return (one/x);
|
||||
} else if (!finite(x)) {
|
||||
if (_IEEE) /* x = NaN, -Inf */
|
||||
return (x*x);
|
||||
else
|
||||
return (infnan(EDOM));
|
||||
} else
|
||||
return (neg_gam(x));
|
||||
}
|
||||
/*
|
||||
* Accurate to max(ulp(1/128) absolute, 2^-66 relative) error.
|
||||
*/
|
||||
static struct Double
|
||||
large_gam(x)
|
||||
double x;
|
||||
{
|
||||
double z, p;
|
||||
int i;
|
||||
struct Double t, u, v;
|
||||
|
||||
z = one/(x*x);
|
||||
p = Pa0+z*(Pa1+z*(Pa2+z*(Pa3+z*(Pa4+z*(Pa5+z*(Pa6+z*Pa7))))));
|
||||
p = p/x;
|
||||
|
||||
u = __log__D(x);
|
||||
u.a -= one;
|
||||
v.a = (x -= .5);
|
||||
TRUNC(v.a);
|
||||
v.b = x - v.a;
|
||||
t.a = v.a*u.a; /* t = (x-.5)*(log(x)-1) */
|
||||
t.b = v.b*u.a + x*u.b;
|
||||
/* return t.a + t.b + lns2pi_hi + lns2pi_lo + p */
|
||||
t.b += lns2pi_lo; t.b += p;
|
||||
u.a = lns2pi_hi + t.b; u.a += t.a;
|
||||
u.b = t.a - u.a;
|
||||
u.b += lns2pi_hi; u.b += t.b;
|
||||
return (u);
|
||||
}
|
||||
/*
|
||||
* Good to < 1 ulp. (provably .90 ulp; .87 ulp on 1,000,000 runs.)
|
||||
* It also has correct monotonicity.
|
||||
*/
|
||||
static double
|
||||
small_gam(x)
|
||||
double x;
|
||||
{
|
||||
double y, ym1, t, x1;
|
||||
struct Double yy, r;
|
||||
y = x - one;
|
||||
ym1 = y - one;
|
||||
if (y <= 1.0 + (LEFT + x0)) {
|
||||
yy = ratfun_gam(y - x0, 0);
|
||||
return (yy.a + yy.b);
|
||||
}
|
||||
r.a = y;
|
||||
TRUNC(r.a);
|
||||
yy.a = r.a - one;
|
||||
y = ym1;
|
||||
yy.b = r.b = y - yy.a;
|
||||
/* Argument reduction: G(x+1) = x*G(x) */
|
||||
for (ym1 = y-one; ym1 > LEFT + x0; y = ym1--, yy.a--) {
|
||||
t = r.a*yy.a;
|
||||
r.b = r.a*yy.b + y*r.b;
|
||||
r.a = t;
|
||||
TRUNC(r.a);
|
||||
r.b += (t - r.a);
|
||||
}
|
||||
/* Return r*gamma(y). */
|
||||
yy = ratfun_gam(y - x0, 0);
|
||||
y = r.b*(yy.a + yy.b) + r.a*yy.b;
|
||||
y += yy.a*r.a;
|
||||
return (y);
|
||||
}
|
||||
/*
|
||||
* Good on (0, 1+x0+LEFT]. Accurate to 1ulp.
|
||||
*/
|
||||
static double
|
||||
smaller_gam(x)
|
||||
double x;
|
||||
{
|
||||
double t, d;
|
||||
struct Double r, xx;
|
||||
if (x < x0 + LEFT) {
|
||||
t = x, TRUNC(t);
|
||||
d = (t+x)*(x-t);
|
||||
t *= t;
|
||||
xx.a = (t + x), TRUNC(xx.a);
|
||||
xx.b = x - xx.a; xx.b += t; xx.b += d;
|
||||
t = (one-x0); t += x;
|
||||
d = (one-x0); d -= t; d += x;
|
||||
x = xx.a + xx.b;
|
||||
} else {
|
||||
xx.a = x, TRUNC(xx.a);
|
||||
xx.b = x - xx.a;
|
||||
t = x - x0;
|
||||
d = (-x0 -t); d += x;
|
||||
}
|
||||
r = ratfun_gam(t, d);
|
||||
d = r.a/x, TRUNC(d);
|
||||
r.a -= d*xx.a; r.a -= d*xx.b; r.a += r.b;
|
||||
return (d + r.a/x);
|
||||
}
|
||||
/*
|
||||
* returns (z+c)^2 * P(z)/Q(z) + a0
|
||||
*/
|
||||
static struct Double
|
||||
ratfun_gam(z, c)
|
||||
double z, c;
|
||||
{
|
||||
int i;
|
||||
double p, q;
|
||||
struct Double r, t;
|
||||
|
||||
q = Q0 +z*(Q1+z*(Q2+z*(Q3+z*(Q4+z*(Q5+z*(Q6+z*(Q7+z*Q8)))))));
|
||||
p = P0 + z*(P1 + z*(P2 + z*(P3 + z*P4)));
|
||||
|
||||
/* return r.a + r.b = a0 + (z+c)^2*p/q, with r.a truncated to 26 bits. */
|
||||
p = p/q;
|
||||
t.a = z, TRUNC(t.a); /* t ~= z + c */
|
||||
t.b = (z - t.a) + c;
|
||||
t.b *= (t.a + z);
|
||||
q = (t.a *= t.a); /* t = (z+c)^2 */
|
||||
TRUNC(t.a);
|
||||
t.b += (q - t.a);
|
||||
r.a = p, TRUNC(r.a); /* r = P/Q */
|
||||
r.b = p - r.a;
|
||||
t.b = t.b*p + t.a*r.b + a0_lo;
|
||||
t.a *= r.a; /* t = (z+c)^2*(P/Q) */
|
||||
r.a = t.a + a0_hi, TRUNC(r.a);
|
||||
r.b = ((a0_hi-r.a) + t.a) + t.b;
|
||||
return (r); /* r = a0 + t */
|
||||
}
|
||||
|
||||
static double
|
||||
neg_gam(x)
|
||||
double x;
|
||||
{
|
||||
int sgn = 1;
|
||||
struct Double lg, lsine;
|
||||
double y, z;
|
||||
|
||||
y = floor(x + .5);
|
||||
if (y == x) /* Negative integer. */
|
||||
if(!_IEEE)
|
||||
return (infnan(ERANGE));
|
||||
else
|
||||
return (one/zero);
|
||||
z = fabs(x - y);
|
||||
y = .5*ceil(x);
|
||||
if (y == ceil(y))
|
||||
sgn = -1;
|
||||
if (z < .25)
|
||||
z = sin(M_PI*z);
|
||||
else
|
||||
z = cos(M_PI*(0.5-z));
|
||||
/* Special case: G(1-x) = Inf; G(x) may be nonzero. */
|
||||
if (x < -170) {
|
||||
if (x < -190)
|
||||
return ((double)sgn*tiny*tiny);
|
||||
y = one - x; /* exact: 128 < |x| < 255 */
|
||||
lg = large_gam(y);
|
||||
lsine = __log__D(M_PI/z); /* = TRUNC(log(u)) + small */
|
||||
lg.a -= lsine.a; /* exact (opposite signs) */
|
||||
lg.b -= lsine.b;
|
||||
y = -(lg.a + lg.b);
|
||||
z = (y + lg.a) + lg.b;
|
||||
y = __exp__D(y, z);
|
||||
if (sgn < 0) y = -y;
|
||||
return (y);
|
||||
}
|
||||
y = one-x;
|
||||
if (one-y == x)
|
||||
y = gamma(y);
|
||||
else /* 1-x is inexact */
|
||||
y = -x*gamma(-x);
|
||||
if (sgn < 0) y = -y;
|
||||
return (M_PI / (y*z));
|
||||
}
|
||||
@ -1,489 +0,0 @@
|
||||
/*
|
||||
* Copyright (c) 1992, 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.
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
__FBSDID("$FreeBSD$");
|
||||
|
||||
#ifndef lint
|
||||
static char sccsid[] = "@(#)log.c 8.2 (Berkeley) 11/30/93";
|
||||
#endif /* not lint */
|
||||
|
||||
#include <math.h>
|
||||
#include <errno.h>
|
||||
|
||||
#include "mathimpl.h"
|
||||
|
||||
/* Table-driven natural logarithm.
|
||||
*
|
||||
* This code was derived, with minor modifications, from:
|
||||
* Peter Tang, "Table-Driven Implementation of the
|
||||
* Logarithm in IEEE Floating-Point arithmetic." ACM Trans.
|
||||
* Math Software, vol 16. no 4, pp 378-400, Dec 1990).
|
||||
*
|
||||
* Calculates log(2^m*F*(1+f/F)), |f/j| <= 1/256,
|
||||
* where F = j/128 for j an integer in [0, 128].
|
||||
*
|
||||
* log(2^m) = log2_hi*m + log2_tail*m
|
||||
* since m is an integer, the dominant term is exact.
|
||||
* m has at most 10 digits (for subnormal numbers),
|
||||
* and log2_hi has 11 trailing zero bits.
|
||||
*
|
||||
* log(F) = logF_hi[j] + logF_lo[j] is in tabular form in log_table.h
|
||||
* logF_hi[] + 512 is exact.
|
||||
*
|
||||
* log(1+f/F) = 2*f/(2*F + f) + 1/12 * (2*f/(2*F + f))**3 + ...
|
||||
* the leading term is calculated to extra precision in two
|
||||
* parts, the larger of which adds exactly to the dominant
|
||||
* m and F terms.
|
||||
* There are two cases:
|
||||
* 1. when m, j are non-zero (m | j), use absolute
|
||||
* precision for the leading term.
|
||||
* 2. when m = j = 0, |1-x| < 1/256, and log(x) ~= (x-1).
|
||||
* In this case, use a relative precision of 24 bits.
|
||||
* (This is done differently in the original paper)
|
||||
*
|
||||
* Special cases:
|
||||
* 0 return signalling -Inf
|
||||
* neg return signalling NaN
|
||||
* +Inf return +Inf
|
||||
*/
|
||||
|
||||
#if defined(vax) || defined(tahoe)
|
||||
#define _IEEE 0
|
||||
#define TRUNC(x) x = (double) (float) (x)
|
||||
#else
|
||||
#define _IEEE 1
|
||||
#define endian (((*(int *) &one)) ? 1 : 0)
|
||||
#define TRUNC(x) *(((int *) &x) + endian) &= 0xf8000000
|
||||
#define infnan(x) 0.0
|
||||
#endif
|
||||
|
||||
#define N 128
|
||||
|
||||
/* Table of log(Fj) = logF_head[j] + logF_tail[j], for Fj = 1+j/128.
|
||||
* Used for generation of extend precision logarithms.
|
||||
* The constant 35184372088832 is 2^45, so the divide is exact.
|
||||
* It ensures correct reading of logF_head, even for inaccurate
|
||||
* decimal-to-binary conversion routines. (Everybody gets the
|
||||
* right answer for integers less than 2^53.)
|
||||
* Values for log(F) were generated using error < 10^-57 absolute
|
||||
* with the bc -l package.
|
||||
*/
|
||||
static double A1 = .08333333333333178827;
|
||||
static double A2 = .01250000000377174923;
|
||||
static double A3 = .002232139987919447809;
|
||||
static double A4 = .0004348877777076145742;
|
||||
|
||||
static double logF_head[N+1] = {
|
||||
0.,
|
||||
.007782140442060381246,
|
||||
.015504186535963526694,
|
||||
.023167059281547608406,
|
||||
.030771658666765233647,
|
||||
.038318864302141264488,
|
||||
.045809536031242714670,
|
||||
.053244514518837604555,
|
||||
.060624621816486978786,
|
||||
.067950661908525944454,
|
||||
.075223421237524235039,
|
||||
.082443669210988446138,
|
||||
.089612158689760690322,
|
||||
.096729626458454731618,
|
||||
.103796793681567578460,
|
||||
.110814366340264314203,
|
||||
.117783035656430001836,
|
||||
.124703478501032805070,
|
||||
.131576357788617315236,
|
||||
.138402322859292326029,
|
||||
.145182009844575077295,
|
||||
.151916042025732167530,
|
||||
.158605030176659056451,
|
||||
.165249572895390883786,
|
||||
.171850256926518341060,
|
||||
.178407657472689606947,
|
||||
.184922338493834104156,
|
||||
.191394852999565046047,
|
||||
.197825743329758552135,
|
||||
.204215541428766300668,
|
||||
.210564769107350002741,
|
||||
.216873938300523150246,
|
||||
.223143551314024080056,
|
||||
.229374101064877322642,
|
||||
.235566071312860003672,
|
||||
.241719936886966024758,
|
||||
.247836163904594286577,
|
||||
.253915209980732470285,
|
||||
.259957524436686071567,
|
||||
.265963548496984003577,
|
||||
.271933715484010463114,
|
||||
.277868451003087102435,
|
||||
.283768173130738432519,
|
||||
.289633292582948342896,
|
||||
.295464212893421063199,
|
||||
.301261330578199704177,
|
||||
.307025035294827830512,
|
||||
.312755710004239517729,
|
||||
.318453731118097493890,
|
||||
.324119468654316733591,
|
||||
.329753286372579168528,
|
||||
.335355541920762334484,
|
||||
.340926586970454081892,
|
||||
.346466767346100823488,
|
||||
.351976423156884266063,
|
||||
.357455888922231679316,
|
||||
.362905493689140712376,
|
||||
.368325561158599157352,
|
||||
.373716409793814818840,
|
||||
.379078352934811846353,
|
||||
.384411698910298582632,
|
||||
.389716751140440464951,
|
||||
.394993808240542421117,
|
||||
.400243164127459749579,
|
||||
.405465108107819105498,
|
||||
.410659924985338875558,
|
||||
.415827895143593195825,
|
||||
.420969294644237379543,
|
||||
.426084395310681429691,
|
||||
.431173464818130014464,
|
||||
.436236766774527495726,
|
||||
.441274560805140936281,
|
||||
.446287102628048160113,
|
||||
.451274644139630254358,
|
||||
.456237433481874177232,
|
||||
.461175715122408291790,
|
||||
.466089729924533457960,
|
||||
.470979715219073113985,
|
||||
.475845904869856894947,
|
||||
.480688529345570714212,
|
||||
.485507815781602403149,
|
||||
.490303988045525329653,
|
||||
.495077266798034543171,
|
||||
.499827869556611403822,
|
||||
.504556010751912253908,
|
||||
.509261901790523552335,
|
||||
.513945751101346104405,
|
||||
.518607764208354637958,
|
||||
.523248143765158602036,
|
||||
.527867089620485785417,
|
||||
.532464798869114019908,
|
||||
.537041465897345915436,
|
||||
.541597282432121573947,
|
||||
.546132437597407260909,
|
||||
.550647117952394182793,
|
||||
.555141507540611200965,
|
||||
.559615787935399566777,
|
||||
.564070138285387656651,
|
||||
.568504735352689749561,
|
||||
.572919753562018740922,
|
||||
.577315365035246941260,
|
||||
.581691739635061821900,
|
||||
.586049045003164792433,
|
||||
.590387446602107957005,
|
||||
.594707107746216934174,
|
||||
.599008189645246602594,
|
||||
.603290851438941899687,
|
||||
.607555250224322662688,
|
||||
.611801541106615331955,
|
||||
.616029877215623855590,
|
||||
.620240409751204424537,
|
||||
.624433288012369303032,
|
||||
.628608659422752680256,
|
||||
.632766669570628437213,
|
||||
.636907462236194987781,
|
||||
.641031179420679109171,
|
||||
.645137961373620782978,
|
||||
.649227946625615004450,
|
||||
.653301272011958644725,
|
||||
.657358072709030238911,
|
||||
.661398482245203922502,
|
||||
.665422632544505177065,
|
||||
.669430653942981734871,
|
||||
.673422675212350441142,
|
||||
.677398823590920073911,
|
||||
.681359224807238206267,
|
||||
.685304003098281100392,
|
||||
.689233281238557538017,
|
||||
.693147180560117703862
|
||||
};
|
||||
|
||||
static double logF_tail[N+1] = {
|
||||
0.,
|
||||
-.00000000000000543229938420049,
|
||||
.00000000000000172745674997061,
|
||||
-.00000000000001323017818229233,
|
||||
-.00000000000001154527628289872,
|
||||
-.00000000000000466529469958300,
|
||||
.00000000000005148849572685810,
|
||||
-.00000000000002532168943117445,
|
||||
-.00000000000005213620639136504,
|
||||
-.00000000000001819506003016881,
|
||||
.00000000000006329065958724544,
|
||||
.00000000000008614512936087814,
|
||||
-.00000000000007355770219435028,
|
||||
.00000000000009638067658552277,
|
||||
.00000000000007598636597194141,
|
||||
.00000000000002579999128306990,
|
||||
-.00000000000004654729747598444,
|
||||
-.00000000000007556920687451336,
|
||||
.00000000000010195735223708472,
|
||||
-.00000000000017319034406422306,
|
||||
-.00000000000007718001336828098,
|
||||
.00000000000010980754099855238,
|
||||
-.00000000000002047235780046195,
|
||||
-.00000000000008372091099235912,
|
||||
.00000000000014088127937111135,
|
||||
.00000000000012869017157588257,
|
||||
.00000000000017788850778198106,
|
||||
.00000000000006440856150696891,
|
||||
.00000000000016132822667240822,
|
||||
-.00000000000007540916511956188,
|
||||
-.00000000000000036507188831790,
|
||||
.00000000000009120937249914984,
|
||||
.00000000000018567570959796010,
|
||||
-.00000000000003149265065191483,
|
||||
-.00000000000009309459495196889,
|
||||
.00000000000017914338601329117,
|
||||
-.00000000000001302979717330866,
|
||||
.00000000000023097385217586939,
|
||||
.00000000000023999540484211737,
|
||||
.00000000000015393776174455408,
|
||||
-.00000000000036870428315837678,
|
||||
.00000000000036920375082080089,
|
||||
-.00000000000009383417223663699,
|
||||
.00000000000009433398189512690,
|
||||
.00000000000041481318704258568,
|
||||
-.00000000000003792316480209314,
|
||||
.00000000000008403156304792424,
|
||||
-.00000000000034262934348285429,
|
||||
.00000000000043712191957429145,
|
||||
-.00000000000010475750058776541,
|
||||
-.00000000000011118671389559323,
|
||||
.00000000000037549577257259853,
|
||||
.00000000000013912841212197565,
|
||||
.00000000000010775743037572640,
|
||||
.00000000000029391859187648000,
|
||||
-.00000000000042790509060060774,
|
||||
.00000000000022774076114039555,
|
||||
.00000000000010849569622967912,
|
||||
-.00000000000023073801945705758,
|
||||
.00000000000015761203773969435,
|
||||
.00000000000003345710269544082,
|
||||
-.00000000000041525158063436123,
|
||||
.00000000000032655698896907146,
|
||||
-.00000000000044704265010452446,
|
||||
.00000000000034527647952039772,
|
||||
-.00000000000007048962392109746,
|
||||
.00000000000011776978751369214,
|
||||
-.00000000000010774341461609578,
|
||||
.00000000000021863343293215910,
|
||||
.00000000000024132639491333131,
|
||||
.00000000000039057462209830700,
|
||||
-.00000000000026570679203560751,
|
||||
.00000000000037135141919592021,
|
||||
-.00000000000017166921336082431,
|
||||
-.00000000000028658285157914353,
|
||||
-.00000000000023812542263446809,
|
||||
.00000000000006576659768580062,
|
||||
-.00000000000028210143846181267,
|
||||
.00000000000010701931762114254,
|
||||
.00000000000018119346366441110,
|
||||
.00000000000009840465278232627,
|
||||
-.00000000000033149150282752542,
|
||||
-.00000000000018302857356041668,
|
||||
-.00000000000016207400156744949,
|
||||
.00000000000048303314949553201,
|
||||
-.00000000000071560553172382115,
|
||||
.00000000000088821239518571855,
|
||||
-.00000000000030900580513238244,
|
||||
-.00000000000061076551972851496,
|
||||
.00000000000035659969663347830,
|
||||
.00000000000035782396591276383,
|
||||
-.00000000000046226087001544578,
|
||||
.00000000000062279762917225156,
|
||||
.00000000000072838947272065741,
|
||||
.00000000000026809646615211673,
|
||||
-.00000000000010960825046059278,
|
||||
.00000000000002311949383800537,
|
||||
-.00000000000058469058005299247,
|
||||
-.00000000000002103748251144494,
|
||||
-.00000000000023323182945587408,
|
||||
-.00000000000042333694288141916,
|
||||
-.00000000000043933937969737844,
|
||||
.00000000000041341647073835565,
|
||||
.00000000000006841763641591466,
|
||||
.00000000000047585534004430641,
|
||||
.00000000000083679678674757695,
|
||||
-.00000000000085763734646658640,
|
||||
.00000000000021913281229340092,
|
||||
-.00000000000062242842536431148,
|
||||
-.00000000000010983594325438430,
|
||||
.00000000000065310431377633651,
|
||||
-.00000000000047580199021710769,
|
||||
-.00000000000037854251265457040,
|
||||
.00000000000040939233218678664,
|
||||
.00000000000087424383914858291,
|
||||
.00000000000025218188456842882,
|
||||
-.00000000000003608131360422557,
|
||||
-.00000000000050518555924280902,
|
||||
.00000000000078699403323355317,
|
||||
-.00000000000067020876961949060,
|
||||
.00000000000016108575753932458,
|
||||
.00000000000058527188436251509,
|
||||
-.00000000000035246757297904791,
|
||||
-.00000000000018372084495629058,
|
||||
.00000000000088606689813494916,
|
||||
.00000000000066486268071468700,
|
||||
.00000000000063831615170646519,
|
||||
.00000000000025144230728376072,
|
||||
-.00000000000017239444525614834
|
||||
};
|
||||
|
||||
double
|
||||
#ifdef _ANSI_SOURCE
|
||||
log(double x)
|
||||
#else
|
||||
log(x) double x;
|
||||
#endif
|
||||
{
|
||||
int m, j;
|
||||
double F, f, g, q, u, u2, v, zero = 0.0, one = 1.0;
|
||||
volatile double u1;
|
||||
|
||||
/* Catch special cases */
|
||||
if (x <= 0)
|
||||
if (_IEEE && x == zero) /* log(0) = -Inf */
|
||||
return (-one/zero);
|
||||
else if (_IEEE) /* log(neg) = NaN */
|
||||
return (zero/zero);
|
||||
else if (x == zero) /* NOT REACHED IF _IEEE */
|
||||
return (infnan(-ERANGE));
|
||||
else
|
||||
return (infnan(EDOM));
|
||||
else if (!finite(x))
|
||||
if (_IEEE) /* x = NaN, Inf */
|
||||
return (x+x);
|
||||
else
|
||||
return (infnan(ERANGE));
|
||||
|
||||
/* Argument reduction: 1 <= g < 2; x/2^m = g; */
|
||||
/* y = F*(1 + f/F) for |f| <= 2^-8 */
|
||||
|
||||
m = logb(x);
|
||||
g = ldexp(x, -m);
|
||||
if (_IEEE && m == -1022) {
|
||||
j = logb(g), m += j;
|
||||
g = ldexp(g, -j);
|
||||
}
|
||||
j = N*(g-1) + .5;
|
||||
F = (1.0/N) * j + 1; /* F*128 is an integer in [128, 512] */
|
||||
f = g - F;
|
||||
|
||||
/* Approximate expansion for log(1+f/F) ~= u + q */
|
||||
g = 1/(2*F+f);
|
||||
u = 2*f*g;
|
||||
v = u*u;
|
||||
q = u*v*(A1 + v*(A2 + v*(A3 + v*A4)));
|
||||
|
||||
/* case 1: u1 = u rounded to 2^-43 absolute. Since u < 2^-8,
|
||||
* u1 has at most 35 bits, and F*u1 is exact, as F has < 8 bits.
|
||||
* It also adds exactly to |m*log2_hi + log_F_head[j] | < 750
|
||||
*/
|
||||
if (m | j)
|
||||
u1 = u + 513, u1 -= 513;
|
||||
|
||||
/* case 2: |1-x| < 1/256. The m- and j- dependent terms are zero;
|
||||
* u1 = u to 24 bits.
|
||||
*/
|
||||
else
|
||||
u1 = u, TRUNC(u1);
|
||||
u2 = (2.0*(f - F*u1) - u1*f) * g;
|
||||
/* u1 + u2 = 2f/(2F+f) to extra precision. */
|
||||
|
||||
/* log(x) = log(2^m*F*(1+f/F)) = */
|
||||
/* (m*log2_hi+logF_head[j]+u1) + (m*log2_lo+logF_tail[j]+q); */
|
||||
/* (exact) + (tiny) */
|
||||
|
||||
u1 += m*logF_head[N] + logF_head[j]; /* exact */
|
||||
u2 = (u2 + logF_tail[j]) + q; /* tiny */
|
||||
u2 += logF_tail[N]*m;
|
||||
return (u1 + u2);
|
||||
}
|
||||
|
||||
/*
|
||||
* Extra precision variant, returning struct {double a, b;};
|
||||
* log(x) = a+b to 63 bits, with a is rounded to 26 bits.
|
||||
*/
|
||||
struct Double
|
||||
#ifdef _ANSI_SOURCE
|
||||
__log__D(double x)
|
||||
#else
|
||||
__log__D(x) double x;
|
||||
#endif
|
||||
{
|
||||
int m, j;
|
||||
double F, f, g, q, u, v, u2, one = 1.0;
|
||||
volatile double u1;
|
||||
struct Double r;
|
||||
|
||||
/* Argument reduction: 1 <= g < 2; x/2^m = g; */
|
||||
/* y = F*(1 + f/F) for |f| <= 2^-8 */
|
||||
|
||||
m = logb(x);
|
||||
g = ldexp(x, -m);
|
||||
if (_IEEE && m == -1022) {
|
||||
j = logb(g), m += j;
|
||||
g = ldexp(g, -j);
|
||||
}
|
||||
j = N*(g-1) + .5;
|
||||
F = (1.0/N) * j + 1;
|
||||
f = g - F;
|
||||
|
||||
g = 1/(2*F+f);
|
||||
u = 2*f*g;
|
||||
v = u*u;
|
||||
q = u*v*(A1 + v*(A2 + v*(A3 + v*A4)));
|
||||
if (m | j)
|
||||
u1 = u + 513, u1 -= 513;
|
||||
else
|
||||
u1 = u, TRUNC(u1);
|
||||
u2 = (2.0*(f - F*u1) - u1*f) * g;
|
||||
|
||||
u1 += m*logF_head[N] + logF_head[j];
|
||||
|
||||
u2 += logF_tail[j]; u2 += q;
|
||||
u2 += logF_tail[N]*m;
|
||||
r.a = u1 + u2; /* Only difference is here */
|
||||
TRUNC(r.a);
|
||||
r.b = (u1 - r.a) + u2;
|
||||
return (r);
|
||||
}
|
||||
@ -1,98 +0,0 @@
|
||||
/*
|
||||
* Copyright (c) 1988, 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.
|
||||
*
|
||||
* @(#)mathimpl.h 8.1 (Berkeley) 6/4/93
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#include <math.h>
|
||||
|
||||
#if defined(vax)||defined(tahoe)
|
||||
|
||||
/* Deal with different ways to concatenate in cpp */
|
||||
# ifdef __STDC__
|
||||
# define cat3(a,b,c) a ## b ## c
|
||||
# else
|
||||
# define cat3(a,b,c) a/**/b/**/c
|
||||
# endif
|
||||
|
||||
/* Deal with vax/tahoe byte order issues */
|
||||
# ifdef vax
|
||||
# define cat3t(a,b,c) cat3(a,b,c)
|
||||
# else
|
||||
# define cat3t(a,b,c) cat3(a,c,b)
|
||||
# endif
|
||||
|
||||
# define vccast(name) (*(const double *)(cat3(name,,x)))
|
||||
|
||||
/*
|
||||
* Define a constant to high precision on a Vax or Tahoe.
|
||||
*
|
||||
* Args are the name to define, the decimal floating point value,
|
||||
* four 16-bit chunks of the float value in hex
|
||||
* (because the vax and tahoe differ in float format!), the power
|
||||
* of 2 of the hex-float exponent, and the hex-float mantissa.
|
||||
* Most of these arguments are not used at compile time; they are
|
||||
* used in a post-check to make sure the constants were compiled
|
||||
* correctly.
|
||||
*
|
||||
* People who want to use the constant will have to do their own
|
||||
* #define foo vccast(foo)
|
||||
* since CPP cannot do this for them from inside another macro (sigh).
|
||||
* We define "vccast" if this needs doing.
|
||||
*/
|
||||
# define vc(name, value, x1,x2,x3,x4, bexp, xval) \
|
||||
const static long cat3(name,,x)[] = {cat3t(0x,x1,x2), cat3t(0x,x3,x4)};
|
||||
|
||||
# define ic(name, value, bexp, xval) ;
|
||||
|
||||
#else /* vax or tahoe */
|
||||
|
||||
/* Hooray, we have an IEEE machine */
|
||||
# undef vccast
|
||||
# define vc(name, value, x1,x2,x3,x4, bexp, xval) ;
|
||||
|
||||
# define ic(name, value, bexp, xval) \
|
||||
const static double name = value;
|
||||
|
||||
#endif /* defined(vax)||defined(tahoe) */
|
||||
|
||||
|
||||
/*
|
||||
* Functions internal to the math package, yet not static.
|
||||
*/
|
||||
extern double __exp__E();
|
||||
extern double __log__L();
|
||||
|
||||
struct Double {double a, b;};
|
||||
double __exp__D __P((double, double));
|
||||
struct Double __log__D __P((double));
|
||||
Loading…
x
Reference in New Issue
Block a user