164 lines
5.3 KiB
C
164 lines
5.3 KiB
C
/*
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* Copyright (c) 1985 Regents of the University of California.
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* 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[] = "@(#)log.c 5.6 (Berkeley) 10/9/90";
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#endif /* not lint */
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/* LOG(X)
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* RETURN THE LOGARITHM OF x
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* DOUBLE PRECISION (VAX D FORMAT 56 bits or IEEE DOUBLE 53 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 2/7/85, 3/7/85, 3/24/85, 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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* logb(x)
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* finite(x)
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*
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* Required kernel function:
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* log__L(z)
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*
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* Method :
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* 1. Argument Reduction: find k and f such that
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* x = 2^k * (1+f),
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* where sqrt(2)/2 < 1+f < sqrt(2) .
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*
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* 2. Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
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* = 2s + 2/3 s**3 + 2/5 s**5 + .....,
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* log(1+f) is computed by
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*
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* log(1+f) = 2s + s*log__L(s*s)
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* where
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* log__L(z) = z*(L1 + z*(L2 + z*(... (L6 + z*L7)...)))
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*
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* See log__L() for the values of the coefficients.
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*
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* 3. Finally, log(x) = k*ln2 + log(1+f). (Here n*ln2 will be stored
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* in two floating point number: n*ln2hi + n*ln2lo, n*ln2hi is exact
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* since the last 20 bits of ln2hi is 0.)
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*
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* Special cases:
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* log(x) is NaN with signal if x < 0 (including -INF) ;
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* log(+INF) is +INF; log(0) is -INF with signal;
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* log(NaN) is that NaN with no signal.
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*
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* Accuracy:
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* log(x) returns the exact log(x) nearly rounded. In a test run with
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* 1,536,000 random arguments on a VAX, the maximum observed error was
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* .826 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 <errno.h>
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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(sqrt2, 1.4142135623730950622E0 ,04f3,40b5,de65,33f9, 1, .B504F333F9DE65)
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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(sqrt2, 1.4142135623730951455E0, 0, 1.6A09E667F3BCD)
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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 sqrt2 vccast(sqrt2)
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#endif
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double log(x)
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double x;
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{
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const static double zero=0.0, negone= -1.0, half=1.0/2.0;
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double s,z,t;
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int k,n;
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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(finite(x)) {
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if( x > zero ) {
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/* argument reduction */
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k=logb(x); x=scalb(x,-k);
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if(k == -1022) /* subnormal no. */
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{n=logb(x); x=scalb(x,-n); k+=n;}
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if(x >= sqrt2 ) {k += 1; x *= half;}
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x += negone ;
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/* compute log(1+x) */
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s=x/(2+x); t=x*x*half;
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z=k*ln2lo+s*(t+log__L(s*s));
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x += (z - t) ;
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return(k*ln2hi+x);
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}
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/* end of if (x > zero) */
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else {
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#if defined(vax)||defined(tahoe)
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if ( x == zero )
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return (infnan(-ERANGE)); /* -INF */
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else
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return (infnan(EDOM)); /* NaN */
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#else /* defined(vax)||defined(tahoe) */
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/* zero argument, return -INF with signal */
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if ( x == zero )
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return( negone/zero );
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/* negative argument, return NaN with signal */
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else
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return ( zero / zero );
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#endif /* defined(vax)||defined(tahoe) */
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}
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}
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/* end of if (finite(x)) */
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/* NOTREACHED if defined(vax)||defined(tahoe) */
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/* log(-INF) is NaN with signal */
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else if (x<0)
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return(zero/zero);
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/* log(+INF) is +INF */
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else return(x);
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}
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