171 lines
5.8 KiB
C
171 lines
5.8 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[] = "@(#)log1p.c 8.1 (Berkeley) 6/4/93";
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#endif /* not lint */
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/* LOG1P(x)
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* RETURN THE LOGARITHM OF 1+x
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* DOUBLE PRECISION (VAX D FORMAT 56 bits, 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 2/6/85, 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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* 1+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(1+x) = k*ln2 + log(1+f).
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*
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* Remarks 1. In step 3 n*ln2 will be stored in two floating point numbers
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* n*ln2hi + n*ln2lo, where ln2hi is chosen such that the last
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* 20 bits (for VAX D format), or the last 21 bits ( for IEEE
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* double) is 0. This ensures n*ln2hi is exactly representable.
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* 2. In step 1, f may not be representable. A correction term c
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* for f is computed. It follows that the correction term for
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* f - t (the leading term of log(1+f) in step 2) is c-c*x. We
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* add this correction term to n*ln2lo to attenuate the error.
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*
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*
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* Special cases:
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* log1p(x) is NaN with signal if x < -1; log1p(NaN) is NaN with no signal;
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* log1p(INF) is +INF; log1p(-1) is -INF with signal;
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* only log1p(0)=0 is exact for finite argument.
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*
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* Accuracy:
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* log1p(x) returns the exact log(1+x) nearly rounded. In a test run
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* with 1,536,000 random arguments on a VAX, the maximum observed
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* error was .846 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 log1p(x)
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double x;
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{
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const static double zero=0.0, negone= -1.0, one=1.0,
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half=1.0/2.0, small=1.0E-20; /* 1+small == 1 */
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double z,s,t,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(finite(x)) {
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if( x > negone ) {
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/* argument reduction */
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if(copysign(x,one)<small) return(x);
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k=logb(one+x); z=scalb(x,-k); t=scalb(one,-k);
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if(z+t >= sqrt2 )
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{ k += 1 ; z *= half; t *= half; }
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t += negone; x = z + t;
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c = (t-x)+z ; /* correction term for x */
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/* compute log(1+x) */
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s = x/(2+x); t = x*x*half;
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c += (k*ln2lo-c*x);
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z = c+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 > negone) */
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else {
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#if defined(vax)||defined(tahoe)
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if ( x == negone )
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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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/* x = -1, return -INF with signal */
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if ( x == negone ) return( negone/zero );
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/* negative argument for log, return NaN with signal */
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else 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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/* log(-INF) is NaN */
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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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