198 lines
6.1 KiB
C
198 lines
6.1 KiB
C
/* log1p.c - math routines */
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/* Copyright 1992 Wind River Systems, Inc. */
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/*
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modification history
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--------------------
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01b,30jul92,kdl marked routine NOMANUAL.
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01a,08jul92,smb documentation.
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*/
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/*
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* DESCRIPTION
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*
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* This file includes a support routine (log1p()) which is used by
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* other portions of the UCB ANSI C library.
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*
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*
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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 are permitted
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* provided that the above copyright notice and this paragraph are
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* duplicated in all such forms and that any documentation,
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* advertising materials, and other materials related to such
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* distribution and use acknowledge that the software was developed
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* by the University of California, Berkeley. The name of the
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* University may not be used to endorse or promote products derived
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* from this software without specific prior written permission.
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* THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
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* IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
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* WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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*
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* All recipients should regard themselves as participants in an ongoing
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* research project and hence should feel obligated to report their
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* experiences (good or bad) with these elementary function codes, using
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* the sendbug(8) program, to the authors.
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*
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* #ifndef lint
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* static char sccsid[] = "@(#)log1p.c 5.3 (Berkeley) 6/30/88";
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* #endif * not lint *
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*
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* SEE ALSO: American National Standard X3.159-1989
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*
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* NOMANUAL
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*
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*/
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#include "vxWorks.h"
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#include "math.h"
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#if defined(vax)||defined(tahoe) /* VAX D format */
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#include <errno.h>
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#ifdef vax
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#define _0x(A,B) 0x/**/A/**/B
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#else /* vax */
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#define _0x(A,B) 0x/**/B/**/A
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#endif /* vax */
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/* static double */
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/* ln2hi = 6.9314718055829871446E-1 , Hex 2^ 0 * .B17217F7D00000 */
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/* ln2lo = 1.6465949582897081279E-12 , Hex 2^-39 * .E7BCD5E4F1D9CC */
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/* sqrt2 = 1.4142135623730950622E0 ; Hex 2^ 1 * .B504F333F9DE65 */
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static long ln2hix[] = { _0x(7217,4031), _0x(0000,f7d0)};
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static long ln2lox[] = { _0x(bcd5,2ce7), _0x(d9cc,e4f1)};
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static long sqrt2x[] = { _0x(04f3,40b5), _0x(de65,33f9)};
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#define ln2hi (*(double*)ln2hix)
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#define ln2lo (*(double*)ln2lox)
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#define sqrt2 (*(double*)sqrt2x)
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#else /* defined(vax)||defined(tahoe) */
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static double
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ln2hi = 6.9314718036912381649E-1 , /*Hex 2^ -1 * 1.62E42FEE00000 */
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ln2lo = 1.9082149292705877000E-10 , /*Hex 2^-33 * 1.A39EF35793C76 */
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sqrt2 = 1.4142135623730951455E0 ; /*Hex 2^ 0 * 1.6A09E667F3BCD */
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#endif /* defined(vax)||defined(tahoe) */
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/**************************************************************************
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* log1p -
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*
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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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* NOMANUAL
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*/
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double log1p(x)
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double x;
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{
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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 logb(),copysign(),scalb(),log__L(),z,s,t,c;
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int k,finite();
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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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extern double infnan();
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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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