log1p.c

VXWORKS源代码

/* log1p.c - math routines */

/* Copyright 1992 Wind River Systems, Inc. */

/*
modification history
--------------------
01b,30jul92,kdl  marked routine NOMANUAL.
01a,08jul92,smb  documentation.
*/

/*
* DESCRIPTION
*
* This file includes a support routine (log1p()) which is used by
* other portions of the UCB ANSI C library.
*
*
* Copyright (c) 1985 Regents of the University of California.
* All rights reserved.
*
* Redistribution and use in source and binary forms are permitted
* provided that the above copyright notice and this paragraph are
* duplicated in all such forms and that any documentation,
* advertising materials, and other materials related to such
* distribution and use acknowledge that the software was developed
* by the University of California, Berkeley.  The name of the
* University may not be used to endorse or promote products derived
* from this software without specific prior written permission.
* THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
* IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
* WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
*
* All recipients should regard themselves as participants in an ongoing
* research project and hence should feel obligated to report their
* experiences (good or bad) with these elementary function codes, using
* the sendbug(8) program, to the authors.
*
* #ifndef lint
* static char sccsid[] = "@(#)log1p.c	5.3 (Berkeley) 6/30/88";
* #endif	* not lint *
* 
* SEE ALSO: American National Standard X3.159-1989
* 
* NOMANUAL
* 
*/

#include "vxWorks.h"
#include "math.h"

#if defined(vax)||defined(tahoe)	/* VAX D format */
#include <errno.h>
#ifdef vax
#define _0x(A,B)	0x/**/A/**/B
#else	/* vax */
#define _0x(A,B)	0x/**/B/**/A
#endif	/* vax */
/* static double */
/* ln2hi  =  6.9314718055829871446E-1    , Hex  2^  0   *  .B17217F7D00000 */
/* ln2lo  =  1.6465949582897081279E-12   , Hex  2^-39   *  .E7BCD5E4F1D9CC */
/* sqrt2  =  1.4142135623730950622E0     ; Hex  2^  1   *  .B504F333F9DE65 */
static long     ln2hix[] = { _0x(7217,4031), _0x(0000,f7d0)};
static long     ln2lox[] = { _0x(bcd5,2ce7), _0x(d9cc,e4f1)};
static long     sqrt2x[] = { _0x(04f3,40b5), _0x(de65,33f9)};
#define    ln2hi    (*(double*)ln2hix)
#define    ln2lo    (*(double*)ln2lox)
#define    sqrt2    (*(double*)sqrt2x)
#else	/* defined(vax)||defined(tahoe) */
static double
ln2hi  =  6.9314718036912381649E-1    , /*Hex  2^ -1   *  1.62E42FEE00000 */
ln2lo  =  1.9082149292705877000E-10   , /*Hex  2^-33   *  1.A39EF35793C76 */
sqrt2  =  1.4142135623730951455E0     ; /*Hex  2^  0   *  1.6A09E667F3BCD */
#endif	/* defined(vax)||defined(tahoe) */

/**************************************************************************
* log1p	-
*
* LOG1P(x)
* RETURN THE LOGARITHM OF 1+x
* DOUBLE PRECISION (VAX D FORMAT 56 bits, IEEE DOUBLE 53 BITS)
* CODED IN C BY K.C. NG, 1/19/85;
* REVISED BY K.C. NG on 2/6/85, 3/7/85, 3/24/85, 4/16/85.
*
* Required system supported functions:
*	scalb(x,n)
*	copysign(x,y)
*	logb(x)
*	finite(x)
*
* Required kernel function:
*	log__L(z)
*
* Method :
*	1. Argument Reduction: find k and f such that
*			1+x  = 2^k * (1+f),
*	   where  sqrt(2)/2 < 1+f < sqrt(2) .
*
*	2. Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
*		 = 2s + 2/3 s**3 + 2/5 s**5 + .....,
*	   log(1+f) is computed by
*
*	     		log(1+f) = 2s + s*log__L(s*s)
*	   where
*		log__L(z) = z*(L1 + z*(L2 + z*(... (L6 + z*L7)...)))
*
*	   See log__L() for the values of the coefficients.
*
*	3. Finally,  log(1+x) = k*ln2 + log(1+f).
*
*	Remarks 1. In step 3 n*ln2 will be stored in two floating point numbers
*		   n*ln2hi + n*ln2lo, where ln2hi is chosen such that the last
*		   20 bits (for VAX D format), or the last 21 bits ( for IEEE
*		   double) is 0. This ensures n*ln2hi is exactly representable.
*		2. In step 1, f may not be representable. A correction term c
*	 	   for f is computed. It follows that the correction term for
*		   f - t (the leading term of log(1+f) in step 2) is c-c*x. We
*		   add this correction term to n*ln2lo to attenuate the error.
*
*
* Special cases:
*	log1p(x) is NaN with signal if x < -1; log1p(NaN) is NaN with no signal;
*	log1p(INF) is +INF; log1p(-1) is -INF with signal;
*	only log1p(0)=0 is exact for finite argument.
*
* Accuracy:
*	log1p(x) returns the exact log(1+x) nearly rounded. In a test run
*	with 1,536,000 random arguments on a VAX, the maximum observed
*	error was .846 ulps (units in the last place).
*
* Constants:
* The hexadecimal values are the intended ones for the following constants.
* The decimal values may be used, provided that the compiler will convert
* from decimal to binary accurately enough to produce the hexadecimal values
* shown.
* 
* NOMANUAL
*/

double log1p(x)
double x;
{
	static double zero=0.0, negone= -1.0, one=1.0,
		      half=1.0/2.0, small=1.0E-20;   /* 1+small == 1 */
	double logb(),copysign(),scalb(),log__L(),z,s,t,c;
	int k,finite();

#if !defined(vax)&&!defined(tahoe)
	if(x!=x) return(x);	/* x is NaN */
#endif	/* !defined(vax)&&!defined(tahoe) */

	if(finite(x)) {
	   if( x > negone ) {

	   /* argument reduction */
	      if(copysign(x,one)<small) return(x);
	      k=logb(one+x); z=scalb(x,-k); t=scalb(one,-k);
	      if(z+t >= sqrt2 )
		  { k += 1 ; z *= half; t *= half; }
	      t += negone; x = z + t;
	      c = (t-x)+z ;		/* correction term for x */

 	   /* compute log(1+x)  */
              s = x/(2+x); t = x*x*half;
	      c += (k*ln2lo-c*x);
	      z = c+s*(t+log__L(s*s));
	      x += (z - t) ;

	      return(k*ln2hi+x);
	   }
	/* end of if (x > negone) */

	    else {
#if defined(vax)||defined(tahoe)
		extern double infnan();
		if ( x == negone )
		    return (infnan(-ERANGE));	/* -INF */
		else
		    return (infnan(EDOM));	/* NaN */
#else	/* defined(vax)||defined(tahoe) */
		/* x = -1, return -INF with signal */
		if ( x == negone ) return( negone/zero );

		/* negative argument for log, return NaN with signal */
	        else return ( zero / zero );
#endif	/* defined(vax)||defined(tahoe) */
	    }
	}
    /* end of if (finite(x)) */

    /* log(-INF) is NaN */
	else if(x<0)
	     return(zero/zero);

    /* log(+INF) is INF */
	else return(x);
}