log__l.c

VXWORKS源代码

/* log__L.c - math routine */

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

/*
modification history
--------------------
01a,08jul92,smb  documentation.
*/

/*
DESCRIPTION
* 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.
*
SEE ALSO: American National Standard X3.159-1989
NOMANUAL
*/

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

#if defined(vax)||defined(tahoe)	/* VAX D format (56 bits) */
#ifdef vax
#define _0x(A,B)	0x/**/A/**/B
#else	/* vax */
#define _0x(A,B)	0x/**/B/**/A
#endif	/* vax */
/* static double */
/* L1     =  6.6666666666666703212E-1    , Hex  2^  0   *  .AAAAAAAAAAAAC5 */
/* L2     =  3.9999999999970461961E-1    , Hex  2^ -1   *  .CCCCCCCCCC2684 */
/* L3     =  2.8571428579395698188E-1    , Hex  2^ -1   *  .92492492F85782 */
/* L4     =  2.2222221233634724402E-1    , Hex  2^ -2   *  .E38E3839B7AF2C */
/* L5     =  1.8181879517064680057E-1    , Hex  2^ -2   *  .BA2EB4CC39655E */
/* L6     =  1.5382888777946145467E-1    , Hex  2^ -2   *  .9D8551E8C5781D */
/* L7     =  1.3338356561139403517E-1    , Hex  2^ -2   *  .8895B3907FCD92 */
/* L8     =  1.2500000000000000000E-1    , Hex  2^ -2   *  .80000000000000 */
static long        L1x[] = { _0x(aaaa,402a), _0x(aac5,aaaa)};
static long        L2x[] = { _0x(cccc,3fcc), _0x(2684,cccc)};
static long        L3x[] = { _0x(4924,3f92), _0x(5782,92f8)};
static long        L4x[] = { _0x(8e38,3f63), _0x(af2c,39b7)};
static long        L5x[] = { _0x(2eb4,3f3a), _0x(655e,cc39)};
static long        L6x[] = { _0x(8551,3f1d), _0x(781d,e8c5)};
static long        L7x[] = { _0x(95b3,3f08), _0x(cd92,907f)};
static long        L8x[] = { _0x(0000,3f00), _0x(0000,0000)};
#define       L1    (*(double*)L1x)
#define       L2    (*(double*)L2x)
#define       L3    (*(double*)L3x)
#define       L4    (*(double*)L4x)
#define       L5    (*(double*)L5x)
#define       L6    (*(double*)L6x)
#define       L7    (*(double*)L7x)
#define       L8    (*(double*)L8x)
#else	/* defined(vax)||defined(tahoe) */
static double
L1     =  6.6666666666667340202E-1    , /*Hex  2^ -1   *  1.5555555555592 */
L2     =  3.9999999999416702146E-1    , /*Hex  2^ -2   *  1.999999997FF24 */
L3     =  2.8571428742008753154E-1    , /*Hex  2^ -2   *  1.24924941E07B4 */
L4     =  2.2222198607186277597E-1    , /*Hex  2^ -3   *  1.C71C52150BEA6 */
L5     =  1.8183562745289935658E-1    , /*Hex  2^ -3   *  1.74663CC94342F */
L6     =  1.5314087275331442206E-1    , /*Hex  2^ -3   *  1.39A1EC014045B */
L7     =  1.4795612545334174692E-1    ; /*Hex  2^ -3   *  1.2F039F0085122 */
#endif	/* defined(vax)||defined(tahoe) */

/*****************************************************************************
* log__l	-
*
* log__L(Z)
*		LOG(1+X) - 2S			       X
* RETURN      ---------------  WHERE Z = S*S,  S = ------- , 0 <= Z <= .0294...
*		      S				     2 + X
*
* DOUBLE PRECISION (VAX D FORMAT 56 bits or IEEE DOUBLE 53 BITS)
* KERNEL FUNCTION FOR LOG; TO BE USED IN LOG1P, LOG, AND POW FUNCTIONS
* CODED IN C BY K.C. NG, 1/19/85;
* REVISED BY K.C. Ng, 2/3/85, 4/16/85.
*
* Method :
*	1. Polynomial approximation: let s = x/(2+x).
*	   Based on log(1+x) = log(1+s) - log(1-s)
*		 = 2s + 2/3 s**3 + 2/5 s**5 + .....,
*
*	   (log(1+x) - 2s)/s is computed by
*
*	       z*(L1 + z*(L2 + z*(... (L7 + z*L8)...)))
*
*	   where z=s*s. (See the listing below for Lk's values.) The
*	   coefficients are obtained by a special Remez algorithm.
*
* Accuracy:
*	Assuming no rounding error, the maximum magnitude of the approximation
*	error (absolute) is 2**(-58.49) for IEEE double, and 2**(-63.63)
*	for VAX D format.
*
* 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 log__L(z)
double z;
{
#if defined(vax)||defined(tahoe)
    return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*(L7+z*L8))))))));
#else	/* defined(vax)||defined(tahoe) */
    return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*L7)))))));
#endif	/* defined(vax)||defined(tahoe) */
}