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libc/math/log__L.c
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128
libc/math/log__L.c
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/* log__L.c - math routine */
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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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01a,08jul92,smb documentation.
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*/
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/*
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DESCRIPTION
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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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SEE ALSO: American National Standard X3.159-1989
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NOMANUAL
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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 (56 bits) */
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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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/* L1 = 6.6666666666666703212E-1 , Hex 2^ 0 * .AAAAAAAAAAAAC5 */
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/* L2 = 3.9999999999970461961E-1 , Hex 2^ -1 * .CCCCCCCCCC2684 */
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/* L3 = 2.8571428579395698188E-1 , Hex 2^ -1 * .92492492F85782 */
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/* L4 = 2.2222221233634724402E-1 , Hex 2^ -2 * .E38E3839B7AF2C */
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/* L5 = 1.8181879517064680057E-1 , Hex 2^ -2 * .BA2EB4CC39655E */
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/* L6 = 1.5382888777946145467E-1 , Hex 2^ -2 * .9D8551E8C5781D */
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/* L7 = 1.3338356561139403517E-1 , Hex 2^ -2 * .8895B3907FCD92 */
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/* L8 = 1.2500000000000000000E-1 , Hex 2^ -2 * .80000000000000 */
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static long L1x[] = { _0x(aaaa,402a), _0x(aac5,aaaa)};
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static long L2x[] = { _0x(cccc,3fcc), _0x(2684,cccc)};
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static long L3x[] = { _0x(4924,3f92), _0x(5782,92f8)};
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static long L4x[] = { _0x(8e38,3f63), _0x(af2c,39b7)};
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static long L5x[] = { _0x(2eb4,3f3a), _0x(655e,cc39)};
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static long L6x[] = { _0x(8551,3f1d), _0x(781d,e8c5)};
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static long L7x[] = { _0x(95b3,3f08), _0x(cd92,907f)};
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static long L8x[] = { _0x(0000,3f00), _0x(0000,0000)};
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#define L1 (*(double*)L1x)
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#define L2 (*(double*)L2x)
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#define L3 (*(double*)L3x)
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#define L4 (*(double*)L4x)
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#define L5 (*(double*)L5x)
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#define L6 (*(double*)L6x)
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#define L7 (*(double*)L7x)
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#define L8 (*(double*)L8x)
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#else /* defined(vax)||defined(tahoe) */
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static double
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L1 = 6.6666666666667340202E-1 , /*Hex 2^ -1 * 1.5555555555592 */
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L2 = 3.9999999999416702146E-1 , /*Hex 2^ -2 * 1.999999997FF24 */
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L3 = 2.8571428742008753154E-1 , /*Hex 2^ -2 * 1.24924941E07B4 */
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L4 = 2.2222198607186277597E-1 , /*Hex 2^ -3 * 1.C71C52150BEA6 */
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L5 = 1.8183562745289935658E-1 , /*Hex 2^ -3 * 1.74663CC94342F */
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L6 = 1.5314087275331442206E-1 , /*Hex 2^ -3 * 1.39A1EC014045B */
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L7 = 1.4795612545334174692E-1 ; /*Hex 2^ -3 * 1.2F039F0085122 */
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#endif /* defined(vax)||defined(tahoe) */
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/*****************************************************************************
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* log__l -
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*
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* log__L(Z)
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* LOG(1+X) - 2S X
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* RETURN --------------- WHERE Z = S*S, S = ------- , 0 <= Z <= .0294...
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* S 2 + X
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*
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* DOUBLE PRECISION (VAX D FORMAT 56 bits or IEEE DOUBLE 53 BITS)
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* KERNEL FUNCTION FOR LOG; TO BE USED IN LOG1P, LOG, AND POW FUNCTIONS
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* CODED IN C BY K.C. NG, 1/19/85;
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* REVISED BY K.C. Ng, 2/3/85, 4/16/85.
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*
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* Method :
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* 1. Polynomial approximation: let s = x/(2+x).
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* Based on log(1+x) = log(1+s) - log(1-s)
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* = 2s + 2/3 s**3 + 2/5 s**5 + .....,
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*
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* (log(1+x) - 2s)/s is computed by
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*
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* z*(L1 + z*(L2 + z*(... (L7 + z*L8)...)))
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*
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* where z=s*s. (See the listing below for Lk's values.) The
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* coefficients are obtained by a special Remez algorithm.
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*
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* Accuracy:
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* Assuming no rounding error, the maximum magnitude of the approximation
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* error (absolute) is 2**(-58.49) for IEEE double, and 2**(-63.63)
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* for VAX D format.
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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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NOMANUAL
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*/
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double log__L(z)
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double z;
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{
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#if defined(vax)||defined(tahoe)
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return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*(L7+z*L8))))))));
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#else /* defined(vax)||defined(tahoe) */
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return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*L7)))))));
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#endif /* defined(vax)||defined(tahoe) */
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}
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