4.4BSD/usr/src/old/libm/libm/log__L.c
/*
* Copyright (c) 1985 Regents of the University of California.
*
* Use and reproduction of this software are granted in accordance with
* the terms and conditions specified in the Berkeley Software License
* Agreement (in particular, this entails acknowledgement of the programs'
* source, and inclusion of this notice) with the additional understanding
* that 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 "sendbug 4bsd-bugs@BERKELEY", to the authors.
*/
#ifndef lint
static char sccsid[] = "@(#)log__L.c 1.2 (Berkeley) 8/21/85";
#endif not lint
/* 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.
*/
#ifdef VAX /* VAX D format (56 bits) */
/* 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[] = { 0xaaaa402a, 0xaac5aaaa};
static long L2x[] = { 0xcccc3fcc, 0x2684cccc};
static long L3x[] = { 0x49243f92, 0x578292f8};
static long L4x[] = { 0x8e383f63, 0xaf2c39b7};
static long L5x[] = { 0x2eb43f3a, 0x655ecc39};
static long L6x[] = { 0x85513f1d, 0x781de8c5};
static long L7x[] = { 0x95b33f08, 0xcd92907f};
static long L8x[] = { 0x00003f00, 0x00000000};
#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 /* IEEE double */
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
double log__L(z)
double z;
{
#ifdef VAX
return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*(L7+z*L8))))))));
#else /* IEEE double */
return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*L7)))))));
#endif
}