111 lines
4.5 KiB
C
111 lines
4.5 KiB
C
/*
|
|
* Copyright (c) 1985, 1993
|
|
* The Regents of the University of California. All rights reserved.
|
|
*
|
|
* Redistribution and use in source and binary forms, with or without
|
|
* modification, are permitted provided that the following conditions
|
|
* are met:
|
|
* 1. Redistributions of source code must retain the above copyright
|
|
* notice, this list of conditions and the following disclaimer.
|
|
* 2. Redistributions in binary form must reproduce the above copyright
|
|
* notice, this list of conditions and the following disclaimer in the
|
|
* documentation and/or other materials provided with the distribution.
|
|
* 3. All advertising materials mentioning features or use of this software
|
|
* must display the following acknowledgement:
|
|
* This product includes software developed by the University of
|
|
* California, Berkeley and its contributors.
|
|
* 4. Neither the name of the University nor the names of its contributors
|
|
* may be used to endorse or promote products derived from this software
|
|
* without specific prior written permission.
|
|
*
|
|
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
|
|
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
|
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
|
* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
|
|
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
|
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
|
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
|
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
|
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
|
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
|
* SUCH DAMAGE.
|
|
*/
|
|
|
|
#ifndef lint
|
|
static char sccsid[] = "@(#)log__L.c 8.1 (Berkeley) 6/4/93";
|
|
#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.
|
|
*/
|
|
|
|
#include "mathimpl.h"
|
|
|
|
vc(L1, 6.6666666666666703212E-1 ,aaaa,402a,aac5,aaaa, 0, .AAAAAAAAAAAAC5)
|
|
vc(L2, 3.9999999999970461961E-1 ,cccc,3fcc,2684,cccc, -1, .CCCCCCCCCC2684)
|
|
vc(L3, 2.8571428579395698188E-1 ,4924,3f92,5782,92f8, -1, .92492492F85782)
|
|
vc(L4, 2.2222221233634724402E-1 ,8e38,3f63,af2c,39b7, -2, .E38E3839B7AF2C)
|
|
vc(L5, 1.8181879517064680057E-1 ,2eb4,3f3a,655e,cc39, -2, .BA2EB4CC39655E)
|
|
vc(L6, 1.5382888777946145467E-1 ,8551,3f1d,781d,e8c5, -2, .9D8551E8C5781D)
|
|
vc(L7, 1.3338356561139403517E-1 ,95b3,3f08,cd92,907f, -2, .8895B3907FCD92)
|
|
vc(L8, 1.2500000000000000000E-1 ,0000,3f00,0000,0000, -2, .80000000000000)
|
|
|
|
ic(L1, 6.6666666666667340202E-1, -1, 1.5555555555592)
|
|
ic(L2, 3.9999999999416702146E-1, -2, 1.999999997FF24)
|
|
ic(L3, 2.8571428742008753154E-1, -2, 1.24924941E07B4)
|
|
ic(L4, 2.2222198607186277597E-1, -3, 1.C71C52150BEA6)
|
|
ic(L5, 1.8183562745289935658E-1, -3, 1.74663CC94342F)
|
|
ic(L6, 1.5314087275331442206E-1, -3, 1.39A1EC014045B)
|
|
ic(L7, 1.4795612545334174692E-1, -3, 1.2F039F0085122)
|
|
|
|
#ifdef vccast
|
|
#define L1 vccast(L1)
|
|
#define L2 vccast(L2)
|
|
#define L3 vccast(L3)
|
|
#define L4 vccast(L4)
|
|
#define L5 vccast(L5)
|
|
#define L6 vccast(L6)
|
|
#define L7 vccast(L7)
|
|
#define L8 vccast(L8)
|
|
#endif
|
|
|
|
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) */
|
|
}
|