1994-05-27 05:00:24 +00:00
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/*
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* Copyright (c) 1985, 1993
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* The Regents of the University of California. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. All advertising materials mentioning features or use of this software
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* must display the following acknowledgement:
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* This product includes software developed by the University of
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* California, Berkeley and its contributors.
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* 4. Neither the name of the University nor the names of its contributors
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* may be used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#ifndef lint
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static char sccsid[] = "@(#)log__L.c 8.1 (Berkeley) 6/4/93";
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#endif /* not lint */
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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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1995-05-30 05:51:47 +00:00
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*
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1994-05-27 05:00:24 +00:00
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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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1995-05-30 05:51:47 +00:00
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* CODED IN C BY K.C. NG, 1/19/85;
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1994-05-27 05:00:24 +00:00
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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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1995-05-30 05:51:47 +00:00
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* 1. Polynomial approximation: let s = x/(2+x).
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1994-05-27 05:00:24 +00:00
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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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1995-05-30 05:51:47 +00:00
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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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1994-05-27 05:00:24 +00:00
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*
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* Accuracy:
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1995-05-30 05:51:47 +00:00
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* Assuming no rounding error, the maximum magnitude of the approximation
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1994-05-27 05:00:24 +00:00
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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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*/
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#include "mathimpl.h"
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vc(L1, 6.6666666666666703212E-1 ,aaaa,402a,aac5,aaaa, 0, .AAAAAAAAAAAAC5)
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vc(L2, 3.9999999999970461961E-1 ,cccc,3fcc,2684,cccc, -1, .CCCCCCCCCC2684)
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vc(L3, 2.8571428579395698188E-1 ,4924,3f92,5782,92f8, -1, .92492492F85782)
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vc(L4, 2.2222221233634724402E-1 ,8e38,3f63,af2c,39b7, -2, .E38E3839B7AF2C)
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vc(L5, 1.8181879517064680057E-1 ,2eb4,3f3a,655e,cc39, -2, .BA2EB4CC39655E)
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vc(L6, 1.5382888777946145467E-1 ,8551,3f1d,781d,e8c5, -2, .9D8551E8C5781D)
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vc(L7, 1.3338356561139403517E-1 ,95b3,3f08,cd92,907f, -2, .8895B3907FCD92)
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vc(L8, 1.2500000000000000000E-1 ,0000,3f00,0000,0000, -2, .80000000000000)
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ic(L1, 6.6666666666667340202E-1, -1, 1.5555555555592)
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ic(L2, 3.9999999999416702146E-1, -2, 1.999999997FF24)
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ic(L3, 2.8571428742008753154E-1, -2, 1.24924941E07B4)
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ic(L4, 2.2222198607186277597E-1, -3, 1.C71C52150BEA6)
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ic(L5, 1.8183562745289935658E-1, -3, 1.74663CC94342F)
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ic(L6, 1.5314087275331442206E-1, -3, 1.39A1EC014045B)
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ic(L7, 1.4795612545334174692E-1, -3, 1.2F039F0085122)
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#ifdef vccast
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#define L1 vccast(L1)
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#define L2 vccast(L2)
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#define L3 vccast(L3)
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#define L4 vccast(L4)
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#define L5 vccast(L5)
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#define L6 vccast(L6)
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#define L7 vccast(L7)
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#define L8 vccast(L8)
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#endif
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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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