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      1 /*      $NetBSD: n_log__L.c,v 1.6 2003/08/07 16:44:52 agc Exp $ */
      2 /*
      3  * Copyright (c) 1985, 1993
      4  *	The Regents of the University of California.  All rights reserved.
      5  *
      6  * Redistribution and use in source and binary forms, with or without
      7  * modification, are permitted provided that the following conditions
      8  * are met:
      9  * 1. Redistributions of source code must retain the above copyright
     10  *    notice, this list of conditions and the following disclaimer.
     11  * 2. Redistributions in binary form must reproduce the above copyright
     12  *    notice, this list of conditions and the following disclaimer in the
     13  *    documentation and/or other materials provided with the distribution.
     14  * 3. Neither the name of the University nor the names of its contributors
     15  *    may be used to endorse or promote products derived from this software
     16  *    without specific prior written permission.
     17  *
     18  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
     19  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
     20  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
     21  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
     22  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
     23  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
     24  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
     25  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
     26  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
     27  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
     28  * SUCH DAMAGE.
     29  */
     30 
     31 #ifndef lint
     32 #if 0
     33 static char sccsid[] = "@(#)log__L.c	8.1 (Berkeley) 6/4/93";
     34 #endif
     35 #endif /* not lint */
     36 
     37 /* log__L(Z)
     38  *		LOG(1+X) - 2S			       X
     39  * RETURN      ---------------  WHERE Z = S*S,  S = ------- , 0 <= Z <= .0294...
     40  *		      S				     2 + X
     41  *
     42  * DOUBLE PRECISION (VAX D FORMAT 56 bits or IEEE DOUBLE 53 BITS)
     43  * KERNEL FUNCTION FOR LOG; TO BE USED IN LOG1P, LOG, AND POW FUNCTIONS
     44  * CODED IN C BY K.C. NG, 1/19/85;
     45  * REVISED BY K.C. Ng, 2/3/85, 4/16/85.
     46  *
     47  * Method :
     48  *	1. Polynomial approximation: let s = x/(2+x).
     49  *	   Based on log(1+x) = log(1+s) - log(1-s)
     50  *		 = 2s + 2/3 s**3 + 2/5 s**5 + .....,
     51  *
     52  *	   (log(1+x) - 2s)/s is computed by
     53  *
     54  *	       z*(L1 + z*(L2 + z*(... (L7 + z*L8)...)))
     55  *
     56  *	   where z=s*s. (See the listing below for Lk's values.) The
     57  *	   coefficients are obtained by a special Remez algorithm.
     58  *
     59  * Accuracy:
     60  *	Assuming no rounding error, the maximum magnitude of the approximation
     61  *	error (absolute) is 2**(-58.49) for IEEE double, and 2**(-63.63)
     62  *	for VAX D format.
     63  *
     64  * Constants:
     65  * The hexadecimal values are the intended ones for the following constants.
     66  * The decimal values may be used, provided that the compiler will convert
     67  * from decimal to binary accurately enough to produce the hexadecimal values
     68  * shown.
     69  */
     70 
     71 #define _LIBM_STATIC
     72 #include "mathimpl.h"
     73 
     74 vc(L1, 6.6666666666666703212E-1 ,aaaa,402a,aac5,aaaa,  0, .AAAAAAAAAAAAC5)
     75 vc(L2, 3.9999999999970461961E-1 ,cccc,3fcc,2684,cccc, -1, .CCCCCCCCCC2684)
     76 vc(L3, 2.8571428579395698188E-1 ,4924,3f92,5782,92f8, -1, .92492492F85782)
     77 vc(L4, 2.2222221233634724402E-1 ,8e38,3f63,af2c,39b7, -2, .E38E3839B7AF2C)
     78 vc(L5, 1.8181879517064680057E-1 ,2eb4,3f3a,655e,cc39, -2, .BA2EB4CC39655E)
     79 vc(L6, 1.5382888777946145467E-1 ,8551,3f1d,781d,e8c5, -2, .9D8551E8C5781D)
     80 vc(L7, 1.3338356561139403517E-1 ,95b3,3f08,cd92,907f, -2, .8895B3907FCD92)
     81 vc(L8, 1.2500000000000000000E-1 ,0000,3f00,0000,0000, -2, .80000000000000)
     82 
     83 ic(L1, 6.6666666666667340202E-1, -1, 1.5555555555592)
     84 ic(L2, 3.9999999999416702146E-1, -2, 1.999999997FF24)
     85 ic(L3, 2.8571428742008753154E-1, -2, 1.24924941E07B4)
     86 ic(L4, 2.2222198607186277597E-1, -3, 1.C71C52150BEA6)
     87 ic(L5, 1.8183562745289935658E-1, -3, 1.74663CC94342F)
     88 ic(L6, 1.5314087275331442206E-1, -3, 1.39A1EC014045B)
     89 ic(L7, 1.4795612545334174692E-1, -3, 1.2F039F0085122)
     90 
     91 #ifdef vccast
     92 #define	L1	vccast(L1)
     93 #define	L2	vccast(L2)
     94 #define	L3	vccast(L3)
     95 #define	L4	vccast(L4)
     96 #define	L5	vccast(L5)
     97 #define	L6	vccast(L6)
     98 #define	L7	vccast(L7)
     99 #define	L8	vccast(L8)
    100 #endif
    101 
    102 double
    103 __log__L(double z)
    104 {
    105 #if defined(__vax__)||defined(tahoe)
    106     return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*(L7+z*L8))))))));
    107 #else	/* defined(__vax__)||defined(tahoe) */
    108     return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*L7)))))));
    109 #endif	/* defined(__vax__)||defined(tahoe) */
    110 }
    111