xref: /netbsd-src/lib/libm/noieee_src/n_log__L.c (revision 76dfffe33547c37f8bdd446e3e4ab0f3c16cea4b)
1 /*      $NetBSD: n_log__L.c,v 1.1 1995/10/10 23:37:01 ragge 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. All advertising materials mentioning features or use of this software
15  *    must display the following acknowledgement:
16  *	This product includes software developed by the University of
17  *	California, Berkeley and its contributors.
18  * 4. Neither the name of the University nor the names of its contributors
19  *    may be used to endorse or promote products derived from this software
20  *    without specific prior written permission.
21  *
22  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
23  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
24  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
25  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
26  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
27  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
28  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
29  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
30  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
31  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
32  * SUCH DAMAGE.
33  */
34 
35 #ifndef lint
36 static char sccsid[] = "@(#)log__L.c	8.1 (Berkeley) 6/4/93";
37 #endif /* not lint */
38 
39 /* log__L(Z)
40  *		LOG(1+X) - 2S			       X
41  * RETURN      ---------------  WHERE Z = S*S,  S = ------- , 0 <= Z <= .0294...
42  *		      S				     2 + X
43  *
44  * DOUBLE PRECISION (VAX D FORMAT 56 bits or IEEE DOUBLE 53 BITS)
45  * KERNEL FUNCTION FOR LOG; TO BE USED IN LOG1P, LOG, AND POW FUNCTIONS
46  * CODED IN C BY K.C. NG, 1/19/85;
47  * REVISED BY K.C. Ng, 2/3/85, 4/16/85.
48  *
49  * Method :
50  *	1. Polynomial approximation: let s = x/(2+x).
51  *	   Based on log(1+x) = log(1+s) - log(1-s)
52  *		 = 2s + 2/3 s**3 + 2/5 s**5 + .....,
53  *
54  *	   (log(1+x) - 2s)/s is computed by
55  *
56  *	       z*(L1 + z*(L2 + z*(... (L7 + z*L8)...)))
57  *
58  *	   where z=s*s. (See the listing below for Lk's values.) The
59  *	   coefficients are obtained by a special Remez algorithm.
60  *
61  * Accuracy:
62  *	Assuming no rounding error, the maximum magnitude of the approximation
63  *	error (absolute) is 2**(-58.49) for IEEE double, and 2**(-63.63)
64  *	for VAX D format.
65  *
66  * Constants:
67  * The hexadecimal values are the intended ones for the following constants.
68  * The decimal values may be used, provided that the compiler will convert
69  * from decimal to binary accurately enough to produce the hexadecimal values
70  * shown.
71  */
72 
73 #include "mathimpl.h"
74 
75 vc(L1, 6.6666666666666703212E-1 ,aaaa,402a,aac5,aaaa,  0, .AAAAAAAAAAAAC5)
76 vc(L2, 3.9999999999970461961E-1 ,cccc,3fcc,2684,cccc, -1, .CCCCCCCCCC2684)
77 vc(L3, 2.8571428579395698188E-1 ,4924,3f92,5782,92f8, -1, .92492492F85782)
78 vc(L4, 2.2222221233634724402E-1 ,8e38,3f63,af2c,39b7, -2, .E38E3839B7AF2C)
79 vc(L5, 1.8181879517064680057E-1 ,2eb4,3f3a,655e,cc39, -2, .BA2EB4CC39655E)
80 vc(L6, 1.5382888777946145467E-1 ,8551,3f1d,781d,e8c5, -2, .9D8551E8C5781D)
81 vc(L7, 1.3338356561139403517E-1 ,95b3,3f08,cd92,907f, -2, .8895B3907FCD92)
82 vc(L8, 1.2500000000000000000E-1 ,0000,3f00,0000,0000, -2, .80000000000000)
83 
84 ic(L1, 6.6666666666667340202E-1, -1, 1.5555555555592)
85 ic(L2, 3.9999999999416702146E-1, -2, 1.999999997FF24)
86 ic(L3, 2.8571428742008753154E-1, -2, 1.24924941E07B4)
87 ic(L4, 2.2222198607186277597E-1, -3, 1.C71C52150BEA6)
88 ic(L5, 1.8183562745289935658E-1, -3, 1.74663CC94342F)
89 ic(L6, 1.5314087275331442206E-1, -3, 1.39A1EC014045B)
90 ic(L7, 1.4795612545334174692E-1, -3, 1.2F039F0085122)
91 
92 #ifdef vccast
93 #define	L1	vccast(L1)
94 #define	L2	vccast(L2)
95 #define	L3	vccast(L3)
96 #define	L4	vccast(L4)
97 #define	L5	vccast(L5)
98 #define	L6	vccast(L6)
99 #define	L7	vccast(L7)
100 #define	L8	vccast(L8)
101 #endif
102 
103 double __log__L(z)
104 double z;
105 {
106 #if defined(vax)||defined(tahoe)
107     return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*(L7+z*L8))))))));
108 #else	/* defined(vax)||defined(tahoe) */
109     return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*L7)))))));
110 #endif	/* defined(vax)||defined(tahoe) */
111 }
112