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
__log__L(double z)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