1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
|
/* $OpenBSD: n_log__L.c,v 1.9 2009/10/27 23:59:29 deraadt Exp $ */
/* $NetBSD: n_log__L.c,v 1.1 1995/10/10 23:37:01 ragge Exp $ */
/*
* 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. 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.
*/
/* 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 Remes 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 "math.h"
#include "mathimpl.h"
static const double L1 = 6.6666666666666703212E-1;
static const double L2 = 3.9999999999970461961E-1;
static const double L3 = 2.8571428579395698188E-1;
static const double L4 = 2.2222221233634724402E-1;
static const double L5 = 1.8181879517064680057E-1;
static const double L6 = 1.5382888777946145467E-1;
static const double L7 = 1.3338356561139403517E-1;
static const double L8 = 1.2500000000000000000E-1;
double
__log__L(double z)
{
#if defined(__vax__)
return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*(L7+z*L8))))))));
#else /* defined(__vax__) */
return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*L7)))))));
#endif /* defined(__vax__) */
}
|
