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1.1 root 1: /*
2: * Copyright (c) 1985 Regents of the University of California.
3: * All rights reserved.
4: *
5: * Redistribution and use in source and binary forms are permitted
6: * provided that: (1) source distributions retain this entire copyright
7: * notice and comment, and (2) distributions including binaries display
8: * the following acknowledgement: ``This product includes software
9: * developed by the University of California, Berkeley and its contributors''
10: * in the documentation or other materials provided with the distribution
11: * and in all advertising materials mentioning features or use of this
12: * software. Neither the name of the University nor the names of its
13: * contributors may be used to endorse or promote products derived
14: * from this software without specific prior written permission.
15: * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
16: * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
17: * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
18: *
19: * All recipients should regard themselves as participants in an ongoing
20: * research project and hence should feel obligated to report their
21: * experiences (good or bad) with these elementary function codes, using
22: * the sendbug(8) program, to the authors.
23: */
24:
25: #ifndef lint
26: static char sccsid[] = "@(#)log__L.c 5.5 (Berkeley) 6/1/90";
27: #endif /* not lint */
28:
29: /* log__L(Z)
30: * LOG(1+X) - 2S X
31: * RETURN --------------- WHERE Z = S*S, S = ------- , 0 <= Z <= .0294...
32: * S 2 + X
33: *
34: * DOUBLE PRECISION (VAX D FORMAT 56 bits or IEEE DOUBLE 53 BITS)
35: * KERNEL FUNCTION FOR LOG; TO BE USED IN LOG1P, LOG, AND POW FUNCTIONS
36: * CODED IN C BY K.C. NG, 1/19/85;
37: * REVISED BY K.C. Ng, 2/3/85, 4/16/85.
38: *
39: * Method :
40: * 1. Polynomial approximation: let s = x/(2+x).
41: * Based on log(1+x) = log(1+s) - log(1-s)
42: * = 2s + 2/3 s**3 + 2/5 s**5 + .....,
43: *
44: * (log(1+x) - 2s)/s is computed by
45: *
46: * z*(L1 + z*(L2 + z*(... (L7 + z*L8)...)))
47: *
48: * where z=s*s. (See the listing below for Lk's values.) The
49: * coefficients are obtained by a special Remez algorithm.
50: *
51: * Accuracy:
52: * Assuming no rounding error, the maximum magnitude of the approximation
53: * error (absolute) is 2**(-58.49) for IEEE double, and 2**(-63.63)
54: * for VAX D format.
55: *
56: * Constants:
57: * The hexadecimal values are the intended ones for the following constants.
58: * The decimal values may be used, provided that the compiler will convert
59: * from decimal to binary accurately enough to produce the hexadecimal values
60: * shown.
61: */
62:
63: #include "mathimpl.h"
64:
65: vc(L1, 6.6666666666666703212E-1 ,aaaa,402a,aac5,aaaa, 0, .AAAAAAAAAAAAC5)
66: vc(L2, 3.9999999999970461961E-1 ,cccc,3fcc,2684,cccc, -1, .CCCCCCCCCC2684)
67: vc(L3, 2.8571428579395698188E-1 ,4924,3f92,5782,92f8, -1, .92492492F85782)
68: vc(L4, 2.2222221233634724402E-1 ,8e38,3f63,af2c,39b7, -2, .E38E3839B7AF2C)
69: vc(L5, 1.8181879517064680057E-1 ,2eb4,3f3a,655e,cc39, -2, .BA2EB4CC39655E)
70: vc(L6, 1.5382888777946145467E-1 ,8551,3f1d,781d,e8c5, -2, .9D8551E8C5781D)
71: vc(L7, 1.3338356561139403517E-1 ,95b3,3f08,cd92,907f, -2, .8895B3907FCD92)
72: vc(L8, 1.2500000000000000000E-1 ,0000,3f00,0000,0000, -2, .80000000000000)
73:
74: ic(L1, 6.6666666666667340202E-1, -1, 1.5555555555592)
75: ic(L2, 3.9999999999416702146E-1, -2, 1.999999997FF24)
76: ic(L3, 2.8571428742008753154E-1, -2, 1.24924941E07B4)
77: ic(L4, 2.2222198607186277597E-1, -3, 1.C71C52150BEA6)
78: ic(L5, 1.8183562745289935658E-1, -3, 1.74663CC94342F)
79: ic(L6, 1.5314087275331442206E-1, -3, 1.39A1EC014045B)
80: ic(L7, 1.4795612545334174692E-1, -3, 1.2F039F0085122)
81:
82: #ifdef vccast
83: #define L1 vccast(L1)
84: #define L2 vccast(L2)
85: #define L3 vccast(L3)
86: #define L4 vccast(L4)
87: #define L5 vccast(L5)
88: #define L6 vccast(L6)
89: #define L7 vccast(L7)
90: #define L8 vccast(L8)
91: #endif
92:
93: double log__L(z)
94: double z;
95: {
96: #if defined(vax)||defined(tahoe)
97: return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*(L7+z*L8))))))));
98: #else /* defined(vax)||defined(tahoe) */
99: return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*L7)))))));
100: #endif /* defined(vax)||defined(tahoe) */
101: }
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