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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 the above copyright notice and this paragraph are
7: * duplicated in all such forms and that any documentation,
8: * advertising materials, and other materials related to such
9: * distribution and use acknowledge that the software was developed
10: * by the University of California, Berkeley. The name of the
11: * University may not be used to endorse or promote products derived
12: * from this software without specific prior written permission.
13: * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
14: * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
15: * WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
16: *
17: * All recipients should regard themselves as participants in an ongoing
18: * research project and hence should feel obligated to report their
19: * experiences (good or bad) with these elementary function codes, using
20: * the sendbug(8) program, to the authors.
21: */
22:
23: #ifndef lint
24: static char sccsid[] = "@(#)log__L.c 5.3 (Berkeley) 6/30/88";
25: #endif /* not lint */
26:
27: /* log__L(Z)
28: * LOG(1+X) - 2S X
29: * RETURN --------------- WHERE Z = S*S, S = ------- , 0 <= Z <= .0294...
30: * S 2 + X
31: *
32: * DOUBLE PRECISION (VAX D FORMAT 56 bits or IEEE DOUBLE 53 BITS)
33: * KERNEL FUNCTION FOR LOG; TO BE USED IN LOG1P, LOG, AND POW FUNCTIONS
34: * CODED IN C BY K.C. NG, 1/19/85;
35: * REVISED BY K.C. Ng, 2/3/85, 4/16/85.
36: *
37: * Method :
38: * 1. Polynomial approximation: let s = x/(2+x).
39: * Based on log(1+x) = log(1+s) - log(1-s)
40: * = 2s + 2/3 s**3 + 2/5 s**5 + .....,
41: *
42: * (log(1+x) - 2s)/s is computed by
43: *
44: * z*(L1 + z*(L2 + z*(... (L7 + z*L8)...)))
45: *
46: * where z=s*s. (See the listing below for Lk's values.) The
47: * coefficients are obtained by a special Remez algorithm.
48: *
49: * Accuracy:
50: * Assuming no rounding error, the maximum magnitude of the approximation
51: * error (absolute) is 2**(-58.49) for IEEE double, and 2**(-63.63)
52: * for VAX D format.
53: *
54: * Constants:
55: * The hexadecimal values are the intended ones for the following constants.
56: * The decimal values may be used, provided that the compiler will convert
57: * from decimal to binary accurately enough to produce the hexadecimal values
58: * shown.
59: */
60:
61: #if defined(vax)||defined(tahoe) /* VAX D format (56 bits) */
62: #ifdef vax
63: #define _0x(A,B) 0x/**/A/**/B
64: #else /* vax */
65: #define _0x(A,B) 0x/**/B/**/A
66: #endif /* vax */
67: /* static double */
68: /* L1 = 6.6666666666666703212E-1 , Hex 2^ 0 * .AAAAAAAAAAAAC5 */
69: /* L2 = 3.9999999999970461961E-1 , Hex 2^ -1 * .CCCCCCCCCC2684 */
70: /* L3 = 2.8571428579395698188E-1 , Hex 2^ -1 * .92492492F85782 */
71: /* L4 = 2.2222221233634724402E-1 , Hex 2^ -2 * .E38E3839B7AF2C */
72: /* L5 = 1.8181879517064680057E-1 , Hex 2^ -2 * .BA2EB4CC39655E */
73: /* L6 = 1.5382888777946145467E-1 , Hex 2^ -2 * .9D8551E8C5781D */
74: /* L7 = 1.3338356561139403517E-1 , Hex 2^ -2 * .8895B3907FCD92 */
75: /* L8 = 1.2500000000000000000E-1 , Hex 2^ -2 * .80000000000000 */
76: static long L1x[] = { _0x(aaaa,402a), _0x(aac5,aaaa)};
77: static long L2x[] = { _0x(cccc,3fcc), _0x(2684,cccc)};
78: static long L3x[] = { _0x(4924,3f92), _0x(5782,92f8)};
79: static long L4x[] = { _0x(8e38,3f63), _0x(af2c,39b7)};
80: static long L5x[] = { _0x(2eb4,3f3a), _0x(655e,cc39)};
81: static long L6x[] = { _0x(8551,3f1d), _0x(781d,e8c5)};
82: static long L7x[] = { _0x(95b3,3f08), _0x(cd92,907f)};
83: static long L8x[] = { _0x(0000,3f00), _0x(0000,0000)};
84: #define L1 (*(double*)L1x)
85: #define L2 (*(double*)L2x)
86: #define L3 (*(double*)L3x)
87: #define L4 (*(double*)L4x)
88: #define L5 (*(double*)L5x)
89: #define L6 (*(double*)L6x)
90: #define L7 (*(double*)L7x)
91: #define L8 (*(double*)L8x)
92: #else /* defined(vax)||defined(tahoe) */
93: static double
94: L1 = 6.6666666666667340202E-1 , /*Hex 2^ -1 * 1.5555555555592 */
95: L2 = 3.9999999999416702146E-1 , /*Hex 2^ -2 * 1.999999997FF24 */
96: L3 = 2.8571428742008753154E-1 , /*Hex 2^ -2 * 1.24924941E07B4 */
97: L4 = 2.2222198607186277597E-1 , /*Hex 2^ -3 * 1.C71C52150BEA6 */
98: L5 = 1.8183562745289935658E-1 , /*Hex 2^ -3 * 1.74663CC94342F */
99: L6 = 1.5314087275331442206E-1 , /*Hex 2^ -3 * 1.39A1EC014045B */
100: L7 = 1.4795612545334174692E-1 ; /*Hex 2^ -3 * 1.2F039F0085122 */
101: #endif /* defined(vax)||defined(tahoe) */
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: }
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