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1 | /* -*-c-*- |
2 | * |
3 | * $Id: maurer.c,v 1.1 2000/06/17 11:29:49 mdw Exp $ |
4 | * |
5 | * Maurer's universal statistical test |
6 | * |
7 | * (c) 2000 Straylight/Edgeware |
8 | */ |
9 | |
10 | /*----- Licensing notice --------------------------------------------------* |
11 | * |
12 | * This file is part of Catacomb. |
13 | * |
14 | * Catacomb is free software; you can redistribute it and/or modify |
15 | * it under the terms of the GNU Library General Public License as |
16 | * published by the Free Software Foundation; either version 2 of the |
17 | * License, or (at your option) any later version. |
18 | * |
19 | * Catacomb is distributed in the hope that it will be useful, |
20 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
21 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
22 | * GNU Library General Public License for more details. |
23 | * |
24 | * You should have received a copy of the GNU Library General Public |
25 | * License along with Catacomb; if not, write to the Free |
26 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
27 | * MA 02111-1307, USA. |
28 | */ |
29 | |
30 | /*----- Revision history --------------------------------------------------* |
31 | * |
32 | * $Log: maurer.c,v $ |
33 | * Revision 1.1 2000/06/17 11:29:49 mdw |
34 | * Maurer's universal statistical test. |
35 | * |
36 | */ |
37 | |
38 | /*----- Header files ------------------------------------------------------*/ |
39 | |
40 | #include <assert.h> |
41 | #include <math.h> |
42 | #include <stdio.h> |
43 | #include <stdlib.h> |
44 | |
45 | #include <mLib/alloc.h> |
46 | #include <mLib/bits.h> |
47 | |
48 | #include "maurer.h" |
49 | |
50 | /*----- Data structures ---------------------------------------------------*/ |
51 | |
52 | typedef struct bitscan { |
53 | const octet *p; |
54 | unsigned b; |
55 | uint32 a; |
56 | } bitscan; |
57 | |
58 | /*----- Main code ---------------------------------------------------------*/ |
59 | |
60 | /* --- @more@ --- * |
61 | * |
62 | * Arguments: @bitscan *b@ = pointer to a bitscanner structure |
63 | * @unsigned l@ = number of bits wanted |
64 | * |
65 | * Returns: An integer representing the next @l@ bits of the stream. |
66 | * |
67 | * Use: Fetches the next @l@ bits of a data stream. The bitscanner |
68 | * has no way of knowing whether it's run out of data, so make |
69 | * sure that doesn't happen. |
70 | */ |
71 | |
72 | static unsigned more(bitscan *b, unsigned l) |
73 | { |
74 | unsigned x, m; |
75 | |
76 | while (b->b < l) { |
77 | b->a |= U8(*b->p++) << b->b; |
78 | b->b += 8; |
79 | } |
80 | m = (1 << l) - 1; |
81 | x = b->a & m; |
82 | b->a >>= l; |
83 | b->b -= l; |
84 | return (x); |
85 | } |
86 | |
87 | /* --- @maurer@ --- * |
88 | * |
89 | * Arguments: @const octet *p@ = pointer to a buffer of data |
90 | * @size_t sz@ = size of the buffer |
91 | * @unsigned l@ = number of bits to take at a time |
92 | * |
93 | * Returns: The statistic %$Z_u = (X_u - \mu)/\sigma$%, which should be |
94 | * normally distributed with a mean of zero and standard |
95 | * deviation of 1. |
96 | * |
97 | * Use: Performs Maurer's universal statistical test on a buffer of |
98 | * data. You must ensure that the buffer size @sz@ is larger |
99 | * than %$11 l \cdot 2^l$% bits long, and ideally much larger. |
100 | * |
101 | * Note that, under Unix systems, this function requires the |
102 | * maths library. |
103 | */ |
104 | |
105 | double maurer(const octet *p, size_t sz, unsigned l) |
106 | { |
107 | size_t *t; /* Table of occurrences */ |
108 | size_t q, k; /* Block counts */ |
109 | size_t i; /* Loop counter */ |
110 | bitscan b; /* Bitscanning context */ |
111 | double x; /* Statistic accumulator */ |
112 | double mu, c, sigma; /* Other useful things */ |
113 | |
114 | /* --- Table for means and variances --- */ |
115 | |
116 | struct { double mu, var_1; } vtab[] = { |
117 | { 0.7326495, 0.690 }, |
118 | { 1.5374383, 1.338 }, |
119 | { 2.4016068, 1.901 }, |
120 | { 3.3112247, 2.358 }, |
121 | { 4.2534266, 2.705 }, |
122 | { 5.2177052, 2.945 }, |
123 | { 6.1962507, 3.125 }, |
124 | { 7.1836656, 3.238 }, |
125 | { 8.1764248, 3.311 }, |
126 | { 9.1723243, 3.356 }, |
127 | { 10.170032 , 3.384 }, |
128 | { 11.168765 , 3.401 }, |
129 | { 12.168070 , 3.410 }, |
130 | { 13.167693 , 3.416 }, |
131 | { 14.167488 , 3.419 }, |
132 | { 15.167379 , 3.421 } |
133 | }; |
134 | |
135 | assert(((void)"bit chunk size out of range", 0 < l && l <= 16)); |
136 | |
137 | /* --- Initialize everything --- */ |
138 | |
139 | t = xmalloc(sizeof(size_t) << l); |
140 | for (i = 0; i < (1 << l); i++) |
141 | t[i] = 0; |
142 | |
143 | b.p = p; |
144 | b.a = 0; |
145 | b.b = 0; |
146 | |
147 | k = (sz * 8)/l; |
148 | q = 10 << l; |
149 | assert(((void)"buffer too small for test", k > q && k - q > (1 << l))); |
150 | |
151 | /* --- Set up the table --- */ |
152 | |
153 | for (i = 0; i < q; i++) { |
154 | unsigned a = more(&b, l); |
155 | t[a] = i; |
156 | } |
157 | |
158 | /* --- Now compute the statistic --- */ |
159 | |
160 | x = 0; |
161 | for (; i < k; i++) { |
162 | unsigned a = more(&b, l); |
163 | x += log(i - t[a]); |
164 | t[a] = i; |
165 | } |
166 | |
167 | /* --- Twiddle at the end --- * |
168 | * |
169 | * This produces %$X_u$%, which should be normally distributed with a mean |
170 | * and variance we can compute. |
171 | */ |
172 | |
173 | k -= q; |
174 | x /= k * log(2); |
175 | |
176 | /* --- Now translate this into %$Z_u$% distributed as %$N(0, 1)$% --- */ |
177 | |
178 | mu = vtab[l - 1].mu; |
179 | c = 0.7 - 0.8/l + (1.6 + 12.8/l) * pow(k, -4.0/l); |
180 | sigma = sqrt(c * c * vtab[l - 1].var_1 / k); |
181 | |
182 | x = (x - mu)/sigma; |
183 | |
184 | /* --- Done (phew!) --- */ |
185 | |
186 | xfree(t); |
187 | return (x); |
188 | } |
189 | |
190 | /*----- That's all, folks -------------------------------------------------*/ |