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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: maurer.c,v 1.2 2000/08/11 21:34:59 mdw Exp $ |
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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 $ |
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33 | * Revision 1.2 2000/08/11 21:34:59 mdw |
34 | * New restartable interface to Maurer testing. |
35 | * |
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36 | * Revision 1.1 2000/06/17 11:29:49 mdw |
37 | * Maurer's universal statistical test. |
38 | * |
39 | */ |
40 | |
41 | /*----- Header files ------------------------------------------------------*/ |
42 | |
43 | #include <assert.h> |
44 | #include <math.h> |
45 | #include <stdio.h> |
46 | #include <stdlib.h> |
47 | |
48 | #include <mLib/alloc.h> |
49 | #include <mLib/bits.h> |
50 | |
51 | #include "maurer.h" |
52 | |
53 | /*----- Data structures ---------------------------------------------------*/ |
54 | |
55 | typedef struct bitscan { |
56 | const octet *p; |
57 | unsigned b; |
58 | uint32 a; |
59 | } bitscan; |
60 | |
61 | /*----- Main code ---------------------------------------------------------*/ |
62 | |
63 | /* --- @more@ --- * |
64 | * |
65 | * Arguments: @bitscan *b@ = pointer to a bitscanner structure |
66 | * @unsigned l@ = number of bits wanted |
67 | * |
68 | * Returns: An integer representing the next @l@ bits of the stream. |
69 | * |
70 | * Use: Fetches the next @l@ bits of a data stream. The bitscanner |
71 | * has no way of knowing whether it's run out of data, so make |
72 | * sure that doesn't happen. |
73 | */ |
74 | |
75 | static unsigned more(bitscan *b, unsigned l) |
76 | { |
77 | unsigned x, m; |
78 | |
79 | while (b->b < l) { |
80 | b->a |= U8(*b->p++) << b->b; |
81 | b->b += 8; |
82 | } |
83 | m = (1 << l) - 1; |
84 | x = b->a & m; |
85 | b->a >>= l; |
86 | b->b -= l; |
87 | return (x); |
88 | } |
89 | |
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90 | /* --- @maurer_init@ --- * |
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91 | * |
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92 | * Arguments: @maurer_ctx *m@ = pointer to a context to initialize |
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93 | * @unsigned l@ = number of bits to take at a time |
94 | * |
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95 | * Returns: Minimum recommended amount of data to test. |
96 | * |
97 | * Use: Initializes a Maurer testing context. Note that @l@ values |
98 | * larger than 16 are not supported, and values less than 6 can |
99 | * give bizarre results. |
100 | */ |
101 | |
102 | unsigned long maurer_init(maurer_ctx *m, unsigned l) |
103 | { |
104 | size_t i; |
105 | |
106 | assert(((void)"(maurer_init): chunks larger than 16 bits not supported", |
107 | 0 < l && l <= 16)); |
108 | |
109 | m->l = l; |
110 | m->a = 0; |
111 | m->b = 0; |
112 | m->n = 0; |
113 | m->x = 0; |
114 | |
115 | m->t = xmalloc(sizeof(unsigned long) << l); |
116 | for (i = 0; i < (1 << l); i++) |
117 | m->t[i] = 0; |
118 | return (((1000ul << l) * l + 7)/8); |
119 | } |
120 | |
121 | /* --- @bits@ --- * |
122 | * |
123 | * Arguments: @maurer_ctx *m@ = pointer to testing context |
124 | * @const octet **p@ = address of a buffer pointer |
125 | * @const octet *q@ = limit of the buffer pointer |
126 | * @unsigned *x@ = address to store next chunk |
127 | * |
128 | * Returns: Nonzero if some more bits arrived. |
129 | * |
130 | * Use: Reads some bits from a buffer. |
131 | */ |
132 | |
133 | static int bits(maurer_ctx *m, const octet **p, const octet *q, unsigned *x) |
134 | { |
135 | while (m->b < m->l) { |
136 | if (*p >= q) |
137 | return (0); |
138 | m->a |= U8(*(*p)++) << m->b; |
139 | m->b += 8; |
140 | } |
141 | *x = m->a & ((1 << m->l) - 1); |
142 | m->a >>= m->l; |
143 | m->b -= m->l; |
144 | m->n++; |
145 | return (1); |
146 | } |
147 | |
148 | /* --- @maurer_test@ --- * |
149 | * |
150 | * Arguments: @maurer_ctx *m@ = pointer to a Maurer testing context |
151 | * @const void *buf@ = pointer to a buffer of data |
152 | * @size_t sz@ = size of the buffer |
153 | * |
154 | * Returns: --- |
155 | * |
156 | * Use: Scans a buffer of data and updates the testing context. |
157 | */ |
158 | |
159 | void maurer_test(maurer_ctx *m, const void *buf, size_t sz) |
160 | { |
161 | const octet *p = buf, *l = p + sz; |
162 | unsigned long q = 10 << m->l; |
163 | unsigned x; |
164 | |
165 | /* --- Initialize the table --- */ |
166 | |
167 | while (m->n < q) { |
168 | if (!bits(m, &p, l, &x)) |
169 | return; |
170 | m->t[x] = m->n; |
171 | } |
172 | |
173 | /* --- Update the statistic --- */ |
174 | |
175 | while (bits(m, &p, l, &x)) { |
176 | m->x += log(m->n - m->t[x]); |
177 | m->t[x] = m->n; |
178 | } |
179 | } |
180 | |
181 | /* --- @maurer_done@ --- * |
182 | * |
183 | * Arguments: @maurer_ctx *m@ = pointer to a Maurer testing context |
184 | * |
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185 | * Returns: The statistic %$Z_u = (X_u - \mu)/\sigma$%, which should be |
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186 | * normally distributed with a mean of 0 and variance of 1. |
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187 | * |
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188 | * Use: Returns the result of Maurer's universal statistical test. |
189 | * Also frees the memory allocated during initialization. |
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190 | * |
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191 | * If insufficient data was received, the value @HUGE_VAL@ is |
192 | * returned. |
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193 | */ |
194 | |
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195 | double maurer_done(maurer_ctx *m) |
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196 | { |
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197 | double x, mu, c, sigma; |
198 | unsigned long q = 10 << m->l, k; |
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199 | |
200 | /* --- Table for means and variances --- */ |
201 | |
202 | struct { double mu, var_1; } vtab[] = { |
203 | { 0.7326495, 0.690 }, |
204 | { 1.5374383, 1.338 }, |
205 | { 2.4016068, 1.901 }, |
206 | { 3.3112247, 2.358 }, |
207 | { 4.2534266, 2.705 }, |
208 | { 5.2177052, 2.945 }, |
209 | { 6.1962507, 3.125 }, |
210 | { 7.1836656, 3.238 }, |
211 | { 8.1764248, 3.311 }, |
212 | { 9.1723243, 3.356 }, |
213 | { 10.170032 , 3.384 }, |
214 | { 11.168765 , 3.401 }, |
215 | { 12.168070 , 3.410 }, |
216 | { 13.167693 , 3.416 }, |
217 | { 14.167488 , 3.419 }, |
218 | { 15.167379 , 3.421 } |
219 | }; |
220 | |
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221 | /* --- Check for bogus requests --- */ |
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222 | |
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223 | if (m->n < q) { |
224 | x = HUGE_VAL; |
225 | goto done; |
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226 | } |
227 | |
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228 | /* --- Do the maths --- * |
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229 | * |
230 | * This produces %$X_u$%, which should be normally distributed with a mean |
231 | * and variance we can compute. |
232 | */ |
233 | |
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234 | k = m->n - q; |
235 | x = m->x/(k * log(2)); |
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236 | |
237 | /* --- Now translate this into %$Z_u$% distributed as %$N(0, 1)$% --- */ |
238 | |
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239 | mu = vtab[m->l - 1].mu; |
240 | c = 0.7 - 0.8/m->l + (1.6 + 12.8/m->l) * pow(k, -4.0/m->l); |
241 | sigma = sqrt(c * c * vtab[m->l - 1].var_1 / k); |
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242 | x = (x - mu)/sigma; |
243 | |
244 | /* --- Done (phew!) --- */ |
245 | |
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246 | done: |
247 | xfree(m->t); |
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248 | return (x); |
249 | } |
250 | |
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251 | /* --- @maurer@ --- * |
252 | * |
253 | * Arguments: @const octet *p@ = pointer to a buffer of data |
254 | * @size_t sz@ = size of the buffer |
255 | * @unsigned l@ = number of bits to take at a time |
256 | * |
257 | * Returns: The statistic %$Z_u$%. |
258 | * |
259 | * Use: Simple interface to Maurer's universal statistical test. For |
260 | * large %$l$% you should use the more complicated restartable |
261 | * interface. |
262 | */ |
263 | |
264 | double maurer(const octet *p, size_t sz, unsigned l) |
265 | { |
266 | maurer_ctx m; |
267 | |
268 | maurer_init(&m, l); |
269 | maurer_test(&m, p, sz); |
270 | return (maurer_done(&m)); |
271 | } |
272 | |
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273 | /*----- That's all, folks -------------------------------------------------*/ |