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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: maurer.c,v 1.4 2004/04/08 01:36:15 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 | |
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30 | /*----- Header files ------------------------------------------------------*/ |
31 | |
32 | #include <assert.h> |
33 | #include <math.h> |
34 | #include <stdio.h> |
35 | #include <stdlib.h> |
36 | |
37 | #include <mLib/alloc.h> |
38 | #include <mLib/bits.h> |
39 | |
40 | #include "maurer.h" |
41 | |
42 | /*----- Data structures ---------------------------------------------------*/ |
43 | |
44 | typedef struct bitscan { |
45 | const octet *p; |
46 | unsigned b; |
47 | uint32 a; |
48 | } bitscan; |
49 | |
50 | /*----- Main code ---------------------------------------------------------*/ |
51 | |
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52 | /* --- @maurer_init@ --- * |
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53 | * |
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54 | * Arguments: @maurer_ctx *m@ = pointer to a context to initialize |
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55 | * @unsigned l@ = number of bits to take at a time |
56 | * |
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57 | * Returns: Minimum recommended amount of data to test. |
58 | * |
59 | * Use: Initializes a Maurer testing context. Note that @l@ values |
60 | * larger than 16 are not supported, and values less than 6 can |
61 | * give bizarre results. |
62 | */ |
63 | |
64 | unsigned long maurer_init(maurer_ctx *m, unsigned l) |
65 | { |
66 | size_t i; |
67 | |
68 | assert(((void)"(maurer_init): chunks larger than 16 bits not supported", |
69 | 0 < l && l <= 16)); |
70 | |
71 | m->l = l; |
72 | m->a = 0; |
73 | m->b = 0; |
74 | m->n = 0; |
75 | m->x = 0; |
76 | |
77 | m->t = xmalloc(sizeof(unsigned long) << l); |
78 | for (i = 0; i < (1 << l); i++) |
79 | m->t[i] = 0; |
80 | return (((1000ul << l) * l + 7)/8); |
81 | } |
82 | |
83 | /* --- @bits@ --- * |
84 | * |
85 | * Arguments: @maurer_ctx *m@ = pointer to testing context |
86 | * @const octet **p@ = address of a buffer pointer |
87 | * @const octet *q@ = limit of the buffer pointer |
88 | * @unsigned *x@ = address to store next chunk |
89 | * |
90 | * Returns: Nonzero if some more bits arrived. |
91 | * |
92 | * Use: Reads some bits from a buffer. |
93 | */ |
94 | |
95 | static int bits(maurer_ctx *m, const octet **p, const octet *q, unsigned *x) |
96 | { |
97 | while (m->b < m->l) { |
98 | if (*p >= q) |
99 | return (0); |
100 | m->a |= U8(*(*p)++) << m->b; |
101 | m->b += 8; |
102 | } |
103 | *x = m->a & ((1 << m->l) - 1); |
104 | m->a >>= m->l; |
105 | m->b -= m->l; |
106 | m->n++; |
107 | return (1); |
108 | } |
109 | |
110 | /* --- @maurer_test@ --- * |
111 | * |
112 | * Arguments: @maurer_ctx *m@ = pointer to a Maurer testing context |
113 | * @const void *buf@ = pointer to a buffer of data |
114 | * @size_t sz@ = size of the buffer |
115 | * |
116 | * Returns: --- |
117 | * |
118 | * Use: Scans a buffer of data and updates the testing context. |
119 | */ |
120 | |
121 | void maurer_test(maurer_ctx *m, const void *buf, size_t sz) |
122 | { |
123 | const octet *p = buf, *l = p + sz; |
124 | unsigned long q = 10 << m->l; |
125 | unsigned x; |
126 | |
127 | /* --- Initialize the table --- */ |
128 | |
129 | while (m->n < q) { |
130 | if (!bits(m, &p, l, &x)) |
131 | return; |
132 | m->t[x] = m->n; |
133 | } |
134 | |
135 | /* --- Update the statistic --- */ |
136 | |
137 | while (bits(m, &p, l, &x)) { |
138 | m->x += log(m->n - m->t[x]); |
139 | m->t[x] = m->n; |
140 | } |
141 | } |
142 | |
143 | /* --- @maurer_done@ --- * |
144 | * |
145 | * Arguments: @maurer_ctx *m@ = pointer to a Maurer testing context |
146 | * |
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147 | * Returns: The statistic %$Z_u = (X_u - \mu)/\sigma$%, which should be |
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148 | * normally distributed with a mean of 0 and variance of 1. |
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149 | * |
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150 | * Use: Returns the result of Maurer's universal statistical test. |
151 | * Also frees the memory allocated during initialization. |
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152 | * |
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153 | * If insufficient data was received, the value @HUGE_VAL@ is |
154 | * returned. |
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155 | */ |
156 | |
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157 | double maurer_done(maurer_ctx *m) |
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158 | { |
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159 | double x, mu, c, sigma; |
160 | unsigned long q = 10 << m->l, k; |
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161 | |
162 | /* --- Table for means and variances --- */ |
163 | |
164 | struct { double mu, var_1; } vtab[] = { |
165 | { 0.7326495, 0.690 }, |
166 | { 1.5374383, 1.338 }, |
167 | { 2.4016068, 1.901 }, |
168 | { 3.3112247, 2.358 }, |
169 | { 4.2534266, 2.705 }, |
170 | { 5.2177052, 2.945 }, |
171 | { 6.1962507, 3.125 }, |
172 | { 7.1836656, 3.238 }, |
173 | { 8.1764248, 3.311 }, |
174 | { 9.1723243, 3.356 }, |
175 | { 10.170032 , 3.384 }, |
176 | { 11.168765 , 3.401 }, |
177 | { 12.168070 , 3.410 }, |
178 | { 13.167693 , 3.416 }, |
179 | { 14.167488 , 3.419 }, |
180 | { 15.167379 , 3.421 } |
181 | }; |
182 | |
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183 | /* --- Check for bogus requests --- */ |
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184 | |
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185 | if (m->n < q) { |
186 | x = HUGE_VAL; |
187 | goto done; |
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188 | } |
189 | |
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190 | /* --- Do the maths --- * |
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191 | * |
192 | * This produces %$X_u$%, which should be normally distributed with a mean |
193 | * and variance we can compute. |
194 | */ |
195 | |
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196 | k = m->n - q; |
197 | x = m->x/(k * log(2)); |
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198 | |
199 | /* --- Now translate this into %$Z_u$% distributed as %$N(0, 1)$% --- */ |
200 | |
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201 | mu = vtab[m->l - 1].mu; |
202 | c = 0.7 - 0.8/m->l + (1.6 + 12.8/m->l) * pow(k, -4.0/m->l); |
203 | sigma = sqrt(c * c * vtab[m->l - 1].var_1 / k); |
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204 | x = (x - mu)/sigma; |
205 | |
206 | /* --- Done (phew!) --- */ |
207 | |
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208 | done: |
209 | xfree(m->t); |
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210 | return (x); |
211 | } |
212 | |
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213 | /* --- @maurer@ --- * |
214 | * |
215 | * Arguments: @const octet *p@ = pointer to a buffer of data |
216 | * @size_t sz@ = size of the buffer |
217 | * @unsigned l@ = number of bits to take at a time |
218 | * |
219 | * Returns: The statistic %$Z_u$%. |
220 | * |
221 | * Use: Simple interface to Maurer's universal statistical test. For |
222 | * large %$l$% you should use the more complicated restartable |
223 | * interface. |
224 | */ |
225 | |
226 | double maurer(const octet *p, size_t sz, unsigned l) |
227 | { |
228 | maurer_ctx m; |
229 | |
230 | maurer_init(&m, l); |
231 | maurer_test(&m, p, sz); |
232 | return (maurer_done(&m)); |
233 | } |
234 | |
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235 | /*----- That's all, folks -------------------------------------------------*/ |