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1 | /* -*-c-*- |
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2 | * |
3 | * Maurer's universal statistical test |
4 | * |
5 | * (c) 2000 Straylight/Edgeware |
6 | */ |
7 | |
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8 | /*----- Licensing notice --------------------------------------------------* |
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9 | * |
10 | * This file is part of Catacomb. |
11 | * |
12 | * Catacomb is free software; you can redistribute it and/or modify |
13 | * it under the terms of the GNU Library General Public License as |
14 | * published by the Free Software Foundation; either version 2 of the |
15 | * License, or (at your option) any later version. |
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16 | * |
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17 | * Catacomb is distributed in the hope that it will be useful, |
18 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
19 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
20 | * GNU Library General Public License for more details. |
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21 | * |
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22 | * You should have received a copy of the GNU Library General Public |
23 | * License along with Catacomb; if not, write to the Free |
24 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
25 | * MA 02111-1307, USA. |
26 | */ |
27 | |
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28 | /*----- Header files ------------------------------------------------------*/ |
29 | |
30 | #include <assert.h> |
31 | #include <math.h> |
32 | #include <stdio.h> |
33 | #include <stdlib.h> |
34 | |
35 | #include <mLib/alloc.h> |
36 | #include <mLib/bits.h> |
37 | |
38 | #include "maurer.h" |
39 | |
40 | /*----- Data structures ---------------------------------------------------*/ |
41 | |
42 | typedef struct bitscan { |
43 | const octet *p; |
44 | unsigned b; |
45 | uint32 a; |
46 | } bitscan; |
47 | |
48 | /*----- Main code ---------------------------------------------------------*/ |
49 | |
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50 | /* --- @maurer_init@ --- * |
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51 | * |
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52 | * Arguments: @maurer_ctx *m@ = pointer to a context to initialize |
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53 | * @unsigned l@ = number of bits to take at a time |
54 | * |
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55 | * Returns: Minimum recommended amount of data to test. |
56 | * |
57 | * Use: Initializes a Maurer testing context. Note that @l@ values |
58 | * larger than 16 are not supported, and values less than 6 can |
59 | * give bizarre results. |
60 | */ |
61 | |
62 | unsigned long maurer_init(maurer_ctx *m, unsigned l) |
63 | { |
64 | size_t i; |
65 | |
66 | assert(((void)"(maurer_init): chunks larger than 16 bits not supported", |
67 | 0 < l && l <= 16)); |
68 | |
69 | m->l = l; |
70 | m->a = 0; |
71 | m->b = 0; |
72 | m->n = 0; |
73 | m->x = 0; |
74 | |
75 | m->t = xmalloc(sizeof(unsigned long) << l); |
76 | for (i = 0; i < (1 << l); i++) |
77 | m->t[i] = 0; |
78 | return (((1000ul << l) * l + 7)/8); |
79 | } |
80 | |
81 | /* --- @bits@ --- * |
82 | * |
83 | * Arguments: @maurer_ctx *m@ = pointer to testing context |
84 | * @const octet **p@ = address of a buffer pointer |
85 | * @const octet *q@ = limit of the buffer pointer |
86 | * @unsigned *x@ = address to store next chunk |
87 | * |
88 | * Returns: Nonzero if some more bits arrived. |
89 | * |
90 | * Use: Reads some bits from a buffer. |
91 | */ |
92 | |
93 | static int bits(maurer_ctx *m, const octet **p, const octet *q, unsigned *x) |
94 | { |
95 | while (m->b < m->l) { |
96 | if (*p >= q) |
97 | return (0); |
98 | m->a |= U8(*(*p)++) << m->b; |
99 | m->b += 8; |
100 | } |
101 | *x = m->a & ((1 << m->l) - 1); |
102 | m->a >>= m->l; |
103 | m->b -= m->l; |
104 | m->n++; |
105 | return (1); |
106 | } |
107 | |
108 | /* --- @maurer_test@ --- * |
109 | * |
110 | * Arguments: @maurer_ctx *m@ = pointer to a Maurer testing context |
111 | * @const void *buf@ = pointer to a buffer of data |
112 | * @size_t sz@ = size of the buffer |
113 | * |
114 | * Returns: --- |
115 | * |
116 | * Use: Scans a buffer of data and updates the testing context. |
117 | */ |
118 | |
119 | void maurer_test(maurer_ctx *m, const void *buf, size_t sz) |
120 | { |
121 | const octet *p = buf, *l = p + sz; |
122 | unsigned long q = 10 << m->l; |
123 | unsigned x; |
124 | |
125 | /* --- Initialize the table --- */ |
126 | |
127 | while (m->n < q) { |
128 | if (!bits(m, &p, l, &x)) |
129 | return; |
130 | m->t[x] = m->n; |
131 | } |
132 | |
133 | /* --- Update the statistic --- */ |
134 | |
135 | while (bits(m, &p, l, &x)) { |
136 | m->x += log(m->n - m->t[x]); |
137 | m->t[x] = m->n; |
138 | } |
139 | } |
140 | |
141 | /* --- @maurer_done@ --- * |
142 | * |
143 | * Arguments: @maurer_ctx *m@ = pointer to a Maurer testing context |
144 | * |
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145 | * Returns: The statistic %$Z_u = (X_u - \mu)/\sigma$%, which should be |
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146 | * normally distributed with a mean of 0 and variance of 1. |
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147 | * |
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148 | * Use: Returns the result of Maurer's universal statistical test. |
149 | * Also frees the memory allocated during initialization. |
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150 | * |
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151 | * If insufficient data was received, the value @HUGE_VAL@ is |
152 | * returned. |
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153 | */ |
154 | |
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155 | double maurer_done(maurer_ctx *m) |
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156 | { |
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157 | double x, mu, c, sigma; |
158 | unsigned long q = 10 << m->l, k; |
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159 | |
160 | /* --- Table for means and variances --- */ |
161 | |
162 | struct { double mu, var_1; } vtab[] = { |
163 | { 0.7326495, 0.690 }, |
164 | { 1.5374383, 1.338 }, |
165 | { 2.4016068, 1.901 }, |
166 | { 3.3112247, 2.358 }, |
167 | { 4.2534266, 2.705 }, |
168 | { 5.2177052, 2.945 }, |
169 | { 6.1962507, 3.125 }, |
170 | { 7.1836656, 3.238 }, |
171 | { 8.1764248, 3.311 }, |
172 | { 9.1723243, 3.356 }, |
173 | { 10.170032 , 3.384 }, |
174 | { 11.168765 , 3.401 }, |
175 | { 12.168070 , 3.410 }, |
176 | { 13.167693 , 3.416 }, |
177 | { 14.167488 , 3.419 }, |
178 | { 15.167379 , 3.421 } |
179 | }; |
180 | |
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181 | /* --- Check for bogus requests --- */ |
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182 | |
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183 | if (m->n < q) { |
184 | x = HUGE_VAL; |
185 | goto done; |
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186 | } |
187 | |
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188 | /* --- Do the maths --- * |
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189 | * |
190 | * This produces %$X_u$%, which should be normally distributed with a mean |
191 | * and variance we can compute. |
192 | */ |
193 | |
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194 | k = m->n - q; |
195 | x = m->x/(k * log(2)); |
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196 | |
197 | /* --- Now translate this into %$Z_u$% distributed as %$N(0, 1)$% --- */ |
198 | |
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199 | mu = vtab[m->l - 1].mu; |
200 | c = 0.7 - 0.8/m->l + (1.6 + 12.8/m->l) * pow(k, -4.0/m->l); |
201 | sigma = sqrt(c * c * vtab[m->l - 1].var_1 / k); |
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202 | x = (x - mu)/sigma; |
203 | |
204 | /* --- Done (phew!) --- */ |
205 | |
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206 | done: |
207 | xfree(m->t); |
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208 | return (x); |
209 | } |
210 | |
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211 | /* --- @maurer@ --- * |
212 | * |
213 | * Arguments: @const octet *p@ = pointer to a buffer of data |
214 | * @size_t sz@ = size of the buffer |
215 | * @unsigned l@ = number of bits to take at a time |
216 | * |
217 | * Returns: The statistic %$Z_u$%. |
218 | * |
219 | * Use: Simple interface to Maurer's universal statistical test. For |
220 | * large %$l$% you should use the more complicated restartable |
221 | * interface. |
222 | */ |
223 | |
224 | double maurer(const octet *p, size_t sz, unsigned l) |
225 | { |
226 | maurer_ctx m; |
227 | |
228 | maurer_init(&m, l); |
229 | maurer_test(&m, p, sz); |
230 | return (maurer_done(&m)); |
231 | } |
232 | |
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233 | /*----- That's all, folks -------------------------------------------------*/ |