| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id: maurer.c,v 1.2 2000/08/11 21:34:59 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 1.2 2000/08/11 21:34:59 mdw |
| 34 | * New restartable interface to Maurer testing. |
| 35 | * |
| 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 | |
| 90 | /* --- @maurer_init@ --- * |
| 91 | * |
| 92 | * Arguments: @maurer_ctx *m@ = pointer to a context to initialize |
| 93 | * @unsigned l@ = number of bits to take at a time |
| 94 | * |
| 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 | * |
| 185 | * Returns: The statistic %$Z_u = (X_u - \mu)/\sigma$%, which should be |
| 186 | * normally distributed with a mean of 0 and variance of 1. |
| 187 | * |
| 188 | * Use: Returns the result of Maurer's universal statistical test. |
| 189 | * Also frees the memory allocated during initialization. |
| 190 | * |
| 191 | * If insufficient data was received, the value @HUGE_VAL@ is |
| 192 | * returned. |
| 193 | */ |
| 194 | |
| 195 | double maurer_done(maurer_ctx *m) |
| 196 | { |
| 197 | double x, mu, c, sigma; |
| 198 | unsigned long q = 10 << m->l, k; |
| 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 | |
| 221 | /* --- Check for bogus requests --- */ |
| 222 | |
| 223 | if (m->n < q) { |
| 224 | x = HUGE_VAL; |
| 225 | goto done; |
| 226 | } |
| 227 | |
| 228 | /* --- Do the maths --- * |
| 229 | * |
| 230 | * This produces %$X_u$%, which should be normally distributed with a mean |
| 231 | * and variance we can compute. |
| 232 | */ |
| 233 | |
| 234 | k = m->n - q; |
| 235 | x = m->x/(k * log(2)); |
| 236 | |
| 237 | /* --- Now translate this into %$Z_u$% distributed as %$N(0, 1)$% --- */ |
| 238 | |
| 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); |
| 242 | x = (x - mu)/sigma; |
| 243 | |
| 244 | /* --- Done (phew!) --- */ |
| 245 | |
| 246 | done: |
| 247 | xfree(m->t); |
| 248 | return (x); |
| 249 | } |
| 250 | |
| 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 | |
| 273 | /*----- That's all, folks -------------------------------------------------*/ |