| 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 -------------------------------------------------*/ |