--- /dev/null
+/* -*-c-*-
+ *
+ * Maurer's universal statistical test
+ *
+ * (c) 2000 Straylight/Edgeware
+ */
+
+/*----- Licensing notice --------------------------------------------------*
+ *
+ * This file is part of Catacomb.
+ *
+ * Catacomb is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU Library General Public License as
+ * published by the Free Software Foundation; either version 2 of the
+ * License, or (at your option) any later version.
+ *
+ * Catacomb is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU Library General Public License for more details.
+ *
+ * You should have received a copy of the GNU Library General Public
+ * License along with Catacomb; if not, write to the Free
+ * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA.
+ */
+
+/*----- Header files ------------------------------------------------------*/
+
+#include <assert.h>
+#include <math.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+#include <mLib/alloc.h>
+#include <mLib/bits.h>
+
+#include "maurer.h"
+
+/*----- Data structures ---------------------------------------------------*/
+
+typedef struct bitscan {
+ const octet *p;
+ unsigned b;
+ uint32 a;
+} bitscan;
+
+/*----- Main code ---------------------------------------------------------*/
+
+/* --- @maurer_init@ --- *
+ *
+ * Arguments: @maurer_ctx *m@ = pointer to a context to initialize
+ * @unsigned l@ = number of bits to take at a time
+ *
+ * Returns: Minimum recommended amount of data to test.
+ *
+ * Use: Initializes a Maurer testing context. Note that @l@ values
+ * larger than 16 are not supported, and values less than 6 can
+ * give bizarre results.
+ */
+
+unsigned long maurer_init(maurer_ctx *m, unsigned l)
+{
+ size_t i;
+
+ assert(((void)"(maurer_init): chunks larger than 16 bits not supported",
+ 0 < l && l <= 16));
+
+ m->l = l;
+ m->a = 0;
+ m->b = 0;
+ m->n = 0;
+ m->x = 0;
+
+ m->t = xmalloc(sizeof(unsigned long) << l);
+ for (i = 0; i < (1 << l); i++)
+ m->t[i] = 0;
+ return (((1000ul << l) * l + 7)/8);
+}
+
+/* --- @bits@ --- *
+ *
+ * Arguments: @maurer_ctx *m@ = pointer to testing context
+ * @const octet **p@ = address of a buffer pointer
+ * @const octet *q@ = limit of the buffer pointer
+ * @unsigned *x@ = address to store next chunk
+ *
+ * Returns: Nonzero if some more bits arrived.
+ *
+ * Use: Reads some bits from a buffer.
+ */
+
+static int bits(maurer_ctx *m, const octet **p, const octet *q, unsigned *x)
+{
+ while (m->b < m->l) {
+ if (*p >= q)
+ return (0);
+ m->a |= U8(*(*p)++) << m->b;
+ m->b += 8;
+ }
+ *x = m->a & ((1 << m->l) - 1);
+ m->a >>= m->l;
+ m->b -= m->l;
+ m->n++;
+ return (1);
+}
+
+/* --- @maurer_test@ --- *
+ *
+ * Arguments: @maurer_ctx *m@ = pointer to a Maurer testing context
+ * @const void *buf@ = pointer to a buffer of data
+ * @size_t sz@ = size of the buffer
+ *
+ * Returns: ---
+ *
+ * Use: Scans a buffer of data and updates the testing context.
+ */
+
+void maurer_test(maurer_ctx *m, const void *buf, size_t sz)
+{
+ const octet *p = buf, *l = p + sz;
+ unsigned long q = 10 << m->l;
+ unsigned x;
+
+ /* --- Initialize the table --- */
+
+ while (m->n < q) {
+ if (!bits(m, &p, l, &x))
+ return;
+ m->t[x] = m->n;
+ }
+
+ /* --- Update the statistic --- */
+
+ while (bits(m, &p, l, &x)) {
+ m->x += log(m->n - m->t[x]);
+ m->t[x] = m->n;
+ }
+}
+
+/* --- @maurer_done@ --- *
+ *
+ * Arguments: @maurer_ctx *m@ = pointer to a Maurer testing context
+ *
+ * Returns: The statistic %$Z_u = (X_u - \mu)/\sigma$%, which should be
+ * normally distributed with a mean of 0 and variance of 1.
+ *
+ * Use: Returns the result of Maurer's universal statistical test.
+ * Also frees the memory allocated during initialization.
+ *
+ * If insufficient data was received, the value @HUGE_VAL@ is
+ * returned.
+ */
+
+double maurer_done(maurer_ctx *m)
+{
+ double x, mu, c, sigma;
+ unsigned long q = 10 << m->l, k;
+
+ /* --- Table for means and variances --- */
+
+ struct { double mu, var_1; } vtab[] = {
+ { 0.7326495, 0.690 },
+ { 1.5374383, 1.338 },
+ { 2.4016068, 1.901 },
+ { 3.3112247, 2.358 },
+ { 4.2534266, 2.705 },
+ { 5.2177052, 2.945 },
+ { 6.1962507, 3.125 },
+ { 7.1836656, 3.238 },
+ { 8.1764248, 3.311 },
+ { 9.1723243, 3.356 },
+ { 10.170032 , 3.384 },
+ { 11.168765 , 3.401 },
+ { 12.168070 , 3.410 },
+ { 13.167693 , 3.416 },
+ { 14.167488 , 3.419 },
+ { 15.167379 , 3.421 }
+ };
+
+ /* --- Check for bogus requests --- */
+
+ if (m->n < q) {
+ x = HUGE_VAL;
+ goto done;
+ }
+
+ /* --- Do the maths --- *
+ *
+ * This produces %$X_u$%, which should be normally distributed with a mean
+ * and variance we can compute.
+ */
+
+ k = m->n - q;
+ x = m->x/(k * log(2));
+
+ /* --- Now translate this into %$Z_u$% distributed as %$N(0, 1)$% --- */
+
+ mu = vtab[m->l - 1].mu;
+ c = 0.7 - 0.8/m->l + (1.6 + 12.8/m->l) * pow(k, -4.0/m->l);
+ sigma = sqrt(c * c * vtab[m->l - 1].var_1 / k);
+ x = (x - mu)/sigma;
+
+ /* --- Done (phew!) --- */
+
+done:
+ xfree(m->t);
+ return (x);
+}
+
+/* --- @maurer@ --- *
+ *
+ * Arguments: @const octet *p@ = pointer to a buffer of data
+ * @size_t sz@ = size of the buffer
+ * @unsigned l@ = number of bits to take at a time
+ *
+ * Returns: The statistic %$Z_u$%.
+ *
+ * Use: Simple interface to Maurer's universal statistical test. For
+ * large %$l$% you should use the more complicated restartable
+ * interface.
+ */
+
+double maurer(const octet *p, size_t sz, unsigned l)
+{
+ maurer_ctx m;
+
+ maurer_init(&m, l);
+ maurer_test(&m, p, sz);
+ return (maurer_done(&m));
+}
+
+/*----- That's all, folks -------------------------------------------------*/
projects / u / mdw / catacomb / blobdiff