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+/* Substring search in a NUL terminated string of UNIT elements,
+ using the Knuth-Morris-Pratt algorithm.
+ Copyright (C) 2005-2015 Free Software Foundation, Inc.
+ Written by Bruno Haible <bruno@clisp.org>, 2005.
+
+ This program is free software; you can redistribute it and/or modify
+ it under the terms of the GNU Lesser General Public License as published by
+ the Free Software Foundation; either version 2, or (at your option)
+ any later version.
+
+ This program 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 Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public License
+ along with this program; if not, see <http://www.gnu.org/licenses/>. */
+
+/* Before including this file, you need to define:
+ UNIT The element type of the needle and haystack.
+ CANON_ELEMENT(c) A macro that canonicalizes an element right after
+ it has been fetched from needle or haystack.
+ The argument is of type UNIT; the result must be
+ of type UNIT as well. */
+
+/* Knuth-Morris-Pratt algorithm.
+ See http://en.wikipedia.org/wiki/Knuth-Morris-Pratt_algorithm
+ HAYSTACK is the NUL terminated string in which to search for.
+ NEEDLE is the string to search for in HAYSTACK, consisting of NEEDLE_LEN
+ units.
+ Return a boolean indicating success:
+ Return true and set *RESULTP if the search was completed.
+ Return false if it was aborted because not enough memory was available. */
+static bool
+knuth_morris_pratt (const UNIT *haystack,
+ const UNIT *needle, size_t needle_len,
+ const UNIT **resultp)
+{
+ size_t m = needle_len;
+
+ /* Allocate the table. */
+ size_t *table = (size_t *) nmalloca (m, sizeof (size_t));
+ if (table == NULL)
+ return false;
+ /* Fill the table.
+ For 0 < i < m:
+ 0 < table[i] <= i is defined such that
+ forall 0 < x < table[i]: needle[x..i-1] != needle[0..i-1-x],
+ and table[i] is as large as possible with this property.
+ This implies:
+ 1) For 0 < i < m:
+ If table[i] < i,
+ needle[table[i]..i-1] = needle[0..i-1-table[i]].
+ 2) For 0 < i < m:
+ rhaystack[0..i-1] == needle[0..i-1]
+ and exists h, i <= h < m: rhaystack[h] != needle[h]
+ implies
+ forall 0 <= x < table[i]: rhaystack[x..x+m-1] != needle[0..m-1].
+ table[0] remains uninitialized. */
+ {
+ size_t i, j;
+
+ /* i = 1: Nothing to verify for x = 0. */
+ table[1] = 1;
+ j = 0;
+
+ for (i = 2; i < m; i++)
+ {
+ /* Here: j = i-1 - table[i-1].
+ The inequality needle[x..i-1] != needle[0..i-1-x] is known to hold
+ for x < table[i-1], by induction.
+ Furthermore, if j>0: needle[i-1-j..i-2] = needle[0..j-1]. */
+ UNIT b = CANON_ELEMENT (needle[i - 1]);
+
+ for (;;)
+ {
+ /* Invariants: The inequality needle[x..i-1] != needle[0..i-1-x]
+ is known to hold for x < i-1-j.
+ Furthermore, if j>0: needle[i-1-j..i-2] = needle[0..j-1]. */
+ if (b == CANON_ELEMENT (needle[j]))
+ {
+ /* Set table[i] := i-1-j. */
+ table[i] = i - ++j;
+ break;
+ }
+ /* The inequality needle[x..i-1] != needle[0..i-1-x] also holds
+ for x = i-1-j, because
+ needle[i-1] != needle[j] = needle[i-1-x]. */
+ if (j == 0)
+ {
+ /* The inequality holds for all possible x. */
+ table[i] = i;
+ break;
+ }
+ /* The inequality needle[x..i-1] != needle[0..i-1-x] also holds
+ for i-1-j < x < i-1-j+table[j], because for these x:
+ needle[x..i-2]
+ = needle[x-(i-1-j)..j-1]
+ != needle[0..j-1-(x-(i-1-j))] (by definition of table[j])
+ = needle[0..i-2-x],
+ hence needle[x..i-1] != needle[0..i-1-x].
+ Furthermore
+ needle[i-1-j+table[j]..i-2]
+ = needle[table[j]..j-1]
+ = needle[0..j-1-table[j]] (by definition of table[j]). */
+ j = j - table[j];
+ }
+ /* Here: j = i - table[i]. */
+ }
+ }
+
+ /* Search, using the table to accelerate the processing. */
+ {
+ size_t j;
+ const UNIT *rhaystack;
+ const UNIT *phaystack;
+
+ *resultp = NULL;
+ j = 0;
+ rhaystack = haystack;
+ phaystack = haystack;
+ /* Invariant: phaystack = rhaystack + j. */
+ while (*phaystack != 0)
+ if (CANON_ELEMENT (needle[j]) == CANON_ELEMENT (*phaystack))
+ {
+ j++;
+ phaystack++;
+ if (j == m)
+ {
+ /* The entire needle has been found. */
+ *resultp = rhaystack;
+ break;
+ }
+ }
+ else if (j > 0)
+ {
+ /* Found a match of needle[0..j-1], mismatch at needle[j]. */
+ rhaystack += table[j];
+ j -= table[j];
+ }
+ else
+ {
+ /* Found a mismatch at needle[0] already. */
+ rhaystack++;
+ phaystack++;
+ }
+ }
+
+ freea (table);
+ return true;
+}
+
+#undef CANON_ELEMENT