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/* Substring search in a NUL terminated string of UNIT elements,
using the Knuth-Morris-Pratt algorithm.
Copyright (C) 2005-2020 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 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 General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, see <https://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 https://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
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