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+/* Byte-wise substring search, using the Two-Way algorithm.
+ Copyright (C) 2008-2020 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+ Written by Eric Blake <ebb9@byu.net>, 2008.
+
+ 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 3, 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 include <config.h> and
+ <string.h>, and define:
+ RETURN_TYPE A macro that expands to the return type.
+ AVAILABLE(h, h_l, j, n_l)
+ A macro that returns nonzero if there are
+ at least N_L bytes left starting at H[J].
+ H is 'unsigned char *', H_L, J, and N_L
+ are 'size_t'; H_L is an lvalue. For
+ NUL-terminated searches, H_L can be
+ modified each iteration to avoid having
+ to compute the end of H up front.
+
+ For case-insensitivity, you may optionally define:
+ CMP_FUNC(p1, p2, l) A macro that returns 0 iff the first L
+ characters of P1 and P2 are equal.
+ CANON_ELEMENT(c) A macro that canonicalizes an element right after
+ it has been fetched from one of the two strings.
+ The argument is an 'unsigned char'; the result
+ must be an 'unsigned char' as well.
+
+ This file undefines the macros documented above, and defines
+ LONG_NEEDLE_THRESHOLD.
+*/
+
+#include <limits.h>
+#include <stdint.h>
+
+/* We use the Two-Way string matching algorithm (also known as
+ Chrochemore-Perrin), which guarantees linear complexity with
+ constant space. Additionally, for long needles, we also use a bad
+ character shift table similar to the Boyer-Moore algorithm to
+ achieve improved (potentially sub-linear) performance.
+
+ See https://www-igm.univ-mlv.fr/~lecroq/string/node26.html#SECTION00260,
+ https://en.wikipedia.org/wiki/Boyer-Moore_string_search_algorithm,
+ https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.34.6641&rep=rep1&type=pdf
+*/
+
+/* Point at which computing a bad-byte shift table is likely to be
+ worthwhile. Small needles should not compute a table, since it
+ adds (1 << CHAR_BIT) + NEEDLE_LEN computations of preparation for a
+ speedup no greater than a factor of NEEDLE_LEN. The larger the
+ needle, the better the potential performance gain. On the other
+ hand, on non-POSIX systems with CHAR_BIT larger than eight, the
+ memory required for the table is prohibitive. */
+#if CHAR_BIT < 10
+# define LONG_NEEDLE_THRESHOLD 32U
+#else
+# define LONG_NEEDLE_THRESHOLD SIZE_MAX
+#endif
+
+#ifndef MAX
+# define MAX(a, b) ((a < b) ? (b) : (a))
+#endif
+
+#ifndef CANON_ELEMENT
+# define CANON_ELEMENT(c) c
+#endif
+#ifndef CMP_FUNC
+# define CMP_FUNC memcmp
+#endif
+
+/* Perform a critical factorization of NEEDLE, of length NEEDLE_LEN.
+ Return the index of the first byte in the right half, and set
+ *PERIOD to the global period of the right half.
+
+ The global period of a string is the smallest index (possibly its
+ length) at which all remaining bytes in the string are repetitions
+ of the prefix (the last repetition may be a subset of the prefix).
+
+ When NEEDLE is factored into two halves, a local period is the
+ length of the smallest word that shares a suffix with the left half
+ and shares a prefix with the right half. All factorizations of a
+ non-empty NEEDLE have a local period of at least 1 and no greater
+ than NEEDLE_LEN.
+
+ A critical factorization has the property that the local period
+ equals the global period. All strings have at least one critical
+ factorization with the left half smaller than the global period.
+ And while some strings have more than one critical factorization,
+ it is provable that with an ordered alphabet, at least one of the
+ critical factorizations corresponds to a maximal suffix.
+
+ Given an ordered alphabet, a critical factorization can be computed
+ in linear time, with 2 * NEEDLE_LEN comparisons, by computing the
+ shorter of two ordered maximal suffixes. The ordered maximal
+ suffixes are determined by lexicographic comparison while tracking
+ periodicity. */
+static size_t
+critical_factorization (const unsigned char *needle, size_t needle_len,
+ size_t *period)
+{
+ /* Index of last byte of left half, or SIZE_MAX. */
+ size_t max_suffix, max_suffix_rev;
+ size_t j; /* Index into NEEDLE for current candidate suffix. */
+ size_t k; /* Offset into current period. */
+ size_t p; /* Intermediate period. */
+ unsigned char a, b; /* Current comparison bytes. */
+
+ /* Special case NEEDLE_LEN of 1 or 2 (all callers already filtered
+ out 0-length needles. */
+ if (needle_len < 3)
+ {
+ *period = 1;
+ return needle_len - 1;
+ }
+
+ /* Invariants:
+ 0 <= j < NEEDLE_LEN - 1
+ -1 <= max_suffix{,_rev} < j (treating SIZE_MAX as if it were signed)
+ min(max_suffix, max_suffix_rev) < global period of NEEDLE
+ 1 <= p <= global period of NEEDLE
+ p == global period of the substring NEEDLE[max_suffix{,_rev}+1...j]
+ 1 <= k <= p
+ */
+
+ /* Perform lexicographic search. */
+ max_suffix = SIZE_MAX;
+ j = 0;
+ k = p = 1;
+ while (j + k < needle_len)
+ {
+ a = CANON_ELEMENT (needle[j + k]);
+ b = CANON_ELEMENT (needle[max_suffix + k]);
+ if (a < b)
+ {
+ /* Suffix is smaller, period is entire prefix so far. */
+ j += k;
+ k = 1;
+ p = j - max_suffix;
+ }
+ else if (a == b)
+ {
+ /* Advance through repetition of the current period. */
+ if (k != p)
+ ++k;
+ else
+ {
+ j += p;
+ k = 1;
+ }
+ }
+ else /* b < a */
+ {
+ /* Suffix is larger, start over from current location. */
+ max_suffix = j++;
+ k = p = 1;
+ }
+ }
+ *period = p;
+
+ /* Perform reverse lexicographic search. */
+ max_suffix_rev = SIZE_MAX;
+ j = 0;
+ k = p = 1;
+ while (j + k < needle_len)
+ {
+ a = CANON_ELEMENT (needle[j + k]);
+ b = CANON_ELEMENT (needle[max_suffix_rev + k]);
+ if (b < a)
+ {
+ /* Suffix is smaller, period is entire prefix so far. */
+ j += k;
+ k = 1;
+ p = j - max_suffix_rev;
+ }
+ else if (a == b)
+ {
+ /* Advance through repetition of the current period. */
+ if (k != p)
+ ++k;
+ else
+ {
+ j += p;
+ k = 1;
+ }
+ }
+ else /* a < b */
+ {
+ /* Suffix is larger, start over from current location. */
+ max_suffix_rev = j++;
+ k = p = 1;
+ }
+ }
+
+ /* Choose the shorter suffix. Return the index of the first byte of
+ the right half, rather than the last byte of the left half.
+
+ For some examples, 'banana' has two critical factorizations, both
+ exposed by the two lexicographic extreme suffixes of 'anana' and
+ 'nana', where both suffixes have a period of 2. On the other
+ hand, with 'aab' and 'bba', both strings have a single critical
+ factorization of the last byte, with the suffix having a period
+ of 1. While the maximal lexicographic suffix of 'aab' is 'b',
+ the maximal lexicographic suffix of 'bba' is 'ba', which is not a
+ critical factorization. Conversely, the maximal reverse
+ lexicographic suffix of 'a' works for 'bba', but not 'ab' for
+ 'aab'. The shorter suffix of the two will always be a critical
+ factorization. */
+ if (max_suffix_rev + 1 < max_suffix + 1)
+ return max_suffix + 1;
+ *period = p;
+ return max_suffix_rev + 1;
+}
+
+/* Return the first location of non-empty NEEDLE within HAYSTACK, or
+ NULL. HAYSTACK_LEN is the minimum known length of HAYSTACK. This
+ method is optimized for NEEDLE_LEN < LONG_NEEDLE_THRESHOLD.
+ Performance is guaranteed to be linear, with an initialization cost
+ of 2 * NEEDLE_LEN comparisons.
+
+ If AVAILABLE does not modify HAYSTACK_LEN (as in memmem), then at
+ most 2 * HAYSTACK_LEN - NEEDLE_LEN comparisons occur in searching.
+ If AVAILABLE modifies HAYSTACK_LEN (as in strstr), then at most 3 *
+ HAYSTACK_LEN - NEEDLE_LEN comparisons occur in searching. */
+static RETURN_TYPE
+two_way_short_needle (const unsigned char *haystack, size_t haystack_len,
+ const unsigned char *needle, size_t needle_len)
+{
+ size_t i; /* Index into current byte of NEEDLE. */
+ size_t j; /* Index into current window of HAYSTACK. */
+ size_t period; /* The period of the right half of needle. */
+ size_t suffix; /* The index of the right half of needle. */
+
+ /* Factor the needle into two halves, such that the left half is
+ smaller than the global period, and the right half is
+ periodic (with a period as large as NEEDLE_LEN - suffix). */
+ suffix = critical_factorization (needle, needle_len, &period);
+
+ /* Perform the search. Each iteration compares the right half
+ first. */
+ if (CMP_FUNC (needle, needle + period, suffix) == 0)
+ {
+ /* Entire needle is periodic; a mismatch in the left half can
+ only advance by the period, so use memory to avoid rescanning
+ known occurrences of the period in the right half. */
+ size_t memory = 0;
+ j = 0;
+ while (AVAILABLE (haystack, haystack_len, j, needle_len))
+ {
+ /* Scan for matches in right half. */
+ i = MAX (suffix, memory);
+ while (i < needle_len && (CANON_ELEMENT (needle[i])
+ == CANON_ELEMENT (haystack[i + j])))
+ ++i;
+ if (needle_len <= i)
+ {
+ /* Scan for matches in left half. */
+ i = suffix - 1;
+ while (memory < i + 1 && (CANON_ELEMENT (needle[i])
+ == CANON_ELEMENT (haystack[i + j])))
+ --i;
+ if (i + 1 < memory + 1)
+ return (RETURN_TYPE) (haystack + j);
+ /* No match, so remember how many repetitions of period
+ on the right half were scanned. */
+ j += period;
+ memory = needle_len - period;
+ }
+ else
+ {
+ j += i - suffix + 1;
+ memory = 0;
+ }
+ }
+ }
+ else
+ {
+ /* The two halves of needle are distinct; no extra memory is
+ required, and any mismatch results in a maximal shift. */
+ period = MAX (suffix, needle_len - suffix) + 1;
+ j = 0;
+ while (AVAILABLE (haystack, haystack_len, j, needle_len))
+ {
+ /* Scan for matches in right half. */
+ i = suffix;
+ while (i < needle_len && (CANON_ELEMENT (needle[i])
+ == CANON_ELEMENT (haystack[i + j])))
+ ++i;
+ if (needle_len <= i)
+ {
+ /* Scan for matches in left half. */
+ i = suffix - 1;
+ while (i != SIZE_MAX && (CANON_ELEMENT (needle[i])
+ == CANON_ELEMENT (haystack[i + j])))
+ --i;
+ if (i == SIZE_MAX)
+ return (RETURN_TYPE) (haystack + j);
+ j += period;
+ }
+ else
+ j += i - suffix + 1;
+ }
+ }
+ return NULL;
+}
+
+/* Return the first location of non-empty NEEDLE within HAYSTACK, or
+ NULL. HAYSTACK_LEN is the minimum known length of HAYSTACK. This
+ method is optimized for LONG_NEEDLE_THRESHOLD <= NEEDLE_LEN.
+ Performance is guaranteed to be linear, with an initialization cost
+ of 3 * NEEDLE_LEN + (1 << CHAR_BIT) operations.
+
+ If AVAILABLE does not modify HAYSTACK_LEN (as in memmem), then at
+ most 2 * HAYSTACK_LEN - NEEDLE_LEN comparisons occur in searching,
+ and sublinear performance O(HAYSTACK_LEN / NEEDLE_LEN) is possible.
+ If AVAILABLE modifies HAYSTACK_LEN (as in strstr), then at most 3 *
+ HAYSTACK_LEN - NEEDLE_LEN comparisons occur in searching, and
+ sublinear performance is not possible. */
+static RETURN_TYPE
+two_way_long_needle (const unsigned char *haystack, size_t haystack_len,
+ const unsigned char *needle, size_t needle_len)
+{
+ size_t i; /* Index into current byte of NEEDLE. */
+ size_t j; /* Index into current window of HAYSTACK. */
+ size_t period; /* The period of the right half of needle. */
+ size_t suffix; /* The index of the right half of needle. */
+ size_t shift_table[1U << CHAR_BIT]; /* See below. */
+
+ /* Factor the needle into two halves, such that the left half is
+ smaller than the global period, and the right half is
+ periodic (with a period as large as NEEDLE_LEN - suffix). */
+ suffix = critical_factorization (needle, needle_len, &period);
+
+ /* Populate shift_table. For each possible byte value c,
+ shift_table[c] is the distance from the last occurrence of c to
+ the end of NEEDLE, or NEEDLE_LEN if c is absent from the NEEDLE.
+ shift_table[NEEDLE[NEEDLE_LEN - 1]] contains the only 0. */
+ for (i = 0; i < 1U << CHAR_BIT; i++)
+ shift_table[i] = needle_len;
+ for (i = 0; i < needle_len; i++)
+ shift_table[CANON_ELEMENT (needle[i])] = needle_len - i - 1;
+
+ /* Perform the search. Each iteration compares the right half
+ first. */
+ if (CMP_FUNC (needle, needle + period, suffix) == 0)
+ {
+ /* Entire needle is periodic; a mismatch in the left half can
+ only advance by the period, so use memory to avoid rescanning
+ known occurrences of the period in the right half. */
+ size_t memory = 0;
+ size_t shift;
+ j = 0;
+ while (AVAILABLE (haystack, haystack_len, j, needle_len))
+ {
+ /* Check the last byte first; if it does not match, then
+ shift to the next possible match location. */
+ shift = shift_table[CANON_ELEMENT (haystack[j + needle_len - 1])];
+ if (0 < shift)
+ {
+ if (memory && shift < period)
+ {
+ /* Since needle is periodic, but the last period has
+ a byte out of place, there can be no match until
+ after the mismatch. */
+ shift = needle_len - period;
+ }
+ memory = 0;
+ j += shift;
+ continue;
+ }
+ /* Scan for matches in right half. The last byte has
+ already been matched, by virtue of the shift table. */
+ i = MAX (suffix, memory);
+ while (i < needle_len - 1 && (CANON_ELEMENT (needle[i])
+ == CANON_ELEMENT (haystack[i + j])))
+ ++i;
+ if (needle_len - 1 <= i)
+ {
+ /* Scan for matches in left half. */
+ i = suffix - 1;
+ while (memory < i + 1 && (CANON_ELEMENT (needle[i])
+ == CANON_ELEMENT (haystack[i + j])))
+ --i;
+ if (i + 1 < memory + 1)
+ return (RETURN_TYPE) (haystack + j);
+ /* No match, so remember how many repetitions of period
+ on the right half were scanned. */
+ j += period;
+ memory = needle_len - period;
+ }
+ else
+ {
+ j += i - suffix + 1;
+ memory = 0;
+ }
+ }
+ }
+ else
+ {
+ /* The two halves of needle are distinct; no extra memory is
+ required, and any mismatch results in a maximal shift. */
+ size_t shift;
+ period = MAX (suffix, needle_len - suffix) + 1;
+ j = 0;
+ while (AVAILABLE (haystack, haystack_len, j, needle_len))
+ {
+ /* Check the last byte first; if it does not match, then
+ shift to the next possible match location. */
+ shift = shift_table[CANON_ELEMENT (haystack[j + needle_len - 1])];
+ if (0 < shift)
+ {
+ j += shift;
+ continue;
+ }
+ /* Scan for matches in right half. The last byte has
+ already been matched, by virtue of the shift table. */
+ i = suffix;
+ while (i < needle_len - 1 && (CANON_ELEMENT (needle[i])
+ == CANON_ELEMENT (haystack[i + j])))
+ ++i;
+ if (needle_len - 1 <= i)
+ {
+ /* Scan for matches in left half. */
+ i = suffix - 1;
+ while (i != SIZE_MAX && (CANON_ELEMENT (needle[i])
+ == CANON_ELEMENT (haystack[i + j])))
+ --i;
+ if (i == SIZE_MAX)
+ return (RETURN_TYPE) (haystack + j);
+ j += period;
+ }
+ else
+ j += i - suffix + 1;
+ }
+ }
+ return NULL;
+}
+
+#undef AVAILABLE
+#undef CANON_ELEMENT
+#undef CMP_FUNC
+#undef MAX
+#undef RETURN_TYPE