/* Byte-wise substring search, using the Two-Way algorithm. | |

Copyright (C) 2008-2021 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 |