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| -rw-r--r-- | lib/str-two-way.h | 452 |
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diff --git a/lib/str-two-way.h b/lib/str-two-way.h new file mode 100644 index 0000000..85489d1 --- /dev/null +++ b/lib/str-two-way.h @@ -0,0 +1,452 @@ +/* Byte-wise substring search, using the Two-Way algorithm. + Copyright (C) 2008-2018 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: + RESULT_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 http://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 |