| 1 | /* Byte-wise substring search, using the Two-Way algorithm. |
| 2 | Copyright (C) 2008-2020 Free Software Foundation, Inc. |
| 3 | This file is part of the GNU C Library. |
| 4 | Written by Eric Blake <ebb9@byu.net>, 2008. |
| 5 | |
| 6 | This program is free software; you can redistribute it and/or modify |
| 7 | it under the terms of the GNU General Public License as published by |
| 8 | the Free Software Foundation; either version 3, or (at your option) |
| 9 | any later version. |
| 10 | |
| 11 | This program is distributed in the hope that it will be useful, |
| 12 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 13 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| 14 | GNU General Public License for more details. |
| 15 | |
| 16 | You should have received a copy of the GNU General Public License along |
| 17 | with this program; if not, see <https://www.gnu.org/licenses/>. */ |
| 18 | |
| 19 | /* Before including this file, you need to include <config.h> and |
| 20 | <string.h>, and define: |
| 21 | RETURN_TYPE A macro that expands to the return type. |
| 22 | AVAILABLE(h, h_l, j, n_l) |
| 23 | A macro that returns nonzero if there are |
| 24 | at least N_L bytes left starting at H[J]. |
| 25 | H is 'unsigned char *', H_L, J, and N_L |
| 26 | are 'size_t'; H_L is an lvalue. For |
| 27 | NUL-terminated searches, H_L can be |
| 28 | modified each iteration to avoid having |
| 29 | to compute the end of H up front. |
| 30 | |
| 31 | For case-insensitivity, you may optionally define: |
| 32 | CMP_FUNC(p1, p2, l) A macro that returns 0 iff the first L |
| 33 | characters of P1 and P2 are equal. |
| 34 | CANON_ELEMENT(c) A macro that canonicalizes an element right after |
| 35 | it has been fetched from one of the two strings. |
| 36 | The argument is an 'unsigned char'; the result |
| 37 | must be an 'unsigned char' as well. |
| 38 | |
| 39 | This file undefines the macros documented above, and defines |
| 40 | LONG_NEEDLE_THRESHOLD. |
| 41 | */ |
| 42 | |
| 43 | #include <limits.h> |
| 44 | #include <stdint.h> |
| 45 | |
| 46 | /* We use the Two-Way string matching algorithm (also known as |
| 47 | Chrochemore-Perrin), which guarantees linear complexity with |
| 48 | constant space. Additionally, for long needles, we also use a bad |
| 49 | character shift table similar to the Boyer-Moore algorithm to |
| 50 | achieve improved (potentially sub-linear) performance. |
| 51 | |
| 52 | See https://www-igm.univ-mlv.fr/~lecroq/string/node26.html#SECTION00260, |
| 53 | https://en.wikipedia.org/wiki/Boyer-Moore_string_search_algorithm, |
| 54 | https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.34.6641&rep=rep1&type=pdf |
| 55 | */ |
| 56 | |
| 57 | /* Point at which computing a bad-byte shift table is likely to be |
| 58 | worthwhile. Small needles should not compute a table, since it |
| 59 | adds (1 << CHAR_BIT) + NEEDLE_LEN computations of preparation for a |
| 60 | speedup no greater than a factor of NEEDLE_LEN. The larger the |
| 61 | needle, the better the potential performance gain. On the other |
| 62 | hand, on non-POSIX systems with CHAR_BIT larger than eight, the |
| 63 | memory required for the table is prohibitive. */ |
| 64 | #if CHAR_BIT < 10 |
| 65 | # define LONG_NEEDLE_THRESHOLD 32U |
| 66 | #else |
| 67 | # define LONG_NEEDLE_THRESHOLD SIZE_MAX |
| 68 | #endif |
| 69 | |
| 70 | #ifndef MAX |
| 71 | # define MAX(a, b) ((a < b) ? (b) : (a)) |
| 72 | #endif |
| 73 | |
| 74 | #ifndef CANON_ELEMENT |
| 75 | # define CANON_ELEMENT(c) c |
| 76 | #endif |
| 77 | #ifndef CMP_FUNC |
| 78 | # define CMP_FUNC memcmp |
| 79 | #endif |
| 80 | |
| 81 | /* Perform a critical factorization of NEEDLE, of length NEEDLE_LEN. |
| 82 | Return the index of the first byte in the right half, and set |
| 83 | *PERIOD to the global period of the right half. |
| 84 | |
| 85 | The global period of a string is the smallest index (possibly its |
| 86 | length) at which all remaining bytes in the string are repetitions |
| 87 | of the prefix (the last repetition may be a subset of the prefix). |
| 88 | |
| 89 | When NEEDLE is factored into two halves, a local period is the |
| 90 | length of the smallest word that shares a suffix with the left half |
| 91 | and shares a prefix with the right half. All factorizations of a |
| 92 | non-empty NEEDLE have a local period of at least 1 and no greater |
| 93 | than NEEDLE_LEN. |
| 94 | |
| 95 | A critical factorization has the property that the local period |
| 96 | equals the global period. All strings have at least one critical |
| 97 | factorization with the left half smaller than the global period. |
| 98 | And while some strings have more than one critical factorization, |
| 99 | it is provable that with an ordered alphabet, at least one of the |
| 100 | critical factorizations corresponds to a maximal suffix. |
| 101 | |
| 102 | Given an ordered alphabet, a critical factorization can be computed |
| 103 | in linear time, with 2 * NEEDLE_LEN comparisons, by computing the |
| 104 | shorter of two ordered maximal suffixes. The ordered maximal |
| 105 | suffixes are determined by lexicographic comparison while tracking |
| 106 | periodicity. */ |
| 107 | static size_t |
| 108 | critical_factorization (const unsigned char *needle, size_t needle_len, |
| 109 | size_t *period) |
| 110 | { |
| 111 | /* Index of last byte of left half, or SIZE_MAX. */ |
| 112 | size_t max_suffix, max_suffix_rev; |
| 113 | size_t j; /* Index into NEEDLE for current candidate suffix. */ |
| 114 | size_t k; /* Offset into current period. */ |
| 115 | size_t p; /* Intermediate period. */ |
| 116 | unsigned char a, b; /* Current comparison bytes. */ |
| 117 | |
| 118 | /* Special case NEEDLE_LEN of 1 or 2 (all callers already filtered |
| 119 | out 0-length needles. */ |
| 120 | if (needle_len < 3) |
| 121 | { |
| 122 | *period = 1; |
| 123 | return needle_len - 1; |
| 124 | } |
| 125 | |
| 126 | /* Invariants: |
| 127 | 0 <= j < NEEDLE_LEN - 1 |
| 128 | -1 <= max_suffix{,_rev} < j (treating SIZE_MAX as if it were signed) |
| 129 | min(max_suffix, max_suffix_rev) < global period of NEEDLE |
| 130 | 1 <= p <= global period of NEEDLE |
| 131 | p == global period of the substring NEEDLE[max_suffix{,_rev}+1...j] |
| 132 | 1 <= k <= p |
| 133 | */ |
| 134 | |
| 135 | /* Perform lexicographic search. */ |
| 136 | max_suffix = SIZE_MAX; |
| 137 | j = 0; |
| 138 | k = p = 1; |
| 139 | while (j + k < needle_len) |
| 140 | { |
| 141 | a = CANON_ELEMENT (needle[j + k]); |
| 142 | b = CANON_ELEMENT (needle[max_suffix + k]); |
| 143 | if (a < b) |
| 144 | { |
| 145 | /* Suffix is smaller, period is entire prefix so far. */ |
| 146 | j += k; |
| 147 | k = 1; |
| 148 | p = j - max_suffix; |
| 149 | } |
| 150 | else if (a == b) |
| 151 | { |
| 152 | /* Advance through repetition of the current period. */ |
| 153 | if (k != p) |
| 154 | ++k; |
| 155 | else |
| 156 | { |
| 157 | j += p; |
| 158 | k = 1; |
| 159 | } |
| 160 | } |
| 161 | else /* b < a */ |
| 162 | { |
| 163 | /* Suffix is larger, start over from current location. */ |
| 164 | max_suffix = j++; |
| 165 | k = p = 1; |
| 166 | } |
| 167 | } |
| 168 | *period = p; |
| 169 | |
| 170 | /* Perform reverse lexicographic search. */ |
| 171 | max_suffix_rev = SIZE_MAX; |
| 172 | j = 0; |
| 173 | k = p = 1; |
| 174 | while (j + k < needle_len) |
| 175 | { |
| 176 | a = CANON_ELEMENT (needle[j + k]); |
| 177 | b = CANON_ELEMENT (needle[max_suffix_rev + k]); |
| 178 | if (b < a) |
| 179 | { |
| 180 | /* Suffix is smaller, period is entire prefix so far. */ |
| 181 | j += k; |
| 182 | k = 1; |
| 183 | p = j - max_suffix_rev; |
| 184 | } |
| 185 | else if (a == b) |
| 186 | { |
| 187 | /* Advance through repetition of the current period. */ |
| 188 | if (k != p) |
| 189 | ++k; |
| 190 | else |
| 191 | { |
| 192 | j += p; |
| 193 | k = 1; |
| 194 | } |
| 195 | } |
| 196 | else /* a < b */ |
| 197 | { |
| 198 | /* Suffix is larger, start over from current location. */ |
| 199 | max_suffix_rev = j++; |
| 200 | k = p = 1; |
| 201 | } |
| 202 | } |
| 203 | |
| 204 | /* Choose the shorter suffix. Return the index of the first byte of |
| 205 | the right half, rather than the last byte of the left half. |
| 206 | |
| 207 | For some examples, 'banana' has two critical factorizations, both |
| 208 | exposed by the two lexicographic extreme suffixes of 'anana' and |
| 209 | 'nana', where both suffixes have a period of 2. On the other |
| 210 | hand, with 'aab' and 'bba', both strings have a single critical |
| 211 | factorization of the last byte, with the suffix having a period |
| 212 | of 1. While the maximal lexicographic suffix of 'aab' is 'b', |
| 213 | the maximal lexicographic suffix of 'bba' is 'ba', which is not a |
| 214 | critical factorization. Conversely, the maximal reverse |
| 215 | lexicographic suffix of 'a' works for 'bba', but not 'ab' for |
| 216 | 'aab'. The shorter suffix of the two will always be a critical |
| 217 | factorization. */ |
| 218 | if (max_suffix_rev + 1 < max_suffix + 1) |
| 219 | return max_suffix + 1; |
| 220 | *period = p; |
| 221 | return max_suffix_rev + 1; |
| 222 | } |
| 223 | |
| 224 | /* Return the first location of non-empty NEEDLE within HAYSTACK, or |
| 225 | NULL. HAYSTACK_LEN is the minimum known length of HAYSTACK. This |
| 226 | method is optimized for NEEDLE_LEN < LONG_NEEDLE_THRESHOLD. |
| 227 | Performance is guaranteed to be linear, with an initialization cost |
| 228 | of 2 * NEEDLE_LEN comparisons. |
| 229 | |
| 230 | If AVAILABLE does not modify HAYSTACK_LEN (as in memmem), then at |
| 231 | most 2 * HAYSTACK_LEN - NEEDLE_LEN comparisons occur in searching. |
| 232 | If AVAILABLE modifies HAYSTACK_LEN (as in strstr), then at most 3 * |
| 233 | HAYSTACK_LEN - NEEDLE_LEN comparisons occur in searching. */ |
| 234 | static RETURN_TYPE |
| 235 | two_way_short_needle (const unsigned char *haystack, size_t haystack_len, |
| 236 | const unsigned char *needle, size_t needle_len) |
| 237 | { |
| 238 | size_t i; /* Index into current byte of NEEDLE. */ |
| 239 | size_t j; /* Index into current window of HAYSTACK. */ |
| 240 | size_t period; /* The period of the right half of needle. */ |
| 241 | size_t suffix; /* The index of the right half of needle. */ |
| 242 | |
| 243 | /* Factor the needle into two halves, such that the left half is |
| 244 | smaller than the global period, and the right half is |
| 245 | periodic (with a period as large as NEEDLE_LEN - suffix). */ |
| 246 | suffix = critical_factorization (needle, needle_len, &period); |
| 247 | |
| 248 | /* Perform the search. Each iteration compares the right half |
| 249 | first. */ |
| 250 | if (CMP_FUNC (needle, needle + period, suffix) == 0) |
| 251 | { |
| 252 | /* Entire needle is periodic; a mismatch in the left half can |
| 253 | only advance by the period, so use memory to avoid rescanning |
| 254 | known occurrences of the period in the right half. */ |
| 255 | size_t memory = 0; |
| 256 | j = 0; |
| 257 | while (AVAILABLE (haystack, haystack_len, j, needle_len)) |
| 258 | { |
| 259 | /* Scan for matches in right half. */ |
| 260 | i = MAX (suffix, memory); |
| 261 | while (i < needle_len && (CANON_ELEMENT (needle[i]) |
| 262 | == CANON_ELEMENT (haystack[i + j]))) |
| 263 | ++i; |
| 264 | if (needle_len <= i) |
| 265 | { |
| 266 | /* Scan for matches in left half. */ |
| 267 | i = suffix - 1; |
| 268 | while (memory < i + 1 && (CANON_ELEMENT (needle[i]) |
| 269 | == CANON_ELEMENT (haystack[i + j]))) |
| 270 | --i; |
| 271 | if (i + 1 < memory + 1) |
| 272 | return (RETURN_TYPE) (haystack + j); |
| 273 | /* No match, so remember how many repetitions of period |
| 274 | on the right half were scanned. */ |
| 275 | j += period; |
| 276 | memory = needle_len - period; |
| 277 | } |
| 278 | else |
| 279 | { |
| 280 | j += i - suffix + 1; |
| 281 | memory = 0; |
| 282 | } |
| 283 | } |
| 284 | } |
| 285 | else |
| 286 | { |
| 287 | /* The two halves of needle are distinct; no extra memory is |
| 288 | required, and any mismatch results in a maximal shift. */ |
| 289 | period = MAX (suffix, needle_len - suffix) + 1; |
| 290 | j = 0; |
| 291 | while (AVAILABLE (haystack, haystack_len, j, needle_len)) |
| 292 | { |
| 293 | /* Scan for matches in right half. */ |
| 294 | i = suffix; |
| 295 | while (i < needle_len && (CANON_ELEMENT (needle[i]) |
| 296 | == CANON_ELEMENT (haystack[i + j]))) |
| 297 | ++i; |
| 298 | if (needle_len <= i) |
| 299 | { |
| 300 | /* Scan for matches in left half. */ |
| 301 | i = suffix - 1; |
| 302 | while (i != SIZE_MAX && (CANON_ELEMENT (needle[i]) |
| 303 | == CANON_ELEMENT (haystack[i + j]))) |
| 304 | --i; |
| 305 | if (i == SIZE_MAX) |
| 306 | return (RETURN_TYPE) (haystack + j); |
| 307 | j += period; |
| 308 | } |
| 309 | else |
| 310 | j += i - suffix + 1; |
| 311 | } |
| 312 | } |
| 313 | return NULL; |
| 314 | } |
| 315 | |
| 316 | /* Return the first location of non-empty NEEDLE within HAYSTACK, or |
| 317 | NULL. HAYSTACK_LEN is the minimum known length of HAYSTACK. This |
| 318 | method is optimized for LONG_NEEDLE_THRESHOLD <= NEEDLE_LEN. |
| 319 | Performance is guaranteed to be linear, with an initialization cost |
| 320 | of 3 * NEEDLE_LEN + (1 << CHAR_BIT) operations. |
| 321 | |
| 322 | If AVAILABLE does not modify HAYSTACK_LEN (as in memmem), then at |
| 323 | most 2 * HAYSTACK_LEN - NEEDLE_LEN comparisons occur in searching, |
| 324 | and sublinear performance O(HAYSTACK_LEN / NEEDLE_LEN) is possible. |
| 325 | If AVAILABLE modifies HAYSTACK_LEN (as in strstr), then at most 3 * |
| 326 | HAYSTACK_LEN - NEEDLE_LEN comparisons occur in searching, and |
| 327 | sublinear performance is not possible. */ |
| 328 | static RETURN_TYPE |
| 329 | two_way_long_needle (const unsigned char *haystack, size_t haystack_len, |
| 330 | const unsigned char *needle, size_t needle_len) |
| 331 | { |
| 332 | size_t i; /* Index into current byte of NEEDLE. */ |
| 333 | size_t j; /* Index into current window of HAYSTACK. */ |
| 334 | size_t period; /* The period of the right half of needle. */ |
| 335 | size_t suffix; /* The index of the right half of needle. */ |
| 336 | size_t shift_table[1U << CHAR_BIT]; /* See below. */ |
| 337 | |
| 338 | /* Factor the needle into two halves, such that the left half is |
| 339 | smaller than the global period, and the right half is |
| 340 | periodic (with a period as large as NEEDLE_LEN - suffix). */ |
| 341 | suffix = critical_factorization (needle, needle_len, &period); |
| 342 | |
| 343 | /* Populate shift_table. For each possible byte value c, |
| 344 | shift_table[c] is the distance from the last occurrence of c to |
| 345 | the end of NEEDLE, or NEEDLE_LEN if c is absent from the NEEDLE. |
| 346 | shift_table[NEEDLE[NEEDLE_LEN - 1]] contains the only 0. */ |
| 347 | for (i = 0; i < 1U << CHAR_BIT; i++) |
| 348 | shift_table[i] = needle_len; |
| 349 | for (i = 0; i < needle_len; i++) |
| 350 | shift_table[CANON_ELEMENT (needle[i])] = needle_len - i - 1; |
| 351 | |
| 352 | /* Perform the search. Each iteration compares the right half |
| 353 | first. */ |
| 354 | if (CMP_FUNC (needle, needle + period, suffix) == 0) |
| 355 | { |
| 356 | /* Entire needle is periodic; a mismatch in the left half can |
| 357 | only advance by the period, so use memory to avoid rescanning |
| 358 | known occurrences of the period in the right half. */ |
| 359 | size_t memory = 0; |
| 360 | size_t shift; |
| 361 | j = 0; |
| 362 | while (AVAILABLE (haystack, haystack_len, j, needle_len)) |
| 363 | { |
| 364 | /* Check the last byte first; if it does not match, then |
| 365 | shift to the next possible match location. */ |
| 366 | shift = shift_table[CANON_ELEMENT (haystack[j + needle_len - 1])]; |
| 367 | if (0 < shift) |
| 368 | { |
| 369 | if (memory && shift < period) |
| 370 | { |
| 371 | /* Since needle is periodic, but the last period has |
| 372 | a byte out of place, there can be no match until |
| 373 | after the mismatch. */ |
| 374 | shift = needle_len - period; |
| 375 | } |
| 376 | memory = 0; |
| 377 | j += shift; |
| 378 | continue; |
| 379 | } |
| 380 | /* Scan for matches in right half. The last byte has |
| 381 | already been matched, by virtue of the shift table. */ |
| 382 | i = MAX (suffix, memory); |
| 383 | while (i < needle_len - 1 && (CANON_ELEMENT (needle[i]) |
| 384 | == CANON_ELEMENT (haystack[i + j]))) |
| 385 | ++i; |
| 386 | if (needle_len - 1 <= i) |
| 387 | { |
| 388 | /* Scan for matches in left half. */ |
| 389 | i = suffix - 1; |
| 390 | while (memory < i + 1 && (CANON_ELEMENT (needle[i]) |
| 391 | == CANON_ELEMENT (haystack[i + j]))) |
| 392 | --i; |
| 393 | if (i + 1 < memory + 1) |
| 394 | return (RETURN_TYPE) (haystack + j); |
| 395 | /* No match, so remember how many repetitions of period |
| 396 | on the right half were scanned. */ |
| 397 | j += period; |
| 398 | memory = needle_len - period; |
| 399 | } |
| 400 | else |
| 401 | { |
| 402 | j += i - suffix + 1; |
| 403 | memory = 0; |
| 404 | } |
| 405 | } |
| 406 | } |
| 407 | else |
| 408 | { |
| 409 | /* The two halves of needle are distinct; no extra memory is |
| 410 | required, and any mismatch results in a maximal shift. */ |
| 411 | size_t shift; |
| 412 | period = MAX (suffix, needle_len - suffix) + 1; |
| 413 | j = 0; |
| 414 | while (AVAILABLE (haystack, haystack_len, j, needle_len)) |
| 415 | { |
| 416 | /* Check the last byte first; if it does not match, then |
| 417 | shift to the next possible match location. */ |
| 418 | shift = shift_table[CANON_ELEMENT (haystack[j + needle_len - 1])]; |
| 419 | if (0 < shift) |
| 420 | { |
| 421 | j += shift; |
| 422 | continue; |
| 423 | } |
| 424 | /* Scan for matches in right half. The last byte has |
| 425 | already been matched, by virtue of the shift table. */ |
| 426 | i = suffix; |
| 427 | while (i < needle_len - 1 && (CANON_ELEMENT (needle[i]) |
| 428 | == CANON_ELEMENT (haystack[i + j]))) |
| 429 | ++i; |
| 430 | if (needle_len - 1 <= i) |
| 431 | { |
| 432 | /* Scan for matches in left half. */ |
| 433 | i = suffix - 1; |
| 434 | while (i != SIZE_MAX && (CANON_ELEMENT (needle[i]) |
| 435 | == CANON_ELEMENT (haystack[i + j]))) |
| 436 | --i; |
| 437 | if (i == SIZE_MAX) |
| 438 | return (RETURN_TYPE) (haystack + j); |
| 439 | j += period; |
| 440 | } |
| 441 | else |
| 442 | j += i - suffix + 1; |
| 443 | } |
| 444 | } |
| 445 | return NULL; |
| 446 | } |
| 447 | |
| 448 | #undef AVAILABLE |
| 449 | #undef CANON_ELEMENT |
| 450 | #undef CMP_FUNC |
| 451 | #undef MAX |
| 452 | #undef RETURN_TYPE |