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1 /* Byte-wise substring search, using the Two-Way algorithm.
2 Copyright (C) 2008-2012 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 The GNU C Library is free software; you can redistribute it and/or
7 modify it under the terms of the GNU Lesser General Public
8 License as published by the Free Software Foundation; either
9 version 2.1 of the License, or (at your option) any later version.
10
11 The GNU C Library 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 GNU
14 Lesser General Public License for more details.
15
16 You should have received a copy of the GNU Lesser General Public
17 License along with the GNU C Library; if not, see
18 <http://www.gnu.org/licenses/>. */
19
20 /* Before including this file, you need to include <string.h> (and
21 <config.h> before that, if not part of libc), and define:
22 RESULT_TYPE A macro that expands to the return type.
23 AVAILABLE(h, h_l, j, n_l)
24 A macro that returns nonzero if there are
25 at least N_L bytes left starting at H[J].
26 H is 'unsigned char *', H_L, J, and N_L
27 are 'size_t'; H_L is an lvalue. For
28 NUL-terminated searches, H_L can be
29 modified each iteration to avoid having
30 to compute the end of H up front.
31
32 For case-insensitivity, you may optionally define:
33 CMP_FUNC(p1, p2, l) A macro that returns 0 iff the first L
34 characters of P1 and P2 are equal.
35 CANON_ELEMENT(c) A macro that canonicalizes an element right after
36 it has been fetched from one of the two strings.
37 The argument is an 'unsigned char'; the result
38 must be an 'unsigned char' as well.
39
40 This file undefines the macros documented above, and defines
41 LONG_NEEDLE_THRESHOLD.
42 */
43
44 #include <limits.h>
45 #include <stdint.h>
46 #include <sys/param.h> /* Defines MAX. */
47
48 /* We use the Two-Way string matching algorithm, which guarantees
49 linear complexity with constant space. Additionally, for long
50 needles, we also use a bad character shift table similar to the
51 Boyer-Moore algorithm to achieve improved (potentially sub-linear)
52 performance.
53
54 See http://www-igm.univ-mlv.fr/~lecroq/string/node26.html#SECTION00260
55 and http://en.wikipedia.org/wiki/Boyer-Moore_string_search_algorithm
56 */
57
58 /* Point at which computing a bad-byte shift table is likely to be
59 worthwhile. Small needles should not compute a table, since it
60 adds (1 << CHAR_BIT) + NEEDLE_LEN computations of preparation for a
61 speedup no greater than a factor of NEEDLE_LEN. The larger the
62 needle, the better the potential performance gain. On the other
63 hand, on non-POSIX systems with CHAR_BIT larger than eight, the
64 memory required for the table is prohibitive. */
65 #if CHAR_BIT < 10
66 # define LONG_NEEDLE_THRESHOLD 32U
67 #else
68 # define LONG_NEEDLE_THRESHOLD SIZE_MAX
69 #endif
70
71 #ifndef CANON_ELEMENT
72 # define CANON_ELEMENT(c) c
73 #endif
74 #ifndef CMP_FUNC
75 # define CMP_FUNC memcmp
76 #endif
77
78 /* Check for end-of-line in strstr and strcasestr routines.
79 We piggy-back matching procedure for detecting EOL where possible,
80 and use AVAILABLE macro otherwise. */
81 #ifndef CHECK_EOL
82 # define CHECK_EOL (0)
83 #endif
84
85 /* Return NULL if argument is '\0'. */
86 #ifndef RET0_IF_0
87 # define RET0_IF_0(a) /* nothing */
88 #endif
89
90 /* Perform a critical factorization of NEEDLE, of length NEEDLE_LEN.
91 Return the index of the first byte in the right half, and set
92 *PERIOD to the global period of the right half.
93
94 The global period of a string is the smallest index (possibly its
95 length) at which all remaining bytes in the string are repetitions
96 of the prefix (the last repetition may be a subset of the prefix).
97
98 When NEEDLE is factored into two halves, a local period is the
99 length of the smallest word that shares a suffix with the left half
100 and shares a prefix with the right half. All factorizations of a
101 non-empty NEEDLE have a local period of at least 1 and no greater
102 than NEEDLE_LEN.
103
104 A critical factorization has the property that the local period
105 equals the global period. All strings have at least one critical
106 factorization with the left half smaller than the global period.
107
108 Given an ordered alphabet, a critical factorization can be computed
109 in linear time, with 2 * NEEDLE_LEN comparisons, by computing the
110 larger of two ordered maximal suffixes. The ordered maximal
111 suffixes are determined by lexicographic comparison of
112 periodicity. */
113 static size_t
114 critical_factorization (const unsigned char *needle, size_t needle_len,
115 size_t *period)
116 {
117 /* Index of last byte of left half, or SIZE_MAX. */
118 size_t max_suffix, max_suffix_rev;
119 size_t j; /* Index into NEEDLE for current candidate suffix. */
120 size_t k; /* Offset into current period. */
121 size_t p; /* Intermediate period. */
122 unsigned char a, b; /* Current comparison bytes. */
123
124 /* Invariants:
125 0 <= j < NEEDLE_LEN - 1
126 -1 <= max_suffix{,_rev} < j (treating SIZE_MAX as if it were signed)
127 min(max_suffix, max_suffix_rev) < global period of NEEDLE
128 1 <= p <= global period of NEEDLE
129 p == global period of the substring NEEDLE[max_suffix{,_rev}+1...j]
130 1 <= k <= p
131 */
132
133 /* Perform lexicographic search. */
134 max_suffix = SIZE_MAX;
135 j = 0;
136 k = p = 1;
137 while (j + k < needle_len)
138 {
139 a = CANON_ELEMENT (needle[j + k]);
140 b = CANON_ELEMENT (needle[max_suffix + k]);
141 if (a < b)
142 {
143 /* Suffix is smaller, period is entire prefix so far. */
144 j += k;
145 k = 1;
146 p = j - max_suffix;
147 }
148 else if (a == b)
149 {
150 /* Advance through repetition of the current period. */
151 if (k != p)
152 ++k;
153 else
154 {
155 j += p;
156 k = 1;
157 }
158 }
159 else /* b < a */
160 {
161 /* Suffix is larger, start over from current location. */
162 max_suffix = j++;
163 k = p = 1;
164 }
165 }
166 *period = p;
167
168 /* Perform reverse lexicographic search. */
169 max_suffix_rev = SIZE_MAX;
170 j = 0;
171 k = p = 1;
172 while (j + k < needle_len)
173 {
174 a = CANON_ELEMENT (needle[j + k]);
175 b = CANON_ELEMENT (needle[max_suffix_rev + k]);
176 if (b < a)
177 {
178 /* Suffix is smaller, period is entire prefix so far. */
179 j += k;
180 k = 1;
181 p = j - max_suffix_rev;
182 }
183 else if (a == b)
184 {
185 /* Advance through repetition of the current period. */
186 if (k != p)
187 ++k;
188 else
189 {
190 j += p;
191 k = 1;
192 }
193 }
194 else /* a < b */
195 {
196 /* Suffix is larger, start over from current location. */
197 max_suffix_rev = j++;
198 k = p = 1;
199 }
200 }
201
202 /* Choose the longer suffix. Return the first byte of the right
203 half, rather than the last byte of the left half. */
204 if (max_suffix_rev + 1 < max_suffix + 1)
205 return max_suffix + 1;
206 *period = p;
207 return max_suffix_rev + 1;
208 }
209
210 /* Return the first location of non-empty NEEDLE within HAYSTACK, or
211 NULL. HAYSTACK_LEN is the minimum known length of HAYSTACK. This
212 method is optimized for NEEDLE_LEN < LONG_NEEDLE_THRESHOLD.
213 Performance is guaranteed to be linear, with an initialization cost
214 of 2 * NEEDLE_LEN comparisons.
215
216 If AVAILABLE does not modify HAYSTACK_LEN (as in memmem), then at
217 most 2 * HAYSTACK_LEN - NEEDLE_LEN comparisons occur in searching.
218 If AVAILABLE modifies HAYSTACK_LEN (as in strstr), then at most 3 *
219 HAYSTACK_LEN - NEEDLE_LEN comparisons occur in searching. */
220 static RETURN_TYPE
221 two_way_short_needle (const unsigned char *haystack, size_t haystack_len,
222 const unsigned char *needle, size_t needle_len)
223 {
224 size_t i; /* Index into current byte of NEEDLE. */
225 size_t j; /* Index into current window of HAYSTACK. */
226 size_t period; /* The period of the right half of needle. */
227 size_t suffix; /* The index of the right half of needle. */
228
229 /* Factor the needle into two halves, such that the left half is
230 smaller than the global period, and the right half is
231 periodic (with a period as large as NEEDLE_LEN - suffix). */
232 suffix = critical_factorization (needle, needle_len, &period);
233
234 /* Perform the search. Each iteration compares the right half
235 first. */
236 if (CMP_FUNC (needle, needle + period, suffix) == 0)
237 {
238 /* Entire needle is periodic; a mismatch can only advance by the
239 period, so use memory to avoid rescanning known occurrences
240 of the period. */
241 size_t memory = 0;
242 j = 0;
243 while (AVAILABLE (haystack, haystack_len, j, needle_len))
244 {
245 const unsigned char *pneedle;
246 const unsigned char *phaystack;
247
248 /* Scan for matches in right half. */
249 i = MAX (suffix, memory);
250 pneedle = &needle[i];
251 phaystack = &haystack[i + j];
252 while (i < needle_len && (CANON_ELEMENT (*pneedle++)
253 == CANON_ELEMENT (*phaystack++)))
254 ++i;
255 if (needle_len <= i)
256 {
257 /* Scan for matches in left half. */
258 i = suffix - 1;
259 pneedle = &needle[i];
260 phaystack = &haystack[i + j];
261 while (memory < i + 1 && (CANON_ELEMENT (*pneedle--)
262 == CANON_ELEMENT (*phaystack--)))
263 --i;
264 if (i + 1 < memory + 1)
265 return (RETURN_TYPE) (haystack + j);
266 /* No match, so remember how many repetitions of period
267 on the right half were scanned. */
268 j += period;
269 memory = needle_len - period;
270 }
271 else
272 {
273 j += i - suffix + 1;
274 memory = 0;
275 }
276 }
277 }
278 else
279 {
280 const unsigned char *phaystack = &haystack[suffix];
281 /* The comparison always starts from needle[suffix], so cache it
282 and use an optimized first-character loop. */
283 unsigned char needle_suffix = CANON_ELEMENT (needle[suffix]);
284
285 #if CHECK_EOL
286 /* We start matching from the SUFFIX'th element, so make sure we
287 don't hit '\0' before that. */
288 if (haystack_len < suffix + 1
289 && !AVAILABLE (haystack, haystack_len, 0, suffix + 1))
290 return NULL;
291 #endif
292
293 /* The two halves of needle are distinct; no extra memory is
294 required, and any mismatch results in a maximal shift. */
295 period = MAX (suffix, needle_len - suffix) + 1;
296 j = 0;
297 while (1
298 #if !CHECK_EOL
299 && AVAILABLE (haystack, haystack_len, j, needle_len)
300 #endif
301 )
302 {
303 unsigned char haystack_char;
304 const unsigned char *pneedle;
305
306 /* TODO: The first-character loop can be sped up by adapting
307 longword-at-a-time implementation of memchr/strchr. */
308 if (needle_suffix
309 != (haystack_char = CANON_ELEMENT (*phaystack++)))
310 {
311 RET0_IF_0 (haystack_char);
312 #if !CHECK_EOL
313 ++j;
314 #endif
315 continue;
316 }
317
318 #if CHECK_EOL
319 /* Calculate J if it wasn't kept up-to-date in the first-character
320 loop. */
321 j = phaystack - &haystack[suffix] - 1;
322 #endif
323
324 /* Scan for matches in right half. */
325 i = suffix + 1;
326 pneedle = &needle[i];
327 while (i < needle_len)
328 {
329 if (CANON_ELEMENT (*pneedle++)
330 != (haystack_char = CANON_ELEMENT (*phaystack++)))
331 {
332 RET0_IF_0 (haystack_char);
333 break;
334 }
335 ++i;
336 }
337 if (needle_len <= i)
338 {
339 /* Scan for matches in left half. */
340 i = suffix - 1;
341 pneedle = &needle[i];
342 phaystack = &haystack[i + j];
343 while (i != SIZE_MAX)
344 {
345 if (CANON_ELEMENT (*pneedle--)
346 != (haystack_char = CANON_ELEMENT (*phaystack--)))
347 {
348 RET0_IF_0 (haystack_char);
349 break;
350 }
351 --i;
352 }
353 if (i == SIZE_MAX)
354 return (RETURN_TYPE) (haystack + j);
355 j += period;
356 }
357 else
358 j += i - suffix + 1;
359
360 #if CHECK_EOL
361 if (!AVAILABLE (haystack, haystack_len, j, needle_len))
362 break;
363 #endif
364
365 phaystack = &haystack[suffix + j];
366 }
367 }
368 ret0: __attribute__ ((unused))
369 return NULL;
370 }
371
372 /* Return the first location of non-empty NEEDLE within HAYSTACK, or
373 NULL. HAYSTACK_LEN is the minimum known length of HAYSTACK. This
374 method is optimized for LONG_NEEDLE_THRESHOLD <= NEEDLE_LEN.
375 Performance is guaranteed to be linear, with an initialization cost
376 of 3 * NEEDLE_LEN + (1 << CHAR_BIT) operations.
377
378 If AVAILABLE does not modify HAYSTACK_LEN (as in memmem), then at
379 most 2 * HAYSTACK_LEN - NEEDLE_LEN comparisons occur in searching,
380 and sublinear performance O(HAYSTACK_LEN / NEEDLE_LEN) is possible.
381 If AVAILABLE modifies HAYSTACK_LEN (as in strstr), then at most 3 *
382 HAYSTACK_LEN - NEEDLE_LEN comparisons occur in searching, and
383 sublinear performance is not possible. */
384 static RETURN_TYPE
385 two_way_long_needle (const unsigned char *haystack, size_t haystack_len,
386 const unsigned char *needle, size_t needle_len)
387 {
388 size_t i; /* Index into current byte of NEEDLE. */
389 size_t j; /* Index into current window of HAYSTACK. */
390 size_t period; /* The period of the right half of needle. */
391 size_t suffix; /* The index of the right half of needle. */
392 size_t shift_table[1U << CHAR_BIT]; /* See below. */
393
394 /* Factor the needle into two halves, such that the left half is
395 smaller than the global period, and the right half is
396 periodic (with a period as large as NEEDLE_LEN - suffix). */
397 suffix = critical_factorization (needle, needle_len, &period);
398
399 /* Populate shift_table. For each possible byte value c,
400 shift_table[c] is the distance from the last occurrence of c to
401 the end of NEEDLE, or NEEDLE_LEN if c is absent from the NEEDLE.
402 shift_table[NEEDLE[NEEDLE_LEN - 1]] contains the only 0. */
403 for (i = 0; i < 1U << CHAR_BIT; i++)
404 shift_table[i] = needle_len;
405 for (i = 0; i < needle_len; i++)
406 shift_table[CANON_ELEMENT (needle[i])] = needle_len - i - 1;
407
408 /* Perform the search. Each iteration compares the right half
409 first. */
410 if (CMP_FUNC (needle, needle + period, suffix) == 0)
411 {
412 /* Entire needle is periodic; a mismatch can only advance by the
413 period, so use memory to avoid rescanning known occurrences
414 of the period. */
415 size_t memory = 0;
416 size_t shift;
417 j = 0;
418 while (AVAILABLE (haystack, haystack_len, j, needle_len))
419 {
420 const unsigned char *pneedle;
421 const unsigned char *phaystack;
422
423 /* Check the last byte first; if it does not match, then
424 shift to the next possible match location. */
425 shift = shift_table[CANON_ELEMENT (haystack[j + needle_len - 1])];
426 if (0 < shift)
427 {
428 if (memory && shift < period)
429 {
430 /* Since needle is periodic, but the last period has
431 a byte out of place, there can be no match until
432 after the mismatch. */
433 shift = needle_len - period;
434 }
435 memory = 0;
436 j += shift;
437 continue;
438 }
439 /* Scan for matches in right half. The last byte has
440 already been matched, by virtue of the shift table. */
441 i = MAX (suffix, memory);
442 pneedle = &needle[i];
443 phaystack = &haystack[i + j];
444 while (i < needle_len - 1 && (CANON_ELEMENT (*pneedle++)
445 == CANON_ELEMENT (*phaystack++)))
446 ++i;
447 if (needle_len - 1 <= i)
448 {
449 /* Scan for matches in left half. */
450 i = suffix - 1;
451 pneedle = &needle[i];
452 phaystack = &haystack[i + j];
453 while (memory < i + 1 && (CANON_ELEMENT (*pneedle--)
454 == CANON_ELEMENT (*phaystack--)))
455 --i;
456 if (i + 1 < memory + 1)
457 return (RETURN_TYPE) (haystack + j);
458 /* No match, so remember how many repetitions of period
459 on the right half were scanned. */
460 j += period;
461 memory = needle_len - period;
462 }
463 else
464 {
465 j += i - suffix + 1;
466 memory = 0;
467 }
468 }
469 }
470 else
471 {
472 /* The two halves of needle are distinct; no extra memory is
473 required, and any mismatch results in a maximal shift. */
474 size_t shift;
475 period = MAX (suffix, needle_len - suffix) + 1;
476 j = 0;
477 while (AVAILABLE (haystack, haystack_len, j, needle_len))
478 {
479 const unsigned char *pneedle;
480 const unsigned char *phaystack;
481
482 /* Check the last byte first; if it does not match, then
483 shift to the next possible match location. */
484 shift = shift_table[CANON_ELEMENT (haystack[j + needle_len - 1])];
485 if (0 < shift)
486 {
487 j += shift;
488 continue;
489 }
490 /* Scan for matches in right half. The last byte has
491 already been matched, by virtue of the shift table. */
492 i = suffix;
493 pneedle = &needle[i];
494 phaystack = &haystack[i + j];
495 while (i < needle_len - 1 && (CANON_ELEMENT (*pneedle++)
496 == CANON_ELEMENT (*phaystack++)))
497 ++i;
498 if (needle_len - 1 <= i)
499 {
500 /* Scan for matches in left half. */
501 i = suffix - 1;
502 pneedle = &needle[i];
503 phaystack = &haystack[i + j];
504 while (i != SIZE_MAX && (CANON_ELEMENT (*pneedle--)
505 == CANON_ELEMENT (*phaystack--)))
506 --i;
507 if (i == SIZE_MAX)
508 return (RETURN_TYPE) (haystack + j);
509 j += period;
510 }
511 else
512 j += i - suffix + 1;
513 }
514 }
515 return NULL;
516 }
517
518 #undef AVAILABLE
519 #undef AVAILABLE1
520 #undef AVAILABLE2
521 #undef AVAILABLE1_USES_J
522 #undef CANON_ELEMENT
523 #undef CMP_FUNC
524 #undef RET0_IF_0
525 #undef RETURN_TYPE