TLA Line data Source code
1 : /*-------------------------------------------------------------------------
2 : *
3 : * levenshtein.c
4 : * Levenshtein distance implementation.
5 : *
6 : * Original author: Joe Conway <mail@joeconway.com>
7 : *
8 : * This file is included by varlena.c twice, to provide matching code for (1)
9 : * Levenshtein distance with custom costings, and (2) Levenshtein distance with
10 : * custom costings and a "max" value above which exact distances are not
11 : * interesting. Before the inclusion, we rely on the presence of the inline
12 : * function rest_of_char_same().
13 : *
14 : * Written based on a description of the algorithm by Michael Gilleland found
15 : * at http://www.merriampark.com/ld.htm. Also looked at levenshtein.c in the
16 : * PHP 4.0.6 distribution for inspiration. Configurable penalty costs
17 : * extension is introduced by Volkan YAZICI <volkan.yazici@gmail.com.
18 : *
19 : * Copyright (c) 2001-2023, PostgreSQL Global Development Group
20 : *
21 : * IDENTIFICATION
22 : * src/backend/utils/adt/levenshtein.c
23 : *
24 : *-------------------------------------------------------------------------
25 : */
26 : #define MAX_LEVENSHTEIN_STRLEN 255
27 :
28 : /*
29 : * Calculates Levenshtein distance metric between supplied strings, which are
30 : * not necessarily null-terminated.
31 : *
32 : * source: source string, of length slen bytes.
33 : * target: target string, of length tlen bytes.
34 : * ins_c, del_c, sub_c: costs to charge for character insertion, deletion,
35 : * and substitution respectively; (1, 1, 1) costs suffice for common
36 : * cases, but your mileage may vary.
37 : * max_d: if provided and >= 0, maximum distance we care about; see below.
38 : * trusted: caller is trusted and need not obey MAX_LEVENSHTEIN_STRLEN.
39 : *
40 : * One way to compute Levenshtein distance is to incrementally construct
41 : * an (m+1)x(n+1) matrix where cell (i, j) represents the minimum number
42 : * of operations required to transform the first i characters of s into
43 : * the first j characters of t. The last column of the final row is the
44 : * answer.
45 : *
46 : * We use that algorithm here with some modification. In lieu of holding
47 : * the entire array in memory at once, we'll just use two arrays of size
48 : * m+1 for storing accumulated values. At each step one array represents
49 : * the "previous" row and one is the "current" row of the notional large
50 : * array.
51 : *
52 : * If max_d >= 0, we only need to provide an accurate answer when that answer
53 : * is less than or equal to max_d. From any cell in the matrix, there is
54 : * theoretical "minimum residual distance" from that cell to the last column
55 : * of the final row. This minimum residual distance is zero when the
56 : * untransformed portions of the strings are of equal length (because we might
57 : * get lucky and find all the remaining characters matching) and is otherwise
58 : * based on the minimum number of insertions or deletions needed to make them
59 : * equal length. The residual distance grows as we move toward the upper
60 : * right or lower left corners of the matrix. When the max_d bound is
61 : * usefully tight, we can use this property to avoid computing the entirety
62 : * of each row; instead, we maintain a start_column and stop_column that
63 : * identify the portion of the matrix close to the diagonal which can still
64 : * affect the final answer.
65 : */
66 : int
67 : #ifdef LEVENSHTEIN_LESS_EQUAL
68 CBC 1223 : varstr_levenshtein_less_equal(const char *source, int slen,
69 : const char *target, int tlen,
70 : int ins_c, int del_c, int sub_c,
71 : int max_d, bool trusted)
72 : #else
73 2 : varstr_levenshtein(const char *source, int slen,
74 : const char *target, int tlen,
75 : int ins_c, int del_c, int sub_c,
76 : bool trusted)
77 : #endif
78 : {
79 : int m,
80 : n;
81 : int *prev;
82 : int *curr;
83 1225 : int *s_char_len = NULL;
84 : int j;
85 : const char *y;
86 :
87 : /*
88 : * For varstr_levenshtein_less_equal, we have real variables called
89 : * start_column and stop_column; otherwise it's just short-hand for 0 and
90 : * m.
91 : */
92 : #ifdef LEVENSHTEIN_LESS_EQUAL
93 : int start_column,
94 : stop_column;
95 :
96 : #undef START_COLUMN
97 : #undef STOP_COLUMN
98 : #define START_COLUMN start_column
99 : #define STOP_COLUMN stop_column
100 : #else
101 : #undef START_COLUMN
102 : #undef STOP_COLUMN
103 : #define START_COLUMN 0
104 : #define STOP_COLUMN m
105 : #endif
106 :
107 ECB : /* Convert string lengths (in bytes) to lengths in characters */
108 CBC 1225 : m = pg_mbstrlen_with_len(source, slen);
109 GIC 1225 : n = pg_mbstrlen_with_len(target, tlen);
110 :
111 : /*
112 : * We can transform an empty s into t with n insertions, or a non-empty t
113 : * into an empty s with m deletions.
114 ECB : */
115 GBC 1225 : if (!m)
116 LBC 0 : return n * ins_c;
117 GBC 1225 : if (!n)
118 UIC 0 : return m * del_c;
119 :
120 : /*
121 : * For security concerns, restrict excessive CPU+RAM usage. (This
122 : * implementation uses O(m) memory and has O(mn) complexity.) If
123 : * "trusted" is true, caller is responsible for not making excessive
124 : * requests, typically by using a small max_d along with strings that are
125 : * bounded, though not necessarily to MAX_LEVENSHTEIN_STRLEN exactly.
126 ECB : */
127 CBC 1225 : if (!trusted &&
128 GIC 4 : (m > MAX_LEVENSHTEIN_STRLEN ||
129 EUB : n > MAX_LEVENSHTEIN_STRLEN))
130 UIC 0 : ereport(ERROR,
131 : (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
132 : errmsg("levenshtein argument exceeds maximum length of %d characters",
133 : MAX_LEVENSHTEIN_STRLEN)));
134 :
135 : #ifdef LEVENSHTEIN_LESS_EQUAL
136 ECB : /* Initialize start and stop columns. */
137 CBC 1223 : start_column = 0;
138 GIC 1223 : stop_column = m + 1;
139 :
140 : /*
141 : * If max_d >= 0, determine whether the bound is impossibly tight. If so,
142 : * return max_d + 1 immediately. Otherwise, determine whether it's tight
143 : * enough to limit the computation we must perform. If so, figure out
144 : * initial stop column.
145 ECB : */
146 GIC 1223 : if (max_d >= 0)
147 : {
148 : int min_theo_d; /* Theoretical minimum distance. */
149 ECB : int max_theo_d; /* Theoretical maximum distance. */
150 GIC 1223 : int net_inserts = n - m;
151 ECB :
152 CBC 1223 : min_theo_d = net_inserts < 0 ?
153 1223 : -net_inserts * del_c : net_inserts * ins_c;
154 1223 : if (min_theo_d > max_d)
155 415 : return max_d + 1;
156 GBC 808 : if (ins_c + del_c < sub_c)
157 LBC 0 : sub_c = ins_c + del_c;
158 CBC 808 : max_theo_d = min_theo_d + sub_c * Min(m, n);
159 808 : if (max_d >= max_theo_d)
160 252 : max_d = -1;
161 GIC 556 : else if (ins_c + del_c > 0)
162 : {
163 : /*
164 : * Figure out how much of the first row of the notional matrix we
165 : * need to fill in. If the string is growing, the theoretical
166 : * minimum distance already incorporates the cost of deleting the
167 : * number of characters necessary to make the two strings equal in
168 : * length. Each additional deletion forces another insertion, so
169 : * the best-case total cost increases by ins_c + del_c. If the
170 : * string is shrinking, the minimum theoretical cost assumes no
171 : * excess deletions; that is, we're starting no further right than
172 : * column n - m. If we do start further right, the best-case
173 : * total cost increases by ins_c + del_c for each move right.
174 ECB : */
175 CBC 556 : int slack_d = max_d - min_theo_d;
176 GIC 556 : int best_column = net_inserts < 0 ? -net_inserts : 0;
177 ECB :
178 CBC 556 : stop_column = best_column + (slack_d / (ins_c + del_c)) + 1;
179 GBC 556 : if (stop_column > m)
180 UIC 0 : stop_column = m + 1;
181 : }
182 : }
183 : #endif
184 :
185 : /*
186 : * In order to avoid calling pg_mblen() repeatedly on each character in s,
187 : * we cache all the lengths before starting the main loop -- but if all
188 : * the characters in both strings are single byte, then we skip this and
189 : * use a fast-path in the main loop. If only one string contains
190 : * multi-byte characters, we still build the array, so that the fast-path
191 : * needn't deal with the case where the array hasn't been initialized.
192 ECB : */
193 GIC 810 : if (m != slen || n != tlen)
194 : {
195 EUB : int i;
196 UIC 0 : const char *cp = source;
197 EUB :
198 UBC 0 : s_char_len = (int *) palloc((m + 1) * sizeof(int));
199 UIC 0 : for (i = 0; i < m; ++i)
200 EUB : {
201 UBC 0 : s_char_len[i] = pg_mblen(cp);
202 UIC 0 : cp += s_char_len[i];
203 EUB : }
204 UIC 0 : s_char_len[i] = 0;
205 : }
206 :
207 ECB : /* One more cell for initialization column and row. */
208 CBC 810 : ++m;
209 GIC 810 : ++n;
210 :
211 ECB : /* Previous and current rows of notional array. */
212 CBC 810 : prev = (int *) palloc(2 * m * sizeof(int));
213 GIC 810 : curr = prev + m;
214 :
215 : /*
216 : * To transform the first i characters of s into the first 0 characters of
217 : * t, we must perform i deletions.
218 ECB : */
219 GNC 3176 : for (int i = START_COLUMN; i < STOP_COLUMN; i++)
220 GIC 2366 : prev[i] = i * del_c;
221 :
222 ECB : /* Loop through rows of the notional array */
223 GIC 3153 : for (y = target, j = 1; j < n; j++)
224 : {
225 ECB : int *temp;
226 CBC 2804 : const char *x = source;
227 GIC 2804 : int y_char_len = n != tlen + 1 ? pg_mblen(y) : 1;
228 : int i;
229 :
230 : #ifdef LEVENSHTEIN_LESS_EQUAL
231 :
232 : /*
233 : * In the best case, values percolate down the diagonal unchanged, so
234 : * we must increment stop_column unless it's already on the right end
235 : * of the array. The inner loop will read prev[stop_column], so we
236 : * have to initialize it even though it shouldn't affect the result.
237 : */
238 CBC 2792 : if (stop_column < m)
239 : {
240 2206 : prev[stop_column] = max_d + 1;
241 2206 : ++stop_column;
242 : }
243 :
244 : /*
245 : * The main loop fills in curr, but curr[0] needs a special case: to
246 : * transform the first 0 characters of s into the first j characters
247 : * of t, we must perform j insertions. However, if start_column > 0,
248 : * this special case does not apply.
249 : */
250 2792 : if (start_column == 0)
251 : {
252 1763 : curr[0] = j * ins_c;
253 1763 : i = 1;
254 : }
255 : else
256 1029 : i = start_column;
257 : #else
258 12 : curr[0] = j * ins_c;
259 12 : i = 1;
260 : #endif
261 :
262 : /*
263 : * This inner loop is critical to performance, so we include a
264 : * fast-path to handle the (fairly common) case where no multibyte
265 : * characters are in the mix. The fast-path is entitled to assume
266 : * that if s_char_len is not initialized then BOTH strings contain
267 : * only single-byte characters.
268 : */
269 2804 : if (s_char_len != NULL)
270 : {
271 UBC 0 : for (; i < STOP_COLUMN; i++)
272 : {
273 : int ins;
274 : int del;
275 : int sub;
276 0 : int x_char_len = s_char_len[i - 1];
277 :
278 : /*
279 : * Calculate costs for insertion, deletion, and substitution.
280 : *
281 : * When calculating cost for substitution, we compare the last
282 : * character of each possibly-multibyte character first,
283 : * because that's enough to rule out most mis-matches. If we
284 : * get past that test, then we compare the lengths and the
285 : * remaining bytes.
286 : */
287 0 : ins = prev[i] + ins_c;
288 0 : del = curr[i - 1] + del_c;
289 0 : if (x[x_char_len - 1] == y[y_char_len - 1]
290 0 : && x_char_len == y_char_len &&
291 0 : (x_char_len == 1 || rest_of_char_same(x, y, x_char_len)))
292 0 : sub = prev[i - 1];
293 : else
294 0 : sub = prev[i - 1] + sub_c;
295 :
296 : /* Take the one with minimum cost. */
297 0 : curr[i] = Min(ins, del);
298 0 : curr[i] = Min(curr[i], sub);
299 :
300 : /* Point to next character. */
301 0 : x += x_char_len;
302 : }
303 : }
304 : else
305 : {
306 CBC 11494 : for (; i < STOP_COLUMN; i++)
307 : {
308 : int ins;
309 : int del;
310 : int sub;
311 :
312 : /* Calculate costs for insertion, deletion, and substitution. */
313 8690 : ins = prev[i] + ins_c;
314 8690 : del = curr[i - 1] + del_c;
315 8690 : sub = prev[i - 1] + ((*x == *y) ? 0 : sub_c);
316 :
317 : /* Take the one with minimum cost. */
318 8690 : curr[i] = Min(ins, del);
319 8690 : curr[i] = Min(curr[i], sub);
320 :
321 : /* Point to next character. */
322 8690 : x++;
323 : }
324 : }
325 :
326 : /* Swap current row with previous row. */
327 2804 : temp = curr;
328 2804 : curr = prev;
329 2804 : prev = temp;
330 :
331 : /* Point to next character. */
332 12 : y += y_char_len;
333 :
334 : #ifdef LEVENSHTEIN_LESS_EQUAL
335 :
336 : /*
337 : * This chunk of code represents a significant performance hit if used
338 : * in the case where there is no max_d bound. This is probably not
339 : * because the max_d >= 0 test itself is expensive, but rather because
340 : * the possibility of needing to execute this code prevents tight
341 : * optimization of the loop as a whole.
342 : */
343 2792 : if (max_d >= 0)
344 : {
345 : /*
346 : * The "zero point" is the column of the current row where the
347 : * remaining portions of the strings are of equal length. There
348 : * are (n - 1) characters in the target string, of which j have
349 : * been transformed. There are (m - 1) characters in the source
350 : * string, so we want to find the value for zp where (n - 1) - j =
351 : * (m - 1) - zp.
352 : */
353 2276 : int zp = j - (n - m);
354 :
355 : /* Check whether the stop column can slide left. */
356 5408 : while (stop_column > 0)
357 : {
358 4947 : int ii = stop_column - 1;
359 4947 : int net_inserts = ii - zp;
360 :
361 8424 : if (prev[ii] + (net_inserts > 0 ? net_inserts * ins_c :
362 3477 : -net_inserts * del_c) <= max_d)
363 1815 : break;
364 3132 : stop_column--;
365 : }
366 :
367 : /* Check whether the start column can slide right. */
368 3790 : while (start_column < stop_column)
369 : {
370 3329 : int net_inserts = start_column - zp;
371 :
372 3329 : if (prev[start_column] +
373 3329 : (net_inserts > 0 ? net_inserts * ins_c :
374 3149 : -net_inserts * del_c) <= max_d)
375 1815 : break;
376 :
377 : /*
378 : * We'll never again update these values, so we must make sure
379 : * there's nothing here that could confuse any future
380 : * iteration of the outer loop.
381 : */
382 1514 : prev[start_column] = max_d + 1;
383 1514 : curr[start_column] = max_d + 1;
384 1514 : if (start_column != 0)
385 1036 : source += (s_char_len != NULL) ? s_char_len[start_column - 1] : 1;
386 1514 : start_column++;
387 : }
388 :
389 : /* If they cross, we're going to exceed the bound. */
390 2276 : if (start_column >= stop_column)
391 461 : return max_d + 1;
392 : }
393 : #endif
394 : }
395 :
396 : /*
397 : * Because the final value was swapped from the previous row to the
398 : * current row, that's where we'll find it.
399 : */
400 349 : return prev[m - 1];
401 : }
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