Branch data 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) 2001-2026, 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 : 0 : 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 : 0 : 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 : 0 : int m,
80 : : n;
81 : 0 : int *prev;
82 : 0 : int *curr;
83 : 0 : int *s_char_len = NULL;
84 : 0 : int j;
85 : 0 : 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 : 0 : 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 : : /* Convert string lengths (in bytes) to lengths in characters */
108 : 0 : m = pg_mbstrlen_with_len(source, slen);
109 : 0 : 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 : : */
115 [ # # # # ]: 0 : if (!m)
116 : 0 : return n * ins_c;
117 [ # # # # ]: 0 : if (!n)
118 : 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 : : */
127 [ # # # # ]: 0 : if (!trusted &&
128 [ # # # # ]: 0 : (m > MAX_LEVENSHTEIN_STRLEN ||
129 : 0 : n > MAX_LEVENSHTEIN_STRLEN))
130 [ # # # # : 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 : : /* Initialize start and stop columns. */
137 : 0 : start_column = 0;
138 : 0 : 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 : : */
146 [ # # ]: 0 : if (max_d >= 0)
147 : : {
148 : 0 : int min_theo_d; /* Theoretical minimum distance. */
149 : 0 : int max_theo_d; /* Theoretical maximum distance. */
150 : 0 : int net_inserts = n - m;
151 : :
152 [ # # ]: 0 : min_theo_d = net_inserts < 0 ?
153 : 0 : -net_inserts * del_c : net_inserts * ins_c;
154 [ # # ]: 0 : if (min_theo_d > max_d)
155 : 0 : return max_d + 1;
156 [ # # ]: 0 : if (ins_c + del_c < sub_c)
157 : 0 : sub_c = ins_c + del_c;
158 [ # # ]: 0 : max_theo_d = min_theo_d + sub_c * Min(m, n);
159 [ # # ]: 0 : if (max_d >= max_theo_d)
160 : 0 : max_d = -1;
161 [ # # ]: 0 : 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 : : */
175 : 0 : int slack_d = max_d - min_theo_d;
176 [ # # ]: 0 : int best_column = net_inserts < 0 ? -net_inserts : 0;
177 : :
178 : 0 : stop_column = best_column + (slack_d / (ins_c + del_c)) + 1;
179 [ # # ]: 0 : if (stop_column > m)
180 : 0 : stop_column = m + 1;
181 : 0 : }
182 [ # # ]: 0 : }
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 : : */
193 [ # # # # : 0 : if (m != slen || n != tlen)
# # # # ]
194 : : {
195 : 0 : int i;
196 : 0 : const char *cp = source;
197 : :
198 : 0 : s_char_len = (int *) palloc((m + 1) * sizeof(int));
199 [ # # # # ]: 0 : for (i = 0; i < m; ++i)
200 : : {
201 : 0 : s_char_len[i] = pg_mblen(cp);
202 : 0 : cp += s_char_len[i];
203 : 0 : }
204 : 0 : s_char_len[i] = 0;
205 : 0 : }
206 : :
207 : : /* One more cell for initialization column and row. */
208 : 0 : ++m;
209 : 0 : ++n;
210 : :
211 : : /* Previous and current rows of notional array. */
212 : 0 : prev = (int *) palloc(2 * m * sizeof(int));
213 : 0 : 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 : : */
219 [ # # # # ]: 0 : for (int i = START_COLUMN; i < STOP_COLUMN; i++)
220 : 0 : prev[i] = i * del_c;
221 : :
222 : : /* Loop through rows of the notional array */
223 [ # # # # ]: 0 : for (y = target, j = 1; j < n; j++)
224 : : {
225 : 0 : int *temp;
226 : 0 : const char *x = source;
227 [ # # # # ]: 0 : int y_char_len = n != tlen + 1 ? pg_mblen(y) : 1;
228 : 0 : 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 [ # # ]: 0 : if (stop_column < m)
239 : : {
240 : 0 : prev[stop_column] = max_d + 1;
241 : 0 : ++stop_column;
242 : 0 : }
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 [ # # ]: 0 : if (start_column == 0)
251 : : {
252 : 0 : curr[0] = j * ins_c;
253 : 0 : i = 1;
254 : 0 : }
255 : : else
256 : 0 : i = start_column;
257 : : #else
258 : 0 : curr[0] = j * ins_c;
259 : 0 : 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 [ # # # # ]: 0 : if (s_char_len != NULL)
270 : : {
271 [ # # # # ]: 0 : for (; i < STOP_COLUMN; i++)
272 : : {
273 : 0 : int ins;
274 : 0 : int del;
275 : 0 : 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 : 0 : }
303 : 0 : }
304 : : else
305 : : {
306 [ # # # # ]: 0 : for (; i < STOP_COLUMN; i++)
307 : : {
308 : 0 : int ins;
309 : 0 : int del;
310 : 0 : int sub;
311 : :
312 : : /* Calculate costs for insertion, deletion, and substitution. */
313 : 0 : ins = prev[i] + ins_c;
314 : 0 : del = curr[i - 1] + del_c;
315 [ # # # # ]: 0 : sub = prev[i - 1] + ((*x == *y) ? 0 : sub_c);
316 : :
317 : : /* Take the one with minimum cost. */
318 [ # # # # ]: 0 : curr[i] = Min(ins, del);
319 [ # # # # ]: 0 : curr[i] = Min(curr[i], sub);
320 : :
321 : : /* Point to next character. */
322 : 0 : x++;
323 : 0 : }
324 : : }
325 : :
326 : : /* Swap current row with previous row. */
327 : 0 : temp = curr;
328 : 0 : curr = prev;
329 : 0 : prev = temp;
330 : :
331 : : /* Point to next character. */
332 : 0 : 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 [ # # ]: 0 : 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 : 0 : int zp = j - (n - m);
354 : :
355 : : /* Check whether the stop column can slide left. */
356 [ # # ]: 0 : while (stop_column > 0)
357 : : {
358 : 0 : int ii = stop_column - 1;
359 : 0 : int net_inserts = ii - zp;
360 : :
361 [ # # ]: 0 : if (prev[ii] + (net_inserts > 0 ? net_inserts * ins_c :
362 [ # # ]: 0 : -net_inserts * del_c) <= max_d)
363 : 0 : break;
364 : 0 : stop_column--;
365 [ # # ]: 0 : }
366 : :
367 : : /* Check whether the start column can slide right. */
368 [ # # ]: 0 : while (start_column < stop_column)
369 : : {
370 : 0 : int net_inserts = start_column - zp;
371 : :
372 : 0 : if (prev[start_column] +
373 [ # # ]: 0 : (net_inserts > 0 ? net_inserts * ins_c :
374 [ # # ]: 0 : -net_inserts * del_c) <= max_d)
375 : 0 : 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 : 0 : prev[start_column] = max_d + 1;
383 : 0 : curr[start_column] = max_d + 1;
384 [ # # ]: 0 : if (start_column != 0)
385 [ # # ]: 0 : source += (s_char_len != NULL) ? s_char_len[start_column - 1] : 1;
386 : 0 : start_column++;
387 [ # # ]: 0 : }
388 : :
389 : : /* If they cross, we're going to exceed the bound. */
390 [ # # ]: 0 : if (start_column >= stop_column)
391 : 0 : return max_d + 1;
392 [ # # ]: 0 : }
393 : : #endif
394 [ # # ]: 0 : }
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 : 0 : return prev[m - 1];
401 : 0 : }
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