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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 : 1933 : 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 : 1935 : int *s_char_len = NULL;
84 : : int j;
85 : : const char *y;
86 : 1935 : const char *send = source + slen;
87 : 1935 : const char *tend = target + tlen;
88 : :
89 : : /*
90 : : * For varstr_levenshtein_less_equal, we have real variables called
91 : : * start_column and stop_column; otherwise it's just short-hand for 0 and
92 : : * m.
93 : : */
94 : : #ifdef LEVENSHTEIN_LESS_EQUAL
95 : : int start_column,
96 : : stop_column;
97 : :
98 : : #undef START_COLUMN
99 : : #undef STOP_COLUMN
100 : : #define START_COLUMN start_column
101 : : #define STOP_COLUMN stop_column
102 : : #else
103 : : #undef START_COLUMN
104 : : #undef STOP_COLUMN
105 : : #define START_COLUMN 0
106 : : #define STOP_COLUMN m
107 : : #endif
108 : :
109 : : /* Convert string lengths (in bytes) to lengths in characters */
110 : 1935 : m = pg_mbstrlen_with_len(source, slen);
111 : 1935 : n = pg_mbstrlen_with_len(target, tlen);
112 : :
113 : : /*
114 : : * We can transform an empty s into t with n insertions, or a non-empty t
115 : : * into an empty s with m deletions.
116 : : */
117 [ - + - + ]: 1935 : if (!m)
118 : 0 : return n * ins_c;
119 [ - + - + ]: 1935 : if (!n)
120 : 0 : return m * del_c;
121 : :
122 : : /*
123 : : * For security concerns, restrict excessive CPU+RAM usage. (This
124 : : * implementation uses O(m) memory and has O(mn) complexity.) If
125 : : * "trusted" is true, caller is responsible for not making excessive
126 : : * requests, typically by using a small max_d along with strings that are
127 : : * bounded, though not necessarily to MAX_LEVENSHTEIN_STRLEN exactly.
128 : : */
129 [ + + + - : 1935 : if (!trusted &&
+ - + - ]
130 [ - + - + ]: 4 : (m > MAX_LEVENSHTEIN_STRLEN ||
131 : : n > MAX_LEVENSHTEIN_STRLEN))
132 [ # # # # ]: 0 : ereport(ERROR,
133 : : (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
134 : : errmsg("levenshtein argument exceeds maximum length of %d characters",
135 : : MAX_LEVENSHTEIN_STRLEN)));
136 : :
137 : : #ifdef LEVENSHTEIN_LESS_EQUAL
138 : : /* Initialize start and stop columns. */
139 : 1933 : start_column = 0;
140 : 1933 : stop_column = m + 1;
141 : :
142 : : /*
143 : : * If max_d >= 0, determine whether the bound is impossibly tight. If so,
144 : : * return max_d + 1 immediately. Otherwise, determine whether it's tight
145 : : * enough to limit the computation we must perform. If so, figure out
146 : : * initial stop column.
147 : : */
148 [ + - ]: 1933 : if (max_d >= 0)
149 : : {
150 : : int min_theo_d; /* Theoretical minimum distance. */
151 : : int max_theo_d; /* Theoretical maximum distance. */
152 : 1933 : int net_inserts = n - m;
153 : :
154 : 1933 : min_theo_d = net_inserts < 0 ?
155 [ + + ]: 1933 : -net_inserts * del_c : net_inserts * ins_c;
156 [ + + ]: 1933 : if (min_theo_d > max_d)
157 : 693 : return max_d + 1;
158 [ - + ]: 1240 : if (ins_c + del_c < sub_c)
159 : 0 : sub_c = ins_c + del_c;
160 : 1240 : max_theo_d = min_theo_d + sub_c * Min(m, n);
161 [ + + ]: 1240 : if (max_d >= max_theo_d)
162 : 381 : max_d = -1;
163 [ + - ]: 859 : else if (ins_c + del_c > 0)
164 : : {
165 : : /*
166 : : * Figure out how much of the first row of the notional matrix we
167 : : * need to fill in. If the string is growing, the theoretical
168 : : * minimum distance already incorporates the cost of deleting the
169 : : * number of characters necessary to make the two strings equal in
170 : : * length. Each additional deletion forces another insertion, so
171 : : * the best-case total cost increases by ins_c + del_c. If the
172 : : * string is shrinking, the minimum theoretical cost assumes no
173 : : * excess deletions; that is, we're starting no further right than
174 : : * column n - m. If we do start further right, the best-case
175 : : * total cost increases by ins_c + del_c for each move right.
176 : : */
177 : 859 : int slack_d = max_d - min_theo_d;
178 [ + + ]: 859 : int best_column = net_inserts < 0 ? -net_inserts : 0;
179 : :
180 : 859 : stop_column = best_column + (slack_d / (ins_c + del_c)) + 1;
181 [ - + ]: 859 : if (stop_column > m)
182 : 0 : stop_column = m + 1;
183 : : }
184 : : }
185 : : #endif
186 : :
187 : : /*
188 : : * In order to avoid calling pg_mblen_range() repeatedly on each character
189 : : * in s, we cache all the lengths before starting the main loop -- but if
190 : : * all the characters in both strings are single byte, then we skip this
191 : : * and use a fast-path in the main loop. If only one string contains
192 : : * multi-byte characters, we still build the array, so that the fast-path
193 : : * needn't deal with the case where the array hasn't been initialized.
194 : : */
195 [ + - + + : 1242 : if (m != slen || n != tlen)
+ - - + ]
196 : : {
197 : : int i;
198 : 4 : const char *cp = source;
199 : :
200 : 4 : s_char_len = (int *) palloc((m + 1) * sizeof(int));
201 [ + + - - ]: 40 : for (i = 0; i < m; ++i)
202 : : {
203 : 36 : s_char_len[i] = pg_mblen_range(cp, send);
204 : 36 : cp += s_char_len[i];
205 : : }
206 : 4 : s_char_len[i] = 0;
207 : : }
208 : :
209 : : /* One more cell for initialization column and row. */
210 : 1242 : ++m;
211 : 1242 : ++n;
212 : :
213 : : /* Previous and current rows of notional array. */
214 : 1242 : prev = (int *) palloc(2 * m * sizeof(int));
215 : 1242 : curr = prev + m;
216 : :
217 : : /*
218 : : * To transform the first i characters of s into the first 0 characters of
219 : : * t, we must perform i deletions.
220 : : */
221 [ + + + + ]: 4827 : for (int i = START_COLUMN; i < STOP_COLUMN; i++)
222 : 3585 : prev[i] = i * del_c;
223 : :
224 : : /* Loop through rows of the notional array */
225 [ + + + + ]: 4830 : for (y = target, j = 1; j < n; j++)
226 : : {
227 : : int *temp;
228 : 4316 : const char *x = source;
229 [ + + - + ]: 4316 : int y_char_len = n != tlen + 1 ? pg_mblen_range(y, tend) : 1;
230 : : int i;
231 : :
232 : : #ifdef LEVENSHTEIN_LESS_EQUAL
233 : :
234 : : /*
235 : : * In the best case, values percolate down the diagonal unchanged, so
236 : : * we must increment stop_column unless it's already on the right end
237 : : * of the array. The inner loop will read prev[stop_column], so we
238 : : * have to initialize it even though it shouldn't affect the result.
239 : : */
240 [ + + ]: 4304 : if (stop_column < m)
241 : : {
242 : 3442 : prev[stop_column] = max_d + 1;
243 : 3442 : ++stop_column;
244 : : }
245 : :
246 : : /*
247 : : * The main loop fills in curr, but curr[0] needs a special case: to
248 : : * transform the first 0 characters of s into the first j characters
249 : : * of t, we must perform j insertions. However, if start_column > 0,
250 : : * this special case does not apply.
251 : : */
252 [ + + ]: 4304 : if (start_column == 0)
253 : : {
254 : 2758 : curr[0] = j * ins_c;
255 : 2758 : i = 1;
256 : : }
257 : : else
258 : 1546 : i = start_column;
259 : : #else
260 : 12 : curr[0] = j * ins_c;
261 : 12 : i = 1;
262 : : #endif
263 : :
264 : : /*
265 : : * This inner loop is critical to performance, so we include a
266 : : * fast-path to handle the (fairly common) case where no multibyte
267 : : * characters are in the mix. The fast-path is entitled to assume
268 : : * that if s_char_len is not initialized then BOTH strings contain
269 : : * only single-byte characters.
270 : : */
271 [ + + - + ]: 4316 : if (s_char_len != NULL)
272 : : {
273 [ + + - - ]: 248 : for (; i < STOP_COLUMN; i++)
274 : : {
275 : : int ins;
276 : : int del;
277 : : int sub;
278 : 208 : int x_char_len = s_char_len[i - 1];
279 : :
280 : : /*
281 : : * Calculate costs for insertion, deletion, and substitution.
282 : : *
283 : : * When calculating cost for substitution, we compare the last
284 : : * character of each possibly-multibyte character first,
285 : : * because that's enough to rule out most mis-matches. If we
286 : : * get past that test, then we compare the lengths and the
287 : : * remaining bytes.
288 : : */
289 : 208 : ins = prev[i] + ins_c;
290 : 208 : del = curr[i - 1] + del_c;
291 [ + + - - ]: 208 : if (x[x_char_len - 1] == y[y_char_len - 1]
292 [ + - - + : 36 : && x_char_len == y_char_len &&
- - - - ]
293 [ # # # # ]: 0 : (x_char_len == 1 || rest_of_char_same(x, y, x_char_len)))
294 : 36 : sub = prev[i - 1];
295 : : else
296 : 172 : sub = prev[i - 1] + sub_c;
297 : :
298 : : /* Take the one with minimum cost. */
299 : 208 : curr[i] = Min(ins, del);
300 : 208 : curr[i] = Min(curr[i], sub);
301 : :
302 : : /* Point to next character. */
303 : 208 : x += x_char_len;
304 : : }
305 : : }
306 : : else
307 : : {
308 [ + + + + ]: 17292 : for (; i < STOP_COLUMN; i++)
309 : : {
310 : : int ins;
311 : : int del;
312 : : int sub;
313 : :
314 : : /* Calculate costs for insertion, deletion, and substitution. */
315 : 13016 : ins = prev[i] + ins_c;
316 : 13016 : del = curr[i - 1] + del_c;
317 [ + + + + ]: 13016 : sub = prev[i - 1] + ((*x == *y) ? 0 : sub_c);
318 : :
319 : : /* Take the one with minimum cost. */
320 : 13016 : curr[i] = Min(ins, del);
321 : 13016 : curr[i] = Min(curr[i], sub);
322 : :
323 : : /* Point to next character. */
324 : 13016 : x++;
325 : : }
326 : : }
327 : :
328 : : /* Swap current row with previous row. */
329 : 4316 : temp = curr;
330 : 4316 : curr = prev;
331 : 4316 : prev = temp;
332 : :
333 : : /* Point to next character. */
334 : 12 : y += y_char_len;
335 : :
336 : : #ifdef LEVENSHTEIN_LESS_EQUAL
337 : :
338 : : /*
339 : : * This chunk of code represents a significant performance hit if used
340 : : * in the case where there is no max_d bound. This is probably not
341 : : * because the max_d >= 0 test itself is expensive, but rather because
342 : : * the possibility of needing to execute this code prevents tight
343 : : * optimization of the loop as a whole.
344 : : */
345 [ + + ]: 4304 : if (max_d >= 0)
346 : : {
347 : : /*
348 : : * The "zero point" is the column of the current row where the
349 : : * remaining portions of the strings are of equal length. There
350 : : * are (n - 1) characters in the target string, of which j have
351 : : * been transformed. There are (m - 1) characters in the source
352 : : * string, so we want to find the value for zp where (n - 1) - j =
353 : : * (m - 1) - zp.
354 : : */
355 : 3548 : int zp = j - (n - m);
356 : :
357 : : /* Check whether the stop column can slide left. */
358 [ + + ]: 8513 : while (stop_column > 0)
359 : : {
360 : 7785 : int ii = stop_column - 1;
361 : 7785 : int net_inserts = ii - zp;
362 : :
363 [ + + + + ]: 13161 : if (prev[ii] + (net_inserts > 0 ? net_inserts * ins_c :
364 : 5376 : -net_inserts * del_c) <= max_d)
365 : 2820 : break;
366 : 4965 : stop_column--;
367 : : }
368 : :
369 : : /* Check whether the start column can slide right. */
370 [ + + ]: 5853 : while (start_column < stop_column)
371 : : {
372 : 5125 : int net_inserts = start_column - zp;
373 : :
374 [ + + ]: 5125 : if (prev[start_column] +
375 [ + + ]: 5125 : (net_inserts > 0 ? net_inserts * ins_c :
376 : 4813 : -net_inserts * del_c) <= max_d)
377 : 2820 : break;
378 : :
379 : : /*
380 : : * We'll never again update these values, so we must make sure
381 : : * there's nothing here that could confuse any future
382 : : * iteration of the outer loop.
383 : : */
384 : 2305 : prev[start_column] = max_d + 1;
385 : 2305 : curr[start_column] = max_d + 1;
386 [ + + ]: 2305 : if (start_column != 0)
387 [ + + ]: 1580 : source += (s_char_len != NULL) ? s_char_len[start_column - 1] : 1;
388 : 2305 : start_column++;
389 : : }
390 : :
391 : : /* If they cross, we're going to exceed the bound. */
392 [ + + ]: 3548 : if (start_column >= stop_column)
393 : 728 : return max_d + 1;
394 : : }
395 : : #endif
396 : : }
397 : :
398 : : /*
399 : : * Because the final value was swapped from the previous row to the
400 : : * current row, that's where we'll find it.
401 : : */
402 : 514 : return prev[m - 1];
403 : : }
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