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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 : : * functions rest_of_char_same() and levenshtein_result().
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 : 1934 : 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 : 4 : 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 : : int64 *prev;
82 : : int64 *curr;
83 : 1938 : int *s_char_len = NULL;
84 : : int j;
85 : : const char *y;
86 : 1938 : const char *send = source + slen;
87 : 1938 : const char *tend = target + tlen;
88 : 1938 : int64 ins_c_64 = ins_c;
89 : 1938 : int64 del_c_64 = del_c;
90 : 1938 : int64 sub_c_64 = sub_c;
91 : :
92 : : /*
93 : : * For varstr_levenshtein_less_equal, we have real variables called
94 : : * start_column and stop_column; otherwise it's just short-hand for 0 and
95 : : * m.
96 : : */
97 : : #ifdef LEVENSHTEIN_LESS_EQUAL
98 : : int start_column,
99 : : stop_column;
100 : :
101 : : #undef START_COLUMN
102 : : #undef STOP_COLUMN
103 : : #define START_COLUMN start_column
104 : : #define STOP_COLUMN stop_column
105 : : #else
106 : : #undef START_COLUMN
107 : : #undef STOP_COLUMN
108 : : #define START_COLUMN 0
109 : : #define STOP_COLUMN m
110 : : #endif
111 : :
112 : : /* Convert string lengths (in bytes) to lengths in characters */
113 : 1938 : m = pg_mbstrlen_with_len(source, slen);
114 : 1938 : n = pg_mbstrlen_with_len(target, tlen);
115 : :
116 : : /*
117 : : * We can transform an empty s into t with n insertions, or a non-empty t
118 : : * into an empty s with m deletions.
119 : : */
120 [ - + - + ]: 1938 : if (!m)
121 : 0 : return levenshtein_result(n * ins_c_64);
122 [ - + - + ]: 1938 : if (!n)
123 : 0 : return levenshtein_result(m * del_c_64);
124 : :
125 : : /*
126 : : * For security concerns, restrict excessive CPU+RAM usage. (This
127 : : * implementation uses O(m) memory and has O(mn) complexity.) If
128 : : * "trusted" is true, caller is responsible for not making excessive
129 : : * requests, typically by using a small max_d along with strings that are
130 : : * bounded, though not necessarily to MAX_LEVENSHTEIN_STRLEN exactly.
131 : : */
132 [ + + + - : 1938 : if (!trusted &&
+ - + - ]
133 [ - + - + ]: 7 : (m > MAX_LEVENSHTEIN_STRLEN ||
134 : : n > MAX_LEVENSHTEIN_STRLEN))
135 [ # # # # ]: 0 : ereport(ERROR,
136 : : (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
137 : : errmsg("levenshtein argument exceeds maximum length of %d characters",
138 : : MAX_LEVENSHTEIN_STRLEN)));
139 : :
140 : : #ifdef LEVENSHTEIN_LESS_EQUAL
141 : : /* Initialize start and stop columns. */
142 : 1934 : start_column = 0;
143 : 1934 : stop_column = m + 1;
144 : :
145 : : /*
146 : : * If max_d >= 0, determine whether the bound is impossibly tight. If so,
147 : : * return max_d + 1 immediately. Otherwise, determine whether it's tight
148 : : * enough to limit the computation we must perform. If so, figure out
149 : : * initial stop column.
150 : : */
151 [ + - ]: 1934 : if (max_d >= 0)
152 : : {
153 : : int64 min_theo_d; /* Theoretical minimum distance. */
154 : : int64 max_theo_d; /* Theoretical maximum distance. */
155 : 1934 : int net_inserts = n - m;
156 : :
157 : 1934 : min_theo_d = net_inserts < 0 ?
158 [ + + ]: 1934 : -net_inserts * del_c_64 : net_inserts * ins_c_64;
159 [ + + ]: 1934 : if (min_theo_d > max_d)
160 : 694 : return levenshtein_result((int64) max_d + 1);
161 [ - + ]: 1240 : if (ins_c_64 + del_c_64 < sub_c_64)
162 : 0 : sub_c_64 = ins_c_64 + del_c_64;
163 : 1240 : max_theo_d = min_theo_d + sub_c_64 * Min(m, n);
164 [ + + ]: 1240 : if (max_d >= max_theo_d)
165 : 381 : max_d = -1;
166 [ + - ]: 859 : else if (ins_c_64 + del_c_64 > 0)
167 : : {
168 : : /*
169 : : * Figure out how much of the first row of the notional matrix we
170 : : * need to fill in. If the string is growing, the theoretical
171 : : * minimum distance already incorporates the cost of deleting the
172 : : * number of characters necessary to make the two strings equal in
173 : : * length. Each additional deletion forces another insertion, so
174 : : * the best-case total cost increases by ins_c + del_c. If the
175 : : * string is shrinking, the minimum theoretical cost assumes no
176 : : * excess deletions; that is, we're starting no further right than
177 : : * column n - m. If we do start further right, the best-case
178 : : * total cost increases by ins_c + del_c for each move right.
179 : : */
180 : 859 : int64 slack_d = max_d - min_theo_d;
181 [ + + ]: 859 : int best_column = net_inserts < 0 ? -net_inserts : 0;
182 : : int64 tmp;
183 : :
184 : 859 : tmp = best_column + (slack_d / (ins_c_64 + del_c_64)) + 1;
185 : 859 : stop_column = Min(tmp, m + 1);
186 : : }
187 : : }
188 : : #endif
189 : :
190 : : /*
191 : : * In order to avoid calling pg_mblen_range() repeatedly on each character
192 : : * in s, we cache all the lengths before starting the main loop -- but if
193 : : * all the characters in both strings are single byte, then we skip this
194 : : * and use a fast-path in the main loop. If only one string contains
195 : : * multi-byte characters, we still build the array, so that the fast-path
196 : : * needn't deal with the case where the array hasn't been initialized.
197 : : */
198 [ + - + + : 1244 : if (m != slen || n != tlen)
+ - - + ]
199 : : {
200 : : int i;
201 : 4 : const char *cp = source;
202 : :
203 : 4 : s_char_len = (int *) palloc((m + 1) * sizeof(int));
204 [ + + - - ]: 40 : for (i = 0; i < m; ++i)
205 : : {
206 : 36 : s_char_len[i] = pg_mblen_range(cp, send);
207 : 36 : cp += s_char_len[i];
208 : : }
209 : 4 : s_char_len[i] = 0;
210 : : }
211 : :
212 : : /* One more cell for initialization column and row. */
213 : 1244 : ++m;
214 : 1244 : ++n;
215 : :
216 : : /* Previous and current rows of notional array. */
217 : 1244 : prev = (int64 *) palloc(2 * m * sizeof(int64));
218 : 1244 : curr = prev + m;
219 : :
220 : : /*
221 : : * To transform the first i characters of s into the first 0 characters of
222 : : * t, we must perform i deletions.
223 : : */
224 [ + + + + ]: 4841 : for (int i = START_COLUMN; i < STOP_COLUMN; i++)
225 : 3597 : prev[i] = i * del_c_64;
226 : :
227 : : /* Loop through rows of the notional array */
228 [ + + + + ]: 4844 : for (y = target, j = 1; j < n; j++)
229 : : {
230 : : int64 *temp;
231 : 4328 : const char *x = source;
232 [ + + - + ]: 4328 : int y_char_len = n != tlen + 1 ? pg_mblen_range(y, tend) : 1;
233 : : int i;
234 : :
235 : : #ifdef LEVENSHTEIN_LESS_EQUAL
236 : :
237 : : /*
238 : : * In the best case, values percolate down the diagonal unchanged, so
239 : : * we must increment stop_column unless it's already on the right end
240 : : * of the array. The inner loop will read prev[stop_column], so we
241 : : * have to initialize it even though it shouldn't affect the result.
242 : : */
243 [ + + ]: 4304 : if (stop_column < m)
244 : : {
245 : 3442 : prev[stop_column] = (int64) max_d + 1;
246 : 3442 : ++stop_column;
247 : : }
248 : :
249 : : /*
250 : : * The main loop fills in curr, but curr[0] needs a special case: to
251 : : * transform the first 0 characters of s into the first j characters
252 : : * of t, we must perform j insertions. However, if start_column > 0,
253 : : * this special case does not apply.
254 : : */
255 [ + + ]: 4304 : if (start_column == 0)
256 : : {
257 : 2758 : curr[0] = j * ins_c_64;
258 : 2758 : i = 1;
259 : : }
260 : : else
261 : 1546 : i = start_column;
262 : : #else
263 : 24 : curr[0] = j * ins_c_64;
264 : 24 : i = 1;
265 : : #endif
266 : :
267 : : /*
268 : : * This inner loop is critical to performance, so we include a
269 : : * fast-path to handle the (fairly common) case where no multibyte
270 : : * characters are in the mix. The fast-path is entitled to assume
271 : : * that if s_char_len is not initialized then BOTH strings contain
272 : : * only single-byte characters.
273 : : */
274 [ + + - + ]: 4328 : if (s_char_len != NULL)
275 : : {
276 [ + + - - ]: 248 : for (; i < STOP_COLUMN; i++)
277 : : {
278 : : int64 ins;
279 : : int64 del;
280 : : int64 sub;
281 : 208 : int x_char_len = s_char_len[i - 1];
282 : :
283 : : /*
284 : : * Calculate costs for insertion, deletion, and substitution.
285 : : *
286 : : * When calculating cost for substitution, we compare the last
287 : : * character of each possibly-multibyte character first,
288 : : * because that's enough to rule out most mis-matches. If we
289 : : * get past that test, then we compare the lengths and the
290 : : * remaining bytes.
291 : : */
292 : 208 : ins = prev[i] + ins_c_64;
293 : 208 : del = curr[i - 1] + del_c_64;
294 [ + + - - ]: 208 : if (x[x_char_len - 1] == y[y_char_len - 1]
295 [ + - - + : 36 : && x_char_len == y_char_len &&
- - - - ]
296 [ # # # # ]: 0 : (x_char_len == 1 || rest_of_char_same(x, y, x_char_len)))
297 : 36 : sub = prev[i - 1];
298 : : else
299 : 172 : sub = prev[i - 1] + sub_c_64;
300 : :
301 : : /* Take the one with minimum cost. */
302 : 208 : curr[i] = Min(ins, del);
303 : 208 : curr[i] = Min(curr[i], sub);
304 : :
305 : : /* Point to next character. */
306 : 208 : x += x_char_len;
307 : : }
308 : : }
309 : : else
310 : : {
311 [ + + + + ]: 17364 : for (; i < STOP_COLUMN; i++)
312 : : {
313 : : int64 ins;
314 : : int64 del;
315 : : int64 sub;
316 : :
317 : : /* Calculate costs for insertion, deletion, and substitution. */
318 : 13076 : ins = prev[i] + ins_c_64;
319 : 13076 : del = curr[i - 1] + del_c_64;
320 [ + + + + ]: 13076 : sub = prev[i - 1] + ((*x == *y) ? 0 : sub_c_64);
321 : :
322 : : /* Take the one with minimum cost. */
323 : 13076 : curr[i] = Min(ins, del);
324 : 13076 : curr[i] = Min(curr[i], sub);
325 : :
326 : : /* Point to next character. */
327 : 13076 : x++;
328 : : }
329 : : }
330 : :
331 : : /* Swap current row with previous row. */
332 : 4328 : temp = curr;
333 : 4328 : curr = prev;
334 : 4328 : prev = temp;
335 : :
336 : : /* Point to next character. */
337 : 24 : y += y_char_len;
338 : :
339 : : #ifdef LEVENSHTEIN_LESS_EQUAL
340 : :
341 : : /*
342 : : * This chunk of code represents a significant performance hit if used
343 : : * in the case where there is no max_d bound. This is probably not
344 : : * because the max_d >= 0 test itself is expensive, but rather because
345 : : * the possibility of needing to execute this code prevents tight
346 : : * optimization of the loop as a whole.
347 : : */
348 [ + + ]: 4304 : if (max_d >= 0)
349 : : {
350 : : /*
351 : : * The "zero point" is the column of the current row where the
352 : : * remaining portions of the strings are of equal length. There
353 : : * are (n - 1) characters in the target string, of which j have
354 : : * been transformed. There are (m - 1) characters in the source
355 : : * string, so we want to find the value for zp where (n - 1) - j =
356 : : * (m - 1) - zp.
357 : : */
358 : 3548 : int zp = j - (n - m);
359 : :
360 : : /* Check whether the stop column can slide left. */
361 [ + + ]: 8513 : while (stop_column > 0)
362 : : {
363 : 7785 : int ii = stop_column - 1;
364 : 7785 : int net_inserts = ii - zp;
365 : :
366 [ + + ]: 7785 : if (prev[ii] + (net_inserts > 0 ? net_inserts * ins_c_64 :
367 [ + + ]: 7785 : -net_inserts * del_c_64) <= max_d)
368 : 2820 : break;
369 : 4965 : stop_column--;
370 : : }
371 : :
372 : : /* Check whether the start column can slide right. */
373 [ + + ]: 5853 : while (start_column < stop_column)
374 : : {
375 : 5125 : int net_inserts = start_column - zp;
376 : :
377 : 10250 : if (prev[start_column] +
378 [ + + ]: 5125 : (net_inserts > 0 ? net_inserts * ins_c_64 :
379 [ + + ]: 5125 : -net_inserts * del_c_64) <= max_d)
380 : 2820 : break;
381 : :
382 : : /*
383 : : * We'll never again update these values, so we must make sure
384 : : * there's nothing here that could confuse any future
385 : : * iteration of the outer loop.
386 : : */
387 : 2305 : prev[start_column] = (int64) max_d + 1;
388 : 2305 : curr[start_column] = (int64) max_d + 1;
389 [ + + ]: 2305 : if (start_column != 0)
390 [ + + ]: 1580 : source += (s_char_len != NULL) ? s_char_len[start_column - 1] : 1;
391 : 2305 : start_column++;
392 : : }
393 : :
394 : : /* If they cross, we're going to exceed the bound. */
395 [ + + ]: 3548 : if (start_column >= stop_column)
396 : 728 : return levenshtein_result((int64) max_d + 1);
397 : : }
398 : : #endif
399 : : }
400 : :
401 : : /*
402 : : * Because the final value was swapped from the previous row to the
403 : : * current row, that's where we'll find it.
404 : : */
405 : 516 : return levenshtein_result(prev[m - 1]);
406 : : }
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