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) 2001-2019, 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 */
66int
67#ifdef LEVENSHTEIN_LESS_EQUAL
68varstr_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
73varstr_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 int *s_char_len = NULL;
84 int i,
85 j;
86 const char *y;
87
88 /*
89 * For varstr_levenshtein_less_equal, we have real variables called
90 * start_column and stop_column; otherwise it's just short-hand for 0 and
91 * m.
92 */
93#ifdef LEVENSHTEIN_LESS_EQUAL
94 int start_column,
95 stop_column;
96
97#undef START_COLUMN
98#undef STOP_COLUMN
99#define START_COLUMN start_column
100#define STOP_COLUMN stop_column
101#else
102#undef START_COLUMN
103#undef STOP_COLUMN
104#define START_COLUMN 0
105#define STOP_COLUMN m
106#endif
107
108 /* Convert string lengths (in bytes) to lengths in characters */
109 m = pg_mbstrlen_with_len(source, slen);
110 n = pg_mbstrlen_with_len(target, tlen);
111
112 /*
113 * We can transform an empty s into t with n insertions, or a non-empty t
114 * into an empty s with m deletions.
115 */
116 if (!m)
117 return n * ins_c;
118 if (!n)
119 return m * del_c;
120
121 /*
122 * For security concerns, restrict excessive CPU+RAM usage. (This
123 * implementation uses O(m) memory and has O(mn) complexity.) If
124 * "trusted" is true, caller is responsible for not making excessive
125 * requests, typically by using a small max_d along with strings that are
126 * bounded, though not necessarily to MAX_LEVENSHTEIN_STRLEN exactly.
127 */
128 if (!trusted &&
129 (m > MAX_LEVENSHTEIN_STRLEN ||
130 n > MAX_LEVENSHTEIN_STRLEN))
131 ereport(ERROR,
132 (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
133 errmsg("levenshtein argument exceeds maximum length of %d characters",
134 MAX_LEVENSHTEIN_STRLEN)));
135
136#ifdef LEVENSHTEIN_LESS_EQUAL
137 /* Initialize start and stop columns. */
138 start_column = 0;
139 stop_column = m + 1;
140
141 /*
142 * If max_d >= 0, determine whether the bound is impossibly tight. If so,
143 * return max_d + 1 immediately. Otherwise, determine whether it's tight
144 * enough to limit the computation we must perform. If so, figure out
145 * initial stop column.
146 */
147 if (max_d >= 0)
148 {
149 int min_theo_d; /* Theoretical minimum distance. */
150 int max_theo_d; /* Theoretical maximum distance. */
151 int net_inserts = n - m;
152
153 min_theo_d = net_inserts < 0 ?
154 -net_inserts * del_c : net_inserts * ins_c;
155 if (min_theo_d > max_d)
156 return max_d + 1;
157 if (ins_c + del_c < sub_c)
158 sub_c = ins_c + del_c;
159 max_theo_d = min_theo_d + sub_c * Min(m, n);
160 if (max_d >= max_theo_d)
161 max_d = -1;
162 else if (ins_c + del_c > 0)
163 {
164 /*
165 * Figure out how much of the first row of the notional matrix we
166 * need to fill in. If the string is growing, the theoretical
167 * minimum distance already incorporates the cost of deleting the
168 * number of characters necessary to make the two strings equal in
169 * length. Each additional deletion forces another insertion, so
170 * the best-case total cost increases by ins_c + del_c. If the
171 * string is shrinking, the minimum theoretical cost assumes no
172 * excess deletions; that is, we're starting no further right than
173 * column n - m. If we do start further right, the best-case
174 * total cost increases by ins_c + del_c for each move right.
175 */
176 int slack_d = max_d - min_theo_d;
177 int best_column = net_inserts < 0 ? -net_inserts : 0;
178
179 stop_column = best_column + (slack_d / (ins_c + del_c)) + 1;
180 if (stop_column > m)
181 stop_column = m + 1;
182 }
183 }
184#endif
185
186 /*
187 * In order to avoid calling pg_mblen() repeatedly on each character in s,
188 * we cache all the lengths before starting the main loop -- but if all
189 * the characters in both strings are single byte, then we skip this and
190 * use a fast-path in the main loop. If only one string contains
191 * multi-byte characters, we still build the array, so that the fast-path
192 * needn't deal with the case where the array hasn't been initialized.
193 */
194 if (m != slen || n != tlen)
195 {
196 int i;
197 const char *cp = source;
198
199 s_char_len = (int *) palloc((m + 1) * sizeof(int));
200 for (i = 0; i < m; ++i)
201 {
202 s_char_len[i] = pg_mblen(cp);
203 cp += s_char_len[i];
204 }
205 s_char_len[i] = 0;
206 }
207
208 /* One more cell for initialization column and row. */
209 ++m;
210 ++n;
211
212 /* Previous and current rows of notional array. */
213 prev = (int *) palloc(2 * m * sizeof(int));
214 curr = prev + m;
215
216 /*
217 * To transform the first i characters of s into the first 0 characters of
218 * t, we must perform i deletions.
219 */
220 for (i = START_COLUMN; i < STOP_COLUMN; i++)
221 prev[i] = i * del_c;
222
223 /* Loop through rows of the notional array */
224 for (y = target, j = 1; j < n; j++)
225 {
226 int *temp;
227 const char *x = source;
228 int y_char_len = n != tlen + 1 ? pg_mblen(y) : 1;
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 if (stop_column < m)
239 {
240 prev[stop_column] = max_d + 1;
241 ++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 if (start_column == 0)
251 {
252 curr[0] = j * ins_c;
253 i = 1;
254 }
255 else
256 i = start_column;
257#else
258 curr[0] = j * ins_c;
259 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 if (s_char_len != NULL)
270 {
271 for (; i < STOP_COLUMN; i++)
272 {
273 int ins;
274 int del;
275 int sub;
276 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 ins = prev[i] + ins_c;
288 del = curr[i - 1] + del_c;
289 if (x[x_char_len - 1] == y[y_char_len - 1]
290 && x_char_len == y_char_len &&
291 (x_char_len == 1 || rest_of_char_same(x, y, x_char_len)))
292 sub = prev[i - 1];
293 else
294 sub = prev[i - 1] + sub_c;
295
296 /* Take the one with minimum cost. */
297 curr[i] = Min(ins, del);
298 curr[i] = Min(curr[i], sub);
299
300 /* Point to next character. */
301 x += x_char_len;
302 }
303 }
304 else
305 {
306 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 ins = prev[i] + ins_c;
314 del = curr[i - 1] + del_c;
315 sub = prev[i - 1] + ((*x == *y) ? 0 : sub_c);
316
317 /* Take the one with minimum cost. */
318 curr[i] = Min(ins, del);
319 curr[i] = Min(curr[i], sub);
320
321 /* Point to next character. */
322 x++;
323 }
324 }
325
326 /* Swap current row with previous row. */
327 temp = curr;
328 curr = prev;
329 prev = temp;
330
331 /* Point to next character. */
332 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 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 int zp = j - (n - m);
354
355 /* Check whether the stop column can slide left. */
356 while (stop_column > 0)
357 {
358 int ii = stop_column - 1;
359 int net_inserts = ii - zp;
360
361 if (prev[ii] + (net_inserts > 0 ? net_inserts * ins_c :
362 -net_inserts * del_c) <= max_d)
363 break;
364 stop_column--;
365 }
366
367 /* Check whether the start column can slide right. */
368 while (start_column < stop_column)
369 {
370 int net_inserts = start_column - zp;
371
372 if (prev[start_column] +
373 (net_inserts > 0 ? net_inserts * ins_c :
374 -net_inserts * del_c) <= max_d)
375 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 prev[start_column] = max_d + 1;
383 curr[start_column] = max_d + 1;
384 if (start_column != 0)
385 source += (s_char_len != NULL) ? s_char_len[start_column - 1] : 1;
386 start_column++;
387 }
388
389 /* If they cross, we're going to exceed the bound. */
390 if (start_column >= stop_column)
391 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 return prev[m - 1];
401}
402