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levenshtein.c
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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) 2001-2017, 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 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 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  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 ||
131  ereport(ERROR,
132  (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
133  errmsg("levenshtein argument exceeds maximum length of %d characters",
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 }
int varstr_levenshtein(const char *source, int slen, const char *target, int tlen, int ins_c, int del_c, int sub_c, bool trusted)
Definition: levenshtein.c:73
#define Min(x, y)
Definition: c.h:795
int errcode(int sqlerrcode)
Definition: elog.c:575
int pg_mbstrlen_with_len(const char *mbstr, int limit)
Definition: mbutils.c:805
#define STOP_COLUMN
#define ERROR
Definition: elog.h:43
#define START_COLUMN
#define ereport(elevel, rest)
Definition: elog.h:122
#define MAX_LEVENSHTEIN_STRLEN
Definition: levenshtein.c:26
static bool rest_of_char_same(const char *s1, const char *s2, int len)
Definition: varlena.c:5511
int pg_mblen(const char *mbstr)
Definition: mbutils.c:771
int varstr_levenshtein_less_equal(const char *source, int slen, const char *target, int tlen, int ins_c, int del_c, int sub_c, int max_d, bool trusted)
void * palloc(Size size)
Definition: mcxt.c:848
int errmsg(const char *fmt,...)
Definition: elog.c:797
int i