/*------------------------------------------------------------------------- * * levenshtein.c * Levenshtein distance implementation. * * Original author: Joe Conway * * This file is included by varlena.c twice, to provide matching code for (1) * Levenshtein distance with custom costings, and (2) Levenshtein distance with * custom costings and a "max" value above which exact distances are not * interesting. Before the inclusion, we rely on the presence of the inline * function rest_of_char_same(). * * Written based on a description of the algorithm by Michael Gilleland found * at http://www.merriampark.com/ld.htm. Also looked at levenshtein.c in the * PHP 4.0.6 distribution for inspiration. Configurable penalty costs * extension is introduced by Volkan YAZICI = 0, maximum distance we care about; see below. * trusted: caller is trusted and need not obey MAX_LEVENSHTEIN_STRLEN. * * One way to compute Levenshtein distance is to incrementally construct * an (m+1)x(n+1) matrix where cell (i, j) represents the minimum number * of operations required to transform the first i characters of s into * the first j characters of t. The last column of the final row is the * answer. * * We use that algorithm here with some modification. In lieu of holding * the entire array in memory at once, we'll just use two arrays of size * m+1 for storing accumulated values. At each step one array represents * the "previous" row and one is the "current" row of the notional large * array. * * If max_d >= 0, we only need to provide an accurate answer when that answer * is less than or equal to max_d. From any cell in the matrix, there is * theoretical "minimum residual distance" from that cell to the last column * of the final row. This minimum residual distance is zero when the * untransformed portions of the strings are of equal length (because we might * get lucky and find all the remaining characters matching) and is otherwise * based on the minimum number of insertions or deletions needed to make them * equal length. The residual distance grows as we move toward the upper * right or lower left corners of the matrix. When the max_d bound is * usefully tight, we can use this property to avoid computing the entirety * of each row; instead, we maintain a start_column and stop_column that * identify the portion of the matrix close to the diagonal which can still * affect the final answer. */ int #ifdef LEVENSHTEIN_LESS_EQUAL 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) #else varstr_levenshtein(const char *source, int slen, const char *target, int tlen, int ins_c, int del_c, int sub_c, bool trusted) #endif { int m, n; int *prev; int *curr; int *s_char_len = NULL; int i, j; const char *y; /* * For varstr_levenshtein_less_equal, we have real variables called * start_column and stop_column; otherwise it's just short-hand for 0 and * m. */ #ifdef LEVENSHTEIN_LESS_EQUAL int start_column, stop_column; #undef START_COLUMN #undef STOP_COLUMN #define START_COLUMN start_column #define STOP_COLUMN stop_column #else #undef START_COLUMN #undef STOP_COLUMN #define START_COLUMN 0 #define STOP_COLUMN m #endif /* Convert string lengths (in bytes) to lengths in characters */ m = pg_mbstrlen_with_len(source, slen); n = pg_mbstrlen_with_len(target, tlen); /* * We can transform an empty s into t with n insertions, or a non-empty t * into an empty s with m deletions. */ if (!m) return n * ins_c; if (!n) return m * del_c; /* * For security concerns, restrict excessive CPU+RAM usage. (This * implementation uses O(m) memory and has O(mn) complexity.) If * "trusted" is true, caller is responsible for not making excessive * requests, typically by using a small max_d along with strings that are * bounded, though not necessarily to MAX_LEVENSHTEIN_STRLEN exactly. */ if (!trusted && (m > MAX_LEVENSHTEIN_STRLEN || n > MAX_LEVENSHTEIN_STRLEN)) ereport(ERROR, (errcode(ERRCODE_INVALID_PARAMETER_VALUE), errmsg("levenshtein argument exceeds maximum length of %d characters", MAX_LEVENSHTEIN_STRLEN))); #ifdef LEVENSHTEIN_LESS_EQUAL /* Initialize start and stop columns. */ start_column = 0; stop_column = m + 1; /* * If max_d >= 0, determine whether the bound is impossibly tight. If so, * return max_d + 1 immediately. Otherwise, determine whether it's tight * enough to limit the computation we must perform. If so, figure out * initial stop column. */ if (max_d >= 0) { int min_theo_d; /* Theoretical minimum distance. */ int max_theo_d; /* Theoretical maximum distance. */ int net_inserts = n - m; min_theo_d = net_inserts < 0 ? -net_inserts * del_c : net_inserts * ins_c; if (min_theo_d > max_d) return max_d + 1; if (ins_c + del_c < sub_c) sub_c = ins_c + del_c; max_theo_d = min_theo_d + sub_c * Min(m, n); if (max_d >= max_theo_d) max_d = -1; else if (ins_c + del_c > 0) { /* * Figure out how much of the first row of the notional matrix we * need to fill in. If the string is growing, the theoretical * minimum distance already incorporates the cost of deleting the * number of characters necessary to make the two strings equal in * length. Each additional deletion forces another insertion, so * the best-case total cost increases by ins_c + del_c. If the * string is shrinking, the minimum theoretical cost assumes no * excess deletions; that is, we're starting no further right than * column n - m. If we do start further right, the best-case * total cost increases by ins_c + del_c for each move right. */ int slack_d = max_d - min_theo_d; int best_column = net_inserts < 0 ? -net_inserts : 0; stop_column = best_column + (slack_d / (ins_c + del_c)) + 1; if (stop_column > m) stop_column = m + 1; } } #endif /* * In order to avoid calling pg_mblen() repeatedly on each character in s, * we cache all the lengths before starting the main loop -- but if all * the characters in both strings are single byte, then we skip this and * use a fast-path in the main loop. If only one string contains * multi-byte characters, we still build the array, so that the fast-path * needn't deal with the case where the array hasn't been initialized. */ if (m != slen || n != tlen) { int i; const char *cp = source; s_char_len = (int *) palloc((m + 1) * sizeof(int)); for (i = 0; i < m; ++i) { s_char_len[i] = pg_mblen(cp); cp += s_char_len[i]; } s_char_len[i] = 0; } /* One more cell for initialization column and row. */ ++m; ++n; /* Previous and current rows of notional array. */ prev = (int *) palloc(2 * m * sizeof(int)); curr = prev + m; /* * To transform the first i characters of s into the first 0 characters of * t, we must perform i deletions. */ for (i = START_COLUMN; i < STOP_COLUMN; i++) prev[i] = i * del_c; /* Loop through rows of the notional array */ for (y = target, j = 1; j < n; j++) { int *temp; const char *x = source; int y_char_len = n != tlen + 1 ? pg_mblen(y) : 1; #ifdef LEVENSHTEIN_LESS_EQUAL /* * In the best case, values percolate down the diagonal unchanged, so * we must increment stop_column unless it's already on the right end * of the array. The inner loop will read prev[stop_column], so we * have to initialize it even though it shouldn't affect the result. */ if (stop_column < m) { prev[stop_column] = max_d + 1; ++stop_column; } /* * The main loop fills in curr, but curr[0] needs a special case: to * transform the first 0 characters of s into the first j characters * of t, we must perform j insertions. However, if start_column > 0, * this special case does not apply. */ if (start_column == 0) { curr[0] = j * ins_c; i = 1; } else i = start_column; #else curr[0] = j * ins_c; i = 1; #endif /* * This inner loop is critical to performance, so we include a * fast-path to handle the (fairly common) case where no multibyte * characters are in the mix. The fast-path is entitled to assume * that if s_char_len is not initialized then BOTH strings contain * only single-byte characters. */ if (s_char_len != NULL) { for (; i < STOP_COLUMN; i++) { int ins; int del; int sub; int x_char_len = s_char_len[i - 1]; /* * Calculate costs for insertion, deletion, and substitution. * * When calculating cost for substitution, we compare the last * character of each possibly-multibyte character first, * because that's enough to rule out most mis-matches. If we * get past that test, then we compare the lengths and the * remaining bytes. */ ins = prev[i] + ins_c; del = curr[i - 1] + del_c; if (x[x_char_len - 1] == y[y_char_len - 1] && x_char_len == y_char_len && (x_char_len == 1 || rest_of_char_same(x, y, x_char_len))) sub = prev[i - 1]; else sub = prev[i - 1] + sub_c; /* Take the one with minimum cost. */ curr[i] = Min(ins, del); curr[i] = Min(curr[i], sub); /* Point to next character. */ x += x_char_len; } } else { for (; i < STOP_COLUMN; i++) { int ins; int del; int sub; /* Calculate costs for insertion, deletion, and substitution. */ ins = prev[i] + ins_c; del = curr[i - 1] + del_c; sub = prev[i - 1] + ((*x == *y) ? 0 : sub_c); /* Take the one with minimum cost. */ curr[i] = Min(ins, del); curr[i] = Min(curr[i], sub); /* Point to next character. */ x++; } } /* Swap current row with previous row. */ temp = curr; curr = prev; prev = temp; /* Point to next character. */ y += y_char_len; #ifdef LEVENSHTEIN_LESS_EQUAL /* * This chunk of code represents a significant performance hit if used * in the case where there is no max_d bound. This is probably not * because the max_d >= 0 test itself is expensive, but rather because * the possibility of needing to execute this code prevents tight * optimization of the loop as a whole. */ if (max_d >= 0) { /* * The "zero point" is the column of the current row where the * remaining portions of the strings are of equal length. There * are (n - 1) characters in the target string, of which j have * been transformed. There are (m - 1) characters in the source * string, so we want to find the value for zp where (n - 1) - j = * (m - 1) - zp. */ int zp = j - (n - m); /* Check whether the stop column can slide left. */ while (stop_column > 0) { int ii = stop_column - 1; int net_inserts = ii - zp; if (prev[ii] + (net_inserts > 0 ? net_inserts * ins_c : -net_inserts * del_c) <= max_d) break; stop_column--; } /* Check whether the start column can slide right. */ while (start_column < stop_column) { int net_inserts = start_column - zp; if (prev[start_column] + (net_inserts > 0 ? net_inserts * ins_c : -net_inserts * del_c) <= max_d) break; /* * We'll never again update these values, so we must make sure * there's nothing here that could confuse any future * iteration of the outer loop. */ prev[start_column] = max_d + 1; curr[start_column] = max_d + 1; if (start_column != 0) source += (s_char_len != NULL) ? s_char_len[start_column - 1] : 1; start_column++; } /* If they cross, we're going to exceed the bound. */ if (start_column >= stop_column) return max_d + 1; } #endif } /* * Because the final value was swapped from the previous row to the * current row, that's where we'll find it. */ return prev[m - 1]; }