1 /* Analyze differences between two vectors.
3 Copyright (C) 1988-1989, 1992-1995, 2001-2004, 2006-2010 Free Software
6 This program is free software: you can redistribute it and/or modify
7 it under the terms of the GNU General Public License as published by
8 the Free Software Foundation; either version 3 of the License, or
9 (at your option) any later version.
11 This program is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14 GNU General Public License for more details.
16 You should have received a copy of the GNU General Public License
17 along with this program. If not, see <http://www.gnu.org/licenses/>. */
20 /* The basic idea is to consider two vectors as similar if, when
21 transforming the first vector into the second vector through a
22 sequence of edits (inserts and deletes of one element each),
23 this sequence is short - or equivalently, if the ordered list
24 of elements that are untouched by these edits is long. For a
25 good introduction to the subject, read about the "Levenshtein
26 distance" in Wikipedia.
28 The basic algorithm is described in:
29 "An O(ND) Difference Algorithm and its Variations", Eugene Myers,
30 Algorithmica Vol. 1 No. 2, 1986, pp. 251-266;
31 see especially section 4.2, which describes the variation used below.
33 The basic algorithm was independently discovered as described in:
34 "Algorithms for Approximate String Matching", E. Ukkonen,
35 Information and Control Vol. 64, 1985, pp. 100-118.
37 Unless the 'find_minimal' flag is set, this code uses the TOO_EXPENSIVE
38 heuristic, by Paul Eggert, to limit the cost to O(N**1.5 log N)
39 at the price of producing suboptimal output for large inputs with
42 /* Before including this file, you need to define:
43 ELEMENT The element type of the vectors being compared.
44 EQUAL A two-argument macro that tests two elements for
46 OFFSET A signed integer type sufficient to hold the
47 difference between two indices. Usually
48 something like ssize_t.
49 EXTRA_CONTEXT_FIELDS Declarations of fields for 'struct context'.
50 NOTE_DELETE(ctxt, xoff) Record the removal of the object xvec[xoff].
51 NOTE_INSERT(ctxt, yoff) Record the insertion of the object yvec[yoff].
52 EARLY_ABORT(ctxt) (Optional) A boolean expression that triggers an
53 early abort of the computation.
54 USE_HEURISTIC (Optional) Define if you want to support the
55 heuristic for large vectors.
56 It is also possible to use this file with abstract arrays. In this case,
57 xvec and yvec are not represented in memory. They only exist conceptually.
58 In this case, the list of defines above is amended as follows:
61 XVECREF_YVECREF_EQUAL(ctxt, xoff, yoff)
62 A three-argument macro: References xvec[xoff] and
63 yvec[yoff] and tests these elements for equality.
64 Before including this file, you also need to include:
70 /* Maximum value of type OFFSET. */
72 ((((OFFSET)1 << (sizeof (OFFSET) * CHAR_BIT - 2)) - 1) * 2 + 1)
74 /* Default to no early abort. */
76 # define EARLY_ABORT(ctxt) false
79 /* Use this to suppress gcc's `...may be used before initialized' warnings.
80 Beware: The Code argument must not contain commas. */
83 # define IF_LINT(Code) Code
85 # define IF_LINT(Code) /* empty */
89 /* As above, but when Code must contain one comma. */
92 # define IF_LINT2(Code1, Code2) Code1, Code2
94 # define IF_LINT2(Code1, Code2) /* empty */
99 * Context of comparison operation.
104 /* Vectors being compared. */
112 /* Vector, indexed by diagonal, containing 1 + the X coordinate of the point
113 furthest along the given diagonal in the forward search of the edit
117 /* Vector, indexed by diagonal, containing the X coordinate of the point
118 furthest along the given diagonal in the backward search of the edit
123 /* This corresponds to the diff -H flag. With this heuristic, for
124 vectors with a constant small density of changes, the algorithm is
125 linear in the vectors size. */
129 /* Edit scripts longer than this are too expensive to compute. */
130 OFFSET too_expensive;
132 /* Snakes bigger than this are considered `big'. */
133 #define SNAKE_LIMIT 20
138 /* Midpoints of this partition. */
142 /* True if low half will be analyzed minimally. */
145 /* Likewise for high half. */
150 /* Find the midpoint of the shortest edit script for a specified portion
153 Scan from the beginnings of the vectors, and simultaneously from the ends,
154 doing a breadth-first search through the space of edit-sequence.
155 When the two searches meet, we have found the midpoint of the shortest
158 If FIND_MINIMAL is true, find the minimal edit script regardless of
159 expense. Otherwise, if the search is too expensive, use heuristics to
160 stop the search and report a suboptimal answer.
162 Set PART->(xmid,ymid) to the midpoint (XMID,YMID). The diagonal number
163 XMID - YMID equals the number of inserted elements minus the number
164 of deleted elements (counting only elements before the midpoint).
166 Set PART->lo_minimal to true iff the minimal edit script for the
167 left half of the partition is known; similarly for PART->hi_minimal.
169 This function assumes that the first elements of the specified portions
170 of the two vectors do not match, and likewise that the last elements do not
171 match. The caller must trim matching elements from the beginning and end
172 of the portions it is going to specify.
174 If we return the "wrong" partitions, the worst this can do is cause
175 suboptimal diff output. It cannot cause incorrect diff output. */
178 diag (OFFSET xoff, OFFSET xlim, OFFSET yoff, OFFSET ylim, bool find_minimal,
179 struct partition *part, struct context *ctxt)
181 OFFSET *const fd = ctxt->fdiag; /* Give the compiler a chance. */
182 OFFSET *const bd = ctxt->bdiag; /* Additional help for the compiler. */
184 ELEMENT const *const xv = ctxt->xvec; /* Still more help for the compiler. */
185 ELEMENT const *const yv = ctxt->yvec; /* And more and more . . . */
186 #define XREF_YREF_EQUAL(x,y) EQUAL (xv[x], yv[y])
188 #define XREF_YREF_EQUAL(x,y) XVECREF_YVECREF_EQUAL (ctxt, x, y)
190 const OFFSET dmin = xoff - ylim; /* Minimum valid diagonal. */
191 const OFFSET dmax = xlim - yoff; /* Maximum valid diagonal. */
192 const OFFSET fmid = xoff - yoff; /* Center diagonal of top-down search. */
193 const OFFSET bmid = xlim - ylim; /* Center diagonal of bottom-up search. */
195 OFFSET fmax = fmid; /* Limits of top-down search. */
197 OFFSET bmax = bmid; /* Limits of bottom-up search. */
198 OFFSET c; /* Cost. */
199 bool odd = (fmid - bmid) & 1; /* True if southeast corner is on an odd
200 diagonal with respect to the northwest. */
207 OFFSET d; /* Active diagonal. */
208 bool big_snake = false;
210 /* Extend the top-down search by an edit step in each diagonal. */
219 for (d = fmax; d >= fmin; d -= 2)
223 OFFSET tlo = fd[d - 1];
224 OFFSET thi = fd[d + 1];
225 OFFSET x0 = tlo < thi ? thi : tlo + 1;
227 for (x = x0, y = x0 - d;
228 x < xlim && y < ylim && XREF_YREF_EQUAL (x, y);
231 if (x - x0 > SNAKE_LIMIT)
234 if (odd && bmin <= d && d <= bmax && bd[d] <= x)
238 part->lo_minimal = part->hi_minimal = true;
243 /* Similarly extend the bottom-up search. */
245 bd[--bmin - 1] = OFFSET_MAX;
249 bd[++bmax + 1] = OFFSET_MAX;
252 for (d = bmax; d >= bmin; d -= 2)
256 OFFSET tlo = bd[d - 1];
257 OFFSET thi = bd[d + 1];
258 OFFSET x0 = tlo < thi ? tlo : thi - 1;
260 for (x = x0, y = x0 - d;
261 xoff < x && yoff < y && XREF_YREF_EQUAL (x - 1, y - 1);
264 if (x0 - x > SNAKE_LIMIT)
267 if (!odd && fmin <= d && d <= fmax && x <= fd[d])
271 part->lo_minimal = part->hi_minimal = true;
280 /* Heuristic: check occasionally for a diagonal that has made lots
281 of progress compared with the edit distance. If we have any
282 such, find the one that has made the most progress and return it
283 as if it had succeeded.
285 With this heuristic, for vectors with a constant small density
286 of changes, the algorithm is linear in the vector size. */
288 if (200 < c && big_snake && ctxt->heuristic)
293 for (d = fmax; d >= fmin; d -= 2)
295 OFFSET dd = d - fmid;
298 OFFSET v = (x - xoff) * 2 - dd;
300 if (v > 12 * (c + (dd < 0 ? -dd : dd)))
303 && xoff + SNAKE_LIMIT <= x && x < xlim
304 && yoff + SNAKE_LIMIT <= y && y < ylim)
306 /* We have a good enough best diagonal; now insist
307 that it end with a significant snake. */
310 for (k = 1; XREF_YREF_EQUAL (x - k, y - k); k++)
311 if (k == SNAKE_LIMIT)
323 part->lo_minimal = true;
324 part->hi_minimal = false;
332 for (d = bmax; d >= bmin; d -= 2)
334 OFFSET dd = d - bmid;
337 OFFSET v = (xlim - x) * 2 + dd;
339 if (v > 12 * (c + (dd < 0 ? -dd : dd)))
342 && xoff < x && x <= xlim - SNAKE_LIMIT
343 && yoff < y && y <= ylim - SNAKE_LIMIT)
345 /* We have a good enough best diagonal; now insist
346 that it end with a significant snake. */
349 for (k = 0; XREF_YREF_EQUAL (x + k, y + k); k++)
350 if (k == SNAKE_LIMIT - 1)
362 part->lo_minimal = false;
363 part->hi_minimal = true;
368 #endif /* USE_HEURISTIC */
370 /* Heuristic: if we've gone well beyond the call of duty, give up
371 and report halfway between our best results so far. */
372 if (c >= ctxt->too_expensive)
375 OFFSET fxbest IF_LINT (= 0);
377 OFFSET bxbest IF_LINT (= 0);
379 /* Find forward diagonal that maximizes X + Y. */
381 for (d = fmax; d >= fmin; d -= 2)
383 OFFSET x = MIN (fd[d], xlim);
397 /* Find backward diagonal that minimizes X + Y. */
398 bxybest = OFFSET_MAX;
399 for (d = bmax; d >= bmin; d -= 2)
401 OFFSET x = MAX (xoff, bd[d]);
415 /* Use the better of the two diagonals. */
416 if ((xlim + ylim) - bxybest < fxybest - (xoff + yoff))
419 part->ymid = fxybest - fxbest;
420 part->lo_minimal = true;
421 part->hi_minimal = false;
426 part->ymid = bxybest - bxbest;
427 part->lo_minimal = false;
428 part->hi_minimal = true;
433 #undef XREF_YREF_EQUAL
437 /* Compare in detail contiguous subsequences of the two vectors
438 which are known, as a whole, to match each other.
440 The subsequence of vector 0 is [XOFF, XLIM) and likewise for vector 1.
442 Note that XLIM, YLIM are exclusive bounds. All indices into the vectors
445 If FIND_MINIMAL, find a minimal difference no matter how
448 The results are recorded by invoking NOTE_DELETE and NOTE_INSERT.
450 Return false if terminated normally, or true if terminated through early
454 compareseq (OFFSET xoff, OFFSET xlim, OFFSET yoff, OFFSET ylim,
455 bool find_minimal, struct context *ctxt)
458 ELEMENT const *xv = ctxt->xvec; /* Help the compiler. */
459 ELEMENT const *yv = ctxt->yvec;
460 #define XREF_YREF_EQUAL(x,y) EQUAL (xv[x], yv[y])
462 #define XREF_YREF_EQUAL(x,y) XVECREF_YVECREF_EQUAL (ctxt, x, y)
465 /* Slide down the bottom initial diagonal. */
466 while (xoff < xlim && yoff < ylim && XREF_YREF_EQUAL (xoff, yoff))
472 /* Slide up the top initial diagonal. */
473 while (xoff < xlim && yoff < ylim && XREF_YREF_EQUAL (xlim - 1, ylim - 1))
479 /* Handle simple cases. */
483 NOTE_INSERT (ctxt, yoff);
484 if (EARLY_ABORT (ctxt))
488 else if (yoff == ylim)
491 NOTE_DELETE (ctxt, xoff);
492 if (EARLY_ABORT (ctxt))
498 struct partition part IF_LINT2 (= { .xmid = 0, .ymid = 0 });
500 /* Find a point of correspondence in the middle of the vectors. */
501 diag (xoff, xlim, yoff, ylim, find_minimal, &part, ctxt);
503 /* Use the partitions to split this problem into subproblems. */
504 if (compareseq (xoff, part.xmid, yoff, part.ymid, part.lo_minimal, ctxt))
506 if (compareseq (part.xmid, xlim, part.ymid, ylim, part.hi_minimal, ctxt))
511 #undef XREF_YREF_EQUAL
517 #undef EXTRA_CONTEXT_FIELDS
522 #undef XVECREF_YVECREF_EQUAL