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/* Analyze differences between two vectors.
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Copyright (C) 1988-1989, 1992-1995, 2001-2004, 2006-2010 Free Software
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>. */
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/* The basic idea is to consider two vectors as similar if, when
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transforming the first vector into the second vector through a
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sequence of edits (inserts and deletes of one element each),
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this sequence is short - or equivalently, if the ordered list
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of elements that are untouched by these edits is long. For a
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good introduction to the subject, read about the "Levenshtein
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distance" in Wikipedia.
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The basic algorithm is described in:
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"An O(ND) Difference Algorithm and its Variations", Eugene Myers,
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Algorithmica Vol. 1 No. 2, 1986, pp. 251-266;
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see especially section 4.2, which describes the variation used below.
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The basic algorithm was independently discovered as described in:
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"Algorithms for Approximate String Matching", E. Ukkonen,
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Information and Control Vol. 64, 1985, pp. 100-118.
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Unless the 'find_minimal' flag is set, this code uses the TOO_EXPENSIVE
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heuristic, by Paul Eggert, to limit the cost to O(N**1.5 log N)
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at the price of producing suboptimal output for large inputs with
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/* Before including this file, you need to define:
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ELEMENT The element type of the vectors being compared.
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EQUAL A two-argument macro that tests two elements for
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OFFSET A signed integer type sufficient to hold the
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difference between two indices. Usually
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something like ssize_t.
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EXTRA_CONTEXT_FIELDS Declarations of fields for 'struct context'.
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NOTE_DELETE(ctxt, xoff) Record the removal of the object xvec[xoff].
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NOTE_INSERT(ctxt, yoff) Record the insertion of the object yvec[yoff].
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EARLY_ABORT(ctxt) (Optional) A boolean expression that triggers an
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early abort of the computation.
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USE_HEURISTIC (Optional) Define if you want to support the
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heuristic for large vectors.
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It is also possible to use this file with abstract arrays. In this case,
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xvec and yvec are not represented in memory. They only exist conceptually.
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In this case, the list of defines above is amended as follows:
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XVECREF_YVECREF_EQUAL(ctxt, xoff, yoff)
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A three-argument macro: References xvec[xoff] and
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yvec[yoff] and tests these elements for equality.
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Before including this file, you also need to include:
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/* Maximum value of type OFFSET. */
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((((OFFSET)1 << (sizeof (OFFSET) * CHAR_BIT - 2)) - 1) * 2 + 1)
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/* Default to no early abort. */
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# define EARLY_ABORT(ctxt) false
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/* Use this to suppress gcc's `...may be used before initialized' warnings.
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Beware: The Code argument must not contain commas. */
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# define IF_LINT(Code) Code
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# define IF_LINT(Code) /* empty */
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/* As above, but when Code must contain one comma. */
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# define IF_LINT2(Code1, Code2) Code1, Code2
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# define IF_LINT2(Code1, Code2) /* empty */
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* Context of comparison operation.
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/* Vectors being compared. */
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/* Vector, indexed by diagonal, containing 1 + the X coordinate of the point
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furthest along the given diagonal in the forward search of the edit
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/* Vector, indexed by diagonal, containing the X coordinate of the point
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furthest along the given diagonal in the backward search of the edit
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/* This corresponds to the diff -H flag. With this heuristic, for
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vectors with a constant small density of changes, the algorithm is
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linear in the vectors size. */
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/* Edit scripts longer than this are too expensive to compute. */
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OFFSET too_expensive;
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/* Snakes bigger than this are considered `big'. */
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#define SNAKE_LIMIT 20
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/* Midpoints of this partition. */
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/* True if low half will be analyzed minimally. */
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/* Likewise for high half. */
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/* Find the midpoint of the shortest edit script for a specified portion
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Scan from the beginnings of the vectors, and simultaneously from the ends,
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doing a breadth-first search through the space of edit-sequence.
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When the two searches meet, we have found the midpoint of the shortest
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If FIND_MINIMAL is true, find the minimal edit script regardless of
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expense. Otherwise, if the search is too expensive, use heuristics to
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stop the search and report a suboptimal answer.
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Set PART->(xmid,ymid) to the midpoint (XMID,YMID). The diagonal number
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XMID - YMID equals the number of inserted elements minus the number
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of deleted elements (counting only elements before the midpoint).
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Set PART->lo_minimal to true iff the minimal edit script for the
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left half of the partition is known; similarly for PART->hi_minimal.
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This function assumes that the first elements of the specified portions
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of the two vectors do not match, and likewise that the last elements do not
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match. The caller must trim matching elements from the beginning and end
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of the portions it is going to specify.
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If we return the "wrong" partitions, the worst this can do is cause
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suboptimal diff output. It cannot cause incorrect diff output. */
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diag (OFFSET xoff, OFFSET xlim, OFFSET yoff, OFFSET ylim, bool find_minimal,
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struct partition *part, struct context *ctxt)
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OFFSET *const fd = ctxt->fdiag; /* Give the compiler a chance. */
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OFFSET *const bd = ctxt->bdiag; /* Additional help for the compiler. */
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ELEMENT const *const xv = ctxt->xvec; /* Still more help for the compiler. */
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ELEMENT const *const yv = ctxt->yvec; /* And more and more . . . */
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#define XREF_YREF_EQUAL(x,y) EQUAL (xv[x], yv[y])
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#define XREF_YREF_EQUAL(x,y) XVECREF_YVECREF_EQUAL (ctxt, x, y)
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const OFFSET dmin = xoff - ylim; /* Minimum valid diagonal. */
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const OFFSET dmax = xlim - yoff; /* Maximum valid diagonal. */
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const OFFSET fmid = xoff - yoff; /* Center diagonal of top-down search. */
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const OFFSET bmid = xlim - ylim; /* Center diagonal of bottom-up search. */
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OFFSET fmax = fmid; /* Limits of top-down search. */
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OFFSET bmax = bmid; /* Limits of bottom-up search. */
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OFFSET c; /* Cost. */
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bool odd = (fmid - bmid) & 1; /* True if southeast corner is on an odd
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diagonal with respect to the northwest. */
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OFFSET d; /* Active diagonal. */
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bool big_snake = false;
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/* Extend the top-down search by an edit step in each diagonal. */
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for (d = fmax; d >= fmin; d -= 2)
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OFFSET tlo = fd[d - 1];
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OFFSET thi = fd[d + 1];
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OFFSET x0 = tlo < thi ? thi : tlo + 1;
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for (x = x0, y = x0 - d;
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x < xlim && y < ylim && XREF_YREF_EQUAL (x, y);
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if (x - x0 > SNAKE_LIMIT)
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if (odd && bmin <= d && d <= bmax && bd[d] <= x)
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part->lo_minimal = part->hi_minimal = true;
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/* Similarly extend the bottom-up search. */
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bd[--bmin - 1] = OFFSET_MAX;
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bd[++bmax + 1] = OFFSET_MAX;
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for (d = bmax; d >= bmin; d -= 2)
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OFFSET tlo = bd[d - 1];
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OFFSET thi = bd[d + 1];
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OFFSET x0 = tlo < thi ? tlo : thi - 1;
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for (x = x0, y = x0 - d;
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xoff < x && yoff < y && XREF_YREF_EQUAL (x - 1, y - 1);
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if (x0 - x > SNAKE_LIMIT)
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if (!odd && fmin <= d && d <= fmax && x <= fd[d])
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part->lo_minimal = part->hi_minimal = true;
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/* Heuristic: check occasionally for a diagonal that has made lots
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of progress compared with the edit distance. If we have any
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such, find the one that has made the most progress and return it
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as if it had succeeded.
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With this heuristic, for vectors with a constant small density
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of changes, the algorithm is linear in the vector size. */
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if (200 < c && big_snake && ctxt->heuristic)
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for (d = fmax; d >= fmin; d -= 2)
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OFFSET dd = d - fmid;
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OFFSET v = (x - xoff) * 2 - dd;
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if (v > 12 * (c + (dd < 0 ? -dd : dd)))
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&& xoff + SNAKE_LIMIT <= x && x < xlim
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&& yoff + SNAKE_LIMIT <= y && y < ylim)
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/* We have a good enough best diagonal; now insist
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that it end with a significant snake. */
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for (k = 1; XREF_YREF_EQUAL (x - k, y - k); k++)
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if (k == SNAKE_LIMIT)
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part->lo_minimal = true;
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part->hi_minimal = false;
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for (d = bmax; d >= bmin; d -= 2)
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OFFSET dd = d - bmid;
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OFFSET v = (xlim - x) * 2 + dd;
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if (v > 12 * (c + (dd < 0 ? -dd : dd)))
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&& xoff < x && x <= xlim - SNAKE_LIMIT
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&& yoff < y && y <= ylim - SNAKE_LIMIT)
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/* We have a good enough best diagonal; now insist
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that it end with a significant snake. */
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for (k = 0; XREF_YREF_EQUAL (x + k, y + k); k++)
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if (k == SNAKE_LIMIT - 1)
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part->lo_minimal = false;
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part->hi_minimal = true;
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#endif /* USE_HEURISTIC */
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/* Heuristic: if we've gone well beyond the call of duty, give up
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and report halfway between our best results so far. */
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if (c >= ctxt->too_expensive)
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OFFSET fxbest IF_LINT (= 0);
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OFFSET bxbest IF_LINT (= 0);
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/* Find forward diagonal that maximizes X + Y. */
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for (d = fmax; d >= fmin; d -= 2)
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OFFSET x = MIN (fd[d], xlim);
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/* Find backward diagonal that minimizes X + Y. */
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bxybest = OFFSET_MAX;
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for (d = bmax; d >= bmin; d -= 2)
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OFFSET x = MAX (xoff, bd[d]);
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/* Use the better of the two diagonals. */
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if ((xlim + ylim) - bxybest < fxybest - (xoff + yoff))
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part->ymid = fxybest - fxbest;
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part->lo_minimal = true;
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part->hi_minimal = false;
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part->ymid = bxybest - bxbest;
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part->lo_minimal = false;
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part->hi_minimal = true;
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#undef XREF_YREF_EQUAL
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/* Compare in detail contiguous subsequences of the two vectors
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which are known, as a whole, to match each other.
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The subsequence of vector 0 is [XOFF, XLIM) and likewise for vector 1.
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Note that XLIM, YLIM are exclusive bounds. All indices into the vectors
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If FIND_MINIMAL, find a minimal difference no matter how
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The results are recorded by invoking NOTE_DELETE and NOTE_INSERT.
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Return false if terminated normally, or true if terminated through early
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compareseq (OFFSET xoff, OFFSET xlim, OFFSET yoff, OFFSET ylim,
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bool find_minimal, struct context *ctxt)
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ELEMENT const *xv = ctxt->xvec; /* Help the compiler. */
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ELEMENT const *yv = ctxt->yvec;
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#define XREF_YREF_EQUAL(x,y) EQUAL (xv[x], yv[y])
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#define XREF_YREF_EQUAL(x,y) XVECREF_YVECREF_EQUAL (ctxt, x, y)
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/* Slide down the bottom initial diagonal. */
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while (xoff < xlim && yoff < ylim && XREF_YREF_EQUAL (xoff, yoff))
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/* Slide up the top initial diagonal. */
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while (xoff < xlim && yoff < ylim && XREF_YREF_EQUAL (xlim - 1, ylim - 1))
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/* Handle simple cases. */
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NOTE_INSERT (ctxt, yoff);
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if (EARLY_ABORT (ctxt))
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else if (yoff == ylim)
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NOTE_DELETE (ctxt, xoff);
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if (EARLY_ABORT (ctxt))
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struct partition part IF_LINT2 (= { .xmid = 0, .ymid = 0 });
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/* Find a point of correspondence in the middle of the vectors. */
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diag (xoff, xlim, yoff, ylim, find_minimal, &part, ctxt);
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/* Use the partitions to split this problem into subproblems. */
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if (compareseq (xoff, part.xmid, yoff, part.ymid, part.lo_minimal, ctxt))
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if (compareseq (part.xmid, xlim, part.ymid, ylim, part.hi_minimal, ctxt))
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#undef XREF_YREF_EQUAL
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#undef EXTRA_CONTEXT_FIELDS
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#undef XVECREF_YVECREF_EQUAL
added
removed
lib/diffseq.h
