/* The basic idea is to consider two vectors as similar if, when
   transforming the first vector into the second vector through a
   sequence of edits (inserts and deletes of one element each), this
   sequence is short - or equivalently, if the ordered list of
   elements that are untouched by these edits is long.  For a good
   introduction to the subject, read about the ``Levenshtein
   distance'' in Wikipedia.

   The basic algorithm is described in: ``An O(ND) Difference
   Algorithm and its Variations'', Eugene W. Myers, Algorithmica
   Vol. 1, 1986, pp. 251-266,
   \url{http://dx.doi.org/10.1007/BF01840446}.  See especially section
   4.2, which describes the variation used below.

   The basic algorithm was independently discovered as described in:
   ``Algorithms for Approximate String Matching'', Esko Ukkonen,
   Information and Control Vol. 64, 1985, pp. 100-118,
   \url{http://dx.doi.org/10.1016/S0019-9958(85)80046-2}.

   Unless the |find_minimal| flag is set, this code uses the
   |TOO_EXPENSIVE| heuristic, by Paul Eggert, to limit the cost to
   $O(N^1.5 \log N)$ at the price of producing suboptimal output for
   large inputs with many differences.  */

/* Before including this file, you need to define:
     |ELEMENT|                   The element type of the vectors being compared.
     |EQUAL|                     A two-argument macro that tests two elements for
                               equality.
     |OFFSET|                    A signed integer type sufficient to hold the
                               difference between two indices.  Usually
                               something like |ptrdiff_t|.
     |EXTRA_CONTEXT_FIELDS|    Declarations of fields for 'struct context'.
     |NOTE_DELETE(ctxt, xoff)| Record the removal of the object xvec[xoff].
     |NOTE_INSERT(ctxt, yoff)| Record the insertion of the object yvec[yoff].
     |EARLY_ABORT(ctxt)|       (Optional) A boolean expression that triggers an
                               early abort of the computation.
     |USE_HEURISTIC|          (Optional) Define if you want to support the
                               heuristic for large vectors.
   It is also possible to use this file with abstract arrays.  In this case,
   xvec and yvec are not represented in memory.  They only exist conceptually.
   In this case, the list of defines above is amended as follows:
     |ELEMENT|                 Undefined.
     |EQUAL|                   Undefined.
     |XVECREF_YVECREF_EQUAL(ctxt, xoff, yoff)|
                             A three-argument macro: References xvec[xoff] and
                             yvec[yoff] and tests these elements for equality.
   Before including this file, you also need to include:
     |#include <limits.h>
     #include <stdbool.h>|
 */

/* Maximum value of type |OFFSET|.  */
#define OFFSET_MAX \
  ((((OFFSET)1 << (sizeof (OFFSET) * CHAR_BIT - 2)) - 1) * 2 + 1)

/* Default to no early abort.  */
#ifndef EARLY_ABORT
# define EARLY_ABORT(ctxt) false
#endif

/* Use this to suppress gcc's ``...may be used before initialized''
   warnings.  Beware: The Code argument must not contain commas.  */
#ifndef IF_LINT
# if defined GCC_LINT || defined lint
#  define IF_LINT(Code) Code
# else
#  define IF_LINT(Code) /* empty */
# endif
#endif

/* As above, but when Code must contain one comma. */
#ifndef IF_LINT2
# if defined GCC_LINT || defined lint
#  define IF_LINT2(Code1, Code2) Code1, Code2
# else
#  define IF_LINT2(Code1, Code2) /* empty */
# endif
#endif

/*
 * Context of comparison operation.
 */
struct context {
#ifdef ELEMENT
    /* Vectors being compared.  */
    ELEMENT const *xvec;
    ELEMENT const *yvec;
#endif

    /* Extra fields.  */
    EXTRA_CONTEXT_FIELDS

    /* Vector, indexed by diagonal, containing 1 + the X coordinate of
       the point furthest along the given diagonal in the forward
       search of the edit matrix.  */
    OFFSET *fdiag;

    /* Vector, indexed by diagonal, containing the X coordinate of the
       point furthest along the given diagonal in the backward search
       of the edit matrix.  */
    OFFSET *bdiag;

#ifdef USE_HEURISTIC
    /* This corresponds to the |diff --speed-large-files| flag.  With
       this heuristic, for vectors with a constant small density of
       changes, the algorithm is linear in the vector size.  */
    bool heuristic;
#endif

    /* Edit scripts longer than this are too expensive to compute.  */
    OFFSET too_expensive;

    /* Snakes bigger than this are considered "big".  */
#define SNAKE_LIMIT 20
};

struct partition {
    /* Midpoints of this partition.  */
    OFFSET xmid;
    OFFSET ymid;

    /* True if low half will be analyzed minimally.  */
    bool lo_minimal;

    /* Likewise for high half.  */
    bool hi_minimal;
};


/* Find the midpoint of the shortest edit script for a specified
   portion of the two vectors.

   Scan from the beginnings of the vectors, and simultaneously from
   the ends, doing a breadth-first search through the space of
   edit-sequence.  When the two searches meet, we have found the
   midpoint of the shortest edit sequence.

   If |find_minimal| is true, find the minimal edit script regardless
   of expense.  Otherwise, if the search is too expensive, use
   heuristics to stop the search and report a suboptimal answer.

   Set |part->(xmid,ymid)| to the midpoint |(xmid,ymid)|.  The
   diagonal number |xmid - ymid| equals the number of inserted
   elements minus the number of deleted elements (counting only
   elements before the midpoint).

   Set |part->lo_minimal| to true iff the minimal edit script for the
   left half of the partition is known; similarly for
   |part->hi_minimal|.

   This function assumes that the first elements of the specified
   portions of the two vectors do not match, and likewise that the
   last elements do not match.  The caller must trim matching elements
   from the beginning and end of the portions it is going to specify.

   If we return the "wrong" partitions, the worst this can do is cause
   suboptimal diff output.  It cannot cause incorrect diff output.  */

static void
diag(OFFSET xoff, OFFSET xlim, OFFSET yoff, OFFSET ylim, bool find_minimal,
     struct partition *part, struct context *ctxt) {
    OFFSET *const fd = ctxt->fdiag;       /* Give the compiler a chance. */
    OFFSET *const bd = ctxt->bdiag;       /* Additional help for the compiler. */
#ifdef ELEMENT
    ELEMENT const *const xv = ctxt->xvec; /* Still more help for the compiler. */
    ELEMENT const *const yv = ctxt->yvec; /* And more and more . . . */
#define XREF_YREF_EQUAL(x, y)  EQUAL (xv[x], yv[y])
#else
#define XREF_YREF_EQUAL(x,y)  XVECREF_YVECREF_EQUAL (ctxt, x, y)
#endif
    const OFFSET dmin = xoff - ylim;      /* Minimum valid diagonal. */
    const OFFSET dmax = xlim - yoff;      /* Maximum valid diagonal. */
    const OFFSET fmid = xoff - yoff;      /* Center diagonal of top-down search. */
    const OFFSET bmid = xlim - ylim;      /* Center diagonal of bottom-up search. */
    OFFSET fmin = fmid;
    OFFSET fmax = fmid;           /* Limits of top-down search. */
    OFFSET bmin = bmid;
    OFFSET bmax = bmid;           /* Limits of bottom-up search. */
    OFFSET c;                     /* Cost. */
    bool odd = (fmid - bmid) & 1; /* True if southeast corner is on an odd
                                   diagonal with respect to the northwest. */

    fd[fmid] = xoff;
    bd[bmid] = xlim;

    for (c = 1;; ++c) {
        OFFSET d;                 /* Active diagonal. */
        bool big_snake = false;

        /* Extend the top-down search by an edit step in each diagonal. */
        if (fmin > dmin)
            fd[--fmin - 1] = -1;
        else
            ++fmin;
        if (fmax < dmax)
            fd[++fmax + 1] = -1;
        else
            --fmax;
        for (d = fmax; d >= fmin; d -= 2) {
            OFFSET x;
            OFFSET y;
            OFFSET tlo = fd[d - 1];
            OFFSET thi = fd[d + 1];
            OFFSET x0 = tlo < thi ? thi : tlo + 1;

            for (x = x0, y = x0 - d;
                 x < xlim && y < ylim && XREF_YREF_EQUAL (x, y);
                 x++, y++)
                continue;
            if (x - x0 > SNAKE_LIMIT)
                big_snake = true;
            fd[d] = x;
            if (odd && bmin <= d && d <= bmax && bd[d] <= x) {
                part->xmid = x;
                part->ymid = y;
                part->lo_minimal = part->hi_minimal = true;
                return;
            }
        }

        /* Similarly extend the bottom-up search.  */
        if (bmin > dmin)
            bd[--bmin - 1] = OFFSET_MAX;
        else
            ++bmin;
        if (bmax < dmax)
            bd[++bmax + 1] = OFFSET_MAX;
        else
            --bmax;
        for (d = bmax; d >= bmin; d -= 2) {
            OFFSET x;
            OFFSET y;
            OFFSET tlo = bd[d - 1];
            OFFSET thi = bd[d + 1];
            OFFSET x0 = tlo < thi ? tlo : thi - 1;

            for (x = x0, y = x0 - d;
                 xoff < x && yoff < y && XREF_YREF_EQUAL (x - 1, y - 1);
                 x--, y--)
                continue;
            if (x0 - x > SNAKE_LIMIT)
                big_snake = true;
            bd[d] = x;
            if (!odd && fmin <= d && d <= fmax && x <= fd[d]) {
                part->xmid = x;
                part->ymid = y;
                part->lo_minimal = part->hi_minimal = true;
                return;
            }
        }

        if (find_minimal)
            continue;

#ifdef USE_HEURISTIC
        /* Heuristic: check occasionally for a diagonal that has made
           lots of progress compared with the edit distance.  If we
           have any such, find the one that has made the most progress
           and return it as if it had succeeded.

           With this heuristic, for vectors with a constant small
           density of changes, the algorithm is linear in the vector
           size.  */

        if (200 < c && big_snake && ctxt->heuristic) {
            {
                OFFSET best = 0;

                for (d = fmax; d >= fmin; d -= 2) {
                    OFFSET dd = d - fmid;
                    OFFSET x = fd[d];
                    OFFSET y = x - d;
                    OFFSET v = (x - xoff) * 2 - dd;

                    if (v > 12 * (c + (dd < 0 ? -dd : dd))) {
                        if (v > best
                            && xoff + SNAKE_LIMIT <= x && x < xlim
                            && yoff + SNAKE_LIMIT <= y && y < ylim) {
                            /* We have a good enough best diagonal;
                               now insist that it end with a
                               significant snake.  */
                            int k;

                            for (k = 1; XREF_YREF_EQUAL (x - k, y - k); k++)
                                if (k == SNAKE_LIMIT) {
                                    best = v;
                                    part->xmid = x;
                                    part->ymid = y;
                                    break;
                                }
                        }
                    }
                }
                if (best > 0) {
                    part->lo_minimal = true;
                    part->hi_minimal = false;
                    return;
                }
            }

            {
                OFFSET best = 0;

                for (d = bmax; d >= bmin; d -= 2) {
                    OFFSET dd = d - bmid;
                    OFFSET x = bd[d];
                    OFFSET y = x - d;
                    OFFSET v = (xlim - x) * 2 + dd;

                    if (v > 12 * (c + (dd < 0 ? -dd : dd))) {
                        if (v > best
                            && xoff < x && x <= xlim - SNAKE_LIMIT
                            && yoff < y && y <= ylim - SNAKE_LIMIT) {
                            /* We have a good enough best diagonal;
                               now insist that it end with a
                               significant snake.  */
                            int k;

                            for (k = 0; XREF_YREF_EQUAL (x + k, y + k); k++)
                                if (k == SNAKE_LIMIT - 1) {
                                    best = v;
                                    part->xmid = x;
                                    part->ymid = y;
                                    break;
                                }
                        }
                    }
                }
                if (best > 0) {
                    part->lo_minimal = false;
                    part->hi_minimal = true;
                    return;
                }
            }
        }
#endif

        /* Heuristic: if we've gone well beyond the call of duty, give
           up and report halfway between our best results so far.  */
        if (c >= ctxt->too_expensive) {
            OFFSET fxybest;
            OFFSET fxbest IF_LINT (= 0);
            OFFSET bxybest;
            OFFSET bxbest IF_LINT (= 0);

            /* Find forward diagonal that maximizes |X + Y|.  */
            fxybest = -1;
            for (d = fmax; d >= fmin; d -= 2) {
                OFFSET x = MIN (fd[d], xlim);
                OFFSET y = x - d;
                if (ylim < y) {
                    x = ylim + d;
                    y = ylim;
                }
                if (fxybest < x + y) {
                    fxybest = x + y;
                    fxbest = x;
                }
            }

            /* Find backward diagonal that minimizes |X + Y|.  */
            bxybest = OFFSET_MAX;
            for (d = bmax; d >= bmin; d -= 2) {
                OFFSET x = MAX (xoff, bd[d]);
                OFFSET y = x - d;
                if (y < yoff) {
                    x = yoff + d;
                    y = yoff;
                }
                if (x + y < bxybest) {
                    bxybest = x + y;
                    bxbest = x;
                }
            }

            /* Use the better of the two diagonals.  */
            if ((xlim + ylim) - bxybest < fxybest - (xoff + yoff)) {
                part->xmid = fxbest;
                part->ymid = fxybest - fxbest;
                part->lo_minimal = true;
                part->hi_minimal = false;
            } else {
                part->xmid = bxbest;
                part->ymid = bxybest - bxbest;
                part->lo_minimal = false;
                part->hi_minimal = true;
            }
            return;
        }
    }
#undef XREF_YREF_EQUAL
}


/* Compare in detail contiguous subsequences of the two vectors which
   are known, as a whole, to match each other.

   The subsequence of vector 0 is |[xoff, xlim)| and likewise for
   vector 1.

   Note that |xlim, ylim| are exclusive bounds.  All indices into the
   vectors are origin-0.

   If |find_minimal|, find a minimal difference no matter how
   expensive it is.

   The results are recorded by invoking |note_delete| and
   |note_insert|.

   Return false if terminated normally, or true if terminated through
   early abort.  */

static bool
compareseq(OFFSET xoff, OFFSET xlim, OFFSET yoff, OFFSET ylim,
           bool find_minimal, struct context *ctxt) {
#ifdef ELEMENT
    ELEMENT const *xv = ctxt->xvec; /* Help the compiler.  */
    ELEMENT const *yv = ctxt->yvec;
#define XREF_YREF_EQUAL(x, y)  EQUAL (xv[x], yv[y])
#else
#define XREF_YREF_EQUAL(x,y)  XVECREF_YVECREF_EQUAL (ctxt, x, y)
#endif

    /* Slide down the bottom initial diagonal.  */
    while (xoff < xlim && yoff < ylim && XREF_YREF_EQUAL (xoff, yoff)) {
        xoff++;
        yoff++;
    }

    /* Slide up the top initial diagonal. */
    while (xoff < xlim && yoff < ylim && XREF_YREF_EQUAL (xlim - 1, ylim - 1)) {
        xlim--;
        ylim--;
    }

    /* Handle simple cases. */
    if (xoff == xlim)
        while (yoff < ylim) {
            NOTE_INSERT (ctxt, yoff);
            if (EARLY_ABORT (ctxt))
                return true;
            yoff++;
        }
    else if (yoff == ylim)
        while (xoff < xlim) {
            NOTE_DELETE (ctxt, xoff);
            if (EARLY_ABORT (ctxt))
                return true;
            xoff++;
        }
    else {
        struct partition part IF_LINT2 (= { .xmid = 0, .ymid = 0 });

        /* Find a point of correspondence in the middle of the vectors.  */
        diag(xoff, xlim, yoff, ylim, find_minimal, &part, ctxt);

        /* Use the partitions to split this problem into subproblems.  */
        if (compareseq(xoff, part.xmid, yoff, part.ymid, part.lo_minimal, ctxt))
            return true;
        if (compareseq(part.xmid, xlim, part.ymid, ylim, part.hi_minimal, ctxt))
            return true;
    }

    return false;
#undef XREF_YREF_EQUAL
}

#undef ELEMENT
#undef EQUAL
#undef OFFSET
#undef EXTRA_CONTEXT_FIELDS
#undef NOTE_DELETE
#undef NOTE_INSERT
#undef EARLY_ABORT
#undef USE_HEURISTIC
#undef XVECREF_YVECREF_EQUAL
#undef OFFSET_MAX