text: /* Analyze differences between two vectors.
  
     Copyright (C) 1988-1989, 1992-1995, 2001-2004, 2006-2016 Free Software
     Foundation, Inc.
  
     This program is free software: you can redistribute it and/or modify
     it under the terms of the GNU General Public License as published by
     the Free Software Foundation; either version 3 of the License, or
     (at your option) any later version.
  
     This program is distributed in the hope that it will be useful,
     but WITHOUT ANY WARRANTY; without even the implied warranty of
     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
     GNU General Public License for more details.
  
     You should have received a copy of the GNU General Public License
     along with this program.  If not, see <http://www.gnu.org/licenses/>.  */
  
  
  /* 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,
     <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,
     <http://dx.doi.org/10.1016/S0019-9958(85)80046-2>.  */
  
  /* 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>
       #include "minmax.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
  # ifdef 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
  # ifdef 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
  
    /* Snakes bigger than this are considered "big".  */
    #define SNAKE_LIMIT 20
  };
  
  struct partition
  {
    /* Midpoints of this partition.  */
    OFFSET xmid;
    OFFSET ymid;
  };
  
  
  /* 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.
  
     Set *PART 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).
  
     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,
        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 _GL_UNUSED = 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;
                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;
                return;
              }
          }
  
  #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)
  	      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)
  	      return;
            }
          }
  #endif /* USE_HEURISTIC */
      }
    #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.
  
     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,
              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, &part, ctxt);
  
        /* Use the partitions to split this problem into subproblems.  */
        if (compareseq (xoff, part.xmid, yoff, part.ymid, ctxt))
          return true;
        if (compareseq (part.xmid, xlim, part.ymid, ylim, 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
  