diffseq.h 17 KB
Newer Older
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525
/* Analyze differences between two vectors.

   Copyright (C) 1988-1989, 1992-1995, 2001-2004, 2006-2017 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>.

   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>
     #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
# 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 /* USE_HEURISTIC */

      /* 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