Merge Wikidiff3 into DiffEngine

Change-Id: Ib4d083a5200824e4d032de6921c375e455e77fb2

1 files changed, 815 insertions, 0 deletions

diff --git a/includes/diff/DiffEngine.php b/includes/diff/DiffEngine.php
new file mode 100644
index 000000000000..75e8791d5b22
--- /dev/null
+++ b/includes/diff/DiffEngine.php
@@ -0,0 +1,815 @@
+<?php
+/**
+ * New version of the difference engine
+ *
+ * Copyright © 2008 Guy Van den Broeck <guy@guyvdb.eu>
+ *
+ * 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 2 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, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ * http://www.gnu.org/copyleft/gpl.html
+ *
+ * @file
+ * @ingroup DifferenceEngine
+ */
+
+/**
+ * This diff implementation is mainly lifted from the LCS algorithm of the Eclipse project which
+ * in turn is based on Myers' "An O(ND) difference algorithm and its variations"
+ * (http://citeseer.ist.psu.edu/myers86ond.html) with range compression (see Wu et al.'s
+ * "An O(NP) Sequence Comparison Algorithm").
+ *
+ * This implementation supports an upper bound on the execution time.
+ *
+ * Some ideas (and a bit of code) are from analyze.c, from GNU
+ * diffutils-2.7, which can be found at:
+ *     ftp://gnudist.gnu.org/pub/gnu/diffutils/diffutils-2.7.tar.gz
+ *
+ * Complexity: O((M + N)D) worst case time, O(M + N + D^2) expected time, O(M + N) space
+ *
+ * @author Guy Van den Broeck, Geoffrey T. Dairiki, Tim Starling
+ * @ingroup DifferenceEngine
+ */
+class DiffEngine {
+
+	// Input variables
+	private $from;
+	private $to;
+	private $m;
+	private $n;
+
+	private $tooLong;
+	private $powLimit;
+
+	// State variables
+	private $maxDifferences;
+	private $lcsLengthCorrectedForHeuristic = false;
+
+	// Output variables
+	public $length;
+	public $removed;
+	public $added;
+	public $heuristicUsed;
+
+	function __construct( $tooLong = 2000000, $powLimit = 1.45 ) {
+		$this->tooLong = $tooLong;
+		$this->powLimit = $powLimit;
+	}
+
+	/**
+	 * @param string[] $from_lines
+	 * @param string[] $to_lines
+	 *
+	 * @return DiffOp[]
+	 */
+	public function diff( $from_lines, $to_lines ) {
+
+		// Diff and store locally
+		$this->diffInternal( $from_lines, $to_lines );
+
+		// Merge edits when possible
+		$this->shiftBoundaries( $from_lines, $this->removed, $this->added );
+		$this->shiftBoundaries( $to_lines, $this->added, $this->removed );
+
+		// Compute the edit operations.
+		$n_from = count( $from_lines );
+		$n_to = count( $to_lines );
+
+		$edits = [];
+		$xi = $yi = 0;
+		while ( $xi < $n_from || $yi < $n_to ) {
+			assert( $yi < $n_to || $this->removed[$xi] );
+			assert( $xi < $n_from || $this->added[$yi] );
+
+			// Skip matching "snake".
+			$copy = [];
+			while ( $xi < $n_from && $yi < $n_to
+					&& !$this->removed[$xi] && !$this->added[$yi]
+			) {
+				$copy[] = $from_lines[$xi++];
+				++$yi;
+			}
+			if ( $copy ) {
+				$edits[] = new DiffOpCopy( $copy );
+			}
+
+			// Find deletes & adds.
+			$delete = [];
+			while ( $xi < $n_from && $this->removed[$xi] ) {
+				$delete[] = $from_lines[$xi++];
+			}
+
+			$add = [];
+			while ( $yi < $n_to && $this->added[$yi] ) {
+				$add[] = $to_lines[$yi++];
+			}
+
+			if ( $delete && $add ) {
+				$edits[] = new DiffOpChange( $delete, $add );
+			} elseif ( $delete ) {
+				$edits[] = new DiffOpDelete( $delete );
+			} elseif ( $add ) {
+				$edits[] = new DiffOpAdd( $add );
+			}
+		}
+
+		return $edits;
+	}
+
+	/**
+	 * Adjust inserts/deletes of identical lines to join changes
+	 * as much as possible.
+	 *
+	 * We do something when a run of changed lines include a
+	 * line at one end and has an excluded, identical line at the other.
+	 * We are free to choose which identical line is included.
+	 * `compareseq' usually chooses the one at the beginning,
+	 * but usually it is cleaner to consider the following identical line
+	 * to be the "change".
+	 *
+	 * This is extracted verbatim from analyze.c (GNU diffutils-2.7).
+	 */
+	private function shiftBoundaries( $lines, &$changed, $other_changed ) {
+		$i = 0;
+		$j = 0;
+
+		assert( count( $lines ) == count( $changed ) );
+		$len = count( $lines );
+		$other_len = count( $other_changed );
+
+		while ( 1 ) {
+			/*
+			 * Scan forwards to find beginning of another run of changes.
+			 * Also keep track of the corresponding point in the other file.
+			 *
+			 * Throughout this code, $i and $j are adjusted together so that
+			 * the first $i elements of $changed and the first $j elements
+			 * of $other_changed both contain the same number of zeros
+			 * (unchanged lines).
+			 * Furthermore, $j is always kept so that $j == $other_len or
+			 * $other_changed[$j] == false.
+			 */
+			while ( $j < $other_len && $other_changed[$j] ) {
+				$j++;
+			}
+
+			while ( $i < $len && !$changed[$i] ) {
+				assert( $j < $other_len && ! $other_changed[$j] );
+				$i++;
+				$j++;
+				while ( $j < $other_len && $other_changed[$j] ) {
+					$j++;
+				}
+			}
+
+			if ( $i == $len ) {
+				break;
+			}
+
+			$start = $i;
+
+			// Find the end of this run of changes.
+			while ( ++$i < $len && $changed[$i] ) {
+				continue;
+			}
+
+			do {
+				/*
+				 * Record the length of this run of changes, so that
+				 * we can later determine whether the run has grown.
+				 */
+				$runlength = $i - $start;
+
+				/*
+				 * Move the changed region back, so long as the
+				 * previous unchanged line matches the last changed one.
+				 * This merges with previous changed regions.
+				 */
+				while ( $start > 0 && $lines[$start - 1] == $lines[$i - 1] ) {
+					$changed[--$start] = 1;
+					$changed[--$i] = false;
+					while ( $start > 0 && $changed[$start - 1] ) {
+						$start--;
+					}
+					assert( $j > 0 );
+					while ( $other_changed[--$j] ) {
+						continue;
+					}
+					assert( $j >= 0 && !$other_changed[$j] );
+				}
+
+				/*
+				 * Set CORRESPONDING to the end of the changed run, at the last
+				 * point where it corresponds to a changed run in the other file.
+				 * CORRESPONDING == LEN means no such point has been found.
+				 */
+				$corresponding = $j < $other_len ? $i : $len;
+
+				/*
+				 * Move the changed region forward, so long as the
+				 * first changed line matches the following unchanged one.
+				 * This merges with following changed regions.
+				 * Do this second, so that if there are no merges,
+				 * the changed region is moved forward as far as possible.
+				 */
+				while ( $i < $len && $lines[$start] == $lines[$i] ) {
+					$changed[$start++] = false;
+					$changed[$i++] = 1;
+					while ( $i < $len && $changed[$i] ) {
+						$i++;
+					}
+
+					assert( $j < $other_len && ! $other_changed[$j] );
+					$j++;
+					if ( $j < $other_len && $other_changed[$j] ) {
+						$corresponding = $i;
+						while ( $j < $other_len && $other_changed[$j] ) {
+							$j++;
+						}
+					}
+				}
+			} while ( $runlength != $i - $start );
+
+			/*
+			 * If possible, move the fully-merged run of changes
+			 * back to a corresponding run in the other file.
+			 */
+			while ( $corresponding < $i ) {
+				$changed[--$start] = 1;
+				$changed[--$i] = 0;
+				assert( $j > 0 );
+				while ( $other_changed[--$j] ) {
+					continue;
+				}
+				assert( $j >= 0 && !$other_changed[$j] );
+			}
+		}
+	}
+
+	protected function diffInternal( /*array*/ $from, /*array*/ $to ) {
+		// remember initial lengths
+		$m = count( $from );
+		$n = count( $to );
+
+		$this->heuristicUsed = false;
+
+		// output
+		$removed = $m > 0 ? array_fill( 0, $m, true ) : [];
+		$added = $n > 0 ? array_fill( 0, $n, true ) : [];
+
+		// reduce the complexity for the next step (intentionally done twice)
+		// remove common tokens at the start
+		$i = 0;
+		while ( $i < $m && $i < $n && $from[$i] === $to[$i] ) {
+			$removed[$i] = $added[$i] = false;
+			unset( $from[$i], $to[$i] );
+			++$i;
+		}
+
+		// remove common tokens at the end
+		$j = 1;
+		while ( $i + $j <= $m && $i + $j <= $n && $from[$m - $j] === $to[$n - $j] ) {
+			$removed[$m - $j] = $added[$n - $j] = false;
+			unset( $from[$m - $j], $to[$n - $j] );
+			++$j;
+		}
+
+		$this->from = $newFromIndex = $this->to = $newToIndex = [];
+
+		// remove tokens not in both sequences
+		$shared = [];
+		foreach ( $from as $key ) {
+			$shared[$key] = false;
+		}
+
+		foreach ( $to as $index => &$el ) {
+			if ( array_key_exists( $el, $shared ) ) {
+				// keep it
+				$this->to[] = $el;
+				$shared[$el] = true;
+				$newToIndex[] = $index;
+			}
+		}
+		foreach ( $from as $index => &$el ) {
+			if ( $shared[$el] ) {
+				// keep it
+				$this->from[] = $el;
+				$newFromIndex[] = $index;
+			}
+		}
+
+		unset( $shared, $from, $to );
+
+		$this->m = count( $this->from );
+		$this->n = count( $this->to );
+
+		$this->removed = $this->m > 0 ? array_fill( 0, $this->m, true ) : [];
+		$this->added = $this->n > 0 ? array_fill( 0, $this->n, true ) : [];
+
+		if ( $this->m == 0 || $this->n == 0 ) {
+			$this->length = 0;
+		} else {
+			$this->maxDifferences = ceil( ( $this->m + $this->n ) / 2.0 );
+			if ( $this->m * $this->n > $this->tooLong ) {
+				// limit complexity to D^POW_LIMIT for long sequences
+				$this->maxDifferences = floor( pow( $this->maxDifferences, $this->powLimit - 1.0 ) );
+				wfDebug( "Limiting max number of differences to $this->maxDifferences\n" );
+			}
+
+			/*
+			 * The common prefixes and suffixes are always part of some LCS, include
+			 * them now to reduce our search space
+			 */
+			$max = min( $this->m, $this->n );
+			for ( $forwardBound = 0; $forwardBound < $max
+				&& $this->from[$forwardBound] === $this->to[$forwardBound];
+				++$forwardBound
+			) {
+				$this->removed[$forwardBound] = $this->added[$forwardBound] = false;
+			}
+
+			$backBoundL1 = $this->m - 1;
+			$backBoundL2 = $this->n - 1;
+
+			while ( $backBoundL1 >= $forwardBound && $backBoundL2 >= $forwardBound
+				&& $this->from[$backBoundL1] === $this->to[$backBoundL2]
+			) {
+				$this->removed[$backBoundL1--] = $this->added[$backBoundL2--] = false;
+			}
+
+			$temp = array_fill( 0, $this->m + $this->n + 1, 0 );
+			$V = [ $temp, $temp ];
+			$snake = [ 0, 0, 0 ];
+
+			$this->length = $forwardBound + $this->m - $backBoundL1 - 1
+				+ $this->lcs_rec(
+					$forwardBound,
+					$backBoundL1,
+					$forwardBound,
+					$backBoundL2,
+					$V,
+					$snake
+			);
+		}
+
+		$this->m = $m;
+		$this->n = $n;
+
+		$this->length += $i + $j - 1;
+
+		foreach ( $this->removed as $key => &$removed_elem ) {
+			if ( !$removed_elem ) {
+				$removed[$newFromIndex[$key]] = false;
+			}
+		}
+		foreach ( $this->added as $key => &$added_elem ) {
+			if ( !$added_elem ) {
+				$added[$newToIndex[$key]] = false;
+			}
+		}
+		$this->removed = $removed;
+		$this->added = $added;
+	}
+
+	function diff_range( $from_lines, $to_lines ) {
+		// Diff and store locally
+		$this->diff( $from_lines, $to_lines );
+		unset( $from_lines, $to_lines );
+
+		$ranges = [];
+		$xi = $yi = 0;
+		while ( $xi < $this->m || $yi < $this->n ) {
+			// Matching "snake".
+			while ( $xi < $this->m && $yi < $this->n
+				&& !$this->removed[$xi]
+				&& !$this->added[$yi]
+			) {
+				++$xi;
+				++$yi;
+			}
+			// Find deletes & adds.
+			$xstart = $xi;
+			while ( $xi < $this->m && $this->removed[$xi] ) {
+				++$xi;
+			}
+
+			$ystart = $yi;
+			while ( $yi < $this->n && $this->added[$yi] ) {
+				++$yi;
+			}
+
+			if ( $xi > $xstart || $yi > $ystart ) {
+				$ranges[] = new RangeDifference( $xstart, $xi, $ystart, $yi );
+			}
+		}
+
+		return $ranges;
+	}
+
+	private function lcs_rec( $bottoml1, $topl1, $bottoml2, $topl2, &$V, &$snake ) {
+		// check that both sequences are non-empty
+		if ( $bottoml1 > $topl1 || $bottoml2 > $topl2 ) {
+			return 0;
+		}
+
+		$d = $this->find_middle_snake( $bottoml1, $topl1, $bottoml2,
+			$topl2, $V, $snake );
+
+		// need to store these so we don't lose them when they're
+		// overwritten by the recursion
+		$len = $snake[2];
+		$startx = $snake[0];
+		$starty = $snake[1];
+
+		// the middle snake is part of the LCS, store it
+		for ( $i = 0; $i < $len; ++$i ) {
+			$this->removed[$startx + $i] = $this->added[$starty + $i] = false;
+		}
+
+		if ( $d > 1 ) {
+			return $len
+			+ $this->lcs_rec( $bottoml1, $startx - 1, $bottoml2,
+				$starty - 1, $V, $snake )
+			+ $this->lcs_rec( $startx + $len, $topl1, $starty + $len,
+				$topl2, $V, $snake );
+		} elseif ( $d == 1 ) {
+			/*
+			 * In this case the sequences differ by exactly 1 line. We have
+			 * already saved all the lines after the difference in the for loop
+			 * above, now we need to save all the lines before the difference.
+			 */
+			$max = min( $startx - $bottoml1, $starty - $bottoml2 );
+			for ( $i = 0; $i < $max; ++$i ) {
+				$this->removed[$bottoml1 + $i] =
+					$this->added[$bottoml2 + $i] = false;
+			}
+
+			return $max + $len;
+		}
+
+		return $len;
+	}
+
+	private function find_middle_snake( $bottoml1, $topl1, $bottoml2, $topl2, &$V, &$snake ) {
+		$from = &$this->from;
+		$to = &$this->to;
+		$V0 = &$V[0];
+		$V1 = &$V[1];
+		$snake0 = &$snake[0];
+		$snake1 = &$snake[1];
+		$snake2 = &$snake[2];
+		$bottoml1_min_1 = $bottoml1 - 1;
+		$bottoml2_min_1 = $bottoml2 - 1;
+		$N = $topl1 - $bottoml1_min_1;
+		$M = $topl2 - $bottoml2_min_1;
+		$delta = $N - $M;
+		$maxabsx = $N + $bottoml1;
+		$maxabsy = $M + $bottoml2;
+		$limit = min( $this->maxDifferences, ceil( ( $N + $M ) / 2 ) );
+
+		// value_to_add_forward: a 0 or 1 that we add to the start
+		// offset to make it odd/even
+		if ( ( $M & 1 ) == 1 ) {
+			$value_to_add_forward = 1;
+		} else {
+			$value_to_add_forward = 0;
+		}
+
+		if ( ( $N & 1 ) == 1 ) {
+			$value_to_add_backward = 1;
+		} else {
+			$value_to_add_backward = 0;
+		}
+
+		$start_forward = -$M;
+		$end_forward = $N;
+		$start_backward = -$N;
+		$end_backward = $M;
+
+		$limit_min_1 = $limit - 1;
+		$limit_plus_1 = $limit + 1;
+
+		$V0[$limit_plus_1] = 0;
+		$V1[$limit_min_1] = $N;
+		$limit = min( $this->maxDifferences, ceil( ( $N + $M ) / 2 ) );
+
+		if ( ( $delta & 1 ) == 1 ) {
+			for ( $d = 0; $d <= $limit; ++$d ) {
+				$start_diag = max( $value_to_add_forward + $start_forward, -$d );
+				$end_diag = min( $end_forward, $d );
+				$value_to_add_forward = 1 - $value_to_add_forward;
+
+				// compute forward furthest reaching paths
+				for ( $k = $start_diag; $k <= $end_diag; $k += 2 ) {
+					if ( $k == -$d || ( $k < $d
+							&& $V0[$limit_min_1 + $k] < $V0[$limit_plus_1 + $k] )
+					) {
+						$x = $V0[$limit_plus_1 + $k];
+					} else {
+						$x = $V0[$limit_min_1 + $k] + 1;
+					}
+
+					$absx = $snake0 = $x + $bottoml1;
+					$absy = $snake1 = $x - $k + $bottoml2;
+
+					while ( $absx < $maxabsx && $absy < $maxabsy && $from[$absx] === $to[$absy] ) {
+						++$absx;
+						++$absy;
+					}
+					$x = $absx - $bottoml1;
+
+					$snake2 = $absx - $snake0;
+					$V0[$limit + $k] = $x;
+					if ( $k >= $delta - $d + 1 && $k <= $delta + $d - 1
+						&& $x >= $V1[$limit + $k - $delta]
+					) {
+						return 2 * $d - 1;
+					}
+
+					// check to see if we can cut down the diagonal range
+					if ( $x >= $N && $end_forward > $k - 1 ) {
+						$end_forward = $k - 1;
+					} elseif ( $absy - $bottoml2 >= $M ) {
+						$start_forward = $k + 1;
+						$value_to_add_forward = 0;
+					}
+				}
+
+				$start_diag = max( $value_to_add_backward + $start_backward, -$d );
+				$end_diag = min( $end_backward, $d );
+				$value_to_add_backward = 1 - $value_to_add_backward;
+
+				// compute backward furthest reaching paths
+				for ( $k = $start_diag; $k <= $end_diag; $k += 2 ) {
+					if ( $k == $d
+						|| ( $k != -$d && $V1[$limit_min_1 + $k] < $V1[$limit_plus_1 + $k] )
+					) {
+						$x = $V1[$limit_min_1 + $k];
+					} else {
+						$x = $V1[$limit_plus_1 + $k] - 1;
+					}
+
+					$y = $x - $k - $delta;
+
+					$snake2 = 0;
+					while ( $x > 0 && $y > 0
+						&& $from[$x + $bottoml1_min_1] === $to[$y + $bottoml2_min_1]
+					) {
+						--$x;
+						--$y;
+						++$snake2;
+					}
+					$V1[$limit + $k] = $x;
+
+					// check to see if we can cut down our diagonal range
+					if ( $x <= 0 ) {
+						$start_backward = $k + 1;
+						$value_to_add_backward = 0;
+					} elseif ( $y <= 0 && $end_backward > $k - 1 ) {
+						$end_backward = $k - 1;
+					}
+				}
+			}
+		} else {
+			for ( $d = 0; $d <= $limit; ++$d ) {
+				$start_diag = max( $value_to_add_forward + $start_forward, -$d );
+				$end_diag = min( $end_forward, $d );
+				$value_to_add_forward = 1 - $value_to_add_forward;
+
+				// compute forward furthest reaching paths
+				for ( $k = $start_diag; $k <= $end_diag; $k += 2 ) {
+					if ( $k == -$d
+						|| ( $k < $d && $V0[$limit_min_1 + $k] < $V0[$limit_plus_1 + $k] )
+					) {
+						$x = $V0[$limit_plus_1 + $k];
+					} else {
+						$x = $V0[$limit_min_1 + $k] + 1;
+					}
+
+					$absx = $snake0 = $x + $bottoml1;
+					$absy = $snake1 = $x - $k + $bottoml2;
+
+					while ( $absx < $maxabsx && $absy < $maxabsy && $from[$absx] === $to[$absy] ) {
+						++$absx;
+						++$absy;
+					}
+					$x = $absx - $bottoml1;
+					$snake2 = $absx - $snake0;
+					$V0[$limit + $k] = $x;
+
+					// check to see if we can cut down the diagonal range
+					if ( $x >= $N && $end_forward > $k - 1 ) {
+						$end_forward = $k - 1;
+					} elseif ( $absy - $bottoml2 >= $M ) {
+						$start_forward = $k + 1;
+						$value_to_add_forward = 0;
+					}
+				}
+
+				$start_diag = max( $value_to_add_backward + $start_backward, -$d );
+				$end_diag = min( $end_backward, $d );
+				$value_to_add_backward = 1 - $value_to_add_backward;
+
+				// compute backward furthest reaching paths
+				for ( $k = $start_diag; $k <= $end_diag; $k += 2 ) {
+					if ( $k == $d
+						|| ( $k != -$d && $V1[$limit_min_1 + $k] < $V1[$limit_plus_1 + $k] )
+					) {
+						$x = $V1[$limit_min_1 + $k];
+					} else {
+						$x = $V1[$limit_plus_1 + $k] - 1;
+					}
+
+					$y = $x - $k - $delta;
+
+					$snake2 = 0;
+					while ( $x > 0 && $y > 0
+						&& $from[$x + $bottoml1_min_1] === $to[$y + $bottoml2_min_1]
+					) {
+						--$x;
+						--$y;
+						++$snake2;
+					}
+					$V1[$limit + $k] = $x;
+
+					if ( $k >= -$delta - $d && $k <= $d - $delta
+						&& $x <= $V0[$limit + $k + $delta]
+					) {
+						$snake0 = $bottoml1 + $x;
+						$snake1 = $bottoml2 + $y;
+
+						return 2 * $d;
+					}
+
+					// check to see if we can cut down our diagonal range
+					if ( $x <= 0 ) {
+						$start_backward = $k + 1;
+						$value_to_add_backward = 0;
+					} elseif ( $y <= 0 && $end_backward > $k - 1 ) {
+						$end_backward = $k - 1;
+					}
+				}
+			}
+		}
+		/*
+		 * computing the true LCS is too expensive, instead find the diagonal
+		 * with the most progress and pretend a midle snake of length 0 occurs
+		 * there.
+		 */
+
+		$most_progress = self::findMostProgress( $M, $N, $limit, $V );
+
+		$snake0 = $bottoml1 + $most_progress[0];
+		$snake1 = $bottoml2 + $most_progress[1];
+		$snake2 = 0;
+		wfDebug( "Computing the LCS is too expensive. Using a heuristic.\n" );
+		$this->heuristicUsed = true;
+
+		return 5; /*
+		* HACK: since we didn't really finish the LCS computation
+		* we don't really know the length of the SES. We don't do
+		* anything with the result anyway, unless it's <=1. We know
+		* for a fact SES > 1 so 5 is as good a number as any to
+		* return here
+		*/
+	}
+
+	private static function findMostProgress( $M, $N, $limit, $V ) {
+		$delta = $N - $M;
+
+		if ( ( $M & 1 ) == ( $limit & 1 ) ) {
+			$forward_start_diag = max( -$M, -$limit );
+		} else {
+			$forward_start_diag = max( 1 - $M, -$limit );
+		}
+
+		$forward_end_diag = min( $N, $limit );
+
+		if ( ( $N & 1 ) == ( $limit & 1 ) ) {
+			$backward_start_diag = max( -$N, -$limit );
+		} else {
+			$backward_start_diag = max( 1 - $N, -$limit );
+		}
+
+		$backward_end_diag = -min( $M, $limit );
+
+		$temp = [ 0, 0, 0 ];
+
+		$max_progress = array_fill( 0, ceil( max( $forward_end_diag - $forward_start_diag,
+				$backward_end_diag - $backward_start_diag ) / 2 ), $temp );
+		$num_progress = 0; // the 1st entry is current, it is initialized
+		// with 0s
+
+		// first search the forward diagonals
+		for ( $k = $forward_start_diag; $k <= $forward_end_diag; $k += 2 ) {
+			$x = $V[0][$limit + $k];
+			$y = $x - $k;
+			if ( $x > $N || $y > $M ) {
+				continue;
+			}
+
+			$progress = $x + $y;
+			if ( $progress > $max_progress[0][2] ) {
+				$num_progress = 0;
+				$max_progress[0][0] = $x;
+				$max_progress[0][1] = $y;
+				$max_progress[0][2] = $progress;
+			} elseif ( $progress == $max_progress[0][2] ) {
+				++$num_progress;
+				$max_progress[$num_progress][0] = $x;
+				$max_progress[$num_progress][1] = $y;
+				$max_progress[$num_progress][2] = $progress;
+			}
+		}
+
+		$max_progress_forward = true; // initially the maximum
+		// progress is in the forward
+		// direction
+
+		// now search the backward diagonals
+		for ( $k = $backward_start_diag; $k <= $backward_end_diag; $k += 2 ) {
+			$x = $V[1][$limit + $k];
+			$y = $x - $k - $delta;
+			if ( $x < 0 || $y < 0 ) {
+				continue;
+			}
+
+			$progress = $N - $x + $M - $y;
+			if ( $progress > $max_progress[0][2] ) {
+				$num_progress = 0;
+				$max_progress_forward = false;
+				$max_progress[0][0] = $x;
+				$max_progress[0][1] = $y;
+				$max_progress[0][2] = $progress;
+			} elseif ( $progress == $max_progress[0][2] && !$max_progress_forward ) {
+				++$num_progress;
+				$max_progress[$num_progress][0] = $x;
+				$max_progress[$num_progress][1] = $y;
+				$max_progress[$num_progress][2] = $progress;
+			}
+		}
+
+		// return the middle diagonal with maximal progress.
+		return $max_progress[(int)floor( $num_progress / 2 )];
+	}
+
+	/**
+	 * @return mixed
+	 */
+	public function getLcsLength() {
+		if ( $this->heuristicUsed && !$this->lcsLengthCorrectedForHeuristic ) {
+			$this->lcsLengthCorrectedForHeuristic = true;
+			$this->length = $this->m - array_sum( $this->added );
+		}
+
+		return $this->length;
+	}
+
+}
+
+/**
+ * Alternative representation of a set of changes, by the index
+ * ranges that are changed.
+ *
+ * @ingroup DifferenceEngine
+ */
+class RangeDifference {
+
+	/** @var int */
+	public $leftstart;
+
+	/** @var int */
+	public $leftend;
+
+	/** @var int */
+	public $leftlength;
+
+	/** @var int */
+	public $rightstart;
+
+	/** @var int */
+	public $rightend;
+
+	/** @var int */
+	public $rightlength;
+
+	function __construct( $leftstart, $leftend, $rightstart, $rightend ) {
+		$this->leftstart = $leftstart;
+		$this->leftend = $leftend;
+		$this->leftlength = $leftend - $leftstart;
+		$this->rightstart = $rightstart;
+		$this->rightend = $rightend;
+		$this->rightlength = $rightend - $rightstart;
+	}
+
+}