## Variance-Adjusted Patching for Divergent Texts

Karl Fogel `<kfogel@collab.net>`

$LastChangedDate: 2005-12-13 20:49:17 +0100 (Tue, 13 Dec 2005) $
Original Date: 22 May, 2001
Canonical URL: http://svn.collab.net/repos/svn/trunk/www/variance-adjusted-patching.html

Version control systems that use traditional context diff / unidiff format for branch merging tend to fail spuriously in high variance situations. A "high variance" situation is one where the branch text differs from the source text by more than roughly 5-10%, counting lines changed, deleted, and added against the source. This appendix describes a technique called "variance-adjusted patching", by which such applications can be made to succeed, when a common ancestor of the source and destination texts is available.

The problem with straight patch application is that it depends on the affected text hunks and their context not having changed significantly since source. They may "float", that is, text may have been inserted or deleted around them, thus changing their locations in the target file. But they themselves may not have changed, except for whitespace adjustments or other trivial (i.e., automatically ignorable) modifications. If they have changed, the patch application will fail.

Variance adjustment is the process of transforming a patch to account for differences that have arisen in the target text since the patch was generated, so that the new patch will be applicable to the new target text and yet still have the "same" effect as the old patch. It is, in essence, patching a patch. For example, suppose a branch B diverges from a trunk T, and an engineer wants to merge the change from revision T:18 to T:19 into B:10, creating B:11. If B:10 is too dissimilar to T:18, the merge may fail due to textual conflicts, even though there is no logical conflict. Variance adjustment is about changing the diff T:18-T:19 so that it applies cleanly to B:10.

This is possible because for any given line that a patch hunk expects to see in the target text (e.g., in a context diff, these would be the context lines, plus the "before" version of affected lines), the version control system can know that line's history in both source and target, if there is a common ancestor to examine. The process is very similar to the calculations done by "`cvs annotate`". Informally speaking, one of the following is true for each such line, ignoring floating due to out-of-bounds insertion and deletion:

1. The line exists unchanged in both source and target

   If the line is still present in target and source, that means it has not been removed from either since the common ancestor, or if it was removed, it has been restored. Nothing need be done to the diff.

2. The line has been changed in source but not in target

   In the diff hunk, the line should be changed to reflect the target's version of the line, so that the diff will be applicable to the target.

   When we say that the line "has been changed", it just means that a different line appears where this line once appeared. Whether this is because the line has been edited, or because a new line has been inserted in target, does not matter. (Another way to say it is that it need not matter whether the old version of the line still appears somewhere nearby in target.) The important thing is that new text appears where the hunk is expecting old text, and that we have a way to change the hunk to expect the new text instead.

3. The line has been changed in target but not in source

   Same as above: in the diff hunk, the line should be changed to reflect the target's version of the line, so that the diff will be applicable to the target. If this seems counterintuitive, drink the Kool-Aid and read again.

4. The line does not exist in target

   This could be for one of two reasons:

   1. the line is new in source, having been added after target branched, or
   2. the line was removed from target after the branch happened

   Either way, the line needs to be changed to the "corresponding" line in the target text -- that is, the line that, in target, now occupies the place of the obsolete expected line. The version control system has enough information to determine which of the two cases above applies, and can use that to decide which of the lines currently in target is the best candidate to substitute for the missing line.

Note that the case of the line not existing in source is impossible: if it doesn't exist in the current source, it certainly can't appear in the expected-text portions of the diff.

Although the patch program can adjust for floating at application time, the version control system can also adjust the line numbers in hunks to compensate for any insertions or deletions that have happened, in either source or target, outside the areas covered by the hunks. This can result in a patch that applies perfectly, without any offset adjustment, to the target as it is known to the revision control system. Of course, uncommitted local edits to the target cannot be compensated for in the diff -- we must still rely on the patch program's own offset adjustment and fuzz factor to handle those.

The above rules are an informal explanation of how variance adjustment works. Below, the algorithm is described somewhat more formally, to show how the version control system would do variance adjustment in any situation. Note that the algorithm is actually too powerful -- if taken to its logical limits, it can generate patches that apply cleanly even when the user would almost certainly prefer a conflict. Thus it's necessary to offer an adjustment selectivity level; a good default selectivity would probably allow compensation for context variance, but not for variance in expected target lines. Anyway, the complete, unselective algorithm is described below, as it should be obvious where to attach the selectivity knobs if desired.

The Variance Adjustment Algorithm.

Some terminology:

insertion
  A new line that has been added in either source or target since the common ancestor.
deletion
  A line that has been deleted from either source or target since the common ancestor.
edit
  A line that has been changed in either source or target since the common ancestor.
out-range
  An event that happened to either source or target since the common ancestor, but to a line that is not covered in any of the diff hunks in the patch undergoing variance adjustment. For example, an out-range insertion means a line was added in some region not directly touched by any of the hunks in the patch; an out-range deletion means a line was deleted from some region not in any hunk.
in-range
  An event that happened to either source or target since the common ancestor, to a line covered in one of the diff hunks in the patch undergoing variance adjustment. For example, an in-range insertion means a line was added in a region affected by one of the hunks; an in-range deletion means a line that was deleted from some region affected by a hunk.
context
  A line included in a hunk for context only -- such lines are not affected by the patch.
destination line, affected line
  (Used interchangeably). A line that is actually affected by a patch. For lines being edited or deleted, the line is already present in the target text; for lines being added, the line will only be present after the patch is applied. In all cases it is present in a hunk in the patch.

Description of the scenario:

Although there is no requirement that there be a "trunk"/"branch" relationship between the two lines, we will use that terminology below to make the description easier to understand. In reality, there are simply two lines of development with a common ancestory.

Assume that branch B is rooted in trunk T at T:8; thus, T:8 == B:1. The youngest trunk revision is T:20, and the youngest branch revision is B:15. A user with working copy on branch B wants to merge in the change T:19-T:20. For brevity, we will call this change P, for "patch". (We may speak, without loss of generality, as if only one file is being patched, as the same algorithm holds for every file involved in the merge.)

There are two problems that prevent the direct application of the unadjusted P to B:15. P, being based on source text T:19,

1. contains certain changes not present in B:15, namely, changes T:9 through T:19.
2. does not contain certain changes present in B:15, namely, changes B:2 through B:15.

To adjust P, we first walk over the diff T:8-T:19, adjusting hunks as we go. Each line in T:8-T:19 falls into one of the following categories:

1. Out-range added line: decrement the line numbers in every hunk in P that comes after the addition. This undoes the effect of the add, since the add never happened in B.
2. Out-range deleted line: increment the line numbers in every hunk in P that comes after the deletion. This undoes the effect of the deletion, since the deletion never happened in B.
3. Out-range edited line: do nothing. Out-range edits are irrelevant to P.
4. Added line in context range in P: remove the corresponding line from the context, optionally replacing it with new context based on that region in B:15, and adjust line numbers and mappings appropriately.
5. Added line in affected text range in P: this is a dependency problem -- part of the change T:18-T:19 depends on changes introduced to T after B branched. There are several possible behaviors, depending on what the user wants. One is to generate an informative error, stating that T:18-T:19 depends on some other change (T:N-T:M, where N>=8, M<=18, and M-N == 1); the exact revisions can be discovered automatically using the same process as "cvs annotate", though it may take some time to do so. Another option is to include the change in P, as an insertion of the "after" version of the text, and adjust line numbers and mappings accordingly. (And if all this isn't sounding a lot like a directory merge algorithm, try drinking more of the Kool-Aid.) A third option is to include it as an insertion, but with metadata (such as CVS-style conflict markers) indicating that the line attempting to be patched does not exist in B.
6. Deleted line that is in-range in P: request another universe -- this situation can't happen in ours.
7. In-range edited line: reverse that edit in the "before" version of the corresponding line in the appropriate hunk in P, to obtain the version of the line that will be found in B when P is applied.

Now walk over the diff B:1-B:15, further adjusting P:

1. Out-range added line: increment the line numbers in every hunk in P that comes after the addition.
2. Out-range deleted line: decrement the line numbers in every hunk in P that comes after the deletion.
3. Out-range edited line: do nothing. Out-range edits are irrelevant to P.
4. Added line in context range in P: add that line to both sides of the context in the appropriate hunk, adjust line numbers in that hunk and all following hunks.
5. Added line in affected text range in P: add that line to the context in P and adjust numbers appropriately.
6. Deleted line in-range in P: dependency problem; see "Added line in affected text range in P" in the first pass above.
7. In-range edited line: apply that edit to the "before" version of the corresponding line in the appropriate hunk in P.

Now P is ready to apply to B:15, and even has enough context to apply over local edits.

Some of the steps in both loops can be compressed. For example, when the number of added and deleted lines in a hunk is balanced, line number adjustment in later hunks is unnecessary; and balance can be quickly detected by inspecting only the line numbers of the hunk in question.

The algorithm handles inherent conflicts flexibly without losing information. An "inherent" conflict is one where changes in T:8-T:19 overlap with changes in B:1-B:15. They can be either papered over by adjusting context and "before" lines as enthusiastically as possible; reported as errors, with dependency information included; or both sides of the overlap can be handed to the user, surrounded by CVS-style conflict markers. Or if conflict markers are not the desired interface, the patch can hold the conflict in some other metadata markup (using the patch format comment space), and other tools can report on and help resolve it.

Let's take a brief look at what adjustment does to some patches. Here's a simple case, arising from an attempt to port an individual change from trunk to branch. On trunk T, revision 1 looks like this:

    int main (int argc, char **argv)
    {
      /* line minus-five of context */
      /* line minus-four of context */
      /* line minus-three of context */
      /* line minus-two of context */
      /* line minus-one of context */
      printf ("Hello, world!\n");
      /* line plus-one of context */
      /* line plus-two of context */
      /* line plus-three of context */
      /* line plus-four of context */
      /* line plus-five of context */
    }

A branch B also exists, rooted in the trunk at revision T:1. On branch B, we commit a change to the context (we replace the words with numbers), so that B:2 looks like this:

    int main (int argc, char **argv)
    {
      /* line -5 of context */
      /* line -4 of context */
      /* line -3 of context */
      /* line -2 of context */
      /* line -1 of context */
      printf ("Hello, world!\n");
      /* line +1 of context */
      /* line +2 of context */
      /* line +3 of context */
      /* line +4 of context */
      /* line +5 of context */
    }

Meanwhile on the trunk, we change only the middle line, so that T:2 is committed as:

    int main (int argc, char **argv)
    {
      /* line minus-five of context */
      /* line minus-four of context */
      /* line minus-three of context */
      /* line minus-two of context */
      /* line minus-one of context */
      printf ("Good-bye, cruel world!\n");
      /* line plus-one of context */
      /* line plus-two of context */
      /* line plus-three of context */
      /* line plus-four of context */
      /* line plus-five of context */
    }

Using a traditional context-based approach, an attempt to patch B:2 with the difference T:1->T:2 will fail, with a reject file if vanilla ``patch`' was used, or with conflict markers if ``rcsmerge`' was used:

    $ cvs up -j 1.1 -j 1.2 foo.c
    ### Purists will note that -j HEAD would have been sufficient; however, ###
    ### two -j's more clearly reflects the intent of the example.           ###
    RCS file: /usr/local/cvs/vap0/foo.c,v
    retrieving revision 1.1
    retrieving revision 1.2
    Merging differences between 1.1 and 1.2 into foo.c
    rcsmerge: warning: conflicts during merge
    $ cat foo.c
    int main (int argc, char **argv)
    {
    <<<<<<< foo.c
      /* line -5 of context */
      /* line -4 of context */
      /* line -3 of context */
      /* line -2 of context */
      /* line -1 of context */
      printf ("Hello, world!\n");
      /* line +1 of context */
      /* line +2 of context */
      /* line +3 of context */
      /* line +4 of context */
      /* line +5 of context */
    =======
      /* line minus-five of context */
      /* line minus-four of context */
      /* line minus-three of context */
      /* line minus-two of context */
      /* line minus-one of context */
      printf ("Good-bye, cruel world!\n");
      /* line plus-one of context */
      /* line plus-two of context */
      /* line plus-three of context */
      /* line plus-four of context */
      /* line plus-five of context */
    >>>>>>> 1.2
    }

Because the context has changed, the change to the middle line cannot be found. If we adjust the patch T:1->T:2, it would look like this:

    *** foo.c	2001/05/18 08:15:28	1.1
    --- foo.c	2001/05/18 08:20:59	1.2
    ***************
    *** 5,11 ****
        /* line -3 of context */
        /* line -2 of context */
        /* line -1 of context */
    !   printf ("Hello, world!\n");
        /* line +1 of context */
        /* line +2 of context */
        /* line +3 of context */
    --- 5,11 ----
        /* line -3 of context */
        /* line -2 of context */
        /* line -1 of context */
    !   printf ("Goodbye, cruel world!\n");
        /* line +1 of context */
        /* line +2 of context */
        /* line +3 of context */

and would now apply perfectly to B:2, even though this diff never existed between any two committed revisions.

Let's try a slightly more complex case, starting with the same T:1 and B:1:

    int main (int argc, char **argv)
    {
      /* line minus-five of context */
      /* line minus-four of context */
      /* line minus-three of context */
      /* line minus-two of context */
      /* line minus-one of context */
      printf ("Hello, world!\n");
      /* line plus-one of context */
      /* line plus-two of context */
      /* line plus-three of context */
      /* line plus-four of context */
      /* line plus-five of context */
    }

T:2 has some inserted lines near the top:

    #include <stdio.h>

    int main (int argc, char **argv)
    {
      /* line minus-five of context */
      /* line minus-four of context */
      /* line minus-three of context */
      /* line minus-two of context */
      /* line minus-one of context */
      printf ("Hello, world!\n");
      /* line plus-one of context */
      /* line plus-two of context */
      /* line plus-three of context */
      /* line plus-four of context */
      /* line plus-five of context */
    }

And then another change was committed on the trunk, editing the middle line, so that T:3 looks like this:

    #include <stdio.h>

    int main (int argc, char **argv)
    {
      /* line minus-five of context */
      /* line minus-four of context */
      /* line minus-three of context */
      /* line minus-two of context */
      /* line minus-one of context */
      printf ("Good-bye, cruel world!\n");
      /* line plus-one of context */
      /* line plus-two of context */
      /* line plus-three of context */
      /* line plus-four of context */
      /* line plus-five of context */
    }

Meanwhile, one complex change has been committed on the branch, so B:2 looks like this:

    int main (int argc, char **argv)
    {
      /* line minus-five of context */
      /* line minus-four of context */
      /* line minus-three of context */
      /* line -1 of context */
      printf ("Hello, world!\n");
      /* newly inserted line of context */
      /* line plus-one of context */
      /* line plus-two of context */
      /* line plus-three of context */
      /* line plus-four of context */
      /* line plus-five of context */
    }

Line minus-two of context was removed, line minus-one was changed to "-1", and a new line of context was inserted farther down. Now the branch developer wants to merge in the change T:2-T:3. Unadjusted, the patch looks like this:

    Index: foo.c
    ===================================================================
    RCS file: /usr/local/cvs/vap1/foo.c,v
    retrieving revision 1.2
    retrieving revision 1.3
    diff -c -r1.2 -r1.3
    *** foo.c	2001/05/22 21:17:14	1.2
    --- foo.c	2001/05/22 21:19:42	1.3
    ***************
    *** 7,13 ****
        /* line minus-three of context */
        /* line minus-two of context */
        /* line minus-one of context */
    !   printf ("Hello, world!\n");
        /* line plus-one of context */
        /* line plus-two of context */
        /* line plus-three of context */
    --- 7,13 ----
        /* line minus-three of context */
        /* line minus-two of context */
        /* line minus-one of context */
    !   printf ("Good-bye, cruel world!\n");
        /* line plus-one of context */
        /* line plus-two of context */
        /* line plus-three of context */

Following the adjustment algorithm, it looks like this:

    Index: foo.c
    ===================================================================
    RCS file: /usr/local/cvs/vap1/foo.c,v
    retrieving revision 1.2
    retrieving revision 1.3
    diff -c -r1.2 -r1.3
    *** foo.c	2001/05/22 21:17:14	1.2
    --- foo.c	2001/05/22 21:19:42	1.3
    ***************
    *** 5,11 ****
        /* line minus-four of context */
        /* line minus-three of context */
        /* line -1 of context */
    !   printf ("Hello, world!\n");
        /* newly inserted line of context */
        /* line plus-one of context */
        /* line plus-two of context */
    --- 5,11 ----
        /* line minus-four of context */
        /* line minus-three of context */
        /* line -1 of context */
    !   printf ("Good-bye, cruel world!\n");
        /* newly inserted line of context */
        /* line plus-one of context */
        /* line plus-two of context */

Note how the line numbers have been adjusted to compensate for the absence of change T:1-T:2 (since the patch we're applying only concerns T:2-T:3), and the context has been changed to include the difference B:1-B:2.

Again, this patch never existed between any two revisions, but it applies cleanly to B:2.

The cost of the adjustment algorithm is proportional to the size of the diff from branch point to trunk head plus the diff from branch point to branch head, plus the size (for time, number of hunks) in the diff being adjusted. This is comparable to the cost of using reverse-delta storage in the first place. Also, the user consuming the final patch does not need access to all the intermediate changes -- she only needs permissions on the endpoints of the diff, the common ancestor of the two lines, and the revision to which the patch is being applied. Intermediate revisions need not be accessible by the user.

Through variance-adjusted patching, any repository that stores successive revisions can apply patches even between highly divergent branches, as long as there is a common ancestor.