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<title>Variance-Adjusted Patching for Divergent Texts</title> 
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<body>

<h2>Variance-Adjusted Patching for Divergent Texts</h2>
<p>Karl&nbsp;Fogel&nbsp;<tt>&lt;kfogel@collab.net&gt;</tt></p>

<p>Date of First Publication: 22 May, 2001</p>

<p>$LastChangedDate$<br />
Canonical URL: <a href="http://svn.apache.org/repos/asf/subversion/trunk/www/variance-adjusted-patching.html">http://svn.apache.org/repos/asf/subversion/trunk/www/variance-adjusted-patching.html</a></p>

<hr />  <!-- ====================================================== -->

<p>
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.
</p>

<p>
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.
</p>

<p>
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.  
</p>

<p>
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 "<tt>cvs&nbsp;annotate</tt>".
Informally speaking, one of the following is true for each such line,
ignoring floating due to out-of-bounds insertion and deletion:
</p>

   <ol style="list-style-type: lower-alphs">
      <li><p><b>The line exists unchanged in both source and target</b></p>
      <p>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.</p>
      </li>
      <li><p><b>The line has been changed in source but not in target</b></p>
      <p>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.</p>
      <p>
      <i>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.</i></p>
      </li>
      <li><p><b>The line has been changed in target but not in source</b></p>
      <p>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.</p>
      </li>
      <li><p><b>The line does not exist in target</b></p>
      <p>This could be for one of two reasons:</p>
           <ol>
           <li>the line is new in source, having been added after
               target branched, or</li>
           <li>the line was removed from target after the branch
               happened</li>
           </ol>
      <p>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.</p>
      </li>
   </ol>

<p>
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.
</p>

<p>
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.
</p>

<p>
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 <i>too</i>
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.
</p>

<p>
<strong>The Variance Adjustment Algorithm.</strong>
</p>

<p>
Some terminology:
</p>

   <dl>
      <dt><i>insertion</i></dt>
      <dd>A new line that has been added in either source or
      target since the common ancestor.</dd>
      <dt><i>deletion</i></dt>
      <dd>A line that has been deleted from either source or target
      since the common ancestor.</dd>
      <dt><i>edit</i></dt>
      <dd>A line that has been changed in either source or target
      since the common ancestor.</dd>
      <dt><i>out-range</i></dt>
      <dd>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 <i>out-range insertion</i> means a line was added in
      some region not directly touched by any of the hunks in the
      patch; an <i>out-range deletion</i> means a line was deleted
      from some region not in any hunk.</dd>
      <dt><i>in-range</i></dt>
      <dd>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
      <i>in-range insertion</i> means a line was added in a region
      affected by one of the hunks; an <i>in-range deletion</i> means
      a line that was deleted from some region affected by a hunk.</dd>
      <dt><i>context</i></dt>
      <dd>A line included in a hunk for context only -- such lines are
      not affected by the patch.</dd> 
      <dt><i>destination line, affected line</i></dt>
      <dd>(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.</dd>
   </dl>

<p>
Description of the scenario:
</p>

<p>
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.
</p>

<p>
Assume that branch B is rooted in trunk T at T:8; thus,
T:8&nbsp;==&nbsp;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.)
</p>

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

   <ol>
   <li>contains certain changes not present in B:15, namely, changes T:9
   through T:19.
   </li> 
   <li>does not contain certain changes present in B:15, namely,
   changes B:2 through B:15.</li>
   </ol>

<p>
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:
</p>

   <ol>
   <li><i>Out-range added line</i>: 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.</li>
   <li><i>Out-range deleted line</i>: 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.</li> 
   <li><i>Out-range edited line</i>: do nothing.  Out-range edits
       are irrelevant to P.</li> 
   <li><i>Added line in context range in P</i>: remove the
       corresponding line from the context, optionally replacing it
       with new context <i>based on that region in B:15</i>, and
       adjust line numbers and mappings appropriately.</li>
   <li><i>Added line in affected text range in P</i>: 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&gt;=8, M&lt;=18, and
       M-N&nbsp;==&nbsp;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.</li>
   <li><i>Deleted line that is in-range in P</i>: request another
       universe -- this situation can't happen in ours.</li>
   <li><i>In-range edited line</i>: 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.</li> 
   </ol>

<p>
Now walk over the diff B:1-B:15, further adjusting P:
</p>

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

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

<p>
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.
</p>

<p>
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.
</p>

<p>
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:
</p>

<pre>
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 */
}
</pre>

<p>
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:
</p>

<pre>
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 */
}
</pre>

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

<pre>
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 */
}
</pre>

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

<pre>
$ 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)
{
&lt;&lt;&lt;&lt;&lt;&lt;&lt; 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 */
&gt;&gt;&gt;&gt;&gt;&gt;&gt; 1.2
}
</pre>

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

<pre>
*** 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 */
</pre>

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

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

<pre>
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 */
}
</pre>

<p>
T:2 has some inserted lines near the top:
</p>

<pre>
#include &lt;stdio.h&gt;

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 */
}
</pre>

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

<pre>
#include &lt;stdio.h&gt;

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 */
}
</pre>

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

<pre>
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 */
}
</pre>

<p>
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:
</p>

<pre>
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 */
</pre>

<p>
Following the adjustment algorithm, it looks like this:
</p>

<pre>
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 */
</pre>

<p>
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.
</p>

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

<p>
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.
</p>

<p>
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.
</p>

<h4>Addendum</h4>

<p>For clarity, I have used line-based diffs to describe the process
of variance adjustment.  The algorithm applies equally well, of
course, to other kinds of diffs, including arbitrary binary diffs.  In
fact,
<a href="http://www.red-bean.com/pipermail/changesets/2003-April/000097.html"
>Dr. William Uther wrote</a>:</p>

<blockquote>
<p style="font-style: italic;">
I actually gave an example of a binary version of the VAP algorithm on
the svn-dev list a while back.  It used VAP at the byte level, instead
of at the line level.  It was similar to your suggested VAP algorithm
in that you could adjust the 'soft-conflict' zone around the changes.
</p>
</blockquote>

<p>The message he's referring to appears to be this one:</p>

<pre>
   <a href="http://svn.haxx.se/dev/archive-2002-02/1059.shtml">http://svn.haxx.se/dev/archive-2002-02/1059.shtml</a>
   From: William Uther
   To: dev@subversion.tigris.org
   Subject: Re: Merging
   Date: Sat, 16 Feb 2002 21:19:43 -0500
   Message-ID: &lt;B8947D6F.787C%will=subversion@cs.cmu.edu&gt;
   In-Reply-To: &lt;51C7002B020CD411824E009027C469F782259A@cldxch01.hifn.com&gt;
</pre>

<p>I mention this here in order to help anyone using this algorithm as
prior art in a patent challenge.  I doubt I was the first person to
describe variance-adjusted patching, but at the very least we can know
that the method was described as of 22 May 2001&nbsp;&mdash;&nbsp;and
that both I and someone else "proficient in the art" (William Uther)
thought its applicability to binary diffs to be pretty obvious.</p>

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