Where do patches come from?

The open source world runs on patches, and thanks to tools like git pretty much all of us are familiar with them. But patches are something the tools generate for us. Hardly anyone ever thinks about how they are made.

You can use diff FILE1 FILE2 to generate a patch. But how does diff work?

Most diffing tools use a single clever algorithm, known as the Hunt–McIlroy algorithm, after its inventors. Douglas McIlroy first implemented it in the 1970s for Unix diff. It has been implemented over and over again, with many variations. One, by Tim Peters, is in the Python standard library. It’s called difflib.

Today we’ll see how the Hunt–McIlroy algorithm works and what optimizations difflib uses.

It turns out you can implement a simple diff in 50 lines of Python code.

Breaking down the problem

Before you read on, take a moment to think about how you would approach this problem. How do you find the differences between two files?

The first key insight is that diffing involves finding large regions where the two input files are the same. This is something that we can do programmatically—computers are good at matching—and once we have found all the common regions, whatever’s left is the differences.

Knowing that, we can break the problem into three parts:

  1. An algorithm for finding the longest common regions of two files. That is, the longest sequence of lines that appears verbatim in both.
  2. An algorithm for finding a list of all the common regions of two files.
  3. Code for printing out a diff, given the list of common regions.

All three parts are apparent in the final code: Three problems, three functions.

The last two are, I hope, easy enough that you can read them, ponder them, and discover what they do and how they work. Both have some clever surprising bits, so if you enjoy a good puzzle, read the code!

But the first part is where the magic lives.

The code

The core of the diffing algorithm is this function, longest_matching_slice. So even though this is “diff in 50 lines”, really the brains of the operation is just 15 lines long:

def longest_matching_slice(a, a0, a1, b, b0, b1):
    sa, sb, n = a0, b0, 0

    runs = {}
    for i in range(a0, a1):
        new_runs = {}
        for j in range(b0, b1):
            if a[i] == b[j]:
                k = new_runs[j] = runs.get(j-1, 0) + 1
                if k > n:
                    sa, sb, n = i-k+1, j-k+1, k
        runs = new_runs

    assert a[sa:sa+n] == b[sb:sb+n]
    return sa, sb, n

This is the part of the code that implements the Hunt–McIlroy algorithm.

It takes as its arguments two regions in two different arrays: a[a0:a1] and b[b0:b1].

The result is a triple of integers (sa, sb, n), telling where the matching region starts in a, where it starts in b, and how many lines long it is.

The assertion on the next-to-last line explains what we’re doing here better than I could.

How it works

The basic idea here is really simple: we start by setting sa, sb, n to the worst possible “matching slice”, which has length 0. Then, we construct every matching region that the two arrays share, and as we go, we store the longest match in sa, sb, n.

The only remaining question is how to construct every matching region. Here is how the Hunt–McIlroy algorithm does it:

  1. Start at the first line of file A.
  2. Make a list of active runs, initially empty.
  3. For each place *b* where the current line of file A appears in file B:
    • If it extends an active run, that run stays active and its length increases by 1;
    • Otherwise, make a new active run of length 1.
  4. Discard all previously-active runs that did not get extended in step 3 (They are not active anymore; we reached a line that doesn't match.)
  5. If there are any more lines in file A, move on to the next one and go back to step 3.

Note that the code works for lists of arbitrary objects, not just strings.

What difflib does

Could we go faster? Here are some ideas:

  • My code has an inner loop that searches for places where a[i] occurs in b. We could replace that with a dictionary mapping all the values of b to the list of places in b where they appear. difflib does this.

  • Even with that optimization, if any elements of a occur many times in b, the innermost loop will go very slowly. This is especially unfortunate because there are in ordinary text files super-common elements (such as blank lines), and they are the least interesting lines in the whole file! difflib optimizes by treating extremely common elements as “junk” and basically ignoring them when matching.

Want to see?

There’s an easy way to find the source code of difflib:

>>> import difflib
>>> difflib.__file__
'/usr/local/Cellar/python/2.7.3/Frameworks/Python.framework/Versions/2.7/lib/python2.7/difflib.pyc'
>>> import os
>>> os.system('cat ' + _.replace('.pyc', '.py'))

The code quoted above was adapted from this code, in particular this method of SequenceMatcher:

def find_longest_match(self, alo, ahi, blo, bhi):
    """Find longest matching block in a[alo:ahi] and b[blo:bhi].
    ...
    """

    ...

    a, b, b2j, isbjunk = self.a, self.b, self.b2j, self.isbjunk
    besti, bestj, bestsize = alo, blo, 0
    # find longest junk-free match
    # during an iteration of the loop, j2len[j] = length of longest
    # junk-free match ending with a[i-1] and b[j]
    j2len = {}
    nothing = []
    for i in xrange(alo, ahi):
        # look at all instances of a[i] in b; note that because
        # b2j has no junk keys, the loop is skipped if a[i] is junk
        j2lenget = j2len.get
        newj2len = {}
        for j in b2j.get(a[i], nothing):
            # a[i] matches b[j]
            if j < blo:
                continue
            if j >= bhi:
                break
            k = newj2len[j] = j2lenget(j-1, 0) + 1
            if k > bestsize:
                besti, bestj, bestsize = i-k+1, j-k+1, k
        j2len = newj2len

Note another small optimization in this code: Method lookups were once quite slow in Python, so instead of calling j2len.get(...) in the inner loop, Tim sets j2lenget = j2len.get outside of the loop and calls that. Method lookups are faster in CPython now, but they still are not free; at least they allocate an object.

difflib is full of fun stuff: routines for printing diffs in several common formats, other random diffy tools.

I’m a little afraid that I enjoyed this code dive more than you! Maybe, for figuring out how code works, there is just no substitute for rewriting it yourself.

Next week, I’ll describe an algorithm for treeification. See you then!


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