tools/releasetools/blockimgdiff.py

# Copyright (C) 2014 The Android Open Source Project
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#      http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

from __future__ import print_function

from collections import deque, OrderedDict
from hashlib import sha1
import heapq
import itertools
import multiprocessing
import os
import re
import subprocess
import threading
import tempfile

from rangelib import RangeSet


__all__ = ["EmptyImage", "DataImage", "BlockImageDiff"]


def compute_patch(src, tgt, imgdiff=False):
  srcfd, srcfile = tempfile.mkstemp(prefix="src-")
  tgtfd, tgtfile = tempfile.mkstemp(prefix="tgt-")
  patchfd, patchfile = tempfile.mkstemp(prefix="patch-")
  os.close(patchfd)

  try:
    with os.fdopen(srcfd, "wb") as f_src:
      for p in src:
        f_src.write(p)

    with os.fdopen(tgtfd, "wb") as f_tgt:
      for p in tgt:
        f_tgt.write(p)
    try:
      os.unlink(patchfile)
    except OSError:
      pass
    if imgdiff:
      p = subprocess.call(["imgdiff", "-z", srcfile, tgtfile, patchfile],
                          stdout=open("/dev/null", "a"),
                          stderr=subprocess.STDOUT)
    else:
      p = subprocess.call(["bsdiff", srcfile, tgtfile, patchfile])

    if p:
      raise ValueError("diff failed: " + str(p))

    with open(patchfile, "rb") as f:
      return f.read()
  finally:
    try:
      os.unlink(srcfile)
      os.unlink(tgtfile)
      os.unlink(patchfile)
    except OSError:
      pass


class Image(object):
  def ReadRangeSet(self, ranges):
    raise NotImplementedError

  def TotalSha1(self, include_clobbered_blocks=False):
    raise NotImplementedError


class EmptyImage(Image):
  """A zero-length image."""
  blocksize = 4096
  care_map = RangeSet()
  clobbered_blocks = RangeSet()
  extended = RangeSet()
  total_blocks = 0
  file_map = {}
  def ReadRangeSet(self, ranges):
    return ()
  def TotalSha1(self, include_clobbered_blocks=False):
    # EmptyImage always carries empty clobbered_blocks, so
    # include_clobbered_blocks can be ignored.
    assert self.clobbered_blocks.size() == 0
    return sha1().hexdigest()


class DataImage(Image):
  """An image wrapped around a single string of data."""

  def __init__(self, data, trim=False, pad=False):
    self.data = data
    self.blocksize = 4096

    assert not (trim and pad)

    partial = len(self.data) % self.blocksize
    if partial > 0:
      if trim:
        self.data = self.data[:-partial]
      elif pad:
        self.data += '\0' * (self.blocksize - partial)
      else:
        raise ValueError(("data for DataImage must be multiple of %d bytes "
                          "unless trim or pad is specified") %
                         (self.blocksize,))

    assert len(self.data) % self.blocksize == 0

    self.total_blocks = len(self.data) / self.blocksize
    self.care_map = RangeSet(data=(0, self.total_blocks))
    self.clobbered_blocks = RangeSet()
    self.extended = RangeSet()

    zero_blocks = []
    nonzero_blocks = []
    reference = '\0' * self.blocksize

    for i in range(self.total_blocks):
      d = self.data[i*self.blocksize : (i+1)*self.blocksize]
      if d == reference:
        zero_blocks.append(i)
        zero_blocks.append(i+1)
      else:
        nonzero_blocks.append(i)
        nonzero_blocks.append(i+1)

    self.file_map = {"__ZERO": RangeSet(zero_blocks),
                     "__NONZERO": RangeSet(nonzero_blocks)}

  def ReadRangeSet(self, ranges):
    return [self.data[s*self.blocksize:e*self.blocksize] for (s, e) in ranges]

  def TotalSha1(self, include_clobbered_blocks=False):
    # DataImage always carries empty clobbered_blocks, so
    # include_clobbered_blocks can be ignored.
    assert self.clobbered_blocks.size() == 0
    return sha1(self.data).hexdigest()


class Transfer(object):
  def __init__(self, tgt_name, src_name, tgt_ranges, src_ranges, style, by_id):
    self.tgt_name = tgt_name
    self.src_name = src_name
    self.tgt_ranges = tgt_ranges
    self.src_ranges = src_ranges
    self.style = style
    self.intact = (getattr(tgt_ranges, "monotonic", False) and
                   getattr(src_ranges, "monotonic", False))

    # We use OrderedDict rather than dict so that the output is repeatable;
    # otherwise it would depend on the hash values of the Transfer objects.
    self.goes_before = OrderedDict()
    self.goes_after = OrderedDict()

    self.stash_before = []
    self.use_stash = []

    self.id = len(by_id)
    by_id.append(self)

  def NetStashChange(self):
    return (sum(sr.size() for (_, sr) in self.stash_before) -
            sum(sr.size() for (_, sr) in self.use_stash))

  def __str__(self):
    return (str(self.id) + ": <" + str(self.src_ranges) + " " + self.style +
            " to " + str(self.tgt_ranges) + ">")


# BlockImageDiff works on two image objects.  An image object is
# anything that provides the following attributes:
#
#    blocksize: the size in bytes of a block, currently must be 4096.
#
#    total_blocks: the total size of the partition/image, in blocks.
#
#    care_map: a RangeSet containing which blocks (in the range [0,
#      total_blocks) we actually care about; i.e. which blocks contain
#      data.
#
#    file_map: a dict that partitions the blocks contained in care_map
#      into smaller domains that are useful for doing diffs on.
#      (Typically a domain is a file, and the key in file_map is the
#      pathname.)
#
#    clobbered_blocks: a RangeSet containing which blocks contain data
#      but may be altered by the FS. They need to be excluded when
#      verifying the partition integrity.
#
#    ReadRangeSet(): a function that takes a RangeSet and returns the
#      data contained in the image blocks of that RangeSet.  The data
#      is returned as a list or tuple of strings; concatenating the
#      elements together should produce the requested data.
#      Implementations are free to break up the data into list/tuple
#      elements in any way that is convenient.
#
#    TotalSha1(): a function that returns (as a hex string) the SHA-1
#      hash of all the data in the image (ie, all the blocks in the
#      care_map minus clobbered_blocks, or including the clobbered
#      blocks if include_clobbered_blocks is True).
#
# When creating a BlockImageDiff, the src image may be None, in which
# case the list of transfers produced will never read from the
# original image.

class BlockImageDiff(object):
  def __init__(self, tgt, src=None, threads=None, version=3):
    if threads is None:
      threads = multiprocessing.cpu_count() // 2
      if threads == 0:
        threads = 1
    self.threads = threads
    self.version = version
    self.transfers = []
    self.src_basenames = {}
    self.src_numpatterns = {}

    assert version in (1, 2, 3)

    self.tgt = tgt
    if src is None:
      src = EmptyImage()
    self.src = src

    # The updater code that installs the patch always uses 4k blocks.
    assert tgt.blocksize == 4096
    assert src.blocksize == 4096

    # The range sets in each filemap should comprise a partition of
    # the care map.
    self.AssertPartition(src.care_map, src.file_map.values())
    self.AssertPartition(tgt.care_map, tgt.file_map.values())

  def Compute(self, prefix):
    # When looking for a source file to use as the diff input for a
    # target file, we try:
    #   1) an exact path match if available, otherwise
    #   2) a exact basename match if available, otherwise
    #   3) a basename match after all runs of digits are replaced by
    #      "#" if available, otherwise
    #   4) we have no source for this target.
    self.AbbreviateSourceNames()
    self.FindTransfers()

    # Find the ordering dependencies among transfers (this is O(n^2)
    # in the number of transfers).
    self.GenerateDigraph()
    # Find a sequence of transfers that satisfies as many ordering
    # dependencies as possible (heuristically).
    self.FindVertexSequence()
    # Fix up the ordering dependencies that the sequence didn't
    # satisfy.
    if self.version == 1:
      self.RemoveBackwardEdges()
    else:
      self.ReverseBackwardEdges()
      self.ImproveVertexSequence()

    # Double-check our work.
    self.AssertSequenceGood()

    self.ComputePatches(prefix)
    self.WriteTransfers(prefix)

  def HashBlocks(self, source, ranges): # pylint: disable=no-self-use
    data = source.ReadRangeSet(ranges)
    ctx = sha1()

    for p in data:
      ctx.update(p)

    return ctx.hexdigest()

  def WriteTransfers(self, prefix):
    out = []

    total = 0
    performs_read = False

    stashes = {}
    stashed_blocks = 0
    max_stashed_blocks = 0

    free_stash_ids = []
    next_stash_id = 0

    for xf in self.transfers:

      if self.version < 2:
        assert not xf.stash_before
        assert not xf.use_stash

      for s, sr in xf.stash_before:
        assert s not in stashes
        if free_stash_ids:
          sid = heapq.heappop(free_stash_ids)
        else:
          sid = next_stash_id
          next_stash_id += 1
        stashes[s] = sid
        stashed_blocks += sr.size()
        if self.version == 2:
          out.append("stash %d %s\n" % (sid, sr.to_string_raw()))
        else:
          sh = self.HashBlocks(self.src, sr)
          if sh in stashes:
            stashes[sh] += 1
          else:
            stashes[sh] = 1
            out.append("stash %s %s\n" % (sh, sr.to_string_raw()))

      if stashed_blocks > max_stashed_blocks:
        max_stashed_blocks = stashed_blocks

      free_string = []

      if self.version == 1:
        src_str = xf.src_ranges.to_string_raw()
      elif self.version >= 2:

        #   <# blocks> <src ranges>
        #     OR
        #   <# blocks> <src ranges> <src locs> <stash refs...>
        #     OR
        #   <# blocks> - <stash refs...>

        size = xf.src_ranges.size()
        src_str = [str(size)]

        unstashed_src_ranges = xf.src_ranges
        mapped_stashes = []
        for s, sr in xf.use_stash:
          sid = stashes.pop(s)
          stashed_blocks -= sr.size()
          unstashed_src_ranges = unstashed_src_ranges.subtract(sr)
          sh = self.HashBlocks(self.src, sr)
          sr = xf.src_ranges.map_within(sr)
          mapped_stashes.append(sr)
          if self.version == 2:
            src_str.append("%d:%s" % (sid, sr.to_string_raw()))
          else:
            assert sh in stashes
            src_str.append("%s:%s" % (sh, sr.to_string_raw()))
            stashes[sh] -= 1
            if stashes[sh] == 0:
              free_string.append("free %s\n" % (sh))
              stashes.pop(sh)
          heapq.heappush(free_stash_ids, sid)

        if unstashed_src_ranges:
          src_str.insert(1, unstashed_src_ranges.to_string_raw())
          if xf.use_stash:
            mapped_unstashed = xf.src_ranges.map_within(unstashed_src_ranges)
            src_str.insert(2, mapped_unstashed.to_string_raw())
            mapped_stashes.append(mapped_unstashed)
            self.AssertPartition(RangeSet(data=(0, size)), mapped_stashes)
        else:
          src_str.insert(1, "-")
          self.AssertPartition(RangeSet(data=(0, size)), mapped_stashes)

        src_str = " ".join(src_str)

      # all versions:
      #   zero <rangeset>
      #   new <rangeset>
      #   erase <rangeset>
      #
      # version 1:
      #   bsdiff patchstart patchlen <src rangeset> <tgt rangeset>
      #   imgdiff patchstart patchlen <src rangeset> <tgt rangeset>
      #   move <src rangeset> <tgt rangeset>
      #
      # version 2:
      #   bsdiff patchstart patchlen <tgt rangeset> <src_str>
      #   imgdiff patchstart patchlen <tgt rangeset> <src_str>
      #   move <tgt rangeset> <src_str>
      #
      # version 3:
      #   bsdiff patchstart patchlen srchash tgthash <tgt rangeset> <src_str>
      #   imgdiff patchstart patchlen srchash tgthash <tgt rangeset> <src_str>
      #   move hash <tgt rangeset> <src_str>

      tgt_size = xf.tgt_ranges.size()

      if xf.style == "new":
        assert xf.tgt_ranges
        out.append("%s %s\n" % (xf.style, xf.tgt_ranges.to_string_raw()))
        total += tgt_size
      elif xf.style == "move":
        performs_read = True
        assert xf.tgt_ranges
        assert xf.src_ranges.size() == tgt_size
        if xf.src_ranges != xf.tgt_ranges:
          if self.version == 1:
            out.append("%s %s %s\n" % (
                xf.style,
                xf.src_ranges.to_string_raw(), xf.tgt_ranges.to_string_raw()))
          elif self.version == 2:
            out.append("%s %s %s\n" % (
                xf.style,
                xf.tgt_ranges.to_string_raw(), src_str))
          elif self.version >= 3:
            # take into account automatic stashing of overlapping blocks
            if xf.src_ranges.overlaps(xf.tgt_ranges):
              temp_stash_usage = stashed_blocks + xf.src_ranges.size()
              if temp_stash_usage > max_stashed_blocks:
                max_stashed_blocks = temp_stash_usage

            out.append("%s %s %s %s\n" % (
                xf.style,
                self.HashBlocks(self.tgt, xf.tgt_ranges),
                xf.tgt_ranges.to_string_raw(), src_str))
          total += tgt_size
      elif xf.style in ("bsdiff", "imgdiff"):
        performs_read = True
        assert xf.tgt_ranges
        assert xf.src_ranges
        if self.version == 1:
          out.append("%s %d %d %s %s\n" % (
              xf.style, xf.patch_start, xf.patch_len,
              xf.src_ranges.to_string_raw(), xf.tgt_ranges.to_string_raw()))
        elif self.version == 2:
          out.append("%s %d %d %s %s\n" % (
              xf.style, xf.patch_start, xf.patch_len,
              xf.tgt_ranges.to_string_raw(), src_str))
        elif self.version >= 3:
          # take into account automatic stashing of overlapping blocks
          if xf.src_ranges.overlaps(xf.tgt_ranges):
            temp_stash_usage = stashed_blocks + xf.src_ranges.size()
            if temp_stash_usage > max_stashed_blocks:
              max_stashed_blocks = temp_stash_usage

          out.append("%s %d %d %s %s %s %s\n" % (
              xf.style,
              xf.patch_start, xf.patch_len,
              self.HashBlocks(self.src, xf.src_ranges),
              self.HashBlocks(self.tgt, xf.tgt_ranges),
              xf.tgt_ranges.to_string_raw(), src_str))
        total += tgt_size
      elif xf.style == "zero":
        assert xf.tgt_ranges
        to_zero = xf.tgt_ranges.subtract(xf.src_ranges)
        if to_zero:
          out.append("%s %s\n" % (xf.style, to_zero.to_string_raw()))
          total += to_zero.size()
      else:
        raise ValueError("unknown transfer style '%s'\n" % xf.style)

      if free_string:
        out.append("".join(free_string))

      # sanity check: abort if we're going to need more than 512 MB if
      # stash space
      assert max_stashed_blocks * self.tgt.blocksize < (512 << 20)

    # Zero out extended blocks as a workaround for bug 20881595.
    if self.tgt.extended:
      out.append("zero %s\n" % (self.tgt.extended.to_string_raw(),))

    # We erase all the blocks on the partition that a) don't contain useful
    # data in the new image and b) will not be touched by dm-verity.
    all_tgt = RangeSet(data=(0, self.tgt.total_blocks))
    all_tgt_minus_extended = all_tgt.subtract(self.tgt.extended)
    new_dontcare = all_tgt_minus_extended.subtract(self.tgt.care_map)
    if new_dontcare:
      out.append("erase %s\n" % (new_dontcare.to_string_raw(),))

    out.insert(0, "%d\n" % (self.version,))   # format version number
    out.insert(1, str(total) + "\n")
    if self.version >= 2:
      # version 2 only: after the total block count, we give the number
      # of stash slots needed, and the maximum size needed (in blocks)
      out.insert(2, str(next_stash_id) + "\n")
      out.insert(3, str(max_stashed_blocks) + "\n")

    with open(prefix + ".transfer.list", "wb") as f:
      for i in out:
        f.write(i)

    if self.version >= 2:
      print("max stashed blocks: %d  (%d bytes)\n" % (
          max_stashed_blocks, max_stashed_blocks * self.tgt.blocksize))

  def ComputePatches(self, prefix):
    print("Reticulating splines...")
    diff_q = []
    patch_num = 0
    with open(prefix + ".new.dat", "wb") as new_f:
      for xf in self.transfers:
        if xf.style == "zero":
          pass
        elif xf.style == "new":
          for piece in self.tgt.ReadRangeSet(xf.tgt_ranges):
            new_f.write(piece)
        elif xf.style == "diff":
          src = self.src.ReadRangeSet(xf.src_ranges)
          tgt = self.tgt.ReadRangeSet(xf.tgt_ranges)

          # We can't compare src and tgt directly because they may have
          # the same content but be broken up into blocks differently, eg:
          #
          #    ["he", "llo"]  vs  ["h", "ello"]
          #
          # We want those to compare equal, ideally without having to
          # actually concatenate the strings (these may be tens of
          # megabytes).

          src_sha1 = sha1()
          for p in src:
            src_sha1.update(p)
          tgt_sha1 = sha1()
          tgt_size = 0
          for p in tgt:
            tgt_sha1.update(p)
            tgt_size += len(p)

          if src_sha1.digest() == tgt_sha1.digest():
            # These are identical; we don't need to generate a patch,
            # just issue copy commands on the device.
            xf.style = "move"
          else:
            # For files in zip format (eg, APKs, JARs, etc.) we would
            # like to use imgdiff -z if possible (because it usually
            # produces significantly smaller patches than bsdiff).
            # This is permissible if:
            #
            #  - the source and target files are monotonic (ie, the
            #    data is stored with blocks in increasing order), and
            #  - we haven't removed any blocks from the source set.
            #
            # If these conditions are satisfied then appending all the
            # blocks in the set together in order will produce a valid
            # zip file (plus possibly extra zeros in the last block),
            # which is what imgdiff needs to operate.  (imgdiff is
            # fine with extra zeros at the end of the file.)
            imgdiff = (xf.intact and
                       xf.tgt_name.split(".")[-1].lower()
                       in ("apk", "jar", "zip"))
            xf.style = "imgdiff" if imgdiff else "bsdiff"
            diff_q.append((tgt_size, src, tgt, xf, patch_num))
            patch_num += 1

        else:
          assert False, "unknown style " + xf.style

    if diff_q:
      if self.threads > 1:
        print("Computing patches (using %d threads)..." % (self.threads,))
      else:
        print("Computing patches...")
      diff_q.sort()

      patches = [None] * patch_num

      # TODO: Rewrite with multiprocessing.ThreadPool?
      lock = threading.Lock()
      def diff_worker():
        while True:
          with lock:
            if not diff_q:
              return
            tgt_size, src, tgt, xf, patchnum = diff_q.pop()
          patch = compute_patch(src, tgt, imgdiff=(xf.style == "imgdiff"))
          size = len(patch)
          with lock:
            patches[patchnum] = (patch, xf)
            print("%10d %10d (%6.2f%%) %7s %s" % (
                size, tgt_size, size * 100.0 / tgt_size, xf.style,
                xf.tgt_name if xf.tgt_name == xf.src_name else (
                    xf.tgt_name + " (from " + xf.src_name + ")")))

      threads = [threading.Thread(target=diff_worker)
                 for _ in range(self.threads)]
      for th in threads:
        th.start()
      while threads:
        threads.pop().join()
    else:
      patches = []

    p = 0
    with open(prefix + ".patch.dat", "wb") as patch_f:
      for patch, xf in patches:
        xf.patch_start = p
        xf.patch_len = len(patch)
        patch_f.write(patch)
        p += len(patch)

  def AssertSequenceGood(self):
    # Simulate the sequences of transfers we will output, and check that:
    # - we never read a block after writing it, and
    # - we write every block we care about exactly once.

    # Start with no blocks having been touched yet.
    touched = RangeSet()

    # Imagine processing the transfers in order.
    for xf in self.transfers:
      # Check that the input blocks for this transfer haven't yet been touched.

      x = xf.src_ranges
      if self.version >= 2:
        for _, sr in xf.use_stash:
          x = x.subtract(sr)

      assert not touched.overlaps(x)
      # Check that the output blocks for this transfer haven't yet been touched.
      assert not touched.overlaps(xf.tgt_ranges)
      # Touch all the blocks written by this transfer.
      touched = touched.union(xf.tgt_ranges)

    # Check that we've written every target block.
    assert touched == self.tgt.care_map

  def ImproveVertexSequence(self):
    print("Improving vertex order...")

    # At this point our digraph is acyclic; we reversed any edges that
    # were backwards in the heuristically-generated sequence.  The
    # previously-generated order is still acceptable, but we hope to
    # find a better order that needs less memory for stashed data.
    # Now we do a topological sort to generate a new vertex order,
    # using a greedy algorithm to choose which vertex goes next
    # whenever we have a choice.

    # Make a copy of the edge set; this copy will get destroyed by the
    # algorithm.
    for xf in self.transfers:
      xf.incoming = xf.goes_after.copy()
      xf.outgoing = xf.goes_before.copy()

    L = []   # the new vertex order

    # S is the set of sources in the remaining graph; we always choose
    # the one that leaves the least amount of stashed data after it's
    # executed.
    S = [(u.NetStashChange(), u.order, u) for u in self.transfers
         if not u.incoming]
    heapq.heapify(S)

    while S:
      _, _, xf = heapq.heappop(S)
      L.append(xf)
      for u in xf.outgoing:
        del u.incoming[xf]
        if not u.incoming:
          heapq.heappush(S, (u.NetStashChange(), u.order, u))

    # if this fails then our graph had a cycle.
    assert len(L) == len(self.transfers)

    self.transfers = L
    for i, xf in enumerate(L):
      xf.order = i

  def RemoveBackwardEdges(self):
    print("Removing backward edges...")
    in_order = 0
    out_of_order = 0
    lost_source = 0

    for xf in self.transfers:
      lost = 0
      size = xf.src_ranges.size()
      for u in xf.goes_before:
        # xf should go before u
        if xf.order < u.order:
          # it does, hurray!
          in_order += 1
        else:
          # it doesn't, boo.  trim the blocks that u writes from xf's
          # source, so that xf can go after u.
          out_of_order += 1
          assert xf.src_ranges.overlaps(u.tgt_ranges)
          xf.src_ranges = xf.src_ranges.subtract(u.tgt_ranges)
          xf.intact = False

      if xf.style == "diff" and not xf.src_ranges:
        # nothing left to diff from; treat as new data
        xf.style = "new"

      lost = size - xf.src_ranges.size()
      lost_source += lost

    print(("  %d/%d dependencies (%.2f%%) were violated; "
           "%d source blocks removed.") %
          (out_of_order, in_order + out_of_order,
           (out_of_order * 100.0 / (in_order + out_of_order))
           if (in_order + out_of_order) else 0.0,
           lost_source))

  def ReverseBackwardEdges(self):
    print("Reversing backward edges...")
    in_order = 0
    out_of_order = 0
    stashes = 0
    stash_size = 0

    for xf in self.transfers:
      for u in xf.goes_before.copy():
        # xf should go before u
        if xf.order < u.order:
          # it does, hurray!
          in_order += 1
        else:
          # it doesn't, boo.  modify u to stash the blocks that it
          # writes that xf wants to read, and then require u to go
          # before xf.
          out_of_order += 1

          overlap = xf.src_ranges.intersect(u.tgt_ranges)
          assert overlap

          u.stash_before.append((stashes, overlap))
          xf.use_stash.append((stashes, overlap))
          stashes += 1
          stash_size += overlap.size()

          # reverse the edge direction; now xf must go after u
          del xf.goes_before[u]
          del u.goes_after[xf]
          xf.goes_after[u] = None    # value doesn't matter
          u.goes_before[xf] = None

    print(("  %d/%d dependencies (%.2f%%) were violated; "
           "%d source blocks stashed.") %
          (out_of_order, in_order + out_of_order,
           (out_of_order * 100.0 / (in_order + out_of_order))
           if (in_order + out_of_order) else 0.0,
           stash_size))

  def FindVertexSequence(self):
    print("Finding vertex sequence...")

    # This is based on "A Fast & Effective Heuristic for the Feedback
    # Arc Set Problem" by P. Eades, X. Lin, and W.F. Smyth.  Think of
    # it as starting with the digraph G and moving all the vertices to
    # be on a horizontal line in some order, trying to minimize the
    # number of edges that end up pointing to the left.  Left-pointing
    # edges will get removed to turn the digraph into a DAG.  In this
    # case each edge has a weight which is the number of source blocks
    # we'll lose if that edge is removed; we try to minimize the total
    # weight rather than just the number of edges.

    # Make a copy of the edge set; this copy will get destroyed by the
    # algorithm.
    for xf in self.transfers:
      xf.incoming = xf.goes_after.copy()
      xf.outgoing = xf.goes_before.copy()

    # We use an OrderedDict instead of just a set so that the output
    # is repeatable; otherwise it would depend on the hash values of
    # the transfer objects.
    G = OrderedDict()
    for xf in self.transfers:
      G[xf] = None
    s1 = deque()  # the left side of the sequence, built from left to right
    s2 = deque()  # the right side of the sequence, built from right to left

    while G:

      # Put all sinks at the end of the sequence.
      while True:
        sinks = [u for u in G if not u.outgoing]
        if not sinks:
          break
        for u in sinks:
          s2.appendleft(u)
          del G[u]
          for iu in u.incoming:
            del iu.outgoing[u]

      # Put all the sources at the beginning of the sequence.
      while True:
        sources = [u for u in G if not u.incoming]
        if not sources:
          break
        for u in sources:
          s1.append(u)
          del G[u]
          for iu in u.outgoing:
            del iu.incoming[u]

      if not G:
        break

      # Find the "best" vertex to put next.  "Best" is the one that
      # maximizes the net difference in source blocks saved we get by
      # pretending it's a source rather than a sink.

      max_d = None
      best_u = None
      for u in G:
        d = sum(u.outgoing.values()) - sum(u.incoming.values())
        if best_u is None or d > max_d:
          max_d = d
          best_u = u

      u = best_u
      s1.append(u)
      del G[u]
      for iu in u.outgoing:
        del iu.incoming[u]
      for iu in u.incoming:
        del iu.outgoing[u]

    # Now record the sequence in the 'order' field of each transfer,
    # and by rearranging self.transfers to be in the chosen sequence.

    new_transfers = []
    for x in itertools.chain(s1, s2):
      x.order = len(new_transfers)
      new_transfers.append(x)
      del x.incoming
      del x.outgoing

    self.transfers = new_transfers

  def GenerateDigraph(self):
    print("Generating digraph...")
    for a in self.transfers:
      for b in self.transfers:
        if a is b:
          continue

        # If the blocks written by A are read by B, then B needs to go before A.
        i = a.tgt_ranges.intersect(b.src_ranges)
        if i:
          if b.src_name == "__ZERO":
            # the cost of removing source blocks for the __ZERO domain
            # is (nearly) zero.
            size = 0
          else:
            size = i.size()
          b.goes_before[a] = size
          a.goes_after[b] = size

  def FindTransfers(self):
    empty = RangeSet()
    for tgt_fn, tgt_ranges in self.tgt.file_map.items():
      if tgt_fn == "__ZERO":
        # the special "__ZERO" domain is all the blocks not contained
        # in any file and that are filled with zeros.  We have a
        # special transfer style for zero blocks.
        src_ranges = self.src.file_map.get("__ZERO", empty)
        Transfer(tgt_fn, "__ZERO", tgt_ranges, src_ranges,
                 "zero", self.transfers)
        continue

      elif tgt_fn == "__COPY":
        # "__COPY" domain includes all the blocks not contained in any
        # file and that need to be copied unconditionally to the target.
        Transfer(tgt_fn, None, tgt_ranges, empty, "new", self.transfers)
        continue

      elif tgt_fn in self.src.file_map:
        # Look for an exact pathname match in the source.
        Transfer(tgt_fn, tgt_fn, tgt_ranges, self.src.file_map[tgt_fn],
                 "diff", self.transfers)
        continue

      b = os.path.basename(tgt_fn)
      if b in self.src_basenames:
        # Look for an exact basename match in the source.
        src_fn = self.src_basenames[b]
        Transfer(tgt_fn, src_fn, tgt_ranges, self.src.file_map[src_fn],
                 "diff", self.transfers)
        continue

      b = re.sub("[0-9]+", "#", b)
      if b in self.src_numpatterns:
        # Look for a 'number pattern' match (a basename match after
        # all runs of digits are replaced by "#").  (This is useful
        # for .so files that contain version numbers in the filename
        # that get bumped.)
        src_fn = self.src_numpatterns[b]
        Transfer(tgt_fn, src_fn, tgt_ranges, self.src.file_map[src_fn],
                 "diff", self.transfers)
        continue

      Transfer(tgt_fn, None, tgt_ranges, empty, "new", self.transfers)

  def AbbreviateSourceNames(self):
    for k in self.src.file_map.keys():
      b = os.path.basename(k)
      self.src_basenames[b] = k
      b = re.sub("[0-9]+", "#", b)
      self.src_numpatterns[b] = k

  @staticmethod
  def AssertPartition(total, seq):
    """Assert that all the RangeSets in 'seq' form a partition of the
    'total' RangeSet (ie, they are nonintersecting and their union
    equals 'total')."""
    so_far = RangeSet()
    for i in seq:
      assert not so_far.overlaps(i)
      so_far = so_far.union(i)
    assert so_far == total