xref: /build/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 common
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))

      if self.version >= 2:
        # Sanity check: abort if we're going to need more stash space than
        # the allowed size (cache_size * threshold). There are two purposes
        # of having a threshold here. a) Part of the cache may have been
        # occupied by some recovery logs. b) It will buy us some time to deal
        # with the oversize issue.
        cache_size = common.OPTIONS.cache_size
        stash_threshold = common.OPTIONS.stash_threshold
        max_allowed = cache_size * stash_threshold
        assert max_stashed_blocks * self.tgt.blocksize < max_allowed, \
               'Stash size %d (%d * %d) exceeds the limit %d (%d * %.2f)' % (
                   max_stashed_blocks * self.tgt.blocksize, max_stashed_blocks,
                   self.tgt.blocksize, max_allowed, cache_size,
                   stash_threshold)

    # 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:
      max_stashed_size = max_stashed_blocks * self.tgt.blocksize
      max_allowed = common.OPTIONS.cache_size * common.OPTIONS.stash_threshold
      print("max stashed blocks: %d  (%d bytes), limit: %d bytes (%.2f%%)\n" % (
          max_stashed_blocks, max_stashed_size, max_allowed,
          max_stashed_size * 100.0 / max_allowed))

  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