diff --git a/CleanSpec.mk b/CleanSpec.mk
index f348692..a4a44ca 100644
--- a/CleanSpec.mk
+++ b/CleanSpec.mk
@@ -299,6 +299,11 @@
 $(call add-clean-step, rm -rf $(PRODUCT_OUT)/system/app/*)
 $(call add-clean-step, rm -rf $(PRODUCT_OUT)/obj/APPS/*)
 
+# API 22!
+$(call add-clean-step, rm -rf $(PRODUCT_OUT)/system/build.prop)
+$(call add-clean-step, rm -rf $(PRODUCT_OUT)/system/app/*)
+$(call add-clean-step, rm -rf $(PRODUCT_OUT)/obj/APPS/*)
+
 # ************************************************
 # NEWER CLEAN STEPS MUST BE AT THE END OF THE LIST
 # ************************************************
diff --git a/core/Makefile b/core/Makefile
index 72ca56c..0db41c9 100644
--- a/core/Makefile
+++ b/core/Makefile
@@ -1405,6 +1405,7 @@
 	$(hide) echo "use_set_metadata=1" >> $(zip_root)/META/misc_info.txt
 	$(hide) echo "multistage_support=1" >> $(zip_root)/META/misc_info.txt
 	$(hide) echo "update_rename_support=1" >> $(zip_root)/META/misc_info.txt
+	$(hide) echo "blockimgdiff_versions=1,2" >> $(zip_root)/META/misc_info.txt
 ifneq ($(OEM_THUMBPRINT_PROPERTIES),)
 	# OTA scripts are only interested in fingerprint related properties
 	$(hide) echo "oem_fingerprint_properties=$(OEM_THUMBPRINT_PROPERTIES)" >> $(zip_root)/META/misc_info.txt
diff --git a/core/binary.mk b/core/binary.mk
index d339317..1e313ff 100644
--- a/core/binary.mk
+++ b/core/binary.mk
@@ -184,9 +184,11 @@
 
 my_compiler_dependencies :=
 
-####################################################
+##################################################################
 ## Add FDO flags if FDO is turned on and supported
-####################################################
+## Please note that we will do option filtering during FDO build.
+## i.e. Os->O2, remove -fno-early-inline and -finline-limit.
+##################################################################
 ifeq ($(strip $(LOCAL_FDO_SUPPORT)), true)
   ifeq ($(strip $(LOCAL_IS_HOST_MODULE)),)
     my_cflags += $($(LOCAL_2ND_ARCH_VAR_PREFIX)TARGET_FDO_CFLAGS)
@@ -923,6 +925,21 @@
 my_ldflags := $(call $(LOCAL_2ND_ARCH_VAR_PREFIX)convert-to-$(my_host)clang-flags,$(my_ldflags))
 endif
 
+ifeq ($(LOCAL_FDO_SUPPORT), true)
+  build_with_fdo := false
+  ifeq ($(BUILD_FDO_INSTRUMENT), true)
+    build_with_fdo := true
+  endif
+  ifeq ($(BUILD_FDO_OPTIMIZE), true)
+    build_with_fdo := true
+  endif
+  ifeq ($(build_with_fdo), true)
+    my_cflags := $(patsubst -Os,-O2,$(my_cflags))
+    fdo_incompatible_flags=-fno-early-inlining -finline-limit=%
+    my_cflags := $(filter-out $(fdo_incompatible_flags),$(my_cflags))
+  endif
+endif
+
 $(LOCAL_INTERMEDIATE_TARGETS): PRIVATE_YACCFLAGS := $(LOCAL_YACCFLAGS)
 $(LOCAL_INTERMEDIATE_TARGETS): PRIVATE_ASFLAGS := $(my_asflags)
 $(LOCAL_INTERMEDIATE_TARGETS): PRIVATE_CONLYFLAGS := $(LOCAL_CONLYFLAGS)
diff --git a/core/cleanbuild.mk b/core/cleanbuild.mk
index 1bada38..c820ad5 100644
--- a/core/cleanbuild.mk
+++ b/core/cleanbuild.mk
@@ -220,6 +220,7 @@
 	$(PRODUCT_OUT)/obj/JAVA_LIBRARIES \
 	$(PRODUCT_OUT)/obj/FAKE \
 	$(PRODUCT_OUT)/obj/EXECUTABLES/adbd_intermediates \
+	$(PRODUCT_OUT)/obj/STATIC_LIBRARIES/libfs_mgr_intermediates \
 	$(PRODUCT_OUT)/obj/EXECUTABLES/init_intermediates \
 	$(PRODUCT_OUT)/obj/ETC/mac_permissions.xml_intermediates \
 	$(PRODUCT_OUT)/obj/ETC/sepolicy_intermediates \
diff --git a/core/combo/HOST_darwin-x86.mk b/core/combo/HOST_darwin-x86.mk
index 4a2bfe3..ec37993 100644
--- a/core/combo/HOST_darwin-x86.mk
+++ b/core/combo/HOST_darwin-x86.mk
@@ -37,8 +37,8 @@
 ifneq (,$(strip $(wildcard $($(combo_2nd_arch_prefix)HOST_TOOLCHAIN_PREFIX)-gcc)))
 $(combo_2nd_arch_prefix)HOST_CC  := $($(combo_2nd_arch_prefix)HOST_TOOLCHAIN_PREFIX)-gcc
 $(combo_2nd_arch_prefix)HOST_CXX := $($(combo_2nd_arch_prefix)HOST_TOOLCHAIN_PREFIX)-g++
-ifeq ($(mac_sdk_version),10.8)
-# Mac SDK 10.8 no longer has stdarg.h, etc
+ifneq ($(filter 10.8 10.9, $(mac_sdk_version)),)
+# Mac SDK 10.8+ no longer has stdarg.h, etc
 host_toolchain_header := $($(combo_2nd_arch_prefix)HOST_TOOLCHAIN_ROOT)/lib/gcc/i686-apple-darwin$(gcc_darwin_version)/4.2.1/include
 $(combo_2nd_arch_prefix)HOST_GLOBAL_CFLAGS += -isystem $(host_toolchain_header)
 endif
diff --git a/core/combo/HOST_darwin-x86_64.mk b/core/combo/HOST_darwin-x86_64.mk
index 0bc0227..a776a69 100644
--- a/core/combo/HOST_darwin-x86_64.mk
+++ b/core/combo/HOST_darwin-x86_64.mk
@@ -37,8 +37,8 @@
 ifneq (,$(strip $(wildcard $(HOST_TOOLCHAIN_PREFIX)-gcc)))
 HOST_CC  := $(HOST_TOOLCHAIN_PREFIX)-gcc
 HOST_CXX := $(HOST_TOOLCHAIN_PREFIX)-g++
-ifeq ($(mac_sdk_version),10.8)
-# Mac SDK 10.8 no longer has stdarg.h, etc
+ifneq ($(filter 10.8 10.9, $(mac_sdk_version)),)
+# Mac SDK 10.8+ no longer has stdarg.h, etc
 host_toolchain_header := $(HOST_TOOLCHAIN_ROOT)/lib/gcc/i686-apple-darwin$(gcc_darwin_version)/4.2.1/include
 HOST_GLOBAL_CFLAGS += -isystem $(host_toolchain_header)
 endif
diff --git a/core/combo/mac_version.mk b/core/combo/mac_version.mk
index b49feee..6defba7 100644
--- a/core/combo/mac_version.mk
+++ b/core/combo/mac_version.mk
@@ -9,7 +9,7 @@
 
 build_mac_version := $(shell sw_vers -productVersion)
 
-mac_sdk_versions_supported :=  10.6 10.7 10.8
+mac_sdk_versions_supported :=  10.6 10.7 10.8 10.9
 ifneq ($(strip $(MAC_SDK_VERSION)),)
 mac_sdk_version := $(MAC_SDK_VERSION)
 ifeq ($(filter $(mac_sdk_version),$(mac_sdk_versions_supported)),)
diff --git a/core/version_defaults.mk b/core/version_defaults.mk
index 8cb8d26..1acc320 100644
--- a/core/version_defaults.mk
+++ b/core/version_defaults.mk
@@ -41,7 +41,7 @@
   # which is the version that we reveal to the end user.
   # Update this value when the platform version changes (rather
   # than overriding it somewhere else).  Can be an arbitrary string.
-  PLATFORM_VERSION := 5.0
+  PLATFORM_VERSION := LollipopMR1
 endif
 
 ifeq "" "$(PLATFORM_SDK_VERSION)"
@@ -53,7 +53,7 @@
   # intermediate builds).  During development, this number remains at the
   # SDK version the branch is based on and PLATFORM_VERSION_CODENAME holds
   # the code-name of the new development work.
-  PLATFORM_SDK_VERSION := 21
+  PLATFORM_SDK_VERSION := 22
 endif
 
 ifeq "" "$(PLATFORM_VERSION_CODENAME)"
diff --git a/tools/releasetools/blockimgdiff.py b/tools/releasetools/blockimgdiff.py
index 216486c..8b179d5 100644
--- a/tools/releasetools/blockimgdiff.py
+++ b/tools/releasetools/blockimgdiff.py
@@ -16,6 +16,7 @@
 
 from collections import deque, OrderedDict
 from hashlib import sha1
+import heapq
 import itertools
 import multiprocessing
 import os
@@ -142,9 +143,16 @@
     self.goes_before = {}
     self.goes_after = {}
 
+    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) + ">")
@@ -182,11 +190,14 @@
 # original image.
 
 class BlockImageDiff(object):
-  def __init__(self, tgt, src=None, threads=None):
+  def __init__(self, tgt, src=None, threads=None, version=2):
     if threads is None:
       threads = multiprocessing.cpu_count() // 2
       if threads == 0: threads = 1
     self.threads = threads
+    self.version = version
+
+    assert version in (1, 2)
 
     self.tgt = tgt
     if src is None:
@@ -221,7 +232,12 @@
     self.FindVertexSequence()
     # Fix up the ordering dependencies that the sequence didn't
     # satisfy.
-    self.RemoveBackwardEdges()
+    if self.version == 1:
+      self.RemoveBackwardEdges()
+    else:
+      self.ReverseBackwardEdges()
+      self.ImproveVertexSequence()
+
     # Double-check our work.
     self.AssertSequenceGood()
 
@@ -231,18 +247,87 @@
   def WriteTransfers(self, prefix):
     out = []
 
-    out.append("1\n")   # format version number
     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:
 
-      # zero [rangeset]
-      # new [rangeset]
-      # bsdiff patchstart patchlen [src rangeset] [tgt rangeset]
-      # imgdiff patchstart patchlen [src rangeset] [tgt rangeset]
-      # move [src rangeset] [tgt rangeset]
-      # erase [rangeset]
+      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()
+        out.append("stash %d %s\n" % (sid, sr.to_string_raw()))
+
+      if stashed_blocks > max_stashed_blocks:
+        max_stashed_blocks = stashed_blocks
+
+      if self.version == 1:
+        src_string = 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_string = [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)
+          sr = xf.src_ranges.map_within(sr)
+          mapped_stashes.append(sr)
+          src_string.append("%d:%s" % (sid, sr.to_string_raw()))
+          heapq.heappush(free_stash_ids, sid)
+
+        if unstashed_src_ranges:
+          src_string.insert(1, unstashed_src_ranges.to_string_raw())
+          if xf.use_stash:
+            mapped_unstashed = xf.src_ranges.map_within(unstashed_src_ranges)
+            src_string.insert(2, mapped_unstashed.to_string_raw())
+            mapped_stashes.append(mapped_unstashed)
+            self.AssertPartition(RangeSet(data=(0, size)), mapped_stashes)
+        else:
+          src_string.insert(1, "-")
+          self.AssertPartition(RangeSet(data=(0, size)), mapped_stashes)
+
+        src_string = " ".join(src_string)
+
+      # both 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_string>
+      #   imgdiff patchstart patchlen <tgt rangeset> <src_string>
+      #   move <tgt rangeset> <src_string>
 
       tgt_size = xf.tgt_ranges.size()
 
@@ -255,17 +340,27 @@
         assert xf.tgt_ranges
         assert xf.src_ranges.size() == tgt_size
         if xf.src_ranges != xf.tgt_ranges:
-          out.append("%s %s %s\n" % (
-              xf.style,
-              xf.src_ranges.to_string_raw(), xf.tgt_ranges.to_string_raw()))
+          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_string))
           total += tgt_size
       elif xf.style in ("bsdiff", "imgdiff"):
         performs_read = True
         assert xf.tgt_ranges
         assert xf.src_ranges
-        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()))
+        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_string))
         total += tgt_size
       elif xf.style == "zero":
         assert xf.tgt_ranges
@@ -276,7 +371,10 @@
       else:
         raise ValueError, "unknown transfer style '%s'\n" % (xf.style,)
 
-    out.insert(1, str(total) + "\n")
+
+      # 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)
 
     all_tgt = RangeSet(data=(0, self.tgt.total_blocks))
     if performs_read:
@@ -289,12 +387,24 @@
     else:
       # if nothing is read (ie, this is a full OTA), then we can start
       # by erasing the entire partition.
-      out.insert(2, "erase %s\n" % (all_tgt.to_string_raw(),))
+      out.insert(0, "erase %s\n" % (all_tgt.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 = []
@@ -409,7 +519,13 @@
     # Imagine processing the transfers in order.
     for xf in self.transfers:
       # Check that the input blocks for this transfer haven't yet been touched.
-      assert not touched.overlaps(xf.src_ranges)
+
+      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.
@@ -418,6 +534,47 @@
     # 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
@@ -425,19 +582,17 @@
     lost_source = 0
 
     for xf in self.transfers:
-      io = 0
-      ooo = 0
       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!
-          io += 1
+          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.
-          ooo += 1
+          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
@@ -448,8 +603,6 @@
 
       lost = size - xf.src_ranges.size()
       lost_source += lost
-      in_order += io
-      out_of_order += ooo
 
     print(("  %d/%d dependencies (%.2f%%) were violated; "
            "%d source blocks removed.") %
@@ -458,6 +611,48 @@
            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:
+      lost = 0
+      size = xf.src_ranges.size()
+      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...")
 
diff --git a/tools/releasetools/common.py b/tools/releasetools/common.py
index 815c76c..96075a9 100644
--- a/tools/releasetools/common.py
+++ b/tools/releasetools/common.py
@@ -1030,7 +1030,14 @@
     self.partition = partition
     self.check_first_block = check_first_block
 
-    b = blockimgdiff.BlockImageDiff(tgt, src, threads=OPTIONS.worker_threads)
+    version = 1
+    if OPTIONS.info_dict:
+      version = max(
+          int(i) for i in
+          OPTIONS.info_dict.get("blockimgdiff_versions", "1").split(","))
+
+    b = blockimgdiff.BlockImageDiff(tgt, src, threads=OPTIONS.worker_threads,
+                                    version=version)
     tmpdir = tempfile.mkdtemp()
     OPTIONS.tempfiles.append(tmpdir)
     self.path = os.path.join(tmpdir, partition)
diff --git a/tools/releasetools/rangelib.py b/tools/releasetools/rangelib.py
index 8a85d2d..7279c60 100644
--- a/tools/releasetools/rangelib.py
+++ b/tools/releasetools/rangelib.py
@@ -24,7 +24,9 @@
   lots of runs."""
 
   def __init__(self, data=None):
-    if data:
+    if isinstance(data, str):
+      self._parse_internal(data)
+    elif data:
       self.data = tuple(self._remove_pairs(data))
     else:
       self.data = ()
@@ -46,6 +48,9 @@
     else:
       return self.to_string()
 
+  def __repr__(self):
+    return '<RangeSet("' + self.to_string() + '")>'
+
   @classmethod
   def parse(cls, text):
     """Parse a text string consisting of a space-separated list of
@@ -59,7 +64,9 @@
     "15-20 30 10-14" is not, even though they represent the same set
     of blocks (and the two RangeSets will compare equal with ==).
     """
+    return cls(text)
 
+  def _parse_internal(self, text):
     data = []
     last = -1
     monotonic = True
@@ -81,9 +88,8 @@
         else:
           monotonic = True
     data.sort()
-    r = RangeSet(cls._remove_pairs(data))
-    r.monotonic = monotonic
-    return r
+    self.data = tuple(self._remove_pairs(data))
+    self.monotonic = monotonic
 
   @staticmethod
   def _remove_pairs(source):
@@ -113,7 +119,13 @@
 
   def union(self, other):
     """Return a new RangeSet representing the union of this RangeSet
-    with the argument."""
+    with the argument.
+
+    >>> RangeSet("10-19 30-34").union(RangeSet("18-29"))
+    <RangeSet("10-34")>
+    >>> RangeSet("10-19 30-34").union(RangeSet("22 32"))
+    <RangeSet("10-19 22 30-34")>
+    """
     out = []
     z = 0
     for p, d in heapq.merge(zip(self.data, itertools.cycle((+1, -1))),
@@ -125,7 +137,13 @@
 
   def intersect(self, other):
     """Return a new RangeSet representing the intersection of this
-    RangeSet with the argument."""
+    RangeSet with the argument.
+
+    >>> RangeSet("10-19 30-34").intersect(RangeSet("18-32"))
+    <RangeSet("18-19 30-32")>
+    >>> RangeSet("10-19 30-34").intersect(RangeSet("22-28"))
+    <RangeSet("")>
+    """
     out = []
     z = 0
     for p, d in heapq.merge(zip(self.data, itertools.cycle((+1, -1))),
@@ -137,7 +155,13 @@
 
   def subtract(self, other):
     """Return a new RangeSet representing subtracting the argument
-    from this RangeSet."""
+    from this RangeSet.
+
+    >>> RangeSet("10-19 30-34").subtract(RangeSet("18-32"))
+    <RangeSet("10-17 33-34")>
+    >>> RangeSet("10-19 30-34").subtract(RangeSet("22-28"))
+    <RangeSet("10-19 30-34")>
+    """
 
     out = []
     z = 0
@@ -150,7 +174,13 @@
 
   def overlaps(self, other):
     """Returns true if the argument has a nonempty overlap with this
-    RangeSet."""
+    RangeSet.
+
+    >>> RangeSet("10-19 30-34").overlaps(RangeSet("18-32"))
+    True
+    >>> RangeSet("10-19 30-34").overlaps(RangeSet("22-28"))
+    False
+    """
 
     # This is like intersect, but we can stop as soon as we discover the
     # output is going to be nonempty.
@@ -164,7 +194,11 @@
 
   def size(self):
     """Returns the total size of the RangeSet (ie, how many integers
-    are in the set)."""
+    are in the set).
+
+    >>> RangeSet("10-19 30-34").size()
+    15
+    """
 
     total = 0
     for i, p in enumerate(self.data):
@@ -173,3 +207,37 @@
       else:
         total -= p
     return total
+
+  def map_within(self, other):
+    """'other' should be a subset of 'self'.  Returns a RangeSet
+    representing what 'other' would get translated to if the integers
+    of 'self' were translated down to be contiguous starting at zero.
+
+    >>> RangeSet("0-9").map_within(RangeSet("3-4"))
+    <RangeSet("3-4")>
+    >>> RangeSet("10-19").map_within(RangeSet("13-14"))
+    <RangeSet("3-4")>
+    >>> RangeSet("10-19 30-39").map_within(RangeSet("17-19 30-32"))
+    <RangeSet("7-12")>
+    >>> RangeSet("10-19 30-39").map_within(RangeSet("12-13 17-19 30-32"))
+    <RangeSet("2-3 7-12")>
+    """
+
+    out = []
+    offset = 0
+    start = None
+    for p, d in heapq.merge(zip(self.data, itertools.cycle((-5, +5))),
+                            zip(other.data, itertools.cycle((-1, +1)))):
+      if d == -5:
+        start = p
+      elif d == +5:
+        offset += p-start
+        start = None
+      else:
+        out.append(offset + p - start)
+    return RangeSet(data=out)
+
+
+if __name__ == "__main__":
+  import doctest
+  doctest.testmod()