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 b08ad1b..6c49580 100644
--- a/core/Makefile
+++ b/core/Makefile
@@ -1418,6 +1418,7 @@
 	$(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 \
 	$(PRODUCT_OUT)/obj/ETC/sepolicy_intermediates \
diff --git a/core/clear_vars.mk b/core/clear_vars.mk
index f23c4a6..92b3fc4 100644
--- a/core/clear_vars.mk
+++ b/core/clear_vars.mk
@@ -123,6 +123,7 @@
 LOCAL_RENDERSCRIPT_TARGET_API:=
 LOCAL_DEX_PREOPT:= # '',true,false,nostripping
 LOCAL_DEX_PREOPT_IMAGE_LOCATION:=
+LOCAL_DEX_PREOPT_FLAGS:=
 LOCAL_PROTOC_OPTIMIZE_TYPE:= # lite(default),micro,nano,full
 LOCAL_PROTOC_FLAGS:=
 LOCAL_PROTO_JAVA_OUTPUT_PARAMS:=
diff --git a/core/combo/HOST_darwin-x86.mk b/core/combo/HOST_darwin-x86.mk
index 4a2bfe3..ec37993 100644
--- a/core/combo/HOST_darwin-x86.mk
+++ b/core/combo/HOST_darwin-x86.mk
@@ -37,8 +37,8 @@
 ifneq (,$(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 $(host_toolchain_header)
 endif
diff --git a/core/combo/HOST_windows-x86.mk b/core/combo/HOST_windows-x86.mk
index fdb72a7..00e1974 100644
--- a/core/combo/HOST_windows-x86.mk
+++ b/core/combo/HOST_windows-x86.mk
@@ -27,7 +27,7 @@
 ifneq ($(strip $(USE_MINGW)),)
 HOST_ACP_UNAVAILABLE := true
 TOOLS_EXE_SUFFIX :=
-$(combo_2nd_arch_prefix)HOST_GLOBAL_CFLAGS += -DUSE_MINGW
+$(combo_2nd_arch_prefix)HOST_GLOBAL_CFLAGS += -DUSE_MINGW -DWIN32_LEAN_AND_MEAN
 $(combo_2nd_arch_prefix)HOST_GLOBAL_CFLAGS += -Wno-unused-parameter
 $(combo_2nd_arch_prefix)HOST_GLOBAL_CFLAGS += --sysroot=prebuilts/gcc/linux-x86/host/x86_64-w64-mingw32-4.8/x86_64-w64-mingw32
 $(combo_2nd_arch_prefix)HOST_GLOBAL_CFLAGS += -m32
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/dex_preopt_libart.mk b/core/dex_preopt_libart.mk
index 5af2be2..4e43a86 100644
--- a/core/dex_preopt_libart.mk
+++ b/core/dex_preopt_libart.mk
@@ -91,5 +91,6 @@
 	--android-root=$(PRODUCT_OUT)/system \
 	--instruction-set=$($(PRIVATE_2ND_ARCH_VAR_PREFIX)DEX2OAT_TARGET_ARCH) \
 	--instruction-set-features=$($(PRIVATE_2ND_ARCH_VAR_PREFIX)DEX2OAT_TARGET_INSTRUCTION_SET_FEATURES) \
-	--include-patch-information --runtime-arg -Xnorelocate --no-include-debug-symbols
+	--include-patch-information --runtime-arg -Xnorelocate --no-include-debug-symbols \
+	$(PRIVATE_DEX_PREOPT_FLAGS)
 endef
diff --git a/core/dex_preopt_libart_boot.mk b/core/dex_preopt_libart_boot.mk
index fe4c5a4..0714c73 100644
--- a/core/dex_preopt_libart_boot.mk
+++ b/core/dex_preopt_libart_boot.mk
@@ -32,6 +32,11 @@
 $(my_2nd_arch_prefix)DEFAULT_DEX_PREOPT_INSTALLED_IMAGE := $(PRODUCT_OUT)$($(my_2nd_arch_prefix)LIBART_BOOT_IMAGE_FILENAME)
 endif
 
+# Compile boot.oat as position-independent code if WITH_DEXPREOPT_PIC=true
+ifeq (true,$(WITH_DEXPREOPT_PIC))
+  PRODUCT_DEX_PREOPT_BOOT_FLAGS += --compile-pic
+endif
+
 # The rule to install boot.art and boot.oat
 $($(my_2nd_arch_prefix)DEFAULT_DEX_PREOPT_INSTALLED_IMAGE) : $($(my_2nd_arch_prefix)DEFAULT_DEX_PREOPT_BUILT_IMAGE_FILENAME) | $(ACP)
 	$(call copy-file-to-target)
@@ -53,4 +58,5 @@
 		--image=$@ --base=$(LIBART_IMG_TARGET_BASE_ADDRESS) \
 		--instruction-set=$($(PRIVATE_2ND_ARCH_VAR_PREFIX)DEX2OAT_TARGET_ARCH) \
 		--instruction-set-features=$($(PRIVATE_2ND_ARCH_VAR_PREFIX)DEX2OAT_TARGET_INSTRUCTION_SET_FEATURES) \
-		--android-root=$(PRODUCT_OUT)/system --include-patch-information --runtime-arg -Xnorelocate --no-include-debug-symbols
+		--android-root=$(PRODUCT_OUT)/system --include-patch-information --runtime-arg -Xnorelocate --no-include-debug-symbols \
+		$(PRODUCT_DEX_PREOPT_BOOT_FLAGS)
diff --git a/core/dex_preopt_odex_install.mk b/core/dex_preopt_odex_install.mk
index 741f9a3..cb38261 100644
--- a/core/dex_preopt_odex_install.mk
+++ b/core/dex_preopt_odex_install.mk
@@ -11,7 +11,12 @@
     ifndef LOCAL_DEX_PREOPT # LOCAL_DEX_PREOPT undefined
       ifneq ($(filter $(TARGET_OUT)/%,$(my_module_path)),) # Installed to system.img.
         ifeq (,$(LOCAL_APK_LIBRARIES)) # LOCAL_APK_LIBRARIES empty
-          LOCAL_DEX_PREOPT := $(DEX_PREOPT_DEFAULT)
+          # If we have product-specific config for this module?
+          ifeq (disable,$(DEXPREOPT.$(TARGET_PRODUCT).$(LOCAL_MODULE).CONFIG))
+            LOCAL_DEX_PREOPT := false
+          else
+            LOCAL_DEX_PREOPT := $(DEX_PREOPT_DEFAULT)
+          endif
         else # LOCAL_APK_LIBRARIES not empty
           LOCAL_DEX_PREOPT := nostripping
         endif # LOCAL_APK_LIBRARIES not empty
@@ -94,6 +99,20 @@
 endif  # boot jar
 
 ifdef built_odex
+ifndef LOCAL_DEX_PREOPT_FLAGS
+LOCAL_DEX_PREOPT_FLAGS := $(DEXPREOPT.$(TARGET_PRODUCT).$(LOCAL_MODULE).CONFIG)
+ifndef LOCAL_DEX_PREOPT_FLAGS
+LOCAL_DEX_PREOPT_FLAGS := $(PRODUCT_DEX_PREOPT_DEFAULT_FLAGS)
+endif
+endif
+
+# Compile apps with position-independent code if WITH_DEXPREOPT_PIC=true
+ifeq (true,$(WITH_DEXPREOPT_PIC))
+  LOCAL_DEX_PREOPT_FLAGS += --compile-pic
+endif
+
+$(built_odex): PRIVATE_DEX_PREOPT_FLAGS := $(LOCAL_DEX_PREOPT_FLAGS)
+
 # Use pattern rule - we may have multiple installed odex files.
 # Ugly syntax - See the definition get-odex-file-path.
 $(installed_odex) : $(dir $(LOCAL_INSTALLED_MODULE))%$(notdir $(word 1,$(installed_odex))) \
diff --git a/core/product.mk b/core/product.mk
index 0075acd..ed906cb 100644
--- a/core/product.mk
+++ b/core/product.mk
@@ -100,14 +100,18 @@
     PRODUCT_FACTORY_BUNDLE_MODULES \
     PRODUCT_RUNTIMES \
     PRODUCT_BOOT_JARS \
-    PRODUCT_DEX_PREOPT_IMAGE_IN_DATA \
     PRODUCT_SUPPORTS_VERITY \
     PRODUCT_OEM_PROPERTIES \
     PRODUCT_SYSTEM_PROPERTY_BLACKLIST \
     PRODUCT_SYSTEM_SERVER_JARS \
     PRODUCT_VERITY_SIGNING_KEY \
     PRODUCT_SYSTEM_VERITY_PARTITION \
-    PRODUCT_VENDOR_VERITY_PARTITION
+    PRODUCT_VENDOR_VERITY_PARTITION \
+    PRODUCT_DEX_PREOPT_IMAGE_IN_DATA \
+    PRODUCT_DEX_PREOPT_MODULE_CONFIGS \
+    PRODUCT_DEX_PREOPT_DEFAULT_FLAGS \
+    PRODUCT_DEX_PREOPT_BOOT_FLAGS \
+
 
 define dump-product
 $(info ==== $(1) ====)\
@@ -299,3 +303,14 @@
 define add-to-product-copy-files-if-exists
 $(if $(wildcard $(word 1,$(subst :, ,$(1)))),$(1))
 endef
+
+# whitespace placeholder when we record module's dex-preopt config.
+_PDPMC_SP_PLACE_HOLDER := |@SP@|
+# Set up dex-preopt config for a module.
+# $(1) list of module names
+# $(2) the modules' dex-preopt config
+define add-product-dex-preopt-module-config
+$(eval _c := $(subst $(space),$(_PDPMC_SP_PLACE_HOLDER),$(strip $(2))))\
+$(eval PRODUCT_DEX_PREOPT_MODULE_CONFIGS += \
+  $(foreach m,$(1),$(m)=$(_c)))
+endef
diff --git a/core/product_config.mk b/core/product_config.mk
index 32e351c..d4ba364 100644
--- a/core/product_config.mk
+++ b/core/product_config.mk
@@ -416,3 +416,21 @@
 # If there is no room in /system for the image, place it in /data
 PRODUCT_DEX_PREOPT_IMAGE_IN_DATA := \
     $(strip $(PRODUCTS.$(INTERNAL_PRODUCT).PRODUCT_DEX_PREOPT_IMAGE_IN_DATA))
+
+PRODUCT_DEX_PREOPT_DEFAULT_FLAGS := \
+    $(strip $(PRODUCTS.$(INTERNAL_PRODUCT).PRODUCT_DEX_PREOPT_DEFAULT_FLAGS))
+PRODUCT_DEX_PREOPT_BOOT_FLAGS := \
+    $(strip $(PRODUCTS.$(INTERNAL_PRODUCT).PRODUCT_DEX_PREOPT_BOOT_FLAGS))
+# Resolve and setup per-module dex-preopot configs.
+PRODUCT_DEX_PREOPT_MODULE_CONFIGS := \
+    $(strip $(PRODUCTS.$(INTERNAL_PRODUCT).PRODUCT_DEX_PREOPT_MODULE_CONFIGS))
+# If a module has multiple setups, the first takes precedence.
+_pdpmc_modules :=
+$(foreach c,$(PRODUCT_DEX_PREOPT_MODULE_CONFIGS),\
+  $(eval m := $(firstword $(subst =,$(space),$(c))))\
+  $(if $(filter $(_pdpmc_modules),$(m)),,\
+    $(eval _pdpmc_modules += $(m))\
+    $(eval cf := $(patsubst $(m)=%,%,$(c)))\
+    $(eval cf := $(subst $(_PDPMC_SP_PLACE_HOLDER),$(space),$(cf)))\
+    $(eval DEXPREOPT.$(TARGET_PRODUCT).$(m).CONFIG := $(cf))))
+_pdpmc_modules :=
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 "" "$(PLATFORM_VERSION_CODENAME)"
diff --git a/envsetup.sh b/envsetup.sh
index a9bd707..94f0c48 100644
--- a/envsetup.sh
+++ b/envsetup.sh
@@ -570,7 +570,8 @@
 {
     local arch="$(echo $* | xargs -n 1 echo | \grep -E '^(arm|x86|mips|armv5|arm64|x86_64|mips64)$' | xargs)"
     local variant="$(echo $* | xargs -n 1 echo | \grep -E '^(user|userdebug|eng)$' | xargs)"
-    local apps="$(echo $* | xargs -n 1 echo | \grep -E -v '^(user|userdebug|eng|arm|x86|mips|armv5|arm64|x86_64|mips64)$' | xargs)"
+    local density="$(echo $* | xargs -n 1 echo | \grep -E '^(ldpi|mdpi|tvdpi|hdpi|xhdpi|xxhdpi|xxxhdpi|alldpi)$' | xargs)"
+    local apps="$(echo $* | xargs -n 1 echo | \grep -E -v '^(user|userdebug|eng|arm|x86|mips|armv5|arm64|x86_64|mips64|ldpi|mdpi|tvdpi|hdpi|xhdpi|xxhdpi|xxxhdpi|alldpi)$' | xargs)"
 
     if [ $(echo $arch | wc -w) -gt 1 ]; then
         echo "tapas: Error: Multiple build archs supplied: $arch"
@@ -580,6 +581,10 @@
         echo "tapas: Error: Multiple build variants supplied: $variant"
         return
     fi
+    if [ $(echo $density | wc -w) -gt 1 ]; then
+        echo "tapas: Error: Multiple densities supplied: $density"
+        return
+    fi
 
     local product=full
     case $arch in
@@ -599,6 +604,7 @@
 
     export TARGET_PRODUCT=$product
     export TARGET_BUILD_VARIANT=$variant
+    export TARGET_BUILD_DENSITY=$density
     export TARGET_BUILD_TYPE=release
     export TARGET_BUILD_APPS=$apps
 
@@ -884,6 +890,84 @@
     fi
 }
 
+# coredump_setup - enable core dumps globally for any process
+#                  that has the core-file-size limit set correctly
+#
+# NOTE: You must call also coredump-enable for a specific process
+#       if its core-file-size limit is not set already.
+# NOTE: Core dumps are written to ramdisk; they will not survive a reboot!
+
+function coredump_setup()
+{
+	echo "Getting root...";
+	adb root;
+	adb wait-for-device;
+
+	echo "Remounting root parition read-write...";
+	adb shell mount -w -o remount -t rootfs rootfs;
+	sleep 1;
+	adb wait-for-device;
+	adb shell mkdir -p /cores;
+	adb shell chmod 0777 /cores;
+
+	echo "Granting SELinux permission to dump in /cores...";
+	adb shell restorecon -R /cores;
+
+	echo "Set core pattern.";
+	adb shell 'echo /cores/core.%p > /proc/sys/kernel/core_pattern';
+
+	echo "Done."
+}
+
+# coredump-enable - enable core dumps for the specified process
+# $1 = PID of process (e.g., $(pid mediaserver))
+#
+# NOTE: coredump-setup must have been called as well for a core
+#       dump to actually be generated.
+
+function coredump-enable()
+{
+	local PID=$1;
+	if [ -z "$PID" ]; then
+		printf "Expecting a PID!\n";
+		return;
+	fi;
+	echo "Setting core limit for $PID to infinite...";
+	adb shell prlimit $PID 4 -1 -1
+}
+
+# core - send SIGV and pull the core for process
+# $1 = PID of process (e.g., $(pid mediaserver))
+#
+# NOTE: coredump-setup must be called once per boot for core dumps to be
+#       enabled globally.
+
+function core()
+{
+	local PID=$1;
+
+	if [ -z "$PID" ]; then
+		printf "Expecting a PID!\n";
+		return;
+	fi;
+
+	local CORENAME=core.$PID;
+	local COREPATH=/cores/$CORENAME;
+	local SIG=SEGV;
+
+	coredump-enable $1;
+
+	local done=0;
+	while [ $(adb shell "[ -d /proc/$PID ] && echo -n yes") ]; do
+		printf "\tSending SIG%s to %d...\n" $SIG $PID;
+		adb shell kill -$SIG $PID;
+		sleep 1;
+	done;
+
+	adb shell "while [ ! -f $COREPATH ] ; do echo waiting for $COREPATH to be generated; sleep 1; done"
+	echo "Done: core is under $COREPATH on device.";
+}
+
 # systemstack - dump the current stack trace of all threads in the system process
 # to the usual ANR traces file
 function systemstack()
@@ -967,10 +1051,151 @@
     fi
 }
 
+function adb_get_product_device() {
+  echo `adb shell getprop ro.product.device | sed s/.$//`
+}
+
+# returns 0 when process is not traced
+function adb_get_traced_by() {
+  echo `adb shell cat /proc/$1/status | grep -e "^TracerPid:" | sed "s/^TracerPid:\t//" | sed s/.$//`
+}
+
+function gdbclient() {
+  # TODO:
+  # 1. Check for ANDROID_SERIAL/multiple devices
+  local PROCESS_NAME="n/a"
+  local PID=$1
+  local PORT=5039
+  if [ -z "$PID" ]; then
+    echo "Usage: gdbclient <pid|processname> [port number]"
+    return -1
+  fi
+  local DEVICE=$(adb_get_product_device)
+
+  if [ -z "$DEVICE" ]; then
+    echo "Error: Unable to get device name. Please check if device is connected and ANDROID_SERIAL is set."
+    return -2
+  fi
+
+  if [ -n "$2" ]; then
+    PORT=$2
+  fi
+
+  local ROOT=$(gettop)
+  if [ -z "$ROOT" ]; then
+    # This is for the situation with downloaded symbols (from the build server)
+    # we check if they are available.
+    ROOT=`realpath .`
+  fi
+
+  local OUT_ROOT="$ROOT/out/target/product/$DEVICE"
+  local SYMBOLS_DIR="$OUT_ROOT/symbols"
+
+  if [ ! -d $SYMBOLS_DIR ]; then
+    echo "Error: couldn't find symbols: $SYMBOLS_DIR does not exist or is not a directory."
+    return -3
+  fi
+
+  # let's figure out which executable we are about to debug
+
+  # check if user specified a name -> resolve to pid
+  if [[ ! "$PID" =~ ^[0-9]+$ ]] ; then
+    PROCESS_NAME=$PID
+    PID=$(pid --exact $PROCESS_NAME)
+    if [ -z "$PID" ]; then
+      echo "Error: couldn't resolve pid by process name: $PROCESS_NAME"
+      return -4
+    fi
+  fi
+
+  local EXE=`adb shell readlink /proc/$PID/exe | sed s/.$//`
+  # TODO: print error in case there is no such pid
+  local LOCAL_EXE_PATH=$SYMBOLS_DIR$EXE
+
+  if [ ! -f $LOCAL_EXE_PATH ]; then
+    echo "Error: unable to find symbols for executable $EXE: file $LOCAL_EXE_PATH does not exist"
+    return -5
+  fi
+
+  local USE64BIT=""
+
+  if [[ "$(file $LOCAL_EXE_PATH)" =~ 64-bit ]]; then
+    USE64BIT="64"
+  fi
+
+  local GDB=
+  local GDB64=
+  local CPU_ABI=`adb shell getprop ro.product.cpu.abilist | sed s/.$//`
+  # TODO: we assume these are available via $PATH
+  if [[ $CPU_ABI =~ (^|,)arm64 ]]; then
+    GDB=arm-linux-androideabi-gdb
+    GDB64=aarch64-linux-android-gdb
+  elif [[ $CPU_ABI =~ (^|,)arm ]]; then
+    GDB=arm-linux-androideabi-gdb
+  elif [[ $CPU_ABI =~ (^|,)x86_64 ]]; then
+    GDB=x86_64-linux-androideabi-gdb
+  elif [[ $CPU_ABI =~ (^|,)x86 ]]; then
+    GDB=x86_64-linux-androideabi-gdb
+  elif [[ $CPU_ABI =~ (^|,)mips64 ]]; then
+    GDB=mipsel-linux-android-gdb
+    GDB64=mips64el-linux-android-gdb
+  elif [[ $CPU_ABI =~ (^|,)mips ]]; then
+    GDB=mipsel-linux-android-gdb
+  else
+    echo "Error: unrecognized cpu.abilist: $CPU_ABI"
+    return -6
+  fi
+
+  # TODO: check if tracing process is gdbserver and not some random strace...
+  if [ $(adb_get_traced_by $PID) -eq 0 ]; then
+    # start gdbserver
+    echo "Starting gdbserver..."
+    # TODO: check if adb is already listening $PORT
+    # to avoid unnecessary calls
+    echo ". adb forward for port=$PORT..."
+    adb forward tcp:$PORT tcp:$PORT
+    echo ". starting gdbserver to attach to pid=$PID..."
+    adb shell gdbserver$USE64BIT :$PORT --attach $PID &
+    echo ". give it couple of seconds to start..."
+    sleep 2
+    echo ". done"
+  else
+    echo "It looks like gdbserver is already attached to $PID (process is traced), trying to connect to it using local port=$PORT"
+  fi
+
+  local OUT_SO_SYMBOLS=$SYMBOLS_DIR/system/lib$USE64BIT
+  local OUT_VENDOR_SO_SYMBOLS=$SYMBOLS_DIR/vendor/lib$USE64BIT
+  local ART_CMD=""
+
+  echo >|"$OUT_ROOT/gdbclient.cmds" "set solib-absolute-prefix $SYMBOLS_DIR"
+  echo >>"$OUT_ROOT/gdbclient.cmds" "set solib-search-path $OUT_SO_SYMBOLS:$OUT_SO_SYMBOLS/hw:$OUT_SO_SYMBOLS/ssl/engines:$OUT_SO_SYMBOLS/drm:$OUT_SO_SYMBOLS/egl:$OUT_SO_SYMBOLS/soundfx:$OUT_VENDOR_SO_SYMBOLS:$OUT_VENDOR_SO_SYMBOLS/hw:$OUT_VENDOR_SO_SYMBOLS/egl"
+  local DALVIK_GDB_SCRIPT=$ROOT/development/scripts/gdb/dalvik.gdb
+  if [ -f $DALVIK_GDB_SCRIPT ]; then
+    echo >>"$OUT_ROOT/gdbclient.cmds" "source $DALVIK_GDB_SCRIPT"
+    ART_CMD="art-on"
+  else
+    echo "Warning: couldn't find $DALVIK_GDB_SCRIPT - ART debugging options will not be available"
+  fi
+  echo >>"$OUT_ROOT/gdbclient.cmds" "target remote :$PORT"
+  if [[ $EXE =~ (^|/)(app_process|dalvikvm)(|32|64)$ ]]; then
+    echo >> "$OUT_ROOT/gdbclient.cmds" $ART_CMD
+  fi
+
+  echo >>"$OUT_ROOT/gdbclient.cmds" ""
+
+  local WHICH_GDB=$GDB
+
+  if [ -n "$USE64BIT" -a -n "$GDB64" ]; then
+    WHICH_GDB=$GDB64
+  fi
+
+  gdbwrapper $WHICH_GDB "$OUT_ROOT/gdbclient.cmds" "$LOCAL_EXE_PATH"
+}
+
 # gdbclient now determines whether the user wants to debug a 32-bit or 64-bit
 # executable, set up the approriate gdbserver, then invokes the proper host
 # gdb.
-function gdbclient()
+function gdbclient_old()
 {
    local OUT_ROOT=$(get_abs_build_var PRODUCT_OUT)
    local OUT_SYMBOLS=$(get_abs_build_var TARGET_OUT_UNSTRIPPED)
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()