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Network Working Group D. Korn
Request for Comments: 3284 AT&T Labs
Category: Standards Track J. MacDonald
UC Berkeley
J. Mogul
Hewlett-Packard Company
K. Vo
AT&T Labs
June 2002
The VCDIFF Generic Differencing and Compression Data Format
Status of this Memo
This document specifies an Internet standards track protocol for the
Internet community, and requests discussion and suggestions for
improvements. Please refer to the current edition of the "Internet
Official Protocol Standards" (STD 1) for the standardization state
and status of this protocol. Distribution of this memo is unlimited.
Copyright Notice
Copyright (C) The Internet Society (2002). All Rights Reserved.
...Network Working Group D. Korn
Request for Comments: 3284 AT&T Labs
Category: Standards Track J. MacDonald
UC Berkeley
J. Mogul
Hewlett-Packard Company
K. Vo
AT&T Labs
June 2002
The VCDIFF Generic Differencing and Compression Data Format
Status of this Memo
This document specifies an Internet standards track protocol for the
Internet community, and requests discussion and suggestions for
improvements. Please refer to the current edition of the "Internet
Official Protocol Standards" (STD 1) for the standardization state
and status of this protocol. Distribution of this memo is unlimited.
Copyright Notice
Copyright (C) The Internet Society (2002). All Rights Reserved.
Abstract
This memo describes VCDIFF, a general, efficient and portable data
format suitable for encoding compressed and/or differencing data so
that they can be easily transported among computers.
Korn, et. al. Standards Track [Page 1]
RFC 3284 VCDIFF June 2002
Table of Contents
1. Executive Summary ........................................... 2
2. Conventions ................................................. 4
3. Delta Instructions .......................................... 5
4. Delta File Organization ..................................... 6
5. Delta Instruction Encoding .................................. 12
6. Decoding a Target Window .................................... 20
7. Application-Defined Code Tables ............................. 21
8. Performance ................................................. 22
9. Further Issues .............................................. 24
10. Summary ..................................................... 25
11. Acknowledgements ............................................ 25
12. Security Considerations ..................................... 25
13. Source Code Availability .................................... 25
14. Intellectual Property Rights ................................ 26
15. IANA Considerations ......................................... 26
16. References .................................................. 26
17. Authors' Addresses .......................................... 28
18. Full Copyright Statement .................................... 29
1. Executive Summary
Compression and differencing techniques can greatly improve storage
and transmission of files and file versions. Since files are often
transported across machines with distinct architectures and
performance characteristics, such data should be encoded in a form
that is portable and can be decoded with little or no knowledge of
the encoders. This document describes Vcdiff, a compact portable
encoding format designed for these purposes.
Data differencing is the process of computing a compact and
invertible encoding of a "target file" given a "source file". Data
compression is similar, but without the use of source data. The UNIX
utilities diff, compress, and gzip are well-known examples of data
differencing and compression tools. For data differencing, the
computed encoding is called a "delta file", and for data compression,
it is called a "compressed file". Delta and compressed files are
good for storage and transmission as they are often smaller than the
originals.
Data differencing and data compression are traditionally treated as
distinct types of data processing. However, as shown in the Vdelta
technique by Korn and Vo [1], compression can be thought of as a
special case of differencing in which the source data is empty. The
basic idea is to unify the string parsing scheme used in the Lempel-
Ziv'77 (LZ'77) style compressors [2] and the block-move technique of
Tichy [3]. Loosely speaking, this works as follows:
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a. Concatenate source and target data.
b. Parse the data from left to right as in LZ'77 but make sure
that a parsed segment starts the target data.
c. Start to output when reaching target data.
Parsing is based on string matching algorithms, such as suffix trees
[4] or hashing with different time and space performance
characteristics. Vdelta uses a fast string matching algorithm that
requires less memory than other techniques [5,6]. However, even with
this algorithm, the memory requirement can still be prohibitive for
large files. A common way to deal with memory limitation is to
partition an input file into chunks called "windows" and process them
separately. Here, except for unpublished work by Vo, little has been
done on designing effective windowing schemes. Current techniques,
including Vdelta, simply use source and target windows with
corresponding addresses across source and target files.
String matching and windowing algorithms have great influence on the
compression rate of delta and compressed files. However, it is
desirable to have a portable encoding format that is independent of
such algorithms. This enables the construction of client-server
applications in which a server may serve clients with unknown
computing characteristics. Unfortunately, all current differencing
and compressing tools, including Vdelta, fall short in this respect.
Their storage formats are closely intertwined with the implemented
string matching and/or windowing algorithms.
The encoding format Vcdiff proposed here addresses the above issues.
Vcdiff achieves the characteristics below:
Output compactness:
The basic encoding format compactly represents compressed or
delta files. Applications can further extend the basic
encoding format with "secondary encoders" to achieve more
compression.
Data portability:
The basic encoding format is free from machine byte order and
word size issues. This allows data to be encoded on one
machine and decoded on a different machine with different
architecture.
Algorithm genericity:
The decoding algorithm is independent from string matching and
windowing algorithms. This allows competition among
implementations of the encoder while keeping the same decoder.
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Decoding efficiency:
Except for secondary encoder issues, the decoding algorithm
runs in time proportionate to the size of the target file and
uses space proportionate to the maximal window size. Vcdiff
differs from more conventional compressors in that it uses only
byte-aligned data, thus avoiding bit-level operations, which
improves decoding speed at the slight cost of compression
efficiency.
The combined differencing and compression method is called "delta
compression" [14]. As this way of data processing treats compression
as a special case of differencing, we shall use the term "delta file"
to indicate the compressed output for both cases.
2. Conventions
The basic data unit is a byte. For portability, Vcdiff shall limit a
byte to its lower eight bits even on machines with larger bytes. The
bits in a byte are ordered from right to left so that the least
significant bit (LSB) has value 1, and the most significant bit
(MSB), has value 128.
For purposes of exposition in this document, we adopt the convention
that the LSB is numbered 0, and the MSB is numbered 7. Bit numbers
never appear in the encoded format itself.
Vcdiff encodes unsigned integer values using a portable, variable-
sized format (originally introduced in the Sfio library [7]). This
encoding treats an integer as a number in base 128. Then, each digit
in this representation is encoded in the lower seven bits of a byte.
Except for the least significant byte, other bytes have their most
significant bit turned on to indicate that there are still more
digits in the encoding. The two key properties of this integer
encoding that are beneficial to a data compression format are:
a. The encoding is portable among systems using 8-bit bytes, and
b. Small values are encoded compactly.
For example, consider the value 123456789, which can be represented
with four 7-bit digits whose values are 58, 111, 26, 21 in order from
most to least significant. Below is the 8-bit byte encoding of these
digits. Note that the MSBs of 58, 111 and 26 are on.
+-------------------------------------------+
| 10111010 | 11101111 | 10011010 | 00010101 |
+-------------------------------------------+
MSB+58 MSB+111 MSB+26 0+21
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Henceforth, the terms "byte" and "integer" will refer to a byte and
an unsigned integer as described.
Algorithms in the C language are occasionally exhibited to clarify
the descriptions. Such C code is meant for clarification only, and
is not part of the actual specification of the Vcdiff format.
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in BCP 14, RFC 2119 [12].
3. Delta Instructions
A large target file is partitioned into non-overlapping sections
called "target windows". These target windows are processed
separately and sequentially based on their order in the target file.
A target window T, of length t, may be compared against some source
data segment S, of length s. By construction, this source data
segment S comes either from the source file, if one is used, or from
a part of the target file earlier than T. In this way, during
decoding, S is completely known when T is being decoded.
The choices of T, t, S and s are made by some window selection
algorithm, which can greatly affect the size of the encoding.
However, as seen later, these choices are encoded so that no
knowledge of the window selection algorithm is needed during
decoding.
Assume that S[j] represents the jth byte in S, and T[k] represents
the kth byte in T. Then, for the delta instructions, we treat the
data windows S and T as substrings of a superstring U, formed by
concatenating them like this:
S[0]S[1]...S[s-1]T[0]T[1]...T[t-1]
The "address" of a byte in S or T is referred to by its location in
U. For example, the address of T[k] is s+k.
The instructions to encode and direct the reconstruction of a target
window are called delta instructions. There are three types:
ADD: This instruction has two arguments, a size x and a sequence
of x bytes to be copied.
COPY: This instruction has two arguments, a size x and an address
p in the string U. The arguments specify the substring of U
that must be copied. We shall assert that such a substring
must be entirely contained in either S or T.
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RUN: This instruction has two arguments, a size x and a byte b,
that will be repeated x times.
Below are example source and target windows and the delta
instructions that encode the target window in terms of the source
window.
a b c d e f g h i j k l m n o p
a b c d w x y z e f g h e f g h e f g h e f g h z z z z
COPY 4, 0
ADD 4, w x y z
COPY 4, 4
COPY 12, 24
RUN 4, z
Thus, the first letter 'a' in the target window is at location 16 in
the superstring. Note that the fourth instruction, "COPY 12, 24",
copies data from T itself since address 24 is position 8 in T. This
instruction also shows that it is fine to overlap the data to be
copied with the data being copied from, as long as the latter starts
earlier. This enables efficient encoding of periodic sequences,
i.e., sequences with regularly repeated subsequences. The RUN
instruction is a compact way to encode a sequence repeating the same
byte even though such a sequence can be thought of as a periodic
sequence with period 1.
To reconstruct the target window, one simply processes one delta
instruction at a time and copies the data, either from the source
window or the target window being reconstructed, based on the type of
the instruction and the associated address, if any.
4. Delta File Organization
A Vcdiff delta file starts with a Header section followed by a
sequence of Window sections. The Header section includes magic bytes
to identify the file type, and information concerning data processing
beyond the basic encoding format. The Window sections encode the
target windows.
Below is the overall organization of a delta file. The indented
items refine the ones immediately above them. An item in square
brackets may or may not be present in the file depending on the
information encoded in the Indicator byte above it.
Korn, et. al. Standards Track [Page 6]
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Header
Header1 - byte
Header2 - byte
Header3 - byte
Header4 - byte
Hdr_Indicator - byte
[Secondary compressor ID] - byte
[Length of code table data] - integer
[Code table data]
Size of near cache - byte
Size of same cache - byte
Compressed code table data
Window1
Win_Indicator - byte
[Source segment size] - integer
[Source segment position] - integer
The delta encoding of the target window
Length of the delta encoding - integer
The delta encoding
Size of the target window - integer
Delta_Indicator - byte
Length of data for ADDs and RUNs - integer
Length of instructions and sizes - integer
Length of addresses for COPYs - integer
Data section for ADDs and RUNs - array of bytes
Instructions and sizes section - array of bytes
Addresses section for COPYs - array of bytes
Window2
...
4.1 The Header Section
Each delta file starts with a header section organized as below.
Note the convention that square-brackets enclose optional items.
Header1 - byte = 0xD6
Header2 - byte = 0xC3
Header3 - byte = 0xC4
Header4 - byte
Hdr_Indicator - byte
[Secondary compressor ID] - byte
[Length of code table data] - integer
[Code table data]
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The first three Header bytes are the ASCII characters 'V', 'C' and
'D' with their most significant bits turned on (in hexadecimal, the
values are 0xD6, 0xC3, and 0xC4). The fourth Header byte is
currently set to zero. In the future, it might be used to indicate
the version of Vcdiff.
The Hdr_Indicator byte shows if there is any initialization data
required to aid in the reconstruction of data in the Window sections.
This byte MAY have non-zero values for either, both, or neither of
the two bits VCD_DECOMPRESS and VCD_CODETABLE below:
7 6 5 4 3 2 1 0
+-+-+-+-+-+-+-+-+
| | | | | | | | |
+-+-+-+-+-+-+-+-+
^ ^
| |
| +-- VCD_DECOMPRESS
+---- VCD_CODETABLE
If bit 0 (VCD_DECOMPRESS) is non-zero, this indicates that a
secondary compressor may have been used to further compress certain
parts of the delta encoding data as described in Sections 4.3 and 6.
In that case, the ID of the secondary compressor is given next. If
this bit is zero, the compressor ID byte is not included.
If bit 1 (VCD_CODETABLE) is non-zero, this indicates that an
application-defined code table is to be used for decoding the delta
instructions. This table itself is compressed. The length of the
data comprising this compressed code table and the data follow next.
Section 7 discusses application-defined code tables. If this bit is
zero, the code table data length and the code table data are not
included.
If both bits are set, then the compressor ID byte is included before
the code table data length and the code table data.
4.2 The Format of a Window Section
Each Window section is organized as follows:
Win_Indicator - byte
[Source segment length] - integer
[Source segment position] - integer
The delta encoding of the target window
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Below are the details of the various items:
Win_Indicator:
This byte is a set of bits, as shown:
7 6 5 4 3 2 1 0
+-+-+-+-+-+-+-+-+
| | | | | | | | |
+-+-+-+-+-+-+-+-+
^ ^
| |
| +-- VCD_SOURCE
+---- VCD_TARGET
If bit 0 (VCD_SOURCE) is non-zero, this indicates that a
segment of data from the "source" file was used as the
corresponding source window of data to encode the target
window. The decoder will use this same source data segment to
decode the target window.
If bit 1 (VCD_TARGET) is non-zero, this indicates that a
segment of data from the "target" file was used as the
corresponding source window of data to encode the target
window. As above, this same source data segment is used to
decode the target window.
The Win_Indicator byte MUST NOT have more than one of the bits
set (non-zero). It MAY have none of these bits set.
If one of these bits is set, the byte is followed by two
integers to indicate respectively, the length and position of
the source data segment in the relevant file. If the indicator
byte is zero, the target window was compressed by itself
without comparing against another data segment, and these two
integers are not included.
The delta encoding of the target window:
This contains the delta encoding of the target window, either
in terms of the source data segment (i.e., VCD_SOURCE or
VCD_TARGET was set) or by itself if no source window is
specified. This data format is discussed next.
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4.3 The Delta Encoding of a Target Window
The delta encoding of a target window is organized as follows:
Length of the delta encoding - integer
The delta encoding
Length of the target window - integer
Delta_Indicator - byte
Length of data for ADDs and RUNs - integer
Length of instructions section - integer
Length of addresses for COPYs - integer
Data section for ADDs and RUNs - array of bytes
Instructions and sizes section - array of bytes
Addresses section for COPYs - array of bytes
Length of the delta encoding:
This integer gives the total number of remaining bytes that
comprise the data of the delta encoding for this target
window.
The delta encoding:
This contains the data representing the delta encoding which
is described next.
Length of the target window:
This integer indicates the actual size of the target window
after decompression. A decoder can use this value to
allocate memory to store the uncompressed data.
Delta_Indicator:
This byte is a set of bits, as shown:
7 6 5 4 3 2 1 0
+-+-+-+-+-+-+-+-+
| | | | | | | | |
+-+-+-+-+-+-+-+-+
^ ^ ^
| | |
| | +-- VCD_DATACOMP
| +---- VCD_INSTCOMP
+------ VCD_ADDRCOMP
VCD_DATACOMP: bit value 1.
VCD_INSTCOMP: bit value 2.
VCD_ADDRCOMP: bit value 4.
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As discussed, the delta encoding consists of COPY, ADD and RUN
instructions. The ADD and RUN instructions have accompanying
unmatched data (that is, data that does not specifically match
any data in the source window or in some earlier part of the
target window) and the COPY instructions have addresses of
where the matches occur. OPTIONALLY, these types of data MAY
be further compressed using a secondary compressor. Thus,
Vcdiff separates the encoding of the delta instructions into
three parts:
a. The unmatched data in the ADD and RUN instructions,
b. The delta instructions and accompanying sizes, and
c. The addresses of the COPY instructions.
If the bit VCD_DECOMPRESS (Section 4.1) was on, each of these
sections may have been compressed using the specified secondary
compressor. The bit positions 0 (VCD_DATACOMP), 1
(VCD_INSTCOMP), and 2 (VCD_ADDRCOMP) respectively indicate, if
non-zero, that the corresponding parts are compressed. Then,
these parts MUST be decompressed before decoding the delta
instructions.
Length of data for ADDs and RUNs:
This is the length (in bytes) of the section of data storing
the unmatched data accompanying the ADD and RUN instructions.
Length of instructions section:
This is the length (in bytes) of the delta instructions and
accompanying sizes.
Length of addresses for COPYs:
This is the length (in bytes) of the section storing the
addresses of the COPY instructions.
Data section for ADDs and RUNs:
This sequence of bytes encodes the unmatched data for the ADD
and RUN instructions.
Instructions and sizes section:
This sequence of bytes encodes the instructions and their
sizes.
Addresses section for COPYs:
This sequence of bytes encodes the addresses of the COPY
instructions.
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5. Delta Instruction Encoding
The delta instructions described in Section 3 represent the results
of string matching. For many data differencing applications in which
the changes between source and target data are small, any
straightforward representation of these instructions would be
adequate. However, for applications including differencing of binary
files or data compression, it is important to encode these
instructions well to achieve good compression rates. The keys to
this achievement is to efficiently encode the addresses of COPY
instructions and the sizes of all delta instructions.
5.1 Address Encoding Modes of COPY Instructions
Addresses of COPY instructions are locations of matches and often
occur close by or even exactly equal to one another. This is because
data in local regions are often replicated with minor changes. In
turn, this means that coding a newly matched address against some
recently matched addresses can be beneficial. To take advantage of
this phenomenon and encode addresses of COPY instructions more
efficiently, the Vcdiff data format supports the use of two different
types of address caches. Both the encoder and decoder maintain these
caches, so that decoder's caches remain synchronized with the
encoder's caches.
a. A "near" cache is an array with "s_near" slots, each containing an
address used for encoding addresses nearby to previously encoded
addresses (in the positive direction only). The near cache also
maintains a "next_slot" index to the near cache. New entries to
the near cache are always inserted in the next_slot index, which
maintains a circular buffer of the s_near most recent addresses.
b. A "same" cache is an array with "s_same", with a multiple of 256
slots, each containing an address. The same cache maintains a
hash table of recent addresses used for repeated encoding of the
exact same address.
By default, the parameters s_near and s_same are respectively set to
4 and 3. An encoder MAY modify these values, but then it MUST encode
the new values in the encoding itself, as discussed in Section 7, so
that the decoder can properly set up its own caches.
At the start of processing a target window, an implementation
(encoder or decoder) initializes all of the slots in both caches to
zero. The next_slot pointer of the near cache is set to point to
slot zero.
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Each time a COPY instruction is processed by the encoder or decoder,
the implementation's caches are updated as follows, where "addr" is
the address in the COPY instruction.
a. The slot in the near cache referenced by the next_slot index is
set to addr. The next_slot index is then incremented modulo
s_near.
b. The slot in the same cache whose index is addr%(s_same*256) is set
to addr. [We use the C notations of % for modulo and * for
multiplication.]
5.2 Example code for maintaining caches
To make clear the above description, below are examples of cache data
structures and algorithms to initialize and update them:
typedef struct _cache_s
{
int* near; /* array of size s_near */
int s_near;
int next_slot; /* the circular index for near */
int* same; /* array of size s_same*256 */
int s_same;
} Cache_t;
cache_init(Cache_t* ka)
{
int i;
ka->next_slot = 0;
for(i = 0; i < ka->s_near; ++i)
ka->near[i] = 0;
for(i = 0; i < ka->s_same*256; ++i)
ka->same[i] = 0;
}
cache_update(Cache_t* ka, int addr)
{
if(ka->s_near > 0)
{ ka->near[ka->next_slot] = addr;
ka->next_slot = (ka->next_slot + 1) % ka->s_near;
}
if(ka->s_same > 0)
ka->same[addr % (ka->s_same*256)] = addr;
}
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5.3 Encoding of COPY instruction addresses
The address of a COPY instruction is encoded using different modes,
depending on the type of cached address used, if any.
Let "addr" be the address of a COPY instruction to be decoded and
"here" be the current location in the target data (i.e., the start of
the data about to be encoded or decoded). Let near[j] be the jth
element in the near cache, and same[k] be the kth element in the same
cache. Below are the possible address modes:
VCD_SELF: This mode has value 0. The address was encoded by
itself as an integer.
VCD_HERE: This mode has value 1. The address was encoded as the
integer value "here - addr".
Near modes: The "near modes" are in the range [2,s_near+1]. Let m
be the mode of the address encoding. The address was encoded
as the integer value "addr - near[m-2]".
Same modes: The "same modes" are in the range
[s_near+2,s_near+s_same+1]. Let m be the mode of the encoding.
The address was encoded as a single byte b such that "addr ==
same[(m - (s_near+2))*256 + b]".
5.4 Example code for encoding and decoding of COPY instruction addresses
We show example algorithms below to demonstrate the use of address
modes more clearly. The encoder has the freedom to choose address
modes, the sample addr_encode() algorithm merely shows one way of
picking the address mode. The decoding algorithm addr_decode() will
uniquely decode addresses, regardless of the encoder's algorithm
choice.
Note that the address caches are updated immediately after an address
is encoded or decoded. In this way, the decoder is always
synchronized with the encoder.
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int addr_encode(Cache_t* ka, int addr, int here, int* mode)
{
int i, d, bestd, bestm;
/* Attempt to find the address mode that yields the
* smallest integer value for "d", the encoded address
* value, thereby minimizing the encoded size of the
* address. */
bestd = addr; bestm = VCD_SELF; /* VCD_SELF == 0 */
if((d = here-addr) < bestd)
{ bestd = d; bestm = VCD_HERE; } /* VCD_HERE == 1 */
for(i = 0; i < ka->s_near; ++i)
if((d = addr - ka->near[i]) >= 0 && d < bestd)
{ bestd = d; bestm = i+2; }
if(ka->s_same > 0 && ka->same[d = addr%(ka->s_same*256)] == addr)
{ bestd = d%256; bestm = ka->s_near + 2 + d/256; }
cache_update(ka,addr);
*mode = bestm; /* this returns the address encoding mode */
return bestd; /* this returns the encoded address */
}
Note that the addr_encode() algorithm chooses the best address mode
using a local optimization, but that may not lead to the best
encoding efficiency because different modes lead to different
instruction encodings, as described below.
The functions addrint() and addrbyte() used in addr_decode(), obtain
from the "Addresses section for COPYs" (Section 4.3), an integer or a
byte, respectively. These utilities will not be described here. We
simply recall that an integer is represented as a compact variable-
sized string of bytes, as described in Section 2 (i.e., base 128).
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int addr_decode(Cache_t* ka, int here, int mode)
{ int addr, m;
if(mode == VCD_SELF)
addr = addrint();
else if(mode == VCD_HERE)
addr = here - addrint();
else if((m = mode - 2) >= 0 && m < ka->s_near) /* near cache */
addr = ka->near[m] + addrint();
else /* same cache */
{ m = mode - (2 + ka->s_near);
addr = ka->same[m*256 + addrbyte()];
}
cache_update(ka, addr);
return addr;
}
5.4 Instruction Codes
Matches are often short in lengths and separated by small amounts of
unmatched data. That is, the lengths of COPY and ADD instructions
are often small. This is particularly true of binary data such as
executable files or structured data, such as HTML or XML. In such
cases, compression can be improved by combining the encoding of the
sizes and the instruction types, as well as combining the encoding of
adjacent delta instructions with sufficiently small data sizes.
Effective choices of when to perform such combinations depend on many
factors including the data being processed and the string matching
algorithm in use. For example, if many COPY instructions have the
same data sizes, it may be worthwhile to encode these instructions
more compactly than others.
The Vcdiff data format is designed so that a decoder does not need to
be aware of the choices made in encoding algorithms. This is
achieved with the notion of an "instruction code table", containing
256 entries. Each entry defines, either a single delta instruction
or a pair of instructions that have been combined. Note that the
code table itself only exists in main memory, not in the delta file
(unless using an application-defined code table, described in Section
7). The encoded data simply includes the index of each instruction
and, since there are only 256 indices, each index can be represented
as a single byte.
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Each instruction code entry contains six fields, each of which is a
single byte with an unsigned value:
+-----------------------------------------------+
| inst1 | size1 | mode1 | inst2 | size2 | mode2 |
+-----------------------------------------------+
Each triple (inst,size,mode) defines a delta instruction. The
meanings of these fields are as follows:
inst: An "inst" field can have one of the four values: NOOP (0),
ADD (1), RUN (2) or COPY (3) to indicate the instruction
types. NOOP means that no instruction is specified. In
this case, both the corresponding size and mode fields will
be zero.
size: A "size" field is zero or positive. A value zero means that
the size associated with the instruction is encoded
separately as an integer in the "Instructions and sizes
section" (Section 6). A positive value for "size" defines
the actual data size. Note that since the size is
restricted to a byte, the maximum value for any instruction
with size implicitly defined in the code table is 255.
mode: A "mode" field is significant only when the associated delta
instruction is a COPY. It defines the mode used to encode
the associated addresses. For other instructions, this is
always zero.
5.6 The Code Table
Following the discussions on address modes and instruction code
tables, we define a "Code Table" to have the data below:
s_near: the size of the near cache,
s_same: the size of the same cache,
i_code: the 256-entry instruction code table.
Vcdiff itself defines a "default code table" in which s_near is 4 and
s_same is 3. Thus, there are 9 address modes for a COPY instruction.
The first two are VCD_SELF (0) and VCD_HERE (1). Modes 2, 3, 4 and 5
are for addresses coded against the near cache. And modes 6, 7 and
8, are for addresses coded against the same cache.
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TYPE SIZE MODE TYPE SIZE MODE INDEX
---------------------------------------------------------------
1. RUN 0 0 NOOP 0 0 0
2. ADD 0, [1,17] 0 NOOP 0 0 [1,18]
3. COPY 0, [4,18] 0 NOOP 0 0 [19,34]
4. COPY 0, [4,18] 1 NOOP 0 0 [35,50]
5. COPY 0, [4,18] 2 NOOP 0 0 [51,66]
6. COPY 0, [4,18] 3 NOOP 0 0 [67,82]
7. COPY 0, [4,18] 4 NOOP 0 0 [83,98]
8. COPY 0, [4,18] 5 NOOP 0 0 [99,114]
9. COPY 0, [4,18] 6 NOOP 0 0 [115,130]
10. COPY 0, [4,18] 7 NOOP 0 0 [131,146]
11. COPY 0, [4,18] 8 NOOP 0 0 [147,162]
12. ADD [1,4] 0 COPY [4,6] 0 [163,174]
13. ADD [1,4] 0 COPY [4,6] 1 [175,186]
14. ADD [1,4] 0 COPY [4,6] 2 [187,198]
15. ADD [1,4] 0 COPY [4,6] 3 [199,210]
16. ADD [1,4] 0 COPY [4,6] 4 [211,222]
17. ADD [1,4] 0 COPY [4,6] 5 [223,234]
18. ADD [1,4] 0 COPY 4 6 [235,238]
19. ADD [1,4] 0 COPY 4 7 [239,242]
20. ADD [1,4] 0 COPY 4 8 [243,246]
21. COPY 4 [0,8] ADD 1 0 [247,255]
---------------------------------------------------------------
The default instruction code table is depicted above, in a compact
representation that we use only for descriptive purposes. See
section 7 for the specification of how an instruction code table is
represented in the Vcdiff encoding format. In the depiction, a zero
value for size indicates that the size is separately coded. The mode
of non-COPY instructions is represented as 0, even though they are
not used.
In the depiction, each numbered line represents one or more entries
in the actual instruction code table (recall that an entry in the
instruction code table may represent up to two combined delta
instructions.) The last column ("INDEX") shows which index value, or
range of index values, of the entries are covered by that line. (The
notation [i,j] means values from i through j, inclusively.) The
first 6 columns of a line in the depiction, describe the pairs of
instructions used for the corresponding index value(s).
If a line in the depiction includes a column entry using the [i,j]
notation, this means that the line is instantiated for each value in
the range from i to j, inclusively. The notation "0, [i,j]" means
that the line is instantiated for the value 0 and for each value in
the range from i to j, inclusively.
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If a line in the depiction includes more than one entry using the
[i,j] notation, implying a "nested loop" to convert the line to a
range of table entries, the first such [i,j] range specifies the
outer loop, and the second specifies the inner loop.
The below examples should make clear the above description:
Line 1 shows the single RUN instruction with index 0. As the size
field is 0, this RUN instruction always has its actual size encoded
separately.
Line 2 shows the 18 single ADD instructions. The ADD instruction
with size field 0 (i.e., the actual size is coded separately) has
index 1. ADD instructions with sizes from 1 to 17 use code indices 2
to 18 and their sizes are as given (so they will not be separately
encoded.)
Following the single ADD instructions are the single COPY
instructions ordered by their address encoding modes. For example,
line 11 shows the COPY instructions with mode 8, i.e., the last of
the same cache. In this case, the COPY instruction with size field 0
has index 147. Again, the actual size of this instruction will be
coded separately.
Lines 12 to 21 show the pairs of instructions that are combined
together. For example, line 12 depicts the 12 entries in which an
ADD instruction is combined with an immediately following COPY
instruction. The entries with indices 163, 164, 165 represent the
pairs in which the ADD instructions all have size 1, while the COPY
instructions have mode 0 (VCD_SELF) and sizes 4, 5 and 6
respectively.
The last line, line 21, shows the eight instruction pairs, where the
first instruction is a COPY and the second is an ADD. In this case,
all COPY instructions have size 4 with mode ranging from 0 to 8 and
all the ADD instructions have size 1. Thus, the entry with the
largest index 255 combines a COPY instruction of size 4 and mode 8
with an ADD instruction of size 1.
The choice of the minimum size 4 for COPY instructions in the default
code table was made from experiments that showed that excluding small
matches (less then 4 bytes long) improved the compression rates.
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6. Decoding a Target Window
Section 4.3 discusses that the delta instructions and associated data
are encoded in three arrays of bytes:
Data section for ADDs and RUNs,
Instructions and sizes section, and
Addresses section for COPYs.
Further, these data sections may have been further compressed by some
secondary compressor. Assuming that any such compressed data has
been decompressed so that we now have three arrays:
inst: bytes coding the instructions and sizes.
data: unmatched data associated with ADDs and RUNs.
addr: bytes coding the addresses of COPYs.
These arrays are organized as follows:
inst: a sequence of (index, [size1], [size2]) tuples, where
"index" is an index into the instruction code table, and
size1 and size2 are integers that MAY or MAY NOT be included
in the tuple as follows. The entry with the given "index"
in the instruction code table potentially defines two delta
instructions. If the first delta instruction is not a
VCD_NOOP and its size is zero, then size1 MUST be present.
Otherwise, size1 MUST be omitted and the size of the
instruction (if it is not VCD_NOOP) is as defined in the
table. The presence or absence of size2 is defined
similarly with respect to the second delta instruction.
data: a sequence of data values, encoded as bytes.
addr: a sequence of address values. Addresses are normally
encoded as integers as described in Section 2 (i.e., base
128). However, since the same cache emits addresses in the
range [0,255], same cache addresses are always encoded as a
single byte.
To summarize, each tuple in the "inst" array includes an index to
some entry in the instruction code table that determines:
a. Whether one or two instructions were encoded and their types.
b. If the instructions have their sizes encoded separately, these
sizes will follow, in order, in the tuple.
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c. If the instructions have accompanying data, i.e., ADDs or RUNs,
their data will be in the array "data".
d. Similarly, if the instructions are COPYs, the coded addresses are
found in the array "addr".
The decoding procedure simply processes the arrays by reading one
code index at a time, looking up the corresponding instruction code
entry, then consuming the respective sizes, data and addresses
following the directions in this entry. In other words, the decoder
maintains an implicit next-element pointer for each array;
"consuming" an instruction tuple, data, or address value implies
incrementing the associated pointer.
For example, if during the processing of the target window, the next
unconsumed tuple in the inst array has an index value of 19, then the
first instruction is a COPY, whose size is found as the immediately
following integer in the inst array. Since the mode of this COPY
instruction is VCD_SELF, the corresponding address is found by
consuming the next integer in the addr array. The data array is left
intact. As the second instruction for code index 19 is a NOOP, this
tuple is finished.
7. APPLICATION-DEFINED CODE TABLES
Although the default code table used in Vcdiff is good for general
purpose encoders, there are times when other code tables may perform
better. For example, to code a file with many identical segments of
data, it may be advantageous to have a COPY instruction with the
specific size of these data segments, so that the instruction can be
encoded in a single byte. Such a special code table MUST then be
encoded in the delta file so that the decoder can reconstruct it
before decoding the data.
Vcdiff allows an application-defined code table to be specified in a
delta file with the following data:
Size of near cache - byte
Size of same cache - byte
Compressed code table data
The "compressed code table data" encodes the delta between the
default code table (source) and the new code table (target) in the
same manner as described in Section 4.3 for encoding a target window
in terms of a source window. This delta is computed using the
following steps:
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a. Convert the new instruction code table into a string, "code", of
1536 bytes using the below steps in order:
i. Add in order the 256 bytes representing the types of the first
instructions in the instruction pairs.
ii. Add in order the 256 bytes representing the types of the
second instructions in the instruction pairs.
iii. Add in order the 256 bytes representing the sizes of the first
instructions in the instruction pairs.
iv. Add in order the 256 bytes representing the sizes of the
second instructions in the instruction pairs.
v. Add in order the 256 bytes representing the modes of the first
instructions in the instruction pairs.
vi. Add in order the 256 bytes representing the modes of the
second instructions in the instruction pairs.
b. Similarly, convert the default code table into a string "dflt".
c. Treat the string "code" as a target window and "dflt" as the
corresponding source data and apply an encoding algorithm to
compute the delta encoding of "code" in terms of "dflt". This
computation MUST use the default code table for encoding the delta
instructions.
The decoder can then reverse the above steps to decode the compressed
table data using the method of Section 6, employing the default code
table, to generate the new code table. Note that the decoder does
not need to know about the details of the encoding algorithm used in
step (c). It is able to decode the new code table because the Vcdiff
format is independent from the choice of encoding algorithm, and
because the encoder in step (c) uses the known, default code table.
8. Performance
The encoding format is compact. For compression only, using the LZ-
77 string parsing strategy and without any secondary compressors, the
typical compression rate is better than Unix compress and close to
gzip. For differencing, the data format is better than all known
methods in terms of its stated goal, which is primarily decoding
speed and encoding efficiency.
We compare the performance of compress, gzip and Vcdiff using the
archives of three versions of the Gnu C compiler, gcc-2.95.1.tar,
gcc-2.95.2.tar and gcc-2.95.3.tar. Gzip was used at its default
compression level. The Vcdiff data were obtained using the
Vcodex/Vcdiff software (Section 13).
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Below are the different Vcdiff runs:
Vcdiff: vcdiff is used as a compressor only.
Vcdiff-d: vcdiff is used as a differencer only. That is, it only
compares target data against source data. Since the files
involved are large, they are broken into windows. In this
case, each target window, starting at some file offset in the
target file, is compared against a source window with the same
file offset (in the source file). The source window is also
slightly larger than the target window to increase matching
opportunities.
Vcdiff-dc: This is similar to Vcdiff-d, but vcdiff can also
compare target data against target data as applicable. Thus,
vcdiff both computes differences and compresses data. The
windowing algorithm is the same as above. However, the above
hint is recinded in this case.
Vcdiff-dcw: This is similar to Vcdiff-dc but the windowing
algorithm uses a content-based heuristic to select a source
window that is more likely to match with a given target window.
Thus, the source data segment selected for a target window
often will not be aligned with the file offsets of this target
window.
gcc-2.95.1 gcc-2.95.2 gcc-2.95.3
---------------------------------------------------------
1. raw size 55,746,560 55,797,760 55,787,520
2. compress - 19,939,390 19,939,453
3. gzip - 12,973,443 12,998,097
4. Vcdiff - 15,358,786 15,371,737
5. Vcdiff-d - 100,971 26,383,849
6. Vcdiff-dc - 97,246 14,461,203
7. Vcdiff-dcw - 256,445 1,248,543
The above table shows the raw sizes of the tar files and the sizes of
the compressed results. The differencing results in the gcc-2.95.2
column were obtained by compressing gcc-2.95.2, given gcc-2.95.1.
The same results for the column gcc-2.95.3 were obtained by
compressing gcc-2.95.3, given gcc-2.95.2.
Rows 2, 3 and 4 show that, for compression only, the compression rate
from Vcdiff is worse than gzip and better than compress.
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The last three rows in the column gcc-2.95.2 show that when two file
versions are very similar, differencing can give dramatically good
compression rates. Vcdiff-d and Vcdiff-dc use the same simple window
selection method of aligning by file offsets, but Vcdiff-dc also does
compression so its output is slightly smaller. Vcdiff-dcw uses a
content-based algorithm to search for source data that likely will
match a given target window. Although it does a good job, the
algorithm does not always find the best matches, which in this case,
are given by the simple algorithm of Vcdiff-d. As a result, the
output size for Vcdiff-dcw is slightly larger.
The situation is reversed in the gcc-2.95.3 column. Here, the files
and their contents were sufficiently rearranged or changed between
the making of the gcc-2.95.3.tar archive and the gcc-2.95.2 archive
so that the simple method of aligning windows by file offsets no
longer works. As a result, Vcdiff-d and Vcdiff-dc do not perform
well. By allowing compression, along with differencing, Vcdiff-dc
manages to beat Vcdiff-c, which does compression only. The content-
based window matching algorithm in Vcdiff-dcw is effective in
matching the right source and target windows so that Vcdiff-dcw is
the overall winner.
9. Further Issues
This document does not address a few issues:
Secondary compressors:
As discussed in Section 4.3, certain sections in the delta
encoding of a window may be further compressed by a secondary
compressor. In our experience, the basic Vcdiff format is
adequate for most purposes so that secondary compressors are
seldom needed. In particular, for normal use of data
differencing, where the files to be compared have long stretches
of matches, much of the gain in compression rate is already
achieved by normal string matching. Thus, the use of secondary
compressors is seldom needed in this case. However, for
applications beyond differencing of such nearly identical files,
secondary compressors may be needed to achieve maximal compressed
results.
Therefore, we recommend leaving the Vcdiff data format defined as
in this document so that the use of secondary compressors can be
implemented when they become needed in the future. The formats of
the compressed data via such compressors or any compressors that
may be defined in the future are left open to their
implementations. These could include Huffman encoding, arithmetic
encoding, and splay tree encoding [8,9].
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