tizen 2.4 release

[external/xdelta3.git] / draft-korn-vcdiff.txt

                                                     David G. Korn, AT&T Labs
                                             Joshua P. MacDonald, UC Berkeley
                                                 Jeffrey C. Mogul, Compaq WRL
Internet-Draft                                       Kiem-Phong Vo, AT&T Labs
Expires: 09 November 2002                                    09 November 2001


        The VCDIFF Generic Differencing and Compression Data Format

                         draft-korn-vcdiff-06.txt



Status of this Memo

    This document is an Internet-Draft and is in full conformance
    with all provisions of Section 10 of RFC2026.

    Internet-Drafts are working documents of the Internet Engineering
    Task Force (IETF), its areas, and its working groups.  Note that
    other groups may also distribute working documents as
    Internet-Drafts.

    Internet-Drafts are draft documents valid for a maximum of six
    months and may be updated, replaced, or obsoleted by other
    documents at any time.  It is inappropriate to use Internet-
    Drafts as reference material or to cite them other than as
    "work in progress."

    The list of current Internet-Drafts can be accessed at
    http://www.ietf.org/ietf/1id-abstracts.txt

    The list of Internet-Draft Shadow Directories can be accessed at
    http://www.ietf.org/shadow.html.


Abstract

    This memo describes a general, efficient and portable data format
    suitable for encoding compressed and/or differencing data so that
    they can be easily transported among computers.


Table of Contents:

    1.  EXECUTIVE SUMMARY ............................................  2
    2.  CONVENTIONS ..................................................  3
    3.  DELTA INSTRUCTIONS ...........................................  4
    4.  DELTA FILE ORGANIZATION ......................................  5
    5.  DELTA INSTRUCTION ENCODING ...................................  9
    6.  DECODING A TARGET WINDOW ..................................... 14
    7.  APPLICATION-DEFINED CODE TABLES .............................. 16
    8.  PERFORMANCE .................................................. 16
    9.  FURTHER ISSUES ............................................... 17
   10.  SUMMARY ...................................................... 18
   11.  ACKNOWLEDGEMENTS ............................................. 18
   12.  SECURITY CONSIDERATIONS ...................................... 18
   13.  SOURCE CODE AVAILABILITY ..................................... 18
   14.  INTELLECTUAL PROPERTY RIGHTS ................................. 18
   15.  IANA CONSIDERATIONS .......................................... 19
   16.  REFERENCES ................................................... 19
   17.  AUTHOR'S ADDRESS ............................................. 20


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 style
    compressors [2], and the block-move technique of Tichy [3].  Loosely
    speaking, this works as follows:

        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 large 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 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 below characteristics:

        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.

        Decoding efficiency:
            Except for secondary encoder issues, the decoding algorithm runs
            in time proportional to the size of the target file and uses space
            proportional 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 Vcdiff data format and the algorithms for decoding data shall be
    described next.  Since Vcdiff 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


    Henceforth, the terms "byte" and "integer" will refer to a byte and an
    unsigned integer as described.


    From time to time, algorithms are exhibited to clarify the descriptions
    of parts of the Vcdiff format. On such occasions, the C language will be
    used to make precise the algorithms.  The C code shown in this
    document is meant for clarification only, and is not part of the
    actual specification of the Vcdiff format.

    In this specification, the key words "MUST", "MUST NOT",
    "SHOULD", "SHOULD NOT", and "MAY" document are to be interpreted as
    described in RFC2119 [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.
        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 copy the data either from the source window
    or the being reconstructed target window 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.

        Header
            Header1                                  - byte
            Header2                                  - byte
            Header3                                  - byte
            Header4                                  - byte
            Hdr_Indicator                            - byte
            [Secondary compressor ID]                - byte

[@@@ Why is compressor ID not an integer? ]
[@@@ If we aren't defining any secondary compressors yet, then it seems
that defining the [Secondary compressor ID] and the corresponding
VCD_DECOMPRESS Hdr_Indicator bit in this draft has no real value.  An
implementation of this specification won't be able to decode a VCDIFF
encoded with this option if it doesn't know about any secondary
compressors.  It seems that you should specify the bits related to
secondary compressors once you have defined the first a secondary
compressor.  I can imagine a secondary-compressor might want to supply
extra information, such as a dictionary of some kind, in which case
this speculative treatment wouldn't go far enough.]

            [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 = 0xE6
            Header2                                  - byte = 0xD3
            Header3                                  - byte = 0xD4

HMMM

0xD6
0xC3
0xC4

            Header4                                  - byte
            Hdr_Indicator                            - byte
            [Secondary compressor ID]                - byte
            [Length of code table data]              - integer
            [Code table data]

    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 0xE6, 0xD3, and 0xD4). 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 are 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 we aren't defining any secondary compressors yet, then it seems
this bit has no real value yet..]

    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


    Below are the detail of the various items:

[@@@ Here, I want to replace the Win_Indicator with a source-count,
followed by source-count length/position pairs?]

        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.


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 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.

            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.


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 data compression, it is important to encode
    these instructions well to achieve good compression rates.  From our
    experience, the following observations can be made:

    a. The addresses in 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
       set of recently matched addresses can be beneficial.

    b. The matches are often short in length 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.

    The below subsections discuss how the Vcdiff data format provides
    mechanisms enabling encoders to use the above observations to improve
    compression rates.


5.1 Address Encoding Modes of COPY Instructions

    As mentioned earlier, addresses of COPY instructions often occur close
    to one another or are exactly equal. 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" 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.

    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 example 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;
        }


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]".


5.3 Example code for encoding and decoding of COPY instruction addresses

    We show example algorithms below to demonstrate use of address modes more
    clearly. The encoder has 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.

        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).

        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

    As noted, the data sizes associated with delta instructions are often
    small. Thus, compression efficiency can be improved by combining the sizes
    and instruction types in a single encoding, as well by combining certain
    pairs of adjacent delta instructions. 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 worth 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.

    Each instruction code entry contains six fields, each of which
    is a single byte with unsigned value:

            +-----------------------------------------------+
            | inst1 | size1 | mode1 | inst2 | size2 | mode2 |
            +-----------------------------------------------+

@@@ could be more compact

    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.


5.5 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.

    The default instruction code table is depicted below, 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.


         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]
        ---------------------------------------------------------------

    In the above 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 covered by that line. The notation
    [i,j] means values from i through j, inclusive. 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, inclusive.  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, inclusive.

    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 has 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 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.


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).
            Since the same cache emits addresses in the range [0,255],
            however, 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.

    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 index value 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:

    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 instruction 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 anything about the details of the encoding algorithm used
    in step (c). The decoder is still 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. The experiments were done on an
    SGI-MIPS3, 400MHZ. Gzip was used at its default compression level.
    Vcdiff timings were done using the Vcodex/Vcdiff software (Section 13).
    As string and window matching typically dominates the computation during
    compression, the Vcdiff compression times were directly due to the
    algorithms used in the Vcodex/Vcdiff software. However, the decompression
    times should be generic and representative of any good implementation
    of the Vcdiff data format. Timing was done by running each program
    three times and taking the average of the total cpu+system times.

    Below are the different Vcdiff runs:

        Vcdiff: vcdiff is used as 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. The -d option also gives
                a hint to the string matching algorithm of Vcdiff that
                the two files are very similar with long stretches of matches.
                The algorithm takes advantage of this to minimize its
                processing of source data and save time.

        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-dcs: This is similar to Vcdiff-dc but the windowing algorithm
                uses a content-based heuristic to select source data segments
                that are 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    compression   decompression
    raw size      55746560      55797760
    compress         -          19939390       13.85s         7.09s
    gzip             -          12973443       42.99s         5.35s
    Vcdiff           -          15358786       20.04s         4.65s
    Vcdiff-d         -            100971       10.93s         1.92s
    Vcdiff-dc        -             97246       20.03s         1.84s
    Vcdiff-dcs       -            256445       44.81s         1.84s

                TABLE 1. Compressing gcc-2.95.2.tar given gcc-2.95.1


    TABLE 1 shows the raw sizes of gcc-2.95.1.tar and gcc-2.95.2.tar and the
    sizes of the compressed results. As a pure compressor, the compression
    rate for Vcdiff is worse than gzip and better than compress. The last
    three rows shows that when two file versions are very similar, differencing
    can have dramatically good compression rates. Vcdiff-d and Vcdiff-dc use
    the same simple window selection method but Vcdiff-dc also does compression
    so its output is slightly smaller. Vcdiff-dcs uses a heuristic based on
    data content to search for source data that likely will match a given target
    window. Although it does a good job, the heuristic did not always find the
    best matches which are given by the simple algorithm of Vcdiff-d.  As a
    result, the output size is slightly larger. Note also that there is a large
    cost in computing matching windows this way. Finally, the compression times
    of Vcdiff-d is nearly half of that of Vcdiff-dc. It is tempting to conclude
    that the compression feature causes the additional time in Vcdiff-dc
    relative to Vcdiff-d.  However, this is not the case. The hint given to
    the Vcdiff string matching algorithm that the two files are likely to
    have very long stretches of matches helps the algorithm to minimize
    processing of the "source data", thus saving half the time. However, as we
    shall see below when this hint is wrong, the result is even longer time.


                gcc-2.95.2    gcc-2.95.3    compression   decompression
    raw size      55797760      55787520
    compress         -          19939453       13.54s         7.00s
    gzip             -          12998097       42.63s         5.62s
    Vcdiff           -          15371737       20.09s         4.74s
    Vcdiff-d         -          26383849       71.41s         6.41s
    Vcdiff-dc        -          14461203       42.48s         4.82s
    Vcdiff-dcs       -           1248543       61.18s         1.99s

                TABLE 2. Compressing gcc-2.95.3.tar given gcc-2.95.2


    TABLE 2 shows the raw sizes of gcc-2.95.2.tar and gcc-2.95.3.tar and
    the sizes of the compressed results. In this case, the tar file of
    gcc-2.95.3 is rearranged in a way that makes the straightforward method
    of matching file offsets for source and target windows fail. As a
    result, Vcdiff-d performs rather dismally both in time and output size.
    The large time for Vcdiff-d is directly due to fact that the string
    matching algorithm has to work much harder to find matches when the hint
    that two files have long matching stretches fails to hold. On the other
    hand, Vcdiff-dc does both differencing and compression resulting in good
    output size. Finally, the window searching heuristic used in Vcdiff-dcs is
    effective in finding the right matching source windows for target windows
    resulting a small output size. This shows why the data format needs to
    have a way to specify matching windows to gain performance. Finally,
    we note that the decoding times are always good regardless of how
    the string matching or window searching algorithms perform.


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 to leave 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].

    Large file system vs. small file system:
        As discussed in Section 4, a target window in a large file may be
        compared against some source window in another file or in the same
        file (from some earlier part). In that case, the file offset of the
        source window is specified as a variable-sized integer in the delta
        encoding. There is a possibility that the encoding was computed on
        a system supporting much larger files than in a system where
        the data may be decoded (e.g., 64-bit file systems vs. 32-bit file
        systems). In that case, some target data may not be recoverable.
        This problem could afflict any compression format, and ought
        to be resolved with a generic negotiation mechanism in the
        appropriate protocol(s).


10.  SUMMARY

    We have described Vcdiff, a general and portable encoding format for
    compression and differencing. The format is good in that it allows
    implementing a decoder without knowledge of the encoders. Further,
    ignoring the use of secondary compressors not defined within the format,
    the decoding algorithms runs in linear time and requires working space
    proportional to window sizes.



11. ACKNOWLEDGEMENTS

    Thanks are due to Balachander Krishnamurthy, Jeff Mogul and Arthur Van Hoff
    who provided much encouragement to publicize Vcdiff. In particular, Jeff
    helped clarifying the description of the data format presented here.



12. SECURITY CONSIDERATIONS

    Vcdiff only provides a format to encode compressed and differenced data.
    It does not address any issues concerning how such data are, in fact,
    stored in a given file system or the run-time memory of a computer system.
    Therefore, we do not anticipate any security issues with respect to Vcdiff.



13. SOURCE CODE AVAILABILITY

    Vcdiff is implemented as a data transforming method in Phong Vo's
    Vcodex library. AT&T Corp. has made the source code for Vcodex available
    for anyone to use to transmit data via HTTP/1.1 Delta Encoding [10,11].
    The source code and according license is accessible at the below URL:

          http://www.research.att.com/sw/tools


14. INTELLECTUAL PROPERTY RIGHTS

   The IETF has been notified of intellectual property rights claimed in
   regard to some or all of the specification contained in this
   document.  For more information consult the online list of claimed
   rights, at <http://www.ietf.org/ipr.html>.

   The IETF takes no position regarding the validity or scope of any
   intellectual property or other rights that might be claimed to
   pertain to the implementation or use of the technology described in
   this document or the extent to which any license under such rights
   might or might not be available; neither does it represent that it
   has made any effort to identify any such rights.  Information on the
   IETF's procedures with respect to rights in standards-track and
   standards-related documentation can be found in BCP-11.  Copies of
   claims of rights made available for publication and any assurances of
   licenses to be made available, or the result of an attempt made to
   obtain a general license or permission for the use of such
   proprietary rights by implementors or users of this specification can
   be obtained from the IETF Secretariat.



15. IANA CONSIDERATIONS

   The Internet Assigned Numbers Authority (IANA) administers the number
   space for Secondary Compressor ID values.  Values and their meaning
   must be documented in an RFC or other peer-reviewed, permanent, and
   readily available reference, in sufficient detail so that
   interoperability between independent implementations is possible.
   Subject to these constraints, name assignments are First Come, First
   Served - see RFC2434 [13].  Legal ID values are in the range 1..255.

   This document does not define any values in this number space.


16. REFERENCES

    [1] D.G. Korn and K.P. Vo, Vdelta: Differencing and Compression,
        Practical Reusable Unix Software, Editor B. Krishnamurthy,
        John Wiley & Sons, Inc., 1995.

    [2] J. Ziv and A. Lempel, A Universal Algorithm for Sequential Data
        Compression, IEEE Trans. on Information Theory, 23(3):337-343, 1977.

    [3] W. Tichy, The String-to-String Correction Problem with Block Moves,
        ACM Transactions on Computer Systems, 2(4):309-321, November 1984.

    [4] E.M. McCreight, A Space-Economical Suffix Tree Construction
        Algorithm, Journal of the ACM, 23:262-272, 1976.

    [5] J.J. Hunt, K.P. Vo, W. Tichy, An Empirical Study of Delta Algorithms,
        IEEE Software Configuration and Maintenance Workshop, 1996.

    [6] J.J. Hunt, K.P. Vo, W. Tichy, Delta Algorithms: An Empirical Analysis,
        ACM Trans. on Software Engineering and Methodology, 7:192-214, 1998.

    [7] D.G. Korn, K.P. Vo, Sfio: A buffered I/O Library,
        Proc. of the Summer '91 Usenix Conference, 1991.

    [8] D. W. Jones, Application of Splay Trees to Data Compression,
        CACM, 31(8):996:1007.

    [9] M. Nelson, J. Gailly, The Data Compression Book, ISBN 1-55851-434-1,
        M&T Books, New York, NY, 1995.

   [10] J.C. Mogul, F. Douglis, A. Feldmann, and B. Krishnamurthy,
        Potential benefits of delta encoding and data compression for HTTP,
        SIGCOMM '97, Cannes, France, 1997.

   [11] J.C. Mogul, B. Krishnamurthy, F. Douglis, A. Feldmann,
        Y. Goland, and A. Van Hoff, Delta Encoding in HTTP,
        IETF, draft-mogul-http-delta-10, 2001.

   [12] S. Bradner, Key words for use in RFCs to Indicate Requirement Levels,
        RFC 2119, March 1997.

   [13] T. Narten, H. Alvestrand, Guidelines for Writing an IANA
        Considerations Section in RFCs, RFC2434, October 1998.



17. AUTHOR'S ADDRESS

    Kiem-Phong Vo (main contact)
    AT&T Labs, Room D223
    180 Park Avenue
    Florham Park, NJ 07932
    Email: kpv@research.att.com
    Phone: 1 973 360 8630

    David G. Korn
    AT&T Labs, Room D237
    180 Park Avenue
    Florham Park, NJ 07932
    Email: dgk@research.att.com
    Phone: 1 973 360 8602

    Jeffrey C. Mogul
    Western Research Laboratory
    Compaq Computer Corporation
    250 University Avenue
    Palo Alto, California, 94305, U.S.A.
    Email: JeffMogul@acm.org
    Phone: 1 650 617 3304 (email preferred)

    Joshua P. MacDonald
    Computer Science Division
    University of California, Berkeley
    345 Soda Hall
    Berkeley, CA 94720
    Email: jmacd@cs.berkeley.edu