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Versions: 00 01                                                         
INTERNET-DRAFT                                          Adam M. Costello
draft-ietf-idn-amc-ace-r-01.txt                              2001-May-31
Expires 2001-Nov-30

                         AMC-ACE-R version 0.2.1

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

    Distribution of this document is unlimited.  Please send comments
    to the author at amc@cs.berkeley.edu, or to the idn working
    group at idn@ops.ietf.org.  A non-paginated (and possibly
    newer) version of this specification may be available at
    http://www.cs.berkeley.edu/~amc/charset/amc-ace-r

Abstract

    AMC-ACE-R is a reversible transformation from a sequence of Unicode
    [UNICODE] code points to a sequence of letters, digits, and hyphens
    (LDH characters).  AMC-ACE-R could be used as an ASCII-Compatible
    Encoding (ACE) for internationalized domain names [IDN] [IDNA].

    Besides domain names, there might also be other contexts where it is
    useful to transform Unicode characters into "safe" (delimiter-free)
    ASCII characters.  (If other contexts consider hyphens to be
    unsafe, a different character could be used to play its role, like
    underscore.)

Contents

    Technical changes from earlier versions
    Features
    Name
    Terminology
    Description
    Base-32 characters
    Encoding and decoding algorithms
    Signature
    Mixed-case annotation
    Comparison with other ACEs
    Example strings
    Security considerations
    Acknowledgements
    References
    Author
    Example implementation

Technical changes from earlier versions

    From 0.0.x to 0.1.x:

        In update(), the test "latest - first == 1" was a bug, changed
        to "latest == first".

        In encode(), "codepoint" was a misspelling of "input[i]".

        Initializing refpoint[1] to 0x60 was a design flaw, because this
        initial value is useless for nameprep'd strings.  The initial
        value is changed to 0xE0.

        encode() now fails if input[i] is not in 0..10FFFF, in order to
        avoid an array bounds error.  This does not affect the encoding
        of valid Unicode strings.

    From 0.1.x to 0.2.x:

        The test "latest == first" tests for the first code point, but
        the intention was to test for the first non-LDH code point,
        or equivalently, for the first time update() is called.  The
        boolean flag "updated" has been introduced for performing the
        proper test.  This alters the encoding of some strings, usually
        for the better.

        The initial value of refpoint[2] has been changed from 0 to
        0xA0, which is more useful in light of nameprep's prohibition of
        non-LDH code points below 0xA0.

        In decode() the number of base-32 characters consumed has been
        limited to 5, to avoid an array bounds error on invalid input.

Features

    Completeness:  Every Unicode string maps to an LDH string.
    Restrictions on which Unicode strings are allowed, and on length,
    may be imposed by higher layers.

    Uniqueness:  Every Unicode string maps to at most one LDH string.

    Reversibility:  Any Unicode string mapped to an LDH string can be
    recovered from that LDH string.

    Efficient encoding:  The ratio of encoded size to original size is
    small for all Unicode strings.  This is important in the context
    of domain names because [RFC1034] restricts the length of a domain
    label to 63 characters.

    Simplicity:  The encoding and decoding algorithms are reasonably
    simple to implement.  The goals of efficiency and simplicity are at
    odds; AMC-ACE-R aims at a reasonable balance between them.

    Mixed-case annotation:  Even if the Unicode string has been
    case-folded prior to encoding, it is possible to used mixed case
    in the encoded string as an annotation telling how to convert the
    folded Unicode string into a mixed-case Unicode string for display
    purposes.  This feature is optional; see section "Mixed-case
    annotation".

    Readability:  The letters A-Z and a-z and the digits 0-9 appearing
    in the Unicode string are represented as themselves in the label.
    This comes for free because it usually the most efficient encoding
    anyway.

Name

    AMC-ACE-R is a working name that should be changed if it is adopted.
    (The R merely indicates that it is the eighteenth ACE devised by
    this author.  BRACE was the third.  Most were not worth releasing.)
    Rather than waste good names on experimental proposals, let's
    wait until one proposal is chosen, then assign it a good name.
    Suggestions:

        UniHost
        NUDE (Normal Unicode Domain Encoding)
        UTF-D ("D" for "domain names")
        UTF-37 (there are 37 characters in the output repertoire)

Terminology

    LDH characters are the letters A-Z and a-z, the digits 0-9, and
    hyphen-minus.

    A quartet is a sequence of four bits (also known as a nibble or
    nybble).

    A quintet is a sequence of five bits.

    Hexadecimal values are shown preceeded by "0x".  For example, 0x60
    is decimal 96.

    As in the Unicode Standard [UNICODE], Unicode code points are
    denoted by "U+" followed by four to six hexadecimal digits, while a
    range of code points is denoted by two hexadecimal numbers separated
    by "..", with no prefixes.

    "x..y" means the range of integers x through y inclusive.

    "x << y" means x left-shifted by y bits (equivalent to x times
    2 to the power y), and "x >> y" means x right-shifted by y bits
    (equivalent to x divided by 2 to the power y, discarding the
    remainder).  These operations are used only with nonnegative
    integral values.

Description

    AMC-ACE-R represents a sequence of Unicode code points as a sequence
    of LDH characters, although implementations will also need to
    represent the LDH characters somehow, typically as ASCII octets.
    The encoder input and decoder output are arrays of Unicode code
    points (integral values in the range 0..10FFFF, but not D800..DFFF,
    which are reserved for use by UTF-16).

    This section describes the representation.  Section "Encoding
    and decoding algorithms" presents the algorithms as commented
    pseudocode.  There is also commented C code in section "Example
    implementation".

    The encoded string alternates between two modes: literal mode and
    base-32 mode.  Unicode code points representing LDH characters
    are encoded as those LDH characters, except that hyphen-minus is
    doubled.  Other Unicode code points are encoded as one or more LDH
    characters using base-32, in which each character of the encoded
    string represents a quintet according to the table in section
    "Base-32 characters".  A mode change is indicated by an unpaired
    hyphen-minus.  A pair of consecutive hyphen-minuses represents a
    hyphen-minus and does not change the mode.

    In base-32 mode a variable-length code sequence of one to five
    quintets represents a delta, which is added to a reference point to
    yield a Unicode code point.  There are five reference points, one
    for each code length.  The delta is represented by the lowest four
    bits of each quintet.  The highest bit of each quintet is 1, except
    for the last quintet, where it is 0, allowing the decoder to detect
    the end of the sequence.

    Code sequences:
        delta from reference point 1: 0xxxx
        delta from reference point 2: 1xxxx 0xxxx
        delta from reference point 3: 1xxxx 1xxxx 0xxxx
        delta from reference point 4: 1xxxx 1xxxx 1xxxx 0xxxx
        delta from reference point 5: 1xxxx 1xxxx 1xxxx 1xxxx 0xxxx

    For reference point k, the delta is constrained by the available
    bits to range from 0 to (1 << (4*k)) - 1, so each reference point is
    the bottom of a window of 1 << (4*k) code points.  A code point is
    encoded as an offset into the smallest window that contains it.

    Reference points 4 and 5 are fixed at 0 and 0x10000 respectively,
    so that windows 4 and 5 always cover the entire Unicode code space
    0..10FFFF.  The other reference points are updated whenever a code
    point has been encoded or decoded in base-32 mode, using following
    heuristic.

    The latest code point is rounded down to a multiple of 0x10 to
    obtain a candidate for replacing reference point 1.  If a non-LDH
    code point falling within the candidate window has appeared more
    recently than one falling within the current window, then the
    reference point is changed.  Otherwise a similar check is performed
    for reference point 2 using 0x100 as the divisor, and failing that,
    reference point 3 is checked using 0x1000.  At most one window is
    changed each time, except that after the very first non-LDH code
    point (when there is no useful history), all three windows are
    changed.

    The initial values of the state variables are:

                     mode:  base-32
        reference point 1:  0xE0
        reference point 2:  0xA0
        reference point 3:  0
        reference point 4:  0
        reference point 5:  0x10000

Base-32 characters

        "a" =  0 = 0x00 = 00000         "s" = 16 = 0x10 = 10000
        "b" =  1 = 0x01 = 00001         "t" = 17 = 0x11 = 10001
        "c" =  2 = 0x02 = 00010         "u" = 18 = 0x12 = 10010
        "d" =  3 = 0x03 = 00011         "v" = 19 = 0x13 = 10011
        "e" =  4 = 0x04 = 00100         "w" = 20 = 0x14 = 10100
        "f" =  5 = 0x05 = 00101         "x" = 21 = 0x15 = 10101
        "g" =  6 = 0x06 = 00110         "y" = 22 = 0x16 = 10110
        "h" =  7 = 0x07 = 00111         "z" = 23 = 0x17 = 10111
        "i" =  8 = 0x08 = 01000         "2" = 24 = 0x18 = 11000
        "j" =  9 = 0x09 = 01001         "3" = 25 = 0x19 = 11001
        "k" = 10 = 0x0A = 01010         "4" = 26 = 0x1A = 11010
        "m" = 11 = 0x0B = 01011         "5" = 27 = 0x1B = 11011
        "n" = 12 = 0x0C = 01100         "6" = 28 = 0x1C = 11100
        "p" = 13 = 0x0D = 01101         "7" = 29 = 0x1D = 11101
        "q" = 14 = 0x0E = 01110         "8" = 30 = 0x1E = 11110
        "r" = 15 = 0x0F = 01111         "9" = 31 = 0x1F = 11111

    The digits "0" and "1" and the letters "o" and "l" are not used, to
    avoid transcription errors.

    All decoders must recognize both the uppercase and lowercase forms
    of the base-32 characters (including mixtures of both forms).
    An encoder should output only lowercase forms or only uppercase
    forms unless it uses the feature described in section "Mixed-case
    annotation").

Encoding and decoding algorithms

    All ordering of bits, quartets, and quintets is big-endian (most
    significant first).  When subroutines alter variables that are
    passed in as arguments, those changes are seen by the caller after
    the subroutine returns.  As in C, "continue" means terminate the
    current iteration of the innermost loop, and "break" means terminate
    the innermost loop.

    procedure initialize(refpoint,literal,updated):
      let refpoint[1..5] = (0xE0, 0xA0, 0, 0, 0x10000)
      let literal = updated = false

    procedure update(refpoint, updated, history[first..latest]):
      # Update the reference points based on the history.
      for k = 1 to 3 do begin
        let b = 4 * k
        # The first time here change all the windows:
        if not updated
        then let refpoint[k] = (history[latest] >> b) << b
        else for i = latest - 1 down to first do begin
          if history[i] represents an LDH character then continue
          # If a code point falling in the existing window has appeared
          # at least as recently as one falling in the candidate window,
          # then leave this window unchanged and go on to the next one:
          if (refpoint[k] XOR history[i]) >> b == 0 then break
          if (history[latest] XOR history[i]) >> b == 0 then begin
            # A code point falling in the candidate window has appeared
            # more recently than one falling in the existing window, so
            # change this window (and no others):
            let refpoint[k] = (history[latest] >> b) << b
            goto update_end
          end
        end
      end
      update_end: let updated = true

    procedure encode(input[first..last]):
      initialize(refpoint,literal,updated)
      for i = first to last do begin
        # Check code point range to avoid array bounds errors later:
        if input[i] is not in 0..10FFFF then fail
        if input[i] == 0x2D then output two hyphen-minuses
        else if input[i] represents an LDH character then begin
          # Letter/digit is encoded literally, so get into literal mode.
          if not literal then output hyphen-minus
          let literal = true
          output the character represented by input[i]
        end
        else begin
          # Non-LDH code point is encoded in base-32.
          # Compute the number of base-32 characters to use:
          for k = 1 to infinity do begin
            let delta = input[i] - refpoint[k]
            if delta >= 0 and delta >> (4*k) == 0 then break
          end
          # Switch to base-32 mode if necessary:
          if literal then output hyphen-minus
          let literal = false
          represent delta in base 16 as k quartets
          prepend 0 to the last quartet and 1 to each of the others
          output a base-32 character corresponding to each quintet
          update(refpoint, updated, input[first..i])
        end
      end

    procedure decode(input string):
      initialize(refpoint,literal,updated)
      let history = the empty array
      while the input string is not exhausted do begin
        read the next character into c
        # Unpaired hyphen-minus toggles the mode:
        if c is hyphen-minus and the next character is not
        then read the next character into c and toggle literal
        # Double hyphen-minus represents 0x2D:
        if c is hyphen-minus
        then read the next character and append 0x2D to history
        else if literal then append the code point of c to history
        else begin
          # Decode a base-32 sequence.
          convert c to a quintet
          while a quintet beginning with 0 has not been seen
          do read and convert up to four more characters
          concatenate the lowest four bits of each quintet to form delta
          append refpoint[number of quintets] + delta to history
          update(refpoint,updated,history)
        end
      end
      # Enforce the uniqueness of the encoding:
      encode history and compare it to the input string
      fail if they are not equal
      output history

    The decoder must always be prepared for premature end-of-input or
    invalid input characters, and must either fail immediately or forge
    ahead and let the comparison at the end fail.  The comparison must
    be case-insensitive if ACEs are always compared case-insensitively
    (which is true of domain names), case-sensitive otherwise.  This
    check is necessary to guarantee the uniqueness property (there
    cannot be two distinct encoded strings representing the same
    sequence of integers).  (If the decoder is one step of a larger
    decoding process, it may be possible to defer the re-encoding and
    comparison to the end of that larger decoding process.)

Signature

    The issue of how to distinguish ACE strings from unencoded strings
    is largely orthogonal to the encoding scheme itself, and is
    therefore not specified here.  In the context of domain name labels,
    a standard prefix and/or suffix (chosen to be unlikely to occur
    naturally) would presumably be attached to ACE labels.

    In order to use AMC-ACE-R in domain names, the choice of signature
    must be mindful of the requirement in [RFC952] that labels never
    begin or end with hyphen-minus.  Since the raw encoded string
    sometimes begins with a hyphen-minus, the signature must include
    a prefix that does not begin with hyphen-minus.  If the Unicode
    strings are forbidden from ending with hyphen-minus (which seems
    prudent anyway), then the raw encoded string will never end with
    hyphen-minus; otherwise, the signature must include a suffix as well
    as a prefix.

Mixed-case annotation

    In order to use AMC-ACE-R to represent case-insensitive Unicode
    strings, higher layers need to case-fold the Unicode strings prior
    to AMC-ACE-R encoding.  The encoded string can, however, use
    mixed-case base-32 (rather than all-lowercase or all-uppercase
    as recommended in section "Base-32 characters") as an annotation
    telling how to convert the folded Unicode string into a mixed-case
    Unicode string for display purposes.

    Each non-LDH code point is represented by a sequence of base-32
    characters, the last of which is always a letter (as opposed to
    a digit).  If that letter is uppercase, it is a suggestion that
    the Unicode character be mapped to uppercase (if possible); if the
    letter is lowercase, it is a suggestion that the Unicode character
    be mapped to lowercase (if possible).

    AMC-ACE-R encoders and decoders are not required to support these
    annotations, and higher layers need not use them.

Comparison with other ACEs

    Please refer to the comparison in [AMCACEW].

Example strings

    In the ACE encodings below, no signatures are shown.  AMC-ACE-R is
    abbreviated AMC-R.  Backslashes show where line breaks have been
    inserted in strings too long for one line.

    The first several examples are all translations of the sentence "Why
    can't they just speak in <language>?" (courtesy of Michael Kaplan's
    "provincial" page [PROVINCIAL]).  Word breaks and punctuation have
    been removed, as is often done in domain names.

    (A) Arabic (Egyptian):
        u+0644 u+064A u+0647 u+0645 u+0627 u+0628 u+062A u+0643 u+0644
        u+0645 u+0648 u+0634 u+0639 u+0631 u+0628 u+064A u+061F
        AMC-R:  ywekhfuhuikwdwefivevjbuiwktr

    (B) Chinese (simplified):
        u+4ED6 u+4EEC u+4E3A u+4EC0 u+4E48 u+4E0D u+8BF4 u+4E2D u+6587
        AMC-R:  w87g8nvk6awisp259eupyx2h

    (C) Czech: Pro<ccaron>prost<ecaron>nemluv<iacute><ccaron>esky
        U+0050 u+0072 u+006F u+010D u+0070 u+0072 u+006F u+0073 u+0074
        u+011B u+006E u+0065 u+006D u+006C u+0075 u+0076 u+00ED u+010D
        u+0065 u+0073 u+006B u+0079
        AMC-R:  -Pro-yp-prost-tm-nemluv-s8pp-esky

    (D) Hebrew:
        u+05DC u+05DE u+05D4 u+05D4 u+05DD u+05E4 u+05E9 u+05D5 u+05D8
        u+05DC u+05D0 u+05DE u+05D3 u+05D1 u+05E8 u+05D9 u+05DD u+05E2
        u+05D1 u+05E8 u+05D9 u+05EA
        AMC-R:  x7nqeep8e8j7f7inaqdb8ijp8cb8ij8k

    (E) Hindi (Devanagari):
        u+092F u+0939 u+0932 u+094B u+0917 u+0939 u+093F u+0928 u+094D
        u+0926 u+0940 u+0915 u+094D u+092F u+094B u+0902 u+0928 u+0939
        u+0940 u+0902 u+092C u+094B u+0932 u+0938 u+0915 u+0924 u+0947
        u+0939 u+0948 u+0902
        AMC-R:  3urvjvcwmthjruiwpugwatfwpurmscuivjascunmvcvitfuewhjwisc

    (F) Japanese (kanji and hiragana):
        u+306A u+305C u+307F u+3093 u+306A u+65E5 u+672C u+8A9E u+3092
        u+8A71 u+3057 u+3066 u+304F u+308C u+306A u+3044 u+306E u+304B
        AMC-R:  vsykxnzr3dkyx8fyzun243q3c24zbxhgwr2nkweqwm

    (G) Korean (Hangul syllables):
        u+C138 u+ACC4 u+C758 u+BAA8 u+B4E0 u+C0AC u+B78C u+B4E4 u+C774
        u+D55C u+AD6D u+C5B4 u+B97C u+C774 u+D574 u+D55C u+B2E4 u+BA74
        u+C5BC u+B9C8 u+B098 u+C88B u+C744 u+AE4C
        AMC-R:  6tvi466ezxi544i5w8a6s4nz2nw8e6zze7xxn47yp6x5e53znze7xze\
                7xxn5u8e54ze6x5n36is3i622m6zwe48wn

    (H) Russian (Cyrillic):
        U+043F u+043E u+0447 u+0435 u+043C u+0443 u+0436 u+0435 u+043E
        u+043D u+0438 u+043D u+0435 u+0433 u+043E u+0432 u+043E u+0440
        u+044F u+0442 u+043F u+043E u+0440 u+0443 u+0441 u+0441 u+043A
        u+0438
        AMC-R:  wvRqwhfnwdgfqpipfdqcqwawrcvrvqwawdbbvkvi

    (I) Spanish: Porqu<eacute>nopuedensimplementehablarenEspa<ntilde>ol
        U+0050 u+006F u+0072 u+0071 u+0075 u+00E9 u+006E u+006F u+0070
        u+0075 u+0065 u+0064 u+0065 u+006E u+0073 u+0069 u+006D u+0070
        u+006C u+0065 u+006D u+0065 u+006E u+0074 u+0065 u+0068 u+0061
        u+0062 u+006C u+0061 u+0072 u+0065 u+006E U+0045 u+0073 u+0070
        u+0061 u+00F1 u+006F u+006C
        AMC-R:  -Porqu-j-nopuedensimplementehablarenEspa-9b-ol

    (J) Taiwanese:
        u+4ED6 u+5011 u+7232 u+4EC0 u+9EBD u+4E0D u+8AAA u+4E2D u+6587
        AMC-R:  w87gxstbzuvc6a385psp244kupyx2h

    (K) Vietnamese:
        Ta<dotbelow>isaoho<dotbelow>kh<ocirc>ngth<ecirc><hookabove>chi\
        <hookabove>no<acute>iti<ecirc><acute>ngVi<ecirc><dotbelow>t
        U+0054 u+0061 u+0323 u+0069 u+0073 u+0061 u+006F u+0068 u+006F
        u+0323 u+006B u+0068 u+00F4 u+006E u+0067 u+0074 u+0068 u+00EA
        u+0309 u+0063 u+0068 u+0069 u+0309 u+006E u+006F u+0301 u+0069
        u+0074 u+0069 u+00EA u+0301 u+006E u+0067 U+0056 u+0069 u+00EA
        u+0323 u+0074
        AMC-R:  -Ta-vud-isaoho-d-kh-s9e-ngth-s8kvsj-chi-vsj-no-b-iti-s8\
                kb-ngVi-s8kud-t

    The next several examples are all names of Japanese music artists,
    song titles, and TV programs, just because the author happens to
    have them handy (but Japanese is useful for providing examples
    of single-row text, two-row text, ideographic text, and various
    mixtures thereof).

    (L) 3<nen>B<gumi><kinpachi><sensei>
        u+0033 u+5E74 U+0042 u+7D44 u+91D1 u+516B u+5148 u+751F
        AMC-R:  -3-x8ze-B-z7we3t7btymtwizxtr

    (M) <amuro><namie>-with-SUPER-MONKEYS
        u+5B89 u+5BA4 u+5948 u+7F8E u+6075 u+002D u+0077 u+0069 u+0074
        u+0068 u+002D U+0053 U+0055 U+0050 U+0045 U+0052 u+002D U+004D
        U+004F U+004E U+004B U+0045 U+0059 U+0053
        AMC-R:  x52j4e3wiz92qyszf---with--SUPER--MONKEYS

    (N) Hello-Another-Way-<sorezore><no><basho>
        U+0048 u+0065 u+006C u+006C u+006F u+002D U+0041 u+006E u+006F
        u+0074 u+0068 u+0065 u+0072 u+002D U+0057 u+0061 u+0079 u+002D
        u+305D u+308C u+305E u+308C u+306E u+5834 u+6240
        AMC-R:  -Hello--Another--Way---vsxp2nq2nyqx2veyuwa

    (O) <hitotsu><yane><no><shita>2
        u+3072 u+3068 u+3064 u+5C4B u+6839 u+306E u+4E0B u+0032
        AMC-R:  vszcyiyex6wmy2vjqw8sm-2

    (P) Maji<de>Koi<suru>5<byou><mae>
        U+004D u+0061 u+006A u+0069 u+3067 U+004B u+006F u+0069 u+3059
        u+308B u+0035 u+79D2 u+524D
        AMC-R:  -Maji-vsyh-Koi-xj2m-5-z37cxuwp

    (Q) <pafii>de<runba>
        u+30D1 u+30D5 u+30A3 u+30FC u+0064 u+0065 u+30EB u+30F3 u+30D0
        AMC-R:  vs7bf4d9n-de-8m9d7a

    (R) <sono><supiido><de>
        u+305D u+306E u+30B9 u+30D4 u+30FC u+30C9 u+3067
        AMC-R:  vsxpyq5j7e9n6jyh

    The last example is an ASCII string that breaks not only the
    existing rules for host name labels but also the rules proposed in
    [NAMEPREP03] for internationalized domain names.

    (S) -> $1.00 <-
        u+002D u+003E u+0020 u+0024 u+0031 u+002E u+0030 u+0030 u+0020
        u+003C u+002D
        AMC-R:  --svquaue-1-q-00-avn--

Security considerations

    Users expect each domain name in DNS to be controlled by a single
    authority.  If a Unicode string intended for use as a domain label
    could map to multiple ACE labels, then an internationalized domain
    name could map to multiple ACE domain names, each controlled by
    a different authority, some of which could be spoofs that hijack
    service requests intended for another.  Therefore AMC-ACE-R is
    designed so that each Unicode string has a unique encoding.

    However, there can still be multiple Unicode representations of the
    "same" text, for various definitions of "same".  This problem is
    addressed to some extent by the Unicode standard under the topic of
    canonicalization, and this work is leveraged for domain names by
    "nameprep" [NAMEPREP03].

Acknowledgements

    AMC-ACE-R reuses a number of preexisting techniques.

    The basic encoding of integers to quartets to quintets to base-32
    comes from UTF-5 [UTF5], and the particular variant used here comes
    from AMC-ACE-M [AMCACEM].

    The idea of avoiding 0, 1, o, and l in base-32 strings was taken
    from SFS [SFS].

    The idea of encoding deltas from reference points was taken from
    RACE (of which the latest version is [RACE03]), which may have
    gotten the idea from Unicode Technical Standard #6 [UTS6].

    The idea of switching between literal mode and base-32 mode comes
    from BRACE [BRACE].

    The general idea of using the alphabetic case of base-32 characters
    to indicate the desired case of the Unicode characters was suggested
    by this author, and first applied to the UTF-5-style encoding in
    DUDE (of which the latest version is [DUDE01]).

    The heuristic used to adapt the reference points based on past code
    points is new in AMC-ACE-R.

References

    [AMCACEM] Adam Costello, "AMC-ACE-M version 0.1.4", 2001-Apr-01,
    update of draft-ietf-idn-amc-ace-m-00, latest version at
    http://www.cs.berkeley.edu/~amc/charset/amc-ace-m.

    [AMCACEW] Adam Costello, "AMC-ACE-W version 0.1.0",
    2001-May-31, draft-ietf-idn-amc-ace-w-00, latest version at
    http://www.cs.berkeley.edu/~amc/charset/amc-ace-w.

    [BRACE] Adam Costello, "BRACE: Bi-mode Row-based
    ASCII-Compatible Encoding for IDN version 0.1.2",
    2000-Sep-19, draft-ietf-idn-brace-00, version at
    http://www.cs.berkeley.edu/~amc/charset/brace.

    [DUDE01] Mark Welter, Brian Spolarich, "DUDE: Differential Unicode
    Domain Encoding", 2001-Mar-02, draft-ietf-idn-dude-01.

    [IDN] Internationalized Domain Names (IETF working group),
    http://www.i-d-n.net/, idn@ops.ietf.org.

    [IDNA] Patrik Faltstrom, Paul Hoffman, "Internationalizing Host
    Names In Applications (IDNA)", draft-ietf-idn-idna-01.

    [NAMEPREP03] Paul Hoffman, Marc Blanchet, "Preparation
    of Internationalized Host Names", 2001-Feb-24,
    draft-ietf-idn-nameprep-03.

    [PROVINCIAL] Michael Kaplan, "The 'anyone can be provincial!' page",
    http://www.trigeminal.com/samples/provincial.html.

    [RACE03] Paul Hoffman, "RACE: Row-based ASCII Compatible Encoding
    for IDN", 2000-Nov-28, draft-ietf-idn-race-03.

    [RFC952] K. Harrenstien, M. Stahl, E. Feinler, "DOD Internet Host
    Table Specification", 1985-Oct, RFC 952.

    [RFC1034] P. Mockapetris, "Domain Names - Concepts and Facilities",
    1987-Nov, RFC 1034.

    [SFS] David Mazieres et al, "Self-certifying File System",
    http://www.fs.net/.

    [UNICODE] The Unicode Consortium, "The Unicode Standard",
    http://www.unicode.org/unicode/standard/standard.html.

    [UTF5] James Seng, Martin Duerst, Tin Wee Tan, "UTF-5, a
    Transformation Format of Unicode and ISO 10646", draft-jseng-utf5-*.

    [UTS6] Misha Wolf, Ken Whistler, Charles Wicksteed,
    Mark Davis, Asmus Freytag, "Unicode Technical Standard
    #6: A Standard Compression Scheme for Unicode",
    http://www.unicode.org/unicode/reports/tr6/.

Author

    Adam M. Costello <amc@cs.berkeley.edu>
    http://www.cs.berkeley.edu/~amc/


Example implementation


/******************************************/
/* amc-ace-r.c 0.2.1 (2001-May-31-Thu)    */
/* Adam M. Costello <amc@cs.berkeley.edu> */
/******************************************/

/* This is ANSI C code (C89) implementing AMC-ACE-R version 0.2.*. */


/************************************************************/
/* Public interface (would normally go in its own .h file): */

#include <limits.h>

enum amc_ace_status {
  amc_ace_success,
  amc_ace_bad_input,
  amc_ace_big_output  /* Output would exceed the space provided. */
};

enum case_sensitivity { case_sensitive, case_insensitive };

#if UINT_MAX >= 0x10FFFF
typedef unsigned int u_code_point;
#else
typedef unsigned long u_code_point;
#endif

enum amc_ace_status amc_ace_r_encode(
  unsigned int input_length,
  const u_code_point input[],
  const unsigned char uppercase_flags[],
  unsigned int *output_size,
  char output[] );

    /* amc_ace_r_encode() converts Unicode to AMC-ACE-R (without      */
    /* any signature).  The input must be represented as an array     */
    /* of Unicode code points (not code units; surrogate pairs        */
    /* are not allowed), and the output will be represented as        */
    /* null-terminated ASCII.  The input_length is the number of      */
    /* code points in the input.  The output_size is an in/out        */
    /* argument: the caller must pass in the maximum number of        */
    /* characters that may be output (including the terminating       */
    /* null), and on successful return it will contain the number of  */
    /* characters actually output (including the terminating null,    */
    /* so it will be one more than strlen() would return, which is    */
    /* why it is called output_size rather than output_length).  The  */
    /* uppercase_flags array must hold input_length boolean values,   */
    /* where nonzero means the corresponding Unicode character should */
    /* be forced to uppercase after being decoded, and zero means it  */
    /* is caseless or should be forced to lowercase.  Alternatively,  */
    /* uppercase_flags may be a null pointer, which is equivalent     */
    /* to all zeros.  The letters a-z and A-Z are always encoded      */
    /* literally, regardless of the corresponding flags.  The encoder */
    /* always outputs lowercase base-32 characters except when        */
    /* nonzero values of uppercase_flags require otherwise.  The      */
    /* return value may be any of the amc_ace_status values defined   */
    /* above; if not amc_ace_success, then output_size and output may */
    /* contain garbage.  On success, the encoder will never need to   */
    /* write an output_size greater than input_length*5+1, because of */
    /* how the encoding is defined.                                   */

enum amc_ace_status amc_ace_r_decode(
  enum case_sensitivity case_sensitivity,
  char scratch_space[],
  const char input[],
  unsigned int *output_length,
  u_code_point output[],
  unsigned char uppercase_flags[] );

    /* amc_ace_r_decode() converts AMC-ACE-R (without any signature)  */
    /* to Unicode.  The input must be represented as null-terminated  */
    /* ASCII, and the output will be represented as an array of       */
    /* Unicode code points.  The case_sensitivity argument influences */
    /* the check on the well-formedness of the input string; it       */
    /* must be case_sensitive if case-sensitive comparisons are       */
    /* allowed on encoded strings, case_insensitive otherwise.        */
    /* The scratch_space must point to space at least as large        */
    /* as the input, which will get overwritten (this allows the      */
    /* decoder to avoid calling malloc()).  The output_length is      */
    /* an in/out argument: the caller must pass in the maximum        */
    /* number of code points that may be output, and on successful    */
    /* return it will contain the actual number of code points        */
    /* output.  The uppercase_flags array must have room for at       */
    /* least output_length values, or it may be a null pointer        */
    /* if the case information is not needed.  A nonzero flag         */
    /* indicates that the corresponding Unicode character should      */
    /* be forced to uppercase by the caller, while zero means it      */
    /* is caseless or should be forced to lowercase.  The letters     */
    /* a-z and A-Z are output already in the proper case, but their   */
    /* flags will be set appropriately so that applying the flags     */
    /* would be harmless.  The return value may be any of the         */
    /* amc_ace_status values defined above; if not amc_ace_success,   */
    /* then output_length, output, and uppercase_flags may contain    */
    /* garbage.  On success, the decoder will never need to write     */
    /* an output_length greater than the length of the input (not     */
    /* counting the null terminator), because of how the encoding is  */
    /* defined.                                                       */


/**********************************************************/
/* Implementation (would normally go in its own .c file): */

#include <string.h>

/* is_ldh(n) returns 1 if the code point n represents an LDH      */
/* character (ASCII letter, digit, or hyphen-minus), 0 otherwise. */

static int is_ldh(u_code_point n)
{
  return n <= 122 && ( n >= 97 || n == 45 ||
         (n >= 48 && n <= 57) || (n >= 65 && n <= 90) );
}

/* base32[q] is the lowercase base-32 character representing  */
/* the number q from the range 0 to 31.  Note that we cannot  */
/* use string literals for ASCII characters because an ANSI C */
/* compiler does not necessarily use ASCII.                   */

static const char base32[] = {
  97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107,     /* a-k */
  109, 110,                                               /* m-n */
  112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122,  /* p-z */
  50, 51, 52, 53, 54, 55, 56, 57                          /* 2-9 */
};

/* base32_decode(c) returns the value of a base-32 character, in the */
/* range 0 to 31, or the constant base32_invalid if c is not a valid */
/* base-32 character.                                                */

enum { base32_invalid = 32 };

static unsigned int base32_decode(char c)
{
  if (c < 50) return base32_invalid;
  if (c <= 57) return c - 26;
  if (c < 97) c += 32;
  if (c < 97 || c == 108 || c == 111 || c > 122) return base32_invalid;
  return c - 97 - (c > 108) - (c > 111);
}

/* unequal(case_sensitivity,s1,s2) returns 0 if the strings s1 and s2 */
/* are equal, 1 otherwise.  If case_sensitivity is case_insensitive,  */
/* then ASCII A-Z are considered equal to a-z respectively.           */

static int unequal( enum case_sensitivity case_sensitivity,
                    const char s1[], const char s2[]        )
{
  char c1, c2;

  if (case_sensitivity != case_insensitive) return strcmp(s1,s2) != 0;

  for (;;) {
    c1 = *s1;
    c2 = *s2;
    if (c1 >= 65 && c1 <= 90) c1 += 32;
    if (c2 >= 65 && c2 <= 90) c2 += 32;
    if (c1 != c2) return 1;
    if (c1 == 0) return 0;
    ++s1, ++s2;
  }
}

/* update(refpoint,updated,history,latest) updates refpoint[1..3] */
/* based on the updated flag and history[0..latest].              */

static void update( u_code_point refpoint[6], unsigned int *updated,
  const u_code_point history[], unsigned int latest )
{
  unsigned int k, b, i;

  for (k = 1;  k <= 3;  ++k) {
    b = k << 2;
    /* The first time here change all the windows: */
    if (!*updated) refpoint[k] = (history[latest] >> b) << b;
    else for (i = latest;  i-- > 0; ) {
      if (is_ldh(history[i])) continue;

      /* If a code point falling in the existing window has appeared  */
      /* at least as recently as one falling in the candidate window, */
      /* then leave this window unchanged and go on to the next one:  */

      if ((refpoint[k] ^ history[i]) >> b == 0) break;

      if ((history[latest] ^ history[i]) >> b == 0) {
        /* A code point falling in the candidate window has appeared */
        /* more recently than one falling in the existing window, so */
        /* change this window (and no others):                       */

        refpoint[k] = (history[latest] >> b) << b;
        goto update_end;
      }
    }
  }

  update_end: *updated = 1;
}

/* Main encode function: */

enum amc_ace_status amc_ace_r_encode(
  unsigned int input_length,
  const u_code_point input[],
  const unsigned char uppercase_flags[],
  unsigned int *output_size,
  char output[] )
{
  unsigned int literal, updated, max_out, in, out, k, j;
  u_code_point n, delta;
  char shift;

  /* Initialize the state: */

  u_code_point refpoint[6] = {0, 0xE0, 0xA0, 0, 0, 0x10000};

  literal = updated = 0;
  max_out = *output_size;

  for (in = out = 0;  in < input_length;  ++in) {

    /* At the start of each iteration, in and out are the number of */
    /* items already input/output, or equivalently, the indices of  */
    /* the next items to be input/output.                           */

    n = input[in];
    /* Check the code point range to avoid array bounds errors later: */
    if (n > 0x10FFFF) return amc_ace_bad_input;

    if (n == 0x2D) {
      /* Hyphen-minus is doubled. */
      if (max_out - out < 2) return amc_ace_big_output;
      output[out++] = 0x2D;
      output[out++] = 0x2D;
    }
    else if (is_ldh(n)) {
      /* Encode an LDH character literally. */
      if (max_out - out < 1 + !literal) return amc_ace_big_output;
      /* Switch to literal mode if necessary: */
      if (!literal) output[out++] = 0x2D;
      literal = 1;
      output[out++] = n;
    }
    else {
      /* Encode a non-LDH character using base-32.           */
      /* First compute the number of base-32 characters (k): */

      for (k = 1; ; ++k) {
        delta = n - refpoint[k];
        if (delta >> (4*k) == 0) break;
      }

      if (max_out - out < k + literal) return amc_ace_big_output;
      /* Switch to base-32 mode if necessary: */
      if (literal) output[out++] = 0x2D;
      literal = 0;
      shift = uppercase_flags && uppercase_flags[in] ? 32 : 0;

      /* Each quintet has the form 1xxxx except the last is 0xxxx. */
      /* Computing the base-32 digits in reverse order is easiest. */

      out += k;
      output[out - 1] = base32[delta & 0xF] - shift;

      for (j = 2;  j <= k;  ++j) {
        delta >>= 4;
        output[out - j] = base32[0x10 | (delta & 0xF)];
      }

      update(refpoint, &updated, input, in);
    }
  }

  /* Append the null terminator: */
  if (max_out - out < 1) return amc_ace_big_output;
  output[out++] = 0;

  *output_size = out;
  return amc_ace_success;
}

/* Main decode function: */

enum amc_ace_status amc_ace_r_decode(
  enum case_sensitivity case_sensitivity,
  char scratch_space[],
  const char input[],
  unsigned int *output_length,
  u_code_point output[],
  unsigned char uppercase_flags[] )
{
  u_code_point q, delta;
  char c;
  unsigned int literal, updated, max_out, in, out, k, scratch_size;
  enum amc_ace_status status;

  /* Initialize the state: */

  u_code_point refpoint[6] = {0, 0xE0, 0xA0, 0, 0, 0x10000};

  literal = updated = 0;
  max_out = *output_length;

  for (c = input[in = 0], out = 0;  c != 0;  c = input[++in], ++out) {

    /* At the start of each iteration, in and out are the number of   */
    /* items already input/output, or equivalently, the indices of    */
    /* the next items to be input/output. c is the same as input[in]. */

    if (c == 0x2D && input[in + 1] != 0x2D) {
      /* Unpaired hyphen-minus toggles mode. */
      literal = !literal;
      c = input[++in];
    }

    if (max_out - out < 1) return amc_ace_big_output;

    if (c == 0x2D) {
      /* Double hyphen-minus represents a hyphen-minus. */
      ++in;
      output[out] = 0x2D;
    }
    else {
      if (literal) output[out] = c;
      else {
        /* Decode a base-32 sequence.                  */
        /* First decode quintets until 0xxxx is found: */

        for (delta = 0, k = 1;  ;  c = input[++in], ++k) {
          q = base32_decode(c);
          if (q == base32_invalid || k > 5) return amc_ace_bad_input;
          delta = (delta << 4) | (q & 0xF);
          if (q >> 4 == 0) break;
        }

        output[out] = refpoint[k] + delta;
        update(refpoint, &updated, output, out);
      }
    }

    /* Case of last character determines uppercase flag: */
    if (uppercase_flags) uppercase_flags[out] = c >= 65 && c <= 90;
  }

  /* Enforce the uniqueness of the encoding by re-encoding */
  /* the output and comparing the result to the input:     */

  scratch_size = ++in;
  status = amc_ace_r_encode(out, output, uppercase_flags,
                            &scratch_size, scratch_space);
  if (status != amc_ace_success || scratch_size != in ||
      unequal(case_sensitivity, scratch_space, input)
     ) return amc_ace_bad_input;

  *output_length = out;
  return amc_ace_success;
}


/******************************************************************/
/* Wrapper for testing (would normally go in a separate .c file): */

#include <assert.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

/* For testing, we'll just set some compile-time limits rather than */
/* use malloc(), and set a compile-time option rather than using a  */
/* command-line option.                                             */

enum {
  unicode_max_length = 256,
  ace_max_size = 256,
  test_case_sensitivity = case_insensitive
                          /* suitable for host names */
};


static void usage(char **argv)
{
  fprintf(stderr,
    "%s -e reads code points and writes an AMC-ACE-R string.\n"
    "%s -d reads an AMC-ACE-R string and writes code points.\n"
    "Input and output are plain text in the native character set.\n"
    "Code points are in the form u+hex separated by whitespace.\n"
    "An AMC-ACE-R string is a newline-terminated sequence of LDH\n"
    "characters (without any signature).\n"
    "The case of the u in u+hex is the force-to-uppercase flag.\n"
    , argv[0], argv[0]);
  exit(EXIT_FAILURE);
}

static void fail(const char *msg)
{
  fputs(msg,stderr);
  exit(EXIT_FAILURE);
}

static const char too_big[] =
  "input or output is too large, recompile with larger limits\n";
static const char invalid_input[] = "invalid input\n";
static const char io_error[] = "I/O error\n";


/* The following string is used to convert LDH      */
/* characters between ASCII and the native charset: */

static const char ldh_ascii[] =
  "................"
  "................"
  ".............-.."
  "0123456789......"
  ".ABCDEFGHIJKLMNO"
  "PQRSTUVWXYZ....."
  ".abcdefghijklmno"
  "pqrstuvwxyz";


int main(int argc, char **argv)
{
  enum amc_ace_status status;
  int r;
  char *p;

  if (argc != 2) usage(argv);
  if (argv[1][0] != '-') usage(argv);
  if (argv[1][2] != 0) usage(argv);

  if (argv[1][1] == 'e') {
    u_code_point input[unicode_max_length];
    unsigned long codept;
    unsigned char uppercase_flags[unicode_max_length];
    char output[ace_max_size], uplus[3];
    unsigned int input_length, output_size, i;

    /* Read the input code points: */

    input_length = 0;

    for (;;) {
      r = scanf("%2s%lx", uplus, &codept);
      if (ferror(stdin)) fail(io_error);
      if (r == EOF || r == 0) break;

      if (r != 2 || uplus[1] != '+' || codept > (u_code_point)-1) {
        fail(invalid_input);
      }

      if (input_length == unicode_max_length) fail(too_big);

      if (uplus[0] == 'u') uppercase_flags[input_length] = 0;
      else if (uplus[0] == 'U') uppercase_flags[input_length] = 1;
      else fail(invalid_input);

      input[input_length++] = codept;
    }

    /* Encode: */

    output_size = ace_max_size;
    status = amc_ace_r_encode(input_length, input, uppercase_flags,
                              &output_size, output);
    if (status == amc_ace_bad_input) fail(invalid_input);
    if (status == amc_ace_big_output) fail(too_big);
    assert(status == amc_ace_success);

    /* Convert to native charset and output: */

    for (p = output;  *p != 0;  ++p) {
      i = *p;
      assert(i <= 122 && ldh_ascii[i] != '.');
      *p = ldh_ascii[i];
    }

    r = puts(output);
    if (r == EOF) fail(io_error);
    return EXIT_SUCCESS;
  }

  if (argv[1][1] == 'd') {
    char input[ace_max_size], scratch[ace_max_size], *pp;
    u_code_point output[unicode_max_length];
    unsigned char uppercase_flags[unicode_max_length];
    unsigned int input_length, output_length, i;

    /* Read the AMC-ACE-R input string and convert to ASCII: */

    fgets(input, ace_max_size, stdin);
    if (ferror(stdin)) fail(io_error);
    if (feof(stdin)) fail(invalid_input);
    input_length = strlen(input);
    if (input[input_length - 1] != '\n') fail(too_big);
    input[--input_length] = 0;

    for (p = input;  *p != 0;  ++p) {
      pp = strchr(ldh_ascii, *p);
      if (pp == 0) fail(invalid_input);
      *p = pp - ldh_ascii;
    }

    /* Decode: */

    output_length = unicode_max_length;
    status = amc_ace_r_decode(test_case_sensitivity, scratch, input,
                              &output_length, output, uppercase_flags);
    if (status == amc_ace_bad_input) fail(invalid_input);
    if (status == amc_ace_big_output) fail(too_big);
    assert(status == amc_ace_success);

    /* Output the result: */

    for (i = 0;  i < output_length;  ++i) {
      r = printf("%s+%04lX\n",
                 uppercase_flags[i] ? "U" : "u",
                 (unsigned long) output[i] );
      if (r < 0) fail(io_error);
    }

    return EXIT_SUCCESS;
  }

  usage(argv);
  return EXIT_SUCCESS;  /* not reached, but quiets compiler warning */
}



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