Punycode: A Bootstring encoding of Unicode for Internationalized Domain Names in Applications (IDNA)
draft-ietf-idn-punycode-02

INTERNET-DRAFT                                          Adam M. Costello
draft-ietf-idn-punycode-02.txt                               2002-May-23
Expires 2002-Nov-23

           Punycode: An encoding of Unicode for use with IDNA

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
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    Distribution of this document is unlimited.

Abstract

    Punycode is a simple and efficient transfer encoding syntax designed
    for use with Internationalized Domain Names in Applications [IDNA].
    It uniquely and reversibly transforms a Unicode string [UNICODE]
    into an ASCII string [ASCII].  ASCII characters in the Unicode
    string are represented literally, and non-ASCII characters are
    represented by ASCII characters that are allowed in host name labels
    (letters, digits, and hyphens).  This document defines a general
    algorithm called Bootstring that allows a string of basic code
    points to uniquely represent any string of code points drawn from
    a larger set.  Punycode is an instance of Bootstring that uses
    particular parameter values specified by this document, appropriate
    for IDNA.


Contents

     1. Introduction
         1.1 Features
         1.2 Interaction of protocol parts
     2. Terminology
     3. Bootstring description
         3.1 Basic code point segregation
         3.2 Insertion unsort coding
         3.3 Generalized variable-length integers
         3.4 Bias adaptation
     4. Bootstring parameters
     5. Parameter values for Punycode
     6. Bootstring algorithms
         6.1 Bias adaptation function
         6.2 Decoding procedure
         6.3 Encoding procedure
         6.4 Overflow handling
     7. Punycode examples
         7.1 Sample strings
         7.2 Decoding traces
         7.3 Encoding traces
     8. Security considerations
     9. References (non-normative)
     A. Author contact information
     B. Mixed-case annotation
     C. Disclaimer and license
     D. Punycode sample implementation

1. Introduction

    [IDNA] describes an architecture for supporting internationalized
    domain names.  Labels containing non-ASCII characters can be
    represented by ACE labels, which begin with a special ACE prefix and
    contain only ASCII characters.  The remainder of the label after the
    prefix is a Punycode encoding of a Unicode string satisfying certain
    constraints.  For the details of the prefix and constraints, see
    [IDNA] and [NAMEPREP].

1.1 Features

    Bootstring has been designed to have the following features:

      * Completeness:  Every extended string (sequence of arbitrary code
        points) can be represented by a basic string (sequence of basic
        code points).  Restrictions on what strings are allowed, and on
        length, can be imposed by higher layers.

      * Uniqueness:  There is at most one basic string that represents a
        given extended string.

      * Reversibility:  Any extended string mapped to a basic string can
        be recovered from that basic string.

      * Efficient encoding:  The ratio of basic string length to
        extended string length is small.  This is important in the
        context of domain names because RFC 1034 [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; Bootstring aims at a good balance between them.

      * Readability:  Basic code points appearing in the extended string
        are represented as themselves in the basic string (although the
        main purpose is to improve efficiency, not readability).

    Punycode can also support an additional feature that is not used
    by the ToASCII and ToUnicode operations of [IDNA].  When extended
    strings are case-folded prior to encoding, the basic string can
    use mixed case to tell how to convert the folded string into a
    mixed-case string.  See appendix B "Mixed-case annotation".

1.2 Interaction of protocol parts

    Punycode is used by the IDNA protocol [IDNA] for converting domain
    labels into ASCII; it is not designed for any other purpose.  It is
    explicitly not designed for processing arbitrary free text.

2. Terminology

    The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
    "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
    document are to be interpreted as described in RFC 2119 [RFC2119].

    A code point is an integral value associated with a character in a
    coded character set.

    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.

    The operators div and mod perform integer division; (x div y) is the
    quotient of x divided by y, discarding the remainder, and (x mod y)
    is the remainder, so (x div y) * y + (x mod y) == x.  Bootstring
    uses these operators only with nonnegative operands, so the quotient
    and remainder are always nonnegative.

    The break statement jumps out of the innermost loop (as in C).

    An overflow is an attempt to compute a value that exceeds the
    maximum value of an integer variable.

3. Bootstring description

    Bootstring represents an arbitrary sequence of code points (the
    "extended string") as a sequence of basic code points (the "basic
    string").  This section describes the representation.  Section 6
    "Bootstring algorithms" presents the algorithms as pseudocode.
    Sections 7.1 "Decoding traces" and 7.2 "Encoding traces" trace the
    algorithms for sample inputs.


    The following sections describe the four techniques used in
    Bootstring.  "Basic code point segregation" is a very simple
    and efficient encoding for basic code points occurring in the
    extended string: they are simply copied all at once.  "Insertion
    unsort coding" encodes the non-basic code points as deltas, and
    processes the code points in numerical order rather than in order of
    appearance, which typically results in smaller deltas.  The deltas
    are represented as "generalized variable-length integers", which use
    basic code points to represent nonnegative integers.  The parameters
    of this integer representation are dynamically adjusted using "bias
    adaptation", to improve efficiency when consecutive deltas have
    similar magnitudes.

3.1 Basic code point segregation

    All basic code points appearing in the extended string are
    represented literally at the beginning of the basic string, in their
    original order, followed by a delimiter if (and only if) the number
    of basic code points is nonzero.  The delimiter is a particular
    basic code point, which never appears in the remainder of the basic
    string.  The decoder can therefore find the end of the literal
    portion (if there is one) by scanning for the last delimiter.

3.2 Insertion unsort coding

    The remainder of the basic string (after the last delimiter if there
    is one) represents a sequence of nonnegative integral deltas as
    generalized variable-length integers, described in section 3.3.  The
    meaning of the deltas is best understood in terms of the decoder.

    The decoder builds the extended string incrementally.  Initially,
    the extended string is a copy of the literal portion of the basic
    string (excluding the last delimiter).  The decoder inserts
    non-basic code points, one for each delta, into the extended string,
    ultimately arriving at the final decoded string.

    At the heart of this process is a state machine with two state
    variables: an index i and a counter n.  The index i refers to
    a position in the extended string; it ranges from 0 (the first
    position) to the current length of the extended string (which refers
    to a potential position beyond the current end).  If the current
    state is <n,i>, the next state is <n,i+1> if i is less than the
    length of the extended string, or <n+1,0> if i equals the length of
    the extended string.  In other words, each state change causes i to
    increment, wrapping around to zero if necessary, and n counts the
    number of wrap-arounds.


    Notice that the state always advances monotonically (there is no
    way for the decoder to return to an earlier state).  At each state,
    an insertion is either performed or not performed.  At most one
    insertion is performed in a given state.  An insertion inserts the
    value of n at position i in the extended string.  The deltas are
    a run-length encoding of this sequence of events: they are the
    lengths of the runs of non-insertion states preceeding the insertion
    states.  Hence, for each delta, the decoder performs delta state
    changes, then an insertion, and then one more state change.  (An
    implementation need not perform each state change individually, but
    can instead use division and remainder calculations to compute the
    next insertion state directly.)  It is an error if the inserted code
    point is a basic code point (because basic code points were supposed
    to be segregated as described in section 3.1).

    The encoder's main task is to derive the sequence of deltas that
    will cause the decoder to construct the desired string.  It can do
    this by repeatedly scanning the extended string for the next code
    point that the decoder would need to insert, and counting the number
    of state changes the decoder would need to perform, mindful of the
    fact that the decoder's extended string will include only those
    code points that have already been inserted.  Section 6.3 "Encoding
    procedure" gives a precise algorithm.

3.3 Generalized variable-length integers

    In a conventional integer representation the base is the number of
    distinct symbols for digits, whose values are 0 through base-1.  Let
    digit_0 denote the least significant digit, digit_1 the next least
    significant, and so on.  The value represented is the sum over j of
    digit_j * w(j), where w(j) = base^j is the weight (scale factor)
    for position j.  For example, in the base 8 integer 437, the digits
    are 7, 3, and 4, and the weights are 1, 8, and 64, so the value is
    7 + 3*8 + 4*64 = 287.  This representation has two disadvantages:
    First, there are multiple encodings of each value (because there
    can be extra zeros in the most significant positions), which is
    inconvenient when unique encodings are needed.  Second, the integer
    is not self-delimiting, so if multiple integers are concatenated the
    boundaries between them are lost.

    The generalized variable-length representation solves these two
    problems.  The digit values are still 0 through base-1, but now
    the integer is self-delimiting by means of thresholds t(j), each
    of which is in the range 0 through base-1.  Exactly one digit, the
    most significant, satisfies digit_j < t(j).  Therefore, if several
    integers are concatenated, it is easy to separate them, starting
    with the first if they are little-endian (least significant digit
    first), or starting with the last if they are big-endian (most
    significant digit first).  As before, the value is the sum over j of
    digit_j * w(j), but the weights are different:

        w(0) = 1
        w(j) = w(j-1) * (base - t(j-1)) for j > 0


    For example, consider the little-endian sequence of base 8 digits
    734251...  Suppose the thresholds are 2, 3, 5, 5, 5, 5...  This
    implies that the weights are 1, 1*(8-2) = 6, 6*(8-3) = 30, 30*(8-5)
    = 90, 90*(8-5) = 270, and so on.  7 is not less than 2, and 3 is
    not less than 3, but 4 is less than 5, so 4 is the last digit.  The
    value of 734 is 7*1 + 3*6 + 4*30 = 145.  The next integer is 251,
    with value 2*1 + 5*6 + 1*30 = 62.  Decoding this representation
    is very similar to decoding a conventional integer:  Start with a
    current value of N = 0 and a weight w = 1.  Fetch the next digit d
    and increase N by d * w.  If d is less than the current threshold
    (t) then stop, otherwise increase w by a factor of (base - t),
    update t for the next position, and repeat.

    Encoding this representation is similar to encoding a conventional
    integer:  If N < t then output one digit for N and stop, otherwise
    output the digit for t + ((N - t) mod (base - t)), then replace N
    with (N - t) div (base - t), update t for the next position, and
    repeat.

    For any particular set of values of t(j), there is exactly one
    generalized variable-length representation of each nonnegative
    integral value.

    Bootstring uses little-endian ordering so that the deltas can be
    separated starting with the first.  The t(j) values are defined in
    terms of the constants base, tmin, and tmax, and a state variable
    called bias:

        t(j) = base * (j + 1) - bias,
        clamped to the range tmin through tmax

    The clamping means that if the formula yields a value less than tmin
    or greater than tmax, then t(j) = tmin or tmax, respectively.  (In
    the pseudocode in section 6 "Bootstring algorithms", the expression
    base * (j + 1) is denoted by k for performance reasons.)  These
    t(j) values cause the representation to favor integers within a
    particular range determined by the bias.

3.4 Bias adaptation

    After each delta is encoded or decoded, bias is set for the next
    delta as follows:

     1. Delta is scaled in order to avoid overflow in the next step:

            let delta = delta div 2

        But when this is the very first delta, the divisor is not 2, but
        instead a constant called damp.  This compensates for the fact
        that the second delta is usually much smaller than the first.

     2. Delta is increased to compensate for the fact that the next
        delta will be inserting into a longer string:


            let delta = delta + (delta div numpoints)

        numpoints is the total number of code points encoded/decoded so
        far (including the one corresponding to this delta itself, and
        including the basic code points).

     3. Delta is repeatedly divided until it falls within a threshold,
        to predict the minimum number of digits needed to represent the
        next delta:

            while delta > ((base - tmin) * tmax) div 2
            do let delta = delta div (base - tmin)

     4. The bias is set:

            let bias =
              (base * the number of divisions performed in step 3) +
              (((base - tmin + 1) * delta) div (delta + skew))

    The motivation for this procedure is that the current delta provides
    a hint about the likely size of the next delta, and so t(j) is
    set to tmax for the more significant digits starting with the one
    expected to be last, tmin for the less significant digits up through
    the one expected to be third-last, and somewhere between tmin and
    tmax for the digit expected to be second-last (balancing the hope of
    the expected-last digit being unnecessary against the danger of it
    being insufficient).

4. Bootstring parameters

    Given a set of basic code points, one needs to be designated as
    the delimiter.  The base cannot be greater than the number of
    distinguishable basic code points remaining.  The digit-values in
    the range 0 through base-1 need to be associated with distinct
    non-delimiter basic code points.  In some cases multiple code points
    need to have the same digit-value; for example, uppercase and
    lowercase versions of the same letter need to be equivalent if basic
    strings are case-insensitive.

    The initial value of n cannot be greater than the minimum non-basic
    code point that could appear in extended strings.

    The remaining five parameters (tmin, tmax, skew, damp, and the
    initial value of bias) need to satisfy the following constraints:

        0 <= tmin <= tmax <= base-1
        skew >= 1
        damp >= 2
        initial_bias mod base <= base - tmin

    Provided the constraints are satisfied, these five parameters affect
    efficiency but not correctness.  They are best chosen empirically.

    If support for mixed-case annotation is desired (see appendix B),
    make sure that the code points corresponding to 0 through tmax-1 all
    have both uppercase and lowercase forms.


5. Parameter values for Punycode

    Punycode uses the following Bootstring parameter values:

        base         = 36
        tmin         = 1
        tmax         = 26
        skew         = 38
        damp         = 700
        initial_bias = 72
        initial_n    = 128 = 0x80

    Although the only restriction Punycode imposes on the input integers
    is that they be nonnegative, these parameters are especially
    designed to work well with Unicode [UNICODE] code points, which
    are integers in the range 0..10FFFF (but not D800..DFFF, which are
    reserved for use by the UTF-16 encoding of Unicode).  The basic code
    points are the ASCII [ASCII] code points (0..7F), of which U+002D
    (-) is the delimiter, and some of the others have digit-values as
    follows:

        code points    digit-values
        ------------   ----------------------
        41..5A (A-Z) =  0 to 25, respectively
        61..7A (a-z) =  0 to 25, respectively
        30..39 (0-9) = 26 to 35, respectively

    Using hyphen-minus as the delimiter implies that the encoded string
    can end with a hyphen-minus only if the Unicode string consists
    entirely of basic code points, but IDNA forbids such strings from
    being encoded.  The encoded string can begin with a hyphen-minus,
    but IDNA prepends a prefix.  Therefore IDNA using Punycode conforms
    to the RFC 952 rule that host name labels neither begin nor end with
    a hyphen-minus [RFC952].

    A decoder MUST recognize the letters in both uppercase and lowercase
    forms (including mixtures of both forms).  An encoder SHOULD output
    only uppercase forms or only lowercase forms, unless it uses
    mixed-case annotation (see appendix B).

    Presumably most users will not manually write or type encoded
    strings (as opposed to cutting and pasting them), but those who do
    will need to be alert to the potential visual ambiguity between the
    following sets of characters:

        G 6
        I l 1
        O 0
        S 5
        U V
        Z 2

    Such ambiguities are usually resolved by context, but in a Punycode
    encoded string there is no context apparent to humans.


6. Bootstring algorithms

    Some parts of the pseudocode can be omitted if the parameters
    satisfy certain conditions (for which Punycode qualifies).  These
    parts are enclosed in {braces}, and notes immediately following the
    pseudocode explain the conditions under which they can be omitted.

    Formally, code points are integers, and hence the pseudocode assumes
    that arithmetic operations can be performed directly on code points.
    In some programming languages, explicit conversion between code
    points and integers might be necessary.

6.1 Bias adaptation function

    function adapt(delta,numpoints,firsttime):
      if firsttime then let delta = delta div damp
      else let delta = delta div 2
      let delta = delta + (delta div numpoints)
      let k = 0
      while delta > ((base - tmin) * tmax) div 2 do begin
        let delta = delta div (base - tmin)
        let k = k + base
      end
      return k + (((base - tmin + 1) * delta) div (delta + skew))

    It does not matter whether the modifications to delta and k
    inside adapt() affect variables of the same name inside the
    encoding/decoding procedures, because after calling adapt() the
    caller does not read those variables before overwriting them.


6.2 Decoding procedure

    let n = initial_n
    let i = 0
    let bias = initial_bias
    let output = an empty string indexed from 0
    consume all code points before the last delimiter (if there is one)
      and copy them to output, fail on any non-basic code point
    if more than zero code points were consumed then consume one more
      (which will be the last delimiter)
    while the input is not exhausted do begin
      let oldi = i
      let w = 1
      for k = base to infinity in steps of base do begin
        consume a code point, or fail if there was none to consume
        let digit = the code point's digit-value, fail if it has none
        let i = i + digit * w, fail on overflow
        let t = tmin if k <= bias {+ tmin}, or
                tmax if k >= bias + tmax, or k - bias otherwise
        if digit < t then break
        let w = w * (base - t), fail on overflow
      end
      let bias = adapt(i - oldi, length(output) + 1, test oldi is 0?)
      let n = n + i div (length(output) + 1), fail on overflow
      let i = i mod (length(output) + 1)
      {if n is a basic code point then fail}
      insert n into output at position i
      increment i
    end

    The full statement enclosed in braces (checking whether n is a basic
    code point) can be omitted if initial_n exceeds all basic code
    points (which is true for Punycode), because n is never less than
    initial_n.

    In the assignment of t, where t is clamped to the range tmin through
    tmax, "+ tmin" can always be omitted.  This makes the clamping
    calculation incorrect when bias < k < bias + tmin, but that cannot
    happen because of the way bias is computed and because of the
    constraints on the parameters.

    Because the decoder state can only advance monotonically, and there
    is only one representation of any delta, there is therefore only
    one encoded string that can represent a given sequence of integers.
    The only error conditions are invalid code points, unexpected
    end-of-input, overflow, and basic code points encoded using deltas
    instead of appearing literally.  If the decoder fails on these
    errors as shown above, then it cannot produce the same output for
    two distinct inputs.  Without this property it would have been
    necessary to re-encode the output and verify that it matches the
    input in order to guarantee the uniqueness of the encoding.


6.3 Encoding procedure

    let n = initial_n
    let delta = 0
    let bias = initial_bias
    let h = b = the number of basic code points in the input
    copy them to the output in order, followed by a delimiter if b > 0
    {if the input contains a non-basic code point < n then fail}
    while h < length(input) do begin
      let m = the minimum {non-basic} code point >= n in the input
      let delta = delta + (m - n) * (h + 1), fail on overflow
      let n = m
      for each code point c in the input (in order) do begin
        if c < n {or c is basic} then increment delta, fail on overflow
        if c == n then begin
          let q = delta
          for k = base to infinity in steps of base do begin
            let t = tmin if k <= bias {+ tmin}, or
                    tmax if k >= bias + tmax, or k - bias otherwise
            if q < t then break
            output the code point for digit t + ((q - t) mod (base - t))
            let q = (q - t) div (base - t)
          end
          output the code point for digit q
          let bias = adapt(delta, h + 1, test h equals b?)
          let delta = 0
          increment h
        end
      end
      increment delta and n
    end

    The full statement enclosed in braces (checking whether the input
    contains a non-basic code point less than n) can be omitted if all
    code points less than initial_n are basic code points (which is true
    for Punycode if code points are unsigned).

    The brace-enclosed conditions "non-basic" and "or m is basic" can be
    omitted if initial_n exceeds all basic code points (which is true
    for Punycode), because the code point being tested is never less
    than initial_n.

    In the assignment of t, where t is clamped to the range tmin through
    tmax, "+ tmin" can always be omitted.  This makes the clamping
    calculation incorrect when bias < k < bias + tmin, but that cannot
    happen because of the way bias is computed and because of the
    constraints on the parameters.

    The checks for overflow are necessary to avoid producing invalid
    output when the input contains very large values or is very long.

    The increment of delta at the bottom of the outer loop cannot
    overflow because delta < length(input) before the increment, and
    length(input) is already assumed to be representable.  The increment
    of n could overflow, but only if h == length(input), in which case
    the procedure is finished anyway.


6.4 Overflow handling

    For IDNA, 26-bit unsigned integers are sufficient to handle all
    valid IDNA labels without overflow, because any string that
    needed a 27-bit delta would have to exceed either the code point
    limit (0..10FFFF) or the label length limit (63 characters).
    However, overflow handling is necessary because the inputs are not
    necessarily valid IDNA labels.

    If the programming language does not provide overflow detection,
    the following technique can be used.  Suppose A, B, and C are
    representable nonnegative integers and C is nonzero.  Then A + B
    overflows if and only if B > maxint - A, and A + (B * C) overflows
    if and only if B > (maxint - A) div C, where maxint is the greatest
    integer for which maxint + 1 cannot be represented.  Refer to
    appendix D "Punycode sample implementation" for demonstrations of
    this technique in the C language.

    The decoding and encoding algorithms shown in sections 6.2 and
    6.3 handle overflow by detecting it whenever it happens.  Another
    approach is to enforce limits on the inputs that prevent overflow
    from happening.  For example, if the encoder were to verify that
    no input code points exceed M and that the input length does not
    exceed L, then no delta could ever exceed (M - initial_n) * (L + 1),
    and hence no overflow could occur if integer variables were capable
    of representing values that large.  This prevention approach would
    impose more restrictions on the input than the detection approach
    does, but might be considered simpler in some programming languages.

    In theory, the decoder could use an analogous approach, limiting the
    number of digits in a variable-length integer (that is, limiting the
    number of iterations in the innermost loop).  However, the number
    of digits that suffice to represent a given delta can sometimes
    represent much larger deltas (because of the adaptation), and hence
    this approach would probably need integers wider than 32 bits.

    Yet another approach for the decoder is to allow overflow to occur,
    but to check the final output string by re-encoding it and comparing
    to the decoder input.  If and only if they do not match (using a
    case-insensitive ASCII comparison) overflow has occurred.  This
    delayed-detection approach would not impose any more restrictions on
    the input than the immediate-detection approach does, and might be
    considered simpler in some programming languages.

    In fact, if the decoder is used only inside the IDNA ToUnicode
    operation [IDNA], then it need not check for overflow at all,
    because ToUnicode performs a higher level re-encoding and
    comparison, and a mismatch has the same consequence as if the
    Punycode decoder had failed.

7. Punycode examples

7.1 Sample strings

    In the Punycode encodings below, the ACE prefix is not shown.
    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
        Punycode: egbpdaj6bu4bxfgehfvwxn

    (B) Chinese (simplified):
        u+4ED6 u+4EEC u+4E3A u+4EC0 u+4E48 u+4E0D u+8BF4 u+4E2D u+6587
        Punycode: ihqwcrb4cv8a8dqg056pqjye

    (C) Chinese (traditional):
        u+4ED6 u+5011 u+7232 u+4EC0 u+9EBD u+4E0D u+8AAA u+4E2D u+6587
        Punycode: ihqwctvzc91f659drss3x8bo0yb

    (D) 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
        Punycode: Proprostnemluvesky-uyb24dma41a

    (E) 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
        Punycode: 4dbcagdahymbxekheh6e0a7fei0b

    (F) 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
        Punycode: i1baa7eci9glrd9b2ae1bj0hfcgg6iyaf8o0a1dig0cd

    (G) 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
        Punycode: n8jok5ay5dzabd5bym9f0cm5685rrjetr6pdxa

    (H) 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
        Punycode: 989aomsvi5e83db1d2a355cv1e0vak1dwrv93d5xbh15a0dt30a5j\
                  psd879ccm6fea98c

    (I) 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
        Punycode: b1abfaaepdrnnbgefbaDotcwatmq2g4l


    (J) 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
        Punycode: PorqunopuedensimplementehablarenEspaol-fmd56a

    (K) Vietnamese:
        T<adotbelow>isaoh<odotbelow>kh<ocirc>ngth<ecirchookabove>ch\
        <ihookabove>n<oacute>iti<ecircacute>ngVi<ecircdotbelow>t
        U+0054 u+1EA1 u+0069 u+0073 u+0061 u+006F u+0068 u+1ECD u+006B
        u+0068 u+00F4 u+006E u+0067 u+0074 u+0068 u+1EC3 u+0063 u+0068
        u+1EC9 u+006E u+00F3 u+0069 u+0074 u+0069 u+1EBF u+006E u+0067
        U+0056 u+0069 u+1EC7 u+0074
        Punycode: TisaohkhngthchnitingVit-kjcr8268qyxafd2f1b9g

    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
        Punycode: 3B-ww4c5e180e575a65lsy2b

    (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
        Punycode: -with-SUPER-MONKEYS-pc58ag80a8qai00g7n9n

    (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
        Punycode: Hello-Another-Way--fc4qua05auwb3674vfr0b

    (O) <hitotsu><yane><no><shita>2
        u+3072 u+3068 u+3064 u+5C4B u+6839 u+306E u+4E0B u+0032
        Punycode: 2-u9tlzr9756bt3uc0v

    (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
        Punycode: MajiKoi5-783gue6qz075azm5e

    (Q) <pafii>de<runba>
        u+30D1 u+30D5 u+30A3 u+30FC u+0064 u+0065 u+30EB u+30F3 u+30D0
        Punycode: de-jg4avhby1noc0d

    (R) <sono><supiido><de>
        u+305D u+306E u+30B9 u+30D4 u+30FC u+30C9 u+3067
        Punycode: d9juau41awczczp


    The last example is an ASCII string that breaks the existing rules
    for host name labels.  (It is not a realistic example for IDNA,
    because IDNA never encodes pure ASCII labels.)

    (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
        Punycode: -> $1.00 <--

7.2 Decoding traces

    In the following traces, the evolving state of the decoder is
    shown as a sequence of hexadecimal values, representing the code
    points in the extended string.  An asterisk appears just after the
    most recently inserted code point, indicating both n (the value
    preceeding the asterisk) and i (the position of the value just after
    the asterisk).  Other numerical values are decimal.

    Decoding trace of example B from section 7.1:

    n is 128, i is 0, bias is 72
    input is "ihqwcrb4cv8a8dqg056pqjye"
    there is no delimiter, so extended string starts empty
    delta "ihq" decodes to 19853
    bias becomes 21
    4E0D *
    delta "wc" decodes to 64
    bias becomes 20
    4E0D 4E2D *
    delta "rb" decodes to 37
    bias becomes 13
    4E3A * 4E0D 4E2D
    delta "4c" decodes to 56
    bias becomes 17
    4E3A 4E48 * 4E0D 4E2D
    delta "v8a" decodes to 599
    bias becomes 32
    4E3A 4EC0 * 4E48 4E0D 4E2D
    delta "8d" decodes to 130
    bias becomes 23
    4ED6 * 4E3A 4EC0 4E48 4E0D 4E2D
    delta "qg" decodes to 154
    bias becomes 25
    4ED6 4EEC * 4E3A 4EC0 4E48 4E0D 4E2D
    delta "056p" decodes to 46301
    bias becomes 84
    4ED6 4EEC 4E3A 4EC0 4E48 4E0D 4E2D 6587 *
    delta "qjye" decodes to 88531
    bias becomes 90
    4ED6 4EEC 4E3A 4EC0 4E48 4E0D 8BF4 * 4E2D 6587


    Decoding trace of example L from section 7.1:

    n is 128, i is 0, bias is 72
    input is "3B-ww4c5e180e575a65lsy2b"
    literal portion is "3B-", so extended string starts as:
    0033 0042
    delta "ww4c" decodes to 62042
    bias becomes 27
    0033 0042 5148 *
    delta "5e" decodes to 139
    bias becomes 24
    0033 0042 516B * 5148
    delta "180e" decodes to 16683
    bias becomes 67
    0033 5E74 * 0042 516B 5148
    delta "575a" decodes to 34821
    bias becomes 82
    0033 5E74 0042 516B 5148 751F *
    delta "65l" decodes to 14592
    bias becomes 67
    0033 5E74 0042 7D44 * 516B 5148 751F
    delta "sy2b" decodes to 42088
    bias becomes 84
    0033 5E74 0042 7D44 91D1 * 516B 5148 751F

7.3 Encoding traces

    In the following traces, code point values are hexadecimal, while
    other numerical values are decimal.


    Encoding trace of example B from section 7.1:

    bias is 72
    input is:
    4ED6 4EEC 4E3A 4EC0 4E48 4E0D 8BF4 4E2D 6587
    there are no basic code points, so no literal portion
    next code point to insert is 4E0D
    needed delta is 19853, encodes as "ihq"
    bias becomes 21
    next code point to insert is 4E2D
    needed delta is 64, encodes as "wc"
    bias becomes 20
    next code point to insert is 4E3A
    needed delta is 37, encodes as "rb"
    bias becomes 13
    next code point to insert is 4E48
    needed delta is 56, encodes as "4c"
    bias becomes 17
    next code point to insert is 4EC0
    needed delta is 599, encodes as "v8a"
    bias becomes 32
    next code point to insert is 4ED6
    needed delta is 130, encodes as "8d"
    bias becomes 23
    next code point to insert is 4EEC
    needed delta is 154, encodes as "qg"
    bias becomes 25
    next code point to insert is 6587
    needed delta is 46301, encodes as "056p"
    bias becomes 84
    next code point to insert is 8BF4
    needed delta is 88531, encodes as "qjye"
    bias becomes 90
    output is "ihqwcrb4cv8a8dqg056pqjye"


    Encoding trace of example L from section 7.1:

    bias is 72
    input is:
    0033 5E74 0042 7D44 91D1 516B 5148 751F
    basic code points (0033, 0042) are copied to literal portion: "3B-"
    next code point to insert is 5148
    needed delta is 62042, encodes as "ww4c"
    bias becomes 27
    next code point to insert is 516B
    needed delta is 139, encodes as "5e"
    bias becomes 24
    next code point to insert is 5E74
    needed delta is 16683, encodes as "180e"
    bias becomes 67
    next code point to insert is 751F
    needed delta is 34821, encodes as "575a"
    bias becomes 82
    next code point to insert is 7D44
    needed delta is 14592, encodes as "65l"
    bias becomes 67
    next code point to insert is 91D1
    needed delta is 42088, encodes as "sy2b"
    bias becomes 84
    output is "3B-ww4c5e180e575a65lsy2b"

8. 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 ASCII domain names, each controlled by
    a different authority, some of which could be spoofs that hijack
    service requests intended for another.  Therefore Punycode 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 [NAMEPREP].

9. References (non-normative)

    [ASCII] Vint Cerf, "ASCII format for Network Interchange",
    1969-Oct-16, RFC 20.

    [IDNA] Patrik Faltstrom, Paul Hoffman, Adam M. Costello,
    "Internationalizing Domain Names In Applications (IDNA)",
    draft-ietf-idn-idna.

    [NAMEPREP] Paul Hoffman, Marc Blanchet, "Nameprep: A
    Stringprep Profile for Internationalized Domain Names",
    draft-ietf-idn-nameprep.

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


    [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.

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

A. Author contact information

    Adam M. Costello
    University of California, Berkeley
    http://www.nicemice.net/amc/

B. Mixed-case annotation

    In order to use Punycode to represent case-insensitive strings,
    higher layers need to case-fold the strings prior to Punycode
    encoding.  The encoded string can use mixed case as an annotation
    telling how to convert the folded string into a mixed-case string
    for display purposes.  Note, however, that mixed-case annotation
    is not used by the ToASCII and ToUnicode operations specified in
    [IDNA], and therefore implementors of IDNA can disregard this
    appendix.

    Basic code points can use mixed case directly, because the decoder
    copies them verbatim, leaving lowercase code points lowercase, and
    leaving uppercase code points uppercase.  Each non-basic code point
    is represented by a delta, which is represented by a sequence of
    basic code points, the last of which provides the annotation.  If it
    is uppercase, it is a suggestion to map the non-basic code point to
    uppercase (if possible); if it is lowercase, it is a suggestion to
    map the non-basic code point to lowercase (if possible).

    These annotations do not alter the code points returned by decoders;
    the annotations are returned separately, for the caller to use or
    ignore.  Encoders can accept annotations in addition to code points,
    but the annotations do not alter the output, except to influence the
    uppercase/lowercase form of ASCII letters.

    Punycode encoders and decoders need not support these annotations,
    and higher layers need not use them.

C. Disclaimer and license

    Regarding this entire document or any portion of it (including
    the pseudocode and C code), the author makes no guarantees and
    is not responsible for any damage resulting from its use.  The
    author grants irrevocable permission to anyone to use, modify,
    and distribute it in any way that does not diminish the rights
    of anyone else to use, modify, and distribute it, provided that
    redistributed derivative works do not contain misleading author or
    version information.  Derivative works need not be licensed under
    similar terms.

D. Punycode sample implementation


/*
punycode.c from draft-ietf-idn-punycode-02
http://www.nicemice.net/idn/
Adam M. Costello
http://www.nicemice.net/amc/

This is ANSI C code (C89) implementing
Punycode (draft-ietf-idn-punycode-02).

*/

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

#include <limits.h>

enum punycode_status {
  punycode_success,
  punycode_bad_input,   /* Input is invalid.                       */
  punycode_big_output,  /* Output would exceed the space provided. */
  punycode_overflow     /* Input needs wider integers to process.  */
};

#if UINT_MAX >= (1 << 26) - 1
typedef unsigned int punycode_uint;
#else
typedef unsigned long punycode_uint;
#endif

enum punycode_status punycode_encode(
  punycode_uint input_length,
  const punycode_uint input[],
  const unsigned char case_flags[],
  punycode_uint *output_length,
  char output[] );


    /* punycode_encode() converts Unicode to Punycode.  The input     */
    /* is represented as an array of Unicode code points (not code    */
    /* units; surrogate pairs are not allowed), and the output        */
    /* will be represented as an array of ASCII code points.  The     */
    /* output string is *not* null-terminated; it will contain        */
    /* zeros if and only if the input contains zeros.  (Of course     */
    /* the caller can leave room for a terminator and add one if      */
    /* needed.)  The input_length is the number of code points in     */
    /* the input.  The output_length is an in/out argument: the       */
    /* caller passes in the maximum number of code points that it     */
    /* can receive, and on successful return it will contain the      */
    /* number of code points actually output.  The case_flags array   */
    /* holds input_length boolean values, where nonzero suggests that */
    /* the corresponding Unicode character be forced to uppercase     */
    /* after being decoded (if possible), and zero suggests that      */
    /* it be forced to lowercase (if possible).  ASCII code points    */
    /* are encoded literally, except that ASCII letters are forced    */
    /* to uppercase or lowercase according to the corresponding       */
    /* uppercase flags.  If case_flags is a null pointer then ASCII   */
    /* letters are left as they are, and other code points are        */
    /* treated as if their uppercase flags were zero.  The return     */
    /* value can be any of the punycode_status values defined above   */
    /* except punycode_bad_input; if not punycode_success, then       */
    /* output_size and output might contain garbage.                  */

enum punycode_status punycode_decode(
  punycode_uint input_length,
  const char input[],
  punycode_uint *output_length,
  punycode_uint output[],
  unsigned char case_flags[] );

    /* punycode_decode() converts Punycode to Unicode.  The input is  */
    /* represented as an array of ASCII code points, and the output   */
    /* will be represented as an array of Unicode code points.  The   */
    /* input_length is the number of code points in the input.  The   */
    /* output_length is an in/out argument: the caller passes in      */
    /* the maximum number of code points that it can receive, and     */
    /* on successful return it will contain the actual number of      */
    /* code points output.  The case_flags array needs room for at    */
    /* least output_length values, or it can be a null pointer if the */
    /* case information is not needed.  A nonzero flag suggests that  */
    /* the corresponding Unicode character be forced to uppercase     */
    /* by the caller (if possible), while zero suggests that it be    */
    /* forced to lowercase (if possible).  ASCII code points 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 can be any of the punycode_status values      */
    /* defined above; if not punycode_success, then output_length,    */
    /* output, and case_flags might contain garbage.  On success, the */
    /* decoder will never need to write an output_length greater than */
    /* input_length, because of how the encoding is defined.          */


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

#include <string.h>

/*** Bootstring parameters for Punycode ***/

enum { base = 36, tmin = 1, tmax = 26, skew = 38, damp = 700,
       initial_bias = 72, initial_n = 0x80, delimiter = 0x2D };

/* basic(cp) tests whether cp is a basic code point: */
#define basic(cp) ((punycode_uint)(cp) < 0x80)

/* delim(cp) tests whether cp is a delimiter: */
#define delim(cp) ((cp) == delimiter)

/* decode_digit(cp) returns the numeric value of a basic code */
/* point (for use in representing integers) in the range 0 to */
/* base-1, or base if cp is does not represent a value.       */

static punycode_uint decode_digit(punycode_uint cp)
{
  return  cp - 48 < 10 ? cp - 22 :  cp - 65 < 26 ? cp - 65 :
          cp - 97 < 26 ? cp - 97 :  base;
}

/* encode_digit(d,flag) returns the basic code point whose value      */
/* (when used for representing integers) is d, which needs to be in   */
/* the range 0 to base-1.  The lowercase form is used unless flag is  */
/* nonzero, in which case the uppercase form is used.  The behavior   */
/* is undefined if flag is nonzero and digit d has no uppercase form. */

static char encode_digit(punycode_uint d, int flag)
{
  return d + 22 + 75 * (d < 26) - ((flag != 0) << 5);
  /*  0..25 map to ASCII a..z or A..Z */
  /* 26..35 map to ASCII 0..9         */
}

/* flagged(bcp) tests whether a basic code point is flagged */
/* (uppercase).  The behavior is undefined if bcp is not a  */
/* basic code point.                                        */

#define flagged(bcp) ((punycode_uint)(bcp) - 65 < 26)

/* encode_basic(bcp,flag) forces a basic code point to lowercase */
/* if flag is zero, uppercase if flag is nonzero, and returns    */
/* the resulting code point.  The code point is unchanged if it  */
/* is caseless.  The behavior is undefined if bcp is not a basic */
/* code point.                                                   */

static char encode_basic(punycode_uint bcp, int flag)
{
  bcp -= (bcp - 97 < 26) << 5;
  return bcp + ((!flag && (bcp - 65 < 26)) << 5);
}


/*** Platform-specific constants ***/

/* maxint is the maximum value of a punycode_uint variable: */
static const punycode_uint maxint = -1;
/* Because maxint is unsigned, -1 becomes the maximum value. */

/*** Bias adaptation function ***/

static punycode_uint adapt(
  punycode_uint delta, punycode_uint numpoints, int firsttime )
{
  punycode_uint k;

  delta = firsttime ? delta / damp : delta >> 1;
  /* delta >> 1 is a faster way of doing delta / 2 */
  delta += delta / numpoints;

  for (k = 0;  delta > ((base - tmin) * tmax) / 2;  k += base) {
    delta /= base - tmin;
  }

  return k + (base - tmin + 1) * delta / (delta + skew);
}

/*** Main encode function ***/

enum punycode_status punycode_encode(
  punycode_uint input_length,
  const punycode_uint input[],
  const unsigned char case_flags[],
  punycode_uint *output_length,
  char output[] )
{
  punycode_uint n, delta, h, b, out, max_out, bias, j, m, q, k, t;

  /* Initialize the state: */

  n = initial_n;
  delta = out = 0;
  max_out = *output_length;
  bias = initial_bias;

  /* Handle the basic code points: */

  for (j = 0;  j < input_length;  ++j) {
    if (basic(input[j])) {
      if (max_out - out < 2) return punycode_big_output;
      output[out++] =
        case_flags ?  encode_basic(input[j], case_flags[j]) : input[j];
    }
    /* else if (input[j] < n) return punycode_bad_input; */
    /* (not needed for Punycode with unsigned code points) */
  }


  h = b = out;

  /* h is the number of code points that have been handled, b is the  */
  /* number of basic code points, and out is the number of characters */
  /* that have been output.                                           */

  if (b > 0) output[out++] = delimiter;

  /* Main encoding loop: */

  while (h < input_length) {
    /* All non-basic code points < n have been     */
    /* handled already.  Find the next larger one: */

    for (m = maxint, j = 0;  j < input_length;  ++j) {
      /* if (basic(input[j])) continue; */
      /* (not needed for Punycode) */
      if (input[j] >= n && input[j] < m) m = input[j];
    }

    /* Increase delta enough to advance the decoder's    */
    /* <n,i> state to <m,0>, but guard against overflow: */

    if (m - n > (maxint - delta) / (h + 1)) return punycode_overflow;
    delta += (m - n) * (h + 1);
    n = m;

    for (j = 0;  j < input_length;  ++j) {
      /* Punycode does not need to check whether input[j] is basic: */
      if (input[j] < n /* || basic(input[j]) */ ) {
        if (++delta == 0) return punycode_overflow;
      }

      if (input[j] == n) {
        /* Represent delta as a generalized variable-length integer: */

        for (q = delta, k = base;  ;  k += base) {
          if (out >= max_out) return punycode_big_output;
          t = k <= bias /* + tmin */ ? tmin :     /* +tmin not needed */
              k >= bias + tmax ? tmax : k - bias;
          if (q < t) break;
          output[out++] = encode_digit(t + (q - t) % (base - t), 0);
          q = (q - t) / (base - t);
        }

        output[out++] = encode_digit(q, case_flags && case_flags[j]);
        bias = adapt(delta, h + 1, h == b);
        delta = 0;
        ++h;
      }
    }

    ++delta, ++n;
  }

  *output_length = out;
  return punycode_success;
}


/*** Main decode function ***/

enum punycode_status punycode_decode(
  punycode_uint input_length,
  const char input[],
  punycode_uint *output_length,
  punycode_uint output[],
  unsigned char case_flags[] )
{
  punycode_uint n, out, i, max_out, bias,
                 b, j, in, oldi, w, k, digit, t;

  /* Initialize the state: */

  n = initial_n;
  out = i = 0;
  max_out = *output_length;
  bias = initial_bias;

  /* Handle the basic code points:  Let b be the number of input code */
  /* points before the last delimiter, or 0 if there is none, then    */
  /* copy the first b code points to the output.                      */

  for (b = j = 0;  j < input_length;  ++j) if (delim(input[j])) b = j;
  if (b > max_out) return punycode_big_output;

  for (j = 0;  j < b;  ++j) {
    if (case_flags) case_flags[out] = flagged(input[j]);
    if (!basic(input[j])) return punycode_bad_input;
    output[out++] = input[j];
  }

  /* Main decoding loop:  Start just after the last delimiter if any  */
  /* basic code points were copied; start at the beginning otherwise. */

  for (in = b > 0 ? b + 1 : 0;  in < input_length;  ++out) {

    /* in is the index of the next character to be consumed, and */
    /* out is the number of code points in the output array.     */

    /* Decode a generalized variable-length integer into delta,  */
    /* which gets added to i.  The overflow checking is easier   */
    /* if we increase i as we go, then subtract off its starting */
    /* value at the end to obtain delta.                         */

    for (oldi = i, w = 1, k = base;  ;  k += base) {
      if (in >= input_length) return punycode_bad_input;
      digit = decode_digit(input[in++]);
      if (digit >= base) return punycode_bad_input;
      if (digit > (maxint - i) / w) return punycode_overflow;
      i += digit * w;
      t = k <= bias /* + tmin */ ? tmin :     /* +tmin not needed */
          k >= bias + tmax ? tmax : k - bias;
      if (digit < t) break;
      if (w > maxint / (base - t)) return punycode_overflow;
      w *= (base - t);
    }


    bias = adapt(i - oldi, out + 1, oldi == 0);

    /* i was supposed to wrap around from out+1 to 0,   */
    /* incrementing n each time, so we'll fix that now: */

    if (i / (out + 1) > maxint - n) return punycode_overflow;
    n += i / (out + 1);
    i %= (out + 1);

    /* Insert n at position i of the output: */

    /* not needed for Punycode: */
    /* if (decode_digit(n) <= base) return punycode_invalid_input; */
    if (out >= max_out) return punycode_big_output;

    if (case_flags) {
      memmove(case_flags + i + 1, case_flags + i, out - i);
      /* Case of last character determines uppercase flag: */
      case_flags[i] = flagged(input[in - 1]);
    }

    memmove(output + i + 1, output + i, (out - i) * sizeof *output);
    output[i++] = n;
  }

  *output_length = out;
  return punycode_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_length = 256
};


static void usage(char **argv)
{
  fprintf(stderr,
    "\n"
    "%s -e reads code points and writes a Punycode string.\n"
    "%s -d reads a Punycode string and writes code points.\n"
    "\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"
    "Although the specification allows Punycode strings to contain\n"
    "any characters from the ASCII repertoire, this test code\n"
    "supports only the printable characters, and needs the Punycode\n"
    "string to be followed by a newline.\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 overflow[] = "arithmetic overflow\n";
static const char io_error[] = "I/O error\n";

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

static const char print_ascii[] =
  "\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n"
  "\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n"
  " !\"#$%&'()*+,-./"
  "0123456789:;<=>?"
  "@ABCDEFGHIJKLMNO"
  "PQRSTUVWXYZ[\\]^_"
  "`abcdefghijklmno"
  "pqrstuvwxyz{|}~\n";

int main(int argc, char **argv)
{
  enum punycode_status status;
  int r;
  unsigned int input_length, output_length, j;
  unsigned char case_flags[unicode_max_length];

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


  if (argv[1][1] == 'e') {
    punycode_uint input[unicode_max_length];
    unsigned long codept;
    char output[ace_max_length+1], uplus[3];
    int c;

    /* 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 > (punycode_uint)-1) {
        fail(invalid_input);
      }

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

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

      input[input_length++] = codept;
    }

    /* Encode: */

    output_length = ace_max_length;
    status = punycode_encode(input_length, input, case_flags,
                             &output_length, output);
    if (status == punycode_bad_input) fail(invalid_input);
    if (status == punycode_big_output) fail(too_big);
    if (status == punycode_overflow) fail(overflow);
    assert(status == punycode_success);

    /* Convert to native charset and output: */

    for (j = 0;  j < output_length;  ++j) {
      c = output[j];
      assert(c >= 0 && c <= 127);
      if (print_ascii[c] == 0) fail(invalid_input);
      output[j] = print_ascii[c];
    }

    output[j] = 0;
    r = puts(output);
    if (r == EOF) fail(io_error);
    return EXIT_SUCCESS;
  }

  if (argv[1][1] == 'd') {
    char input[ace_max_length+2], *p, *pp;
    punycode_uint output[unicode_max_length];


    /* Read the Punycode input string and convert to ASCII: */

    fgets(input, ace_max_length+2, stdin);
    if (ferror(stdin)) fail(io_error);
    if (feof(stdin)) fail(invalid_input);
    input_length = strlen(input) - 1;
    if (input[input_length] != '\n') fail(too_big);
    input[input_length] = 0;

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

    /* Decode: */

    output_length = unicode_max_length;
    status = punycode_decode(input_length, input, &output_length,
                             output, case_flags);
    if (status == punycode_bad_input) fail(invalid_input);
    if (status == punycode_big_output) fail(too_big);
    if (status == punycode_overflow) fail(overflow);
    assert(status == punycode_success);

    /* Output the result: */

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

    return EXIT_SUCCESS;
  }

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

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