[Unicode]  Technical Reports
 

Unicode Standard Annex #15

Unicode Normalization Forms

Version Unicode 4.1.0
Authors Mark Davis (mark.davis@us.ibm.com), Martin Dürst (duerst@w3.org)
Date 2005-03-25
This Version http://www.unicode.org/reports/tr15/tr15-25.html
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Revision 25


Summary

This document describes specifications for four normalized forms of Unicode text. With these forms, equivalent text (canonical or compatibility) will have identical binary representations. When implementations keep strings in a normalized form, they can be assured that equivalent strings have a unique binary representation.

Note: For details on backwards compatibility, see Annex 12: Corrigenda.

Status

This document has been reviewed by Unicode members and other interested parties, and has been approved for publication by the Unicode Consortium. This is a stable document and may be used as reference material or cited as a normative reference by other specifications.

A Unicode Standard Annex (UAX) forms an integral part of the Unicode Standard, but is published as a separate document. The Unicode Standard may require conformance to normative content in a Unicode Standard Annex, if so specified in the Conformance chapter of that version of the Unicode Standard. The version number of a UAX document corresponds to the version number of the Unicode Standard at the last point that the UAX document was updated.

Please submit corrigenda and other comments with the online reporting form [Feedback]. Related information that is useful in understanding this document is found in References. For the latest version of the Unicode Standard see [Unicode]. For a list of current Unicode Technical Reports see [Reports]. For more information about versions of the Unicode Standard, see [Versions].

Contents


1 Introduction

The Unicode Standard defines two equivalences between characters: canonical equivalence and compatibility equivalence. Canonical equivalence is a basic equivalency between characters or sequences of characters. Figure 1: Canonical Equivalence illustrates this equivalence.

Figure 1: Canonical Equivalence

Canonical Equivalence
Combining Sequence    Ç C ¸
Hangul 가
Singleton Ω

For round-trip compatibility with existing standards, Unicode has encoded many entities that are really variants of existing nominal characters. The visual representations of these characters are typically a subset of the possible visual representations of the nominal character. These are given compatibility decompositions in the standard. Because the characters are visually distinguished, replacing a character by a compatibility equivalent may mean this visual distinction is lost. If the visual distinction is stylistic, then markup or styling could be used to represent the formatting information. However, some characters with compatibility decompostions are used in mathematical notation to represent distinction of a semantic nature; replacing the use of distinct character codes by formatting may cause problems. See Figure 2: Compatibility Equivalence for examples of compatibility equivalents.

Figure 2: Compatibility Equivalence

Compatibility Equivalence
Font variants ℌ ℍ
Breaking differences    -
Cursive forms U+FEE5  U+FEE6  U+FEE7  U+FEE8
Circled
Width, size, rotated カ カ ︷ {
Super/subscripts ⁹ ₉
Squared characters
Fractions ¼
Others dž

Both canonical and compatibility equivalences are explained in more detail in The Unicode Standard, Chapters 2 and 3. In addition, the Unicode Standard describes several forms of normalization in Section 5.6, Normalization. These normalization forms are designed to produce a unique normalized form for any given string. Two of these forms are precisely specified in Section 3.7, Decomposition. In particular, the standard defines a canonical decomposition format, which can be used as a normalization for interchanging text. This format allows for binary comparison while maintaining canonical equivalence with the original unnormalized text.

The standard also defines a compatibility decomposition format, which allows for binary comparison while maintaining compatibility equivalence with the original unnormalized text. The latter can also be useful in many circumstances, because it folds the differences between characters which are inappropriate in those circumstances. For example, the half-width and full-width katakana characters will have the same compatibility decomposition and are thus compatibility equivalents; however, they are not canonical equivalents.

Both of these formats are normalizations to decomposed characters. While Section 3.7, Decomposition also discusses normalization to composite characters (also known as decomposable or precomposed characters), it does not precisely specify a format. Because of the nature of the precomposed forms in the Unicode Standard, there is more than one possible specification for a normalized form with composite characters. This document provides a unique specification for normalization, and a label for each normalized form.

The four normalization forms are labeled as shown in Table 1: Normalization Forms.

Table 1: Normalization Forms

Title

Description

Specification

Normalization Form D (NFD) Canonical Decomposition Sections 3.7, 3.11, and 3.12 of The Unicode Standard, also summarized under Annex 4: Decomposition
Normalization Form C (NFC) Canonical Decomposition,
followed by Canonical Composition
see Section 5, Specification
Normalization Form KD (NFKD) Compatibility Decomposition Sections 3.7, 3.11, and 3.12 of The Unicode Standard, also summarized under Annex 4: Decomposition
Normalization Form KC (NFKC) Compatibility Decomposition,
followed by Canonical Composition
see Section 5, Specification

As with decomposition, there are two forms of normalization that convert to composite characters, Normalization Form C and Normalization Form KC. The difference between these depends on whether the resulting text is to be a canonical equivalent to the original unnormalized text, or is to be a compatibility equivalent to the original unnormalized text. (In NFKC and NFKD, a K is used to stand for compatibility to avoid confusion with the C standing for composition.) Both types of normalization can be useful in different circumstances.

Figure 3: Applying Different Normalization Forms to Denormalized Text illustrates the effect of applying different normalization forms to denormalized text. In the diagram, glyphs are colored according to the characters they represent (this will not be visible in black and white printouts).

Figure 3: Applying Different Normalization Forms to Denormalized Text

Figure for different normalizations

With all normalization forms, singleton characters (those with singleton canonical mappings) are replaced. With NFD and NFC, compatibility composites (characters with compatibility decompositions) are retained; with NFKD and NFKC they are replaced. Notice that this sometimes loses significant information, unless supplemented by markup or styling.

With NFD and NFKD, composite characters are mapped to their canonical decompositions. With NFC and NFKC, combining character sequences are mapped to composites, if possible. Notice that there is no composite for e-ring, so it is left decomposed in NFC and NFKC.

All of the definitions in this document depend on the rules for equivalence and decomposition found in Chapter 3 of The Unicode Standard and the decomposition mappings in the Unicode Character Database.

Note: Text exclusively containing only ASCII characters (U+0000 to U+007F) is left unaffected by all of the normalization forms. This is particularly important for programming languages (see Annex 7: Programming Language Identifiers).

Normalization Form C uses canonical composite characters where possible, and maintains the distinction between characters that are compatibility equivalents. Typical strings of composite accented Unicode characters are already in Normalization Form C. Implementations of Unicode which restrict themselves to a repertoire containing no combining marks (such as those that declare themselves to be implementations at Level 1 as defined in ISO/IEC 10646-1) are already typically using Normalization Form C. (Implementations of later versions of 10646 need to be aware of the versioning issues — see Section 3, Versioning and Stability.)

The W3C Character Model for the World Wide Web [CharMod] uses Normalization Form C for XML and related standards (this document is not yet final, but this requirement is not expected to change). See the W3C Requirements for String Identity, Matching, and String Indexing [CharReq] for more background.

Normalization Form KC additionally folds the differences between compatibility-equivalent characters which are inappropriately distinguished in many circumstances. For example, the half-width and full-width katakana characters will normalize to the same strings, as will Roman numerals and their letter equivalents. More complete examples are provided in Annex 1: Examples and Charts.

Normalization forms KC and KD must not be blindly applied to arbitrary text. Because they erase many formatting distinctions, they will prevent round-trip conversion to and from many legacy character sets, and unless supplanted by formatting markup, may remove distinctions that are important to the semantics of the text. It is best to think of these normalization forms as being like uppercase or lowercase mappings: useful in certain contexts for identifying core meanings, but also performing modifications to the text that may not always be appropriate. They can be applied more freely to domains with restricted character sets, such as in Annex 7: Programming Language Identifiers.

To summarize the treatment of compatibility composites that were in the source text:

Note: Normalization Form KC does not attempt to map character sequences to compatibility composites. For example, a compatibility composition of "office" does not produce "o\uFB03ce", even though "\uFB03" is a character that is the compatibility equivalent of the sequence of three characters 'ffi'.

For a list of all characters that may change in any of the normalization forms (aside from reordering), see Normalization Charts [Charts].

1.1 Concatenation

In using normalization functions, it is important to realize that none of the normalization forms are closed under string concatenation. That is, even if two strings X and Y are normalized, their string concatenation X+Y is not guaranteed to be normalized. This even happens in NFD, because accents are canonically ordered, and may rearrange around the point where the strings are joined. Consider the examples shown in Table 2: String Concatenation.

Table 2: String Concatenation

Form String1 String2 Concatenation Correct Normalization
NFC "a" "^" "a"+"^" "â"
NFD "a"+"^" "." (dot under) "a"+"^" + "." "a" + "." +"^"

However, it is possible to produce an optimized function that concatenates two normalized strings, and does guarantee that the result is normalized. Internally, it only needs to normalize characters around the boundary of where the original strings were joined, within stable code points. For more information, see Annex 8.1, Stable Code Points.

However, all of the normalization forms are closed under substringing. For example, if one takes a substring of a normalized string X, from offsets 5 to 10, one is guaranteed that the resulting string is still normalized.

2 Notation

All of the definitions in this document depend on the rules for equivalence and decomposition found in Chapter 3 of The Unicode Standard and the Character Decomposition Mapping and Canonical Combining Class property in [UCD]. Decomposition must be done in accordance with these rules. In particular, the decomposition mappings found in the Unicode Character Database must be applied recursively, and then the string put into canonical order based on the characters' combining classes.

The following notation is used for brevity.

Example Notation Description
combiningClass(X) The combining class of a character X
"...\uXXXX..." the Unicode character U+XXXX embedded within a string
"...\UXXXXXXXX..." the Unicode character U+XXXXXXXX embedded within a string
B-C A single character which is equivalent to the sequence of characters B + C
ki, am, and kf Conjoining jamo of various types (initial, medial, final) represented by subscripts
"c¸" c followed by a nonspacing cedilla: spacing accents (without a dotted circle) may be used to represent nonspacing accents
NFX(S) Any normalization form: NFD(S), NFKD(S), NFC(S), NFKC(S) are the possibilities.
toNFX(s) A function that produces the the normalized form of a string s according to the definition of Normalization Form X
isNFC(s) A binary property of a string s, whereby isNFX(s) is true if and only if toNFX(s) is identical to s. See also Annex 8: Detecting Normalization Forms.
X ≈ Y X is canonically equivalent to Y
X[a, b] The substring of X that includes all code units after offset a and before offset b. For example, if X is "abc", then X[1,2] is "b".

In addition,

  1. A sequence of characters may be represented by using plus signs between the character names, or by using string notation.
  2. An offset into a Unicode string is a number from 0 to n, where n is the length of the string, and indicates a position that is logically between Unicode code units (or at the very front or end in the case of 0 or n respectively).
  3. Unicode names may be shortened, as shown in Table 3: Character Abbreviation.

Table 3: Character Abbreviation

Abbreviation Full Unicode Name
E-grave LATIN CAPITAL LETTER E WITH GRAVE
ka  KATAKANA LETTER KA
hw_ka HALFWIDTH KATAKANA LETTER KA
ten COMBINING KATAKANA-HIRAGANA VOICED SOUND MARK
hw_ten HALFWIDTH KATAKANA VOICED SOUND MARK


3 Versioning and Stability

It is crucial that normalization forms remain stable over time. That is, if a string that does not have any unassigned characters is normalized under one version of Unicode, it must remain normalized under all future versions of Unicode. This is the backwards compatibility requirement. To meet this requirement, a  fixed version for the composition process is specified, called the composition version. The composition version is defined to be Version 3.1.0 of  the Unicode Character Database. For more information, see:

To see what difference the composition version makes, suppose that a future version of Unicode were to add the composite Q-caron. For an implementation that uses that future version of Unicode, strings in Normalization Forms C or KC would continue to contain the sequence Q + caron, and not the new character Q-caron, because a canonical composition for Q-caron was not defined in the composition version. See Section 6, Composition Exclusion Table for more information.

It would be possible to add more compositions in a future version of Unicode, as long as the backward compatibility requirement is met. That requires that for any new composition XY => Z, at most one of X or Y was defined in a previous version of Unicode. That is, Z must be a new character, and either X or Y must be a new character. However, the Unicode Consortium strongly discourages new compositions, even in such restricted cases.

In addition to fixing the composition version, future versions of Unicode must be restricted in terms of the kinds of changes that can be made to character properties. Because of this, the Unicode Consortium has a clear policy to guarantee the stability of normalization forms: for more information, see Annex 12: Corrigenda.

4 Conformance

C1. A process that produces Unicode text that purports to be in a Normalization Form shall do so in accordance with the specifications in this document.

C2. A process that tests Unicode text to determine whether it is in a Normalization Form shall do so in accordance with the specifications in this document.

C3. A process that purports to transform text into a Normalization Form, must be able to pass the conformance test described in Annex 9: Conformance Testing.

Note: The specifications for Normalization Forms are written in terms of a process for producing a decomposition or composition from an arbitrary Unicode string. This is a logical description — particular implementations can have more efficient mechanisms as long as they produce the same result. Similarly, testing for a particular Normalization Form does not require applying the process of normalization, so long as the result of the test is equivalent to applying normalization and then testing for binary identity.

5 Specification

This section specifies the format for Normalization Forms C and KC. It uses the following four definitions D1, D2, D3, D4, and two rules R1 and R2.

All combining character sequences start with a character of combining class zero. For simplicity, the following term is defined for such characters:

D1. A character S is a starter if it has a combining class of zero in the Unicode Character Database.

Because of the definition of canonical equivalence, the order of combining characters with the same combining class makes a difference. For example, a-macron-breve is not the same as a-breve-macron. Characters cannot be composed if that would change the canonical order of the combining characters.

D2. In any character sequence beginning with a starter S, a character C is blocked from S if and only if there is some character B between S and C, and either B is a starter or it has the same or higher combining class as C.

When B blocks C, changing the order of B and C would result in a character sequence that is not canonically equivalent to the original. See Section 3.11, Canonical Ordering Behavior in the Unicode Standard, 4.0.

If a combining character sequence is in canonical order, then testing whether a character is blocked only requires looking at the immediately preceding character.

The process of forming a composition in Normalization Form C or KC involves:

Figure 4: Composition Process shows a sample of how this works. The dark green cubes represent starters, and the light gray cubes represent non-starters. In the first step, the string is fully decomposed, and reordered. In the second step, each character is checked against the last non-starter and starter, and combined if all the conditions are met. Examples are provided in Annex 1: Examples and Charts, and a code sample is provided in Annex 5: Code Sample.

Figure 4: Composition Process

Basic composition process

A precise notion is required for when an unblocked character can be composed with a starter. This uses the following two definitions.

D3. A primary composite is a character that has a canonical decomposition mapping in the Unicode Character Database (or has a canonical Hangul decomposition) but is not in the Section 6, Composition Exclusion Table.

Note: Hangul syllable decomposition is considered a canonical decomposition. See [Unicode]. See Annex 10: Hangul.

D4. A character X can be primary combined with a character Y if and only if there is a primary composite Z which is canonically equivalent to the sequence <X, Y>.

Based upon these definitions, the following rules specify the Normalization Forms C and KC.

R1. Normalization Form C

The Normalization Form C for a string S is obtained by applying the following process, or any other process that leads to the same result:

  1. Generate the canonical decomposition for the source string S according to the decomposition mappings in the latest supported version of the Unicode Character Database.
  2. Iterate through each character C in that decomposition, from first to last. If C is not blocked from the last starter L, and it can be primary combined with L, then replace L by the composite L-C, and remove C.

The result of this process is a new string S' which is in Normalization Form C.

R2. Normalization Form KC

The Normalization Form KC for a string S is obtained by applying the following process, or any other process that leads to the same result:

  1. Generate the compatibility decomposition for the source string S according to the decomposition mappings in the latest supported version of the Unicode Character Database.
  2. Iterate through each character C in that decomposition, from first to last. If C is not blocked from the last starter L, and it can be primary combined with L, then replace L by the composite L-C, and remove C.

The result of this process is a new string S' which is in Normalization Form KC.

6 Composition Exclusion Table

There are four classes of characters that are excluded from composition:

  1. Script-specifics: precomposed characters that are generally not the preferred form for particular scripts.
    • These cannot be computed from information in the Unicode Character Database.
  2. Post Composition Version: precomposed characters that are added after Unicode 3.0 [U3.0]. This set will be updated with each subsequent version of Unicode. For more information, see Section 3, Versioning and Stability.
    • These cannot be computed from information in the Unicode Character Database.
  3. Singletons: characters having decompositions that consist of single characters (as described below).
    • These are computed from information in the Unicode Character Database.
  4. Non-starter decompositions: precomposed characters whose decompositions start with a non-starter.
    • These are computed from information in the Unicode Character Database.

Two characters may have the same canonical decomposition in the Unicode Character Database. Table 4: Same Canonical Decomposition is an example of this.

Table 4: Same Canonical Decomposition

Source Same Decomposition
212B 'Å' ANGSTROM SIGN 0041 'A' LATIN CAPITAL LETTER A + 030A '°' COMBINING RING ABOVE
00C5 'Å' LATIN CAPITAL LETTER A WITH RING ABOVE

The Unicode Character Database will first decompose one of the characters to the other, and then decompose from there. That is, one of the characters (in this case ANGSTROM SIGN) will have a singleton decomposition. Characters with singleton decompositions are included in Unicode essentially for compatibility with certain pre-existing standards. These singleton decompositions are excluded from primary composition.

A machine-readable form data file is found in the Composition Exclusion Table [Exclusions].

All four classes of characters are included in this file, although the singletons and non-starter decompositions are commented out.

A derived property containing the complete list of exclusions, Comp_Ex, is described in the UCD documentation [UCDDoc]. Implementations can avoid computing the singleton and non-starter decompositions from the Unicode Character Database by using the Comp_Ex property instead.


Annex 1: Examples and Charts

This annex provides some detailed examples of the results when each of the normalization forms is applied. The Normalization Charts [Charts] also provide charts of all the characters in Unicode that differ from at least one of their normalization forms (NFC, NFD, NFKC, NFKD).

A1.1 Common Examples

The examples in Table 5: Identical Cases illustrates cases where the NFD and NFKD are identical, and NFC and NFKC are identical.

Table 5: Identical Cases

Original NFD, NFKD NFC, NFKC

Notes

a D-dot_above D + dot_above D-dot_above Both decomposed and precomposed canonical sequences produce the same result.
b D + dot_above D + dot_above D-dot_above
c D-dot_below + dot_above D + dot_below + dot_above D-dot_below + dot_above The dot_above cannot be combined with the D because the D has already combined with the intervening dot_below.

 

d D-dot_above + dot_below D + dot_below + dot_above D-dot_below + dot_above
e D + dot_above + dot_below D + dot_below + dot_above D-dot_below + dot_above
f D + dot_above + horn + dot_below D + horn + dot_below + dot_above D-dot_below + horn + dot_above There may be intervening combining marks, so long as the result of the combination is canonically equivalent.
g E-macron-grave E + macron + grave E-macron-grave Multiple combining characters are combined with the base character.
h E-macron + grave E + macron + grave E-macron-grave
i E-grave + macron E + grave + macron E-grave + macron Characters will not be combined if they would not be canonical equivalents because of their ordering.
j angstrom_sign A + ring A-ring Because Å (A-ring) is the preferred composite, it is the form produced for both characters.
k A-ring A + ring A-ring


A1.2 Normalization Forms D and C Examples

Table 6: Differing Examples offers examples of NFD and NFC that illustrate how they differ from NFKD and NFKC, respectively.

Table 6: Differing Examples

Original NFD NFC

Notes

l "Äffin" "A\u0308ffin" "Äffin" The ffi_ligature (U+FB03) is not decomposed, because it has a compatibility mapping, not a canonical mapping. (See Normalization Forms KD and KC Examples.)
m "Ä\uFB03n" "A\u0308\uFB03n" "Ä\uFB03n"
n "Henry IV" "Henry IV" "Henry IV" Similarly, the ROMAN NUMERAL IV (U+2163) is not decomposed.
o "Henry \u2163" "Henry \u2163" "Henry \u2163"
p ga ka + ten ga Different compatibility equivalents of a single Japanese character will not result in the same string in NFC.
q ka + ten ka + ten ga
r hw_ka + hw_ten hw_ka + hw_ten hw_ka + hw_ten
s ka + hw_ten ka + hw_ten ka + hw_ten
t hw_ka + ten hw_ka + ten hw_ka + ten
u kaks ki + am + ksf kaks

Hangul syllables are maintained under normalization.


A1.3 Normalization Forms KD and KC Examples

The examples of NFKD and NFKC in Table 7: Other Differing Examples illustrate how they differ from NFD and NFC, respectively.

Table 7: Other Differing Examples

Original NFKD NFKC

Notes

l' "Äffin" "A\u0308ffin" "Äffin" The ffi_ligature (U+FB03) is decomposed in NFKC (where it is not in NFC).
m' "Ä\uFB03n" "A\u0308ffin" "Äffin"
n' "Henry IV" "Henry IV" "Henry IV" Similarly, the resulting strings here are identical in NFKC.
o' "Henry \u2163" "Henry IV" "Henry IV"
p' ga ka + ten ga Different compatibility equivalents of a single Japanese character will result in the same string in NFKC.
q' ka + ten ka + ten ga
r' hw_ka + hw_ten ka + ten ga
s' ka + hw_ten ka + ten ga
t' hw_ka + ten ka + ten ga
u' kaks ki + am + ksf kaks

Hangul syllables are maintained under normalization.*

*In earlier versions of Unicode, jamo characters like ksf had compatibility mappings to kf + sf. These mappings were removed in Unicode 2.1.9 to ensure that Hangul syllables are maintained.)

Annex 2: Design Goals

The following are the design goals for the specification of the normalization forms, and are presented here for reference. The first goal is a fundamental conformance feature of the design.

Goal 1: Uniqueness

The first, and by far the most important, design goal for the normalization forms is uniqueness: two equivalent strings will have precisely the same normalized form. More explicitly,

  1. If two strings x and y are canonical equivalents, then
    • toNFC(x) = toNFC(y)
    • toNFD(x) = toNFD(y)
  2. If two strings are compatibility equivalents, then
    • toNFKC(x) = toNFKC(y)
    • toNFKD(x) = toNFKD(y)
  3. All of the transformations are idempotent: that is,
    • toNFC(toNFC(x)) = toNFC(x)
    • toNFD(toNFD(x)) = toNFD(x)
    • toNFKC(toNFKC(x)) = toNFKC(x)
    • toNFKD(toNFKD(x)) = toNFKD(x)

Goal 1.3 falls out from Goal 1.2 and 1.1, but is stated here for clarity.

Goal 2: Stability

The second major design goal for the normalization forms is stability of characters that are not involved in the composition or decomposition process.

  1. If X contains a character with a compatibility decomposition, then toNFD(X) and toNFC(X) still contain that character.
  2. As much as possible, if there are no combining characters in X, then toNFC(X) = X.
  3. Irrelevant combining marks should not affect the results of composition. See example f in Annex 1: Examples and Charts, where the horn character does not affect the results of composition.

Note:

Goal 3: Efficiency

The third major design goal for the normalization forms is to allow efficient implementations.

  1. It is possible to implement efficient code for producing the Normalization Forms. In particular, it should be possible to produce Normalization Form C very quickly from strings that are already in Normalization Form C or are in Normalization Form D.
     
  2. Composition Forms do not have to produce the shortest possible results, because that can be computationally expensive.

Annex 3: Implementation Notes

There are a number of optimizations that can be made in programs that produce Normalization Form C. Rather than first decomposing the text fully, a quick check can be made on each character. If it is already in the proper precomposed form, then no work has to be done. Only if the current character is combining or in the Section 6, Composition Exclusion Table does a slower code path need to be invoked. (This code path will need to look at previous characters, back to the last starter. See Annex 8: Detecting Normalization Forms for more information.)

The majority of the cycles spent in doing composition is spent looking up the appropriate data. The data lookup for Normalization Form C can be very efficiently implemented, because it only has to look up pairs of characters, not arbitrary strings. First a multistage table (also known as trie; see [Unicode] Chapter 5, Implementation Guidelines) is used to map a character c to a small integer i in a contiguous range from 0 to n. The code for doing this looks like:

i = data[index[c >> BLOCKSHIFT] + (c & BLOCKMASK)];

Then a pair of these small integers are simply mapped through a two-dimensional array to get a resulting value. This yields much better performance than a general-purpose string lookup in a hash table.

Because the Hangul compositions and decompositions are algorithmic, memory storage can be significantly reduced if the corresponding operations are done in code. See Annex 10: Hangul for more information.

Note: Any such optimizations must be carefully checked to ensure that they still produce conformant results. In particular, the code must still be able to pass the test described in Annex 9: Conformance Testing.

For more information on useful implementation techniques, see Annex 8: Detecting Normalization Forms, and UTN #5 Canonical Equivalences in Applications.

Annex 4: Decomposition

For those reading this document without access to the Unicode Standard, the following summarizes the canonical decomposition process. For a complete discussion, see Sections 3.7, Decomposition and 3.11, Canonical Ordering Behavior of the Unicode Standard, 4.0.

Canonical decomposition is the process of taking a string, recursively replacing composite characters using the Unicode canonical decomposition mappings (including the algorithmic Hangul canonical decomposition mappings, see Annex 10: Hangul), and putting the result in canonical order.

Compatibility decomposition is the process of taking a string, replacing composite characters using both the Unicode canonical decomposition mappings and the Unicode compatibility decomposition mappings, and putting the result in canonical order.

A string is put into canonical order by repeatedly replacing any exchangeable pair by the pair in reversed order. When there are no remaining exchangeable pairs, then the string is in canonical order. Note that the replacements can be done in any order.

A sequence of two adjacent characters in a string is an exchangeable pair if the combining class (from the Unicode Character Database) for the first character is greater than the combining class for the second, and the second is not a starter; that is, if combiningClass(first) > combiningClass(second) > 0. See Table 8: Examples of Exchangeable Pairs.

Table 8: Examples of Exchangeable Pairs

Sequence Combining classes Status
<acute, cedilla> 230, 202 exchangeable, because 230 > 202
<a, acute> 0, 230 not exchangeable, because 0 <= 230
<diaeresis, acute> 230, 230 not exchangeable, because 230 <= 230
<acute, a> 230, 0 not exchangeable, because the second class is zero.

Example of Decomposition:

  1. Take the string with the characters "ác´¸" (a-acute, c, acute, cedilla)
  2. The data file contains the following relevant information:
    code; name; ... combining class; ... decomposition.
    0061;LATIN SMALL LETTER A;...0;...
    0063;LATIN SMALL LETTER C;...0;...
    00E1;LATIN SMALL LETTER A WITH ACUTE;...0;...0061 0301;...
    0107;LATIN SMALL LETTER C WITH ACUTE;...0;...0063 0301;...
    0301;COMBINING ACUTE ACCENT;...230;...
    0327;COMBINING CEDILLA;...202;...
  3. Applying the canonical decomposition mappings results in "a´c´¸" (a, acute, c, acute, cedilla).
    • This is because 00E1 (a-acute) has a canonical decomposition mapping to 0061 0301 (a, acute)
  4. Applying the canonical ordering, results in "a´c¸´" (a, acute, c, cedilla, acute).
    • This is because cedilla has a lower combining class (202) than acute (230) does. The positions of 'a' and 'c' are not affected, because they are starters.

Annex 5: Code Sample

A code sample is available for the four different normalization forms. For clarity, this sample is not optimized. The implementations for NFKC and NFC transform a string in two passes: pass 1 decomposes, while pass 2 composes by successively composing each unblocked character with the last starter.

In some implementations, people may be working with streaming interfaces that read and write small amounts at a time. In those implementations, the text back to the last starter needs to be buffered. Whenever a second starter would be added to that buffer, the buffer can be flushed.

The sample is written in Java, though for accessibility it avoids the use of object-oriented techniques. For access to the code, and for a live demonstration, see Normalizer.html [Sample]. Equivalent Perl code is available on the W3C site [CharLint].

Annex 6: Legacy Encodings

While the Normalization Forms are specified for Unicode text, they can also be extended to non-Unicode (legacy) character encodings. This is based on mapping the legacy character set strings to and from Unicode using definitions D5 and D6.

D5. An invertible transcoding T for a legacy character set L is a one-to-one mapping from characters encoded in L to characters in Unicode with an associated mapping T-1 such that for any string S in L, T-1(T(S)) = S.

Most legacy character sets have a single invertible transcoding in common use. In a few cases there may be multiple invertible transcodings: for example, Shift-JIS may have two different mappings used in different circumstances: one to preserve the '/' semantics of 5C16, and one to preserve the '¥' semantics.

The character indexes in the legacy character set string may be different from character indexes in the Unicode equivalent. For example, if a legacy string uses visual encoding for Hebrew, then its first character might be the last character in the Unicode string.

If transcoders are implemented for legacy character sets, it is recommended that the result be in Normalization Form C where possible. See UTR #22: Character Mapping Tables for more information.

D6. Given a string S encoded in L and an invertible transcoding T for L, the Normalization Form X of S under T is defined to be the result of mapping to Unicode, normalizing to Unicode Normalization Form X, and mapping back to the legacy character encoding, for example, T-1(NFX(T(S))). Where there is a single invertible transcoding for that character set in common use, one can simply speak of the Normalization Form X of S.

Legacy character sets fall into three categories based on their normalization behavior with accepted transcoders.

Annex 7: Programming Language Identifiers

This section has been moved to [UTR 31].

Annex 8: Detecting Normalization Forms

The Unicode Character Database supplies properties that allow implementations to quickly determine whether a string x is in a particular normalization form, for example isNFC(x). This is, in general, many times faster than normalizing and then comparing.

For each normalization form, the properties provide the following values for each Unicode code point as shown in Table 9: Value and Meaning.

Table 9: Value and Meaning

Value Meaning
NO The code point cannot occur in that normalization form.
YES The code point can occur, subject to canonical ordering, but without any other constraints.
MAYBE The code point can occur, subject to canonical ordering, but with constraints. In particular, the text may not be in the specified normalization form if this code point is preceded by certain other characters.

Code that uses this property can do a very fast first pass over a string to determine the normalization form. The result is also either NO, YES, or MAYBE. For NO or YES, the answer is definite. In the MAYBE case, a more thorough check must be made, typically by putting a copy of the string into the normalization form, and checking for equality with the original.

This check is much faster than simply running the normalization algorithm, because it avoids any memory allocation and copying. The vast majority of strings will return a definitive YES or NO answer, leaving only a small percentage that require more work. The sample below is written in Java, though for accessibility it avoids the use of object-oriented techniques.

public int quickCheck(String source) {
    short lastCanonicalClass = 0;
    int result = YES;
    for (int i = 0; i < source.length(); ++i) {
        char ch = source.charAt(i);
        short canonicalClass = getCanonicalClass(ch);
        if (lastCanonicalClass > canonicalClass && canonicalClass != 0) {
            return NO;
        }
        int check = isAllowed(ch);
        if (check == NO) return NO;
        if (check == MAYBE) result = MAYBE;
        lastCanonicalClass = canonicalClass;
    }
    return result;
}
public static final int NO = 0, YES = 1, MAYBE = -1;

The isAllowed() call should access the data from Derived Normalization Properties file [NormProps] for the normalization form in question.  (For more information, see the UCD documentation [UCDDoc].) For example, here is a segment of the data for NFC:

...
0338       ; NFC_MAYBE # Mn     COMBINING LONG SOLIDUS OVERLAY
...
F900..FA0D ; NFC_NO    # Lo [270] CJK COMPATIBILITY IDEOGRAPH-F900..CJK COMPATIBILITY IDEOGRAPH-FA0D
...

These lines assign the value NFC_MAYBE to the code point U+0338, and the value NFC_NO to the code points in the range U+F900 .. U+FA0D. Note that there are no MAYBE values for NFD and NFKD: the quickCheck function will always produce a precise result for these normalization forms. All characters that are not specifically mentioned in the file have the values YES.

The data for the implementation of the isAllowed() call can be accessed in memory with a hashtable or a trie (see Annex 3: Implementation Notes); the latter will be the fastest.

A8.1 Stable Code Points

It may also be useful to distinguish the set of code points that are stable under a particular normalization form. They are the set of code points never affected by that particular normalization process. This property is very useful for skipping over text that does not need to be considered at all, either when normalizing or when testing normalization. Formally, each stable code point CP fulfills all the following conditions:

  1. CP has canonical combining class 0, and
  2. CP is (as a single character) not changed by this normalization form, and
    if NFC or NFKC, ALL of the following:
  3. CP can never compose with a previous character, and
  4. CP can never compose with a following character, and
  5. CP can never change if another character is added.

Example: In NFC, a-breve satisfies all but (e), but if you add an ogonek it changes to a-ogonek + breve. So a-breve is not stable in NFC. However, a-ogonek is stable in NFC, because it does satisfy (a-e).

Annex 9: Conformance Testing (Normative)

Implementations must be thoroughly tested for conformance to the normalization specification. The Normalization Conformance Test [Test] file is available for testing conformance. This file consists of a series of fields. When normalization forms are applied to the different fields, the results shall be as specified in the header of that file.

Annex 10: Hangul

Because the Hangul compositions and decompositions are algorithmic, memory storage can be significantly reduced if the corresponding operations are done in code rather than by simply storing the data in the general purpose tables. Here is sample code illustrating algorithmic Hangul canonical decomposition and composition done according to the specification in Section 3.12, Combining Jamo Behavior in [Unicode]. Although coded in Java, the same structure can be used in other programming languages.

The canonical Hangul decompositions specified here and in Section 3.12, Combining Jamo Behavior directly decomposes precomposed Hangul syllable characters into two or three Hangul Jamo characters. This differs from all other canonical decompositions in two ways. First is that they are arithmetically specified, and second is they directly map to more than two characters. The canonical decomposition mapping for all other characters maps each character to one or two others. A character may have a canonical decomposition to more than two characters, but it is expressed as the recursive application of mappings to at most a pair of characters at a time.

Hangul decomposition could also be expressed this way. All LVT syllables decompose into an LV syllable plus an T jamo. The LV syllables themselves decompose into an L jamo plus a T jamo. Thus the Hangul canonical decompositions are fundamentally the same as the other canonical decompositions in terms of the way they decompose. This analysis can also be used to produce more compact code than what is given below.

A10.1 Common Constants

    static final int
        SBase = 0xAC00, LBase = 0x1100, VBase = 0x1161, TBase = 0x11A7,
        LCount = 19, VCount = 21, TCount = 28,
        NCount = VCount * TCount,   // 588
        SCount = LCount * NCount;   // 11172

A10.2 Hangul Decomposition

    public static String decomposeHangul(char s) {
        int SIndex = s - SBase;
        if (SIndex < 0 || SIndex >= SCount) {
            return String.valueOf(s);
        }
        StringBuffer result = new StringBuffer();
        int L = LBase + SIndex / NCount;
        int V = VBase + (SIndex % NCount) / TCount;
        int T = TBase + SIndex % TCount;
        result.append((char)L);
        result.append((char)V);
        if (T != TBase) result.append((char)T);
        return result.toString();
    }

A10.3 Hangul Composition

Notice an important feature of Hangul composition: whenever the source string is not in Normalization Form D, you can not just detect character sequences of the form <L, V> and <L, V, T>. It is also necessary to catch the sequences of the form <LV, T>. To guarantee uniqueness, these sequences must also be composed. This is illustrated in Step 2 below.

    public static String composeHangul(String source) {
        int len = source.length();
        if (len == 0) return "";
        StringBuffer result = new StringBuffer();
        char last = source.charAt(0);            // copy first char
        result.append(last);

        for (int i = 1; i < len; ++i) {
            char ch = source.charAt(i);

            // 1. check to see if two current characters are L and V

            int LIndex = last - LBase;
            if (0 <= LIndex && LIndex < LCount) {
                int VIndex = ch - VBase;
                if (0 <= VIndex && VIndex < VCount) {

                    // make syllable of form LV

                    last = (char)(SBase + (LIndex * VCount + VIndex) * TCount);
                    result.setCharAt(result.length()-1, last); // reset last
                    continue; // discard ch
                }
            }

            // 2. check to see if two current characters are LV and T

            int SIndex = last - SBase;
            if (0 <= SIndex && SIndex < SCount && (SIndex % TCount) == 0) {
                int TIndex = ch - TBase;
                if (0 < TIndex && TIndex < TCount) {

                    // make syllable of form LVT

                    last += TIndex;
                    result.setCharAt(result.length()-1, last); // reset last
                    continue; // discard ch
                }
            }

            // if neither case was true, just add the character

            last = ch;
            result.append(ch);
        }
        return result.toString();
    }

Additional transformations can be performed on sequences of Hangul jamo for various purposes. For example, to regularize sequences of Hangul jamo into standard syllables, the choseong and jungseong fillers can be inserted, as described in Chapter 3 Conformance, of the Unicode Standard [Unicode]. For keyboard input, additional compositions may be performed. For example, the trailing consonants kf + sf may be combined into ksf. In addition, some Hangul input methods do not require a distinction on input between initial and final consonants, and change between them on the basis of context. For example, in the keyboard sequence mi + em + ni + si + am, the consonant ni would be reinterpreted as nf, because there is no possible syllable nsa. This results in the two syllables men and sa.

However, none of these additional transformations are considered part of the Unicode Normalization Formats.

A10.4 Hangul Character Names

Hangul decomposition is also used to form the character names for the Hangul syllables. While the sample code that illustrates this process is not directly related to normalization, it is worth including because it is so similar to the decomposition code.

    public static String getHangulName(char s) {
        int SIndex = s - SBase;
        if (0 > SIndex || SIndex >= SCount) {
            throw new IllegalArgumentException("Not a Hangul Syllable: " + s);
        }
        StringBuffer result = new StringBuffer();
        int LIndex = SIndex / NCount;
        int VIndex = (SIndex % NCount) / TCount;
        int TIndex = SIndex % TCount;
        return "HANGUL SYLLABLE " + JAMO_L_TABLE[LIndex]
          + JAMO_V_TABLE[VIndex] + JAMO_T_TABLE[TIndex];
    }

    static private String[] JAMO_L_TABLE = {
        "G", "GG", "N", "D", "DD", "R", "M", "B", "BB",
        "S", "SS", "", "J", "JJ", "C", "K", "T", "P", "H"
    };

    static private String[] JAMO_V_TABLE = {
        "A", "AE", "YA", "YAE", "EO", "E", "YEO", "YE", "O",
        "WA", "WAE", "OE", "YO", "U", "WEO", "WE", "WI",
        "YU", "EU", "YI", "I"
    };

    static private String[] JAMO_T_TABLE = {
        "", "G", "GG", "GS", "N", "NJ", "NH", "D", "L", "LG", "LM",
        "LB", "LS", "LT", "LP", "LH", "M", "B", "BS",
        "S", "SS", "NG", "J", "C", "K", "T", "P", "H"
    };

Annex 11: Intellectual Property

Transcript of letter regarding disclosure of IBM Technology
(Hard copy is on file with the Chair of UTC and the Chair of NCITS/L2)
Transcribed on 1999-03-10

February 26, 1999

 

The Chair, Unicode Technical Committee

Subject: Disclosure of IBM Technology - Unicode Normalization Forms

The attached document entitled "Unicode Normalization Forms" does not require IBM technology, but may be implemented using IBM technology that has been filed for US Patent. However, IBM believes that the technology could be beneficial to the software community at large, especially with respect to usage on the Internet, allowing the community to derive the enormous benefits provided by Unicode.

This letter is to inform you that IBM is pleased to make the Unicode normalization technology that has been filed for patent freely available to anyone using them in implementing to the Unicode standard.

Sincerely,

 

W. J. Sullivan,
Acting Director of National Language Support
and Information Development

 

Annex 12: Corrigenda

The Unicode Consortium has well-defined policies in place to govern changes that affect backwards compatibility. For information on these stability policies, especially regarding normalization, see Unicode Policies [Policies]. In particular:

Once a character is encoded, its canonical combining class and decomposition mapping will not be changed in a way that will destabilize normalization.

What this means is:

If a string contains only characters from a given version of the Unicode Standard (for example, Unicode 3.1.1), and it is put into a normalized form in accordance with that version of Unicode, then it will be in normalized form according to any past or future versions of Unicode.

This guarantee has been in place for Unicode 3.1 and after. It has been necessary to correct the decompositions of a small number of characters since Unicode 3.1, as listed in the Normalization Corrections data file [Corrections], but such corrections are in accordance with the above principles: all text normalized on old systems will test as normalized in future systems. All text normalized in future systems will test as normalized on past systems. What may change, for those few characters, is that unnormalized text may normalize differently on past and future systems.

It is straightforward for any implementation with a future version of Unicode to support all past versions of normalization. For an implementation of Unicode Version X to support a version of NFC that precisely matches a older Unicode Version Y, the following two steps are taken:

  1. Before applying the normalization algorithm, map the characters that were corrected to their old values in Unicode Version Y.
    • Use the table in [Corrections] for this step, by including any code points that have a version later than Y and less than or equal to X.
    • For example, for a Unicode 4.0 implementation to duplicate Unicode 3.2 results, exactly 5 characters must be mapped.
  2. In applying the normalization algorithm, handle any code points that were not defined in Unicode Version X as if they were unassigned.
    • That is, the code points will not decompose or compose, and their canonical combining class will be zero.
    • The Derived_Age property in the Unicode Character Database [UCD] can be used for the set of code points in question.

There was a change in version 4.1 to correct a definitional problem with D2. For more information, see Public Review Issue #29.

Annex 13: Canonical Equivalence

This section describes the relationship of normalization to respecting (or preserving) canonical equivalence. A process (or function) respects canonical equivalence when canonical equivalent inputs always produce canonically equivalent outputs. For a function that transforms one string into another, this may also be called preserving canonical equivalence. There are a number of important aspects to this concept:

The canonically equivalent inputs or outputs are not just limited to strings, but are also relevant to the offsets within strings, because those play a fundamental role in Unicode string processing.

Offset P into string X is canonically equivalent to offset Q into string Y if and only if both of the following conditions are true:

This can be written as PX ≈ QY. Note that whenever X and Y are canonically equivalent, it follows that 0X ≈ 0Y, and len(X)X ≈ len(Y)Y.

Example:

  1. Given X = <angstrom sign, semicolon> and Y = <A, combining ring above, greek question mark>,
    • 0X ≈ 0Y
    • 1X ≈ 2Y
    • 2X ≈ 3Y
    • 1Y has no canonically equivalent offset in X

The following are examples of processes that involve canonically equivalent strings and/or offsets.

Examples:

  1. When isWordBreak(string, offset) respects canonical equivalence,  then
    • isWordBreak(<A-ring, semicolon>, 1) = isWordBreak(<A, ring, semicolon>, 2)
  2. When nextWordBreak(string, offset) respects canonical equivalence,  then
    • nextWordBreak(<A-ring, semicolon>, 0) = 1 if and only if nextWordBreak(<A, ring, semicolon>, 0) = 2.

Respecting canonical equivalence is related to, but different from, preserving a canonical normalization form NFx (where NFx means either NFD or NFC). In a process that preserves a normalization form, whenever any input string is normalized according to that normalization form, then every output string is also normalized according to that form. If a process preserves a canonical normalization form, then it respects canonical equivalence, but not necessarily vice versa.

In building a system that as a whole respects canonical equivalence, there are two basic strategies, with some variations on the second strategy. These strategies are:

  1. Ensure that each system component respects canonical equivalence,
  2. Ensure that each system component preserves NFx, and one of the following:
    1. Reject any non-NFx text on input to the whole system
    2. Reject any non-NFx text on input to each component
    3. Normalize to NFx all text on input to the whole system
    4. Normalize to NFx all text on input to each component
    5. All three of the following:
      1. Allow text to be marked as NFx when generated.
      2. Normalize any unmarked text on input to each component to NFx
      3. Reject any marked text that is not NFx

There are trade-offs for each of these strategies. The best choice or mixture of strategies will depend on the structure of the components and their interrelations, and how fine-grained or low-level those components are. One key piece of information is that it is much faster to check that text is NFx than it is to convert it. This is especially true in the case of NFC. So even where it says "normalize" above, a good technique is to first check if normalization is required, and only perform the extra processing if necessary.

Acknowledgements

Thanks to Kent Karlsson, Marcin Kowalczyk, Rick Kunst, Sadahiro Tomoyuki, Markus Scherer, Dick Sites, and Ken Whistler for feedback on the previous version of this document.

References

[CharLint] Charlint - A Character Normalization Tool
http://www.w3.org/International/charlint/
[CharMod] W3C Character Model for the World Wide Web
http://www.w3.org/TR/charmod/
[CharReq] W3C Requirements for String Identity Matching and String Indexing
http://www.w3.org/TR/WD-charreq
[Charts] Normalization Charts
http://www.unicode.org/reports/tr15/charts
[Corrections] Normalization Corrections
Latest Version:
http://www.unicode.org/Public/UNIDATA/NormalizationCorrections.txt
Unicode 4.1.0 Version:
http://www.unicode.org/Public/4.1.0/ucd/NormalizationCorrections.txt

Unicode 4.0 Version:
http://www.unicode.org/Public/4.0-Update/NormalizationCorrections-4.0.0.txt
Unicode 3.2 Version:
http://www.unicode.org/Public/3.2-Update/NormalizationCorrections-3.2.0.txt
[UCDDoc Unicode Character Database Documentation
http://www.unicode.org/Public/UNIDATA/UCD.html
[Exclusions] Composition Exclusion Table
Latest Version:
http://www.unicode.org/Public/UNIDATA/CompositionExclusions.txt
Unicode 4.1.0 Version:
http://www.unicode.org/Public/4.1.0/ucd/CompositionExclusions.txt
Unicode 4.0 Version:
http://www.unicode.org/Public/4.0-Update/CompositionExclusions-4.0.0.txt
Unicode 3.2 Version:
http://www.unicode.org/Public/3.2-Update/CompositionExclusions-3.2.0.txt
Unicode 3.1 Version:

http://www.unicode.org/Public/3.1-Update/CompositionExclusions-3.txt
Unicode 3.0 Version:
http://www.unicode.org/Public/3.0-Update1/CompositionExclusions-2.txt
[FAQ] Unicode Frequently Asked Questions
http://www.unicode.org/faq/
For answers to common questions on technical issues.
[Feedback] Reporting Errors and Requesting Information Online
http://www.unicode.org/reporting.html
[Glossary] Unicode Glossary
http://www.unicode.org/glossary/
For explanations of terminology used in this and other documents.
[NormProps Derived Normalization Properties
Latest Version:
http://www.unicode.org/Public/UNIDATA/DerivedNormalizationProps.txt
Unicode 4.1.0 Version:
http://www.unicode.org/Public/4.1.0/ucd/DerivedNormalizationProps.txt
Unicode 4.0 Version:
http://www.unicode.org/Public/4.0-Update/DerivedNormalizationProps-4.0.0.txt
[Policies] Unicode Policies
http://www.unicode.org/policies/
[Reports] Unicode Technical Reports
http://www.unicode.org/reports/
For information on the status and development process for technical reports, and for a list of technical reports.
[Sample] Sample Normalizer code
http://www.unicode.org/reports/tr15/Normalizer.html
[Test] Normalization Conformance Test
Latest Version:
http://www.unicode.org/Public/UNIDATA/NormalizationTest.txt
Unicode 4.1.0 Version:
http://www.unicode.org/Public/4.1.0/ucd/NormalizationTest.txt
Unicode 4.0 Version:
http://www.unicode.org/Public/4.0-Update/NormalizationTest-4.0.0.txt
[UCD] Unicode Character Database
http://www.unicode.org/ucd/
[U3.0] The Unicode Consortium. The Unicode Standard, Version 3.0. Reading, MA, Addison-Wesley, 2000. 0-201-61633-5
[U3.1] Unicode 3.1
http://www.unicode.org/reports/tr27/
[U3.2] Unicode 3.2
http://www.unicode.org/reports/tr28/
[Unicode] The Unicode Consortium. The Unicode Standard, Version 4.0. Reading, MA, Addison-Wesley, 2003. 0-321-18578-1.
[UAX31] UAX #31, Identifier and Pattern Syntax
http://www.unicode.org/reports/tr31/
[Versions] Versions of the Unicode Standard
http://www.unicode.org/versions/
For information on version numbering, and citing and referencing the Unicode Standard, the Unicode Character Database, and Unicode Technical Reports.


Modifications

The following summarizes modifications from previous revisions of this document.

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