Unicode Technical Standard #10

Unicode Collation Algorithm

Summary

This report provides the specification of the Unicode Collation Algorithm, which provides a specification for how to compare two Unicode strings while remaining conformant to the requirements of The Unicode Standard. The UCA also supplies the Default Unicode Collation Element Table (DUCET) as the data specifying the default collation order for all Unicode characters.

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 Technical Standard (UTS) is an independent specification. Conformance to the Unicode Standard does not imply conformance to any UTS.

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
  • 1.1 Multi-Level Comparison
  • 1.2 Canonical Equivalence
  • 1.3 Contextual Sensitivity
  • 1.4 Customization
  • 1.5 Other Applications of Collation
  • 1.6 Interleaved Levels
  • 1.7 Performance
  • 1.8 Common Misperceptions
  • 1.9 The Unicode Collation Algorithm
    • 1.9.1 Goals
    • 1.9.2 Non-Goals
• 2 Conformance
• 3 Collation Element Table
  • 3.1 Linguistic Features
    • 3.1.1 Multiple Mappings
      • 3.1.1.1 Expansions
      • 3.1.1.2 Contractions
      • 3.1.1.3 Other Multiple Mappings
    • 3.1.2 French Accents
    • 3.1.3 Rearrangement
    • 3.1.4 Default Values
    • 3.1.5 Collation Graphemes
    • 3.1.6 Combining Grapheme Joiner
  • 3.2 Default Unicode Collation Element Table
    • 3.2.1 File Format
    • 3.2.2 Variable Weighting
  • 3.3 Well-Formed Collation Element Tables
  • 3.4 Stability
• 4 Main Algorithm
  • 4.1 Normalize
  • 4.2 Produce Array
  • 4.3 Form Sort Key
  • 4.4 Compare
• 5 Tailoring
  • 5.1 Preprocessing
• 6 Implementation Notes
  • 6.1 Reducing Sort Key Lengths
    • 6.1.1 Eliminating Level Separators
    • 6.1.2 L2/L3 in 8 Bits
    • 6.1.3 Machine Words
    • 6.1.4 Run-Length Compression
  • 6.2 Large Weight Values
  • 6.3 Reducing Table Sizes
    • 6.3.1 Contiguous Weight Ranges
    • 6.3.2 Escape Hatch
    • 6.3.3 Leveraging Unicode Tables
    • 6.3.4 Reducing the Repertoire
    • 6.3.5 Memory Table Size
  • 6.4 Avoiding Zero Bytes
  • 6.5 Avoiding Normalization
  • 6.6 Case Comparisons
  • 6.7 Incremental Comparison
  • 6.8 Catching Mismatches
  • 6.9 Tailoring Example: Java
  • 6.10 Flat File Example
    • 6.10.1 Collation Element Format
    • 6.10.2 Sample Code
• 7 Weight Derivation
  • 7.1 Derived Collation Elements
    • 7.1.1 Illegal Code Points
    • 7.1.2 Legal Code Points
    • 7.1.3 Implicit Weights
    • 7.1.4 Trailing Weights
  • 7.2 Canonical Decompositions
  • 7.3 Compatibility Decompositions
    • 7.3.1 Tertiary Weight Table
• 8 Searching and Matching
• Appendix A: Deterministic_Sorting
• Acknowledgements
• References
• Modifications

1 Introduction

Collation is the general term for the process and function of determining the sorting order of strings of characters. It is a key function in computer systems; whenever a list of strings is presented to users, they are likely to want it in a sorted order so that they can easily and reliably find individual strings. Thus it is widely used in user interfaces. It is also crucial for the operation of databases, not only in sorting records but also in selecting sets of records with fields within given bounds.

However, collation is not uniform; it varies according to language and culture: Germans, French and Swedes sort the same characters differently. It may also vary by specific application: even within the same language, dictionaries may sort differently than phonebooks or book indices. For non-alphabetic scripts such as East Asian ideographs, collation can be either phonetic or based on the appearance of the character. Collation can also be commonly customized or configured according to user preference, such as ignoring punctuation or not, putting uppercase before lowercase (or vice versa), and so on. Linguistically correct searching also needs to use the same mechanisms: just as "v" and "w" sort as if they were the same base letter in Swedish, a loose search should pick up words with either one of them.

Thus collation implementations must deal with the often-complex linguistic conventions that communities of people have developed over the centuries for ordering text in their language, and provide for common customizations based on user preferences. And while doing all of this, of course, performance is critical.

The following table shows some examples of cases where sort order differs by language, by usage, or by another customization.

The conventions that people have developed over the centuries for collating text in their language are often quite complex.  Sorting all Unicode characters in a uniform and consistent manner presents a number of challenges. And for any collation mechanisms to be accepted in the marketplace, algorithms that allow for good performance are crucial.

Languages vary not only regarding which types of sorts to use (and in which order they are to be applied), but also in what constitutes a fundamental element for sorting. For example, Swedish treats ä as an individual letter, sorting it after z in the alphabet; German, however, sorts it either like ae or like other accented forms of a, thus following a. In Slovak, the digraph ch sorts as if it were a separate letter after h. Examples from other languages (and scripts) abound. Languages whose writing systems use uppercase and lowercase typically ignore the differences in case, unless there are no other differences in the text.

It is important to ensure that collation meets user expectations as fully as possible. For example, in the majority of Latin languages, ø sorts as an accented variant of o, meaning that most users would expect ø alongside o. However, there are a few languages (Norwegian and Danish for example) that sort ø as a unique sorting element after z. Sorting "Søren" after "Sylt" in a long list — that is, as would be expected in Norwegian or Danish — will cause problems if the user expects ø as a variant of o. A user will look for "Søren" between "Sorem" and "Soret", not see it in the selection, and assume the string is missing - fooled by the fact that it has sorted in a completely different location. In matching, the same can occur, which can cause significant problems for software customers; and as with database selection, the user may not realize what he is missing. See Section 1.5 Other Applications of Collation.

With Unicode being deployed so widely, multilingual data becomes the rule, not the exception. Furthermore, it is increasingly common to see users with many different sorting expectations accessing the data. For example, a French company with customers all over Europe will include names from many different languages - French, German, Polish, Swedish, and so on. If a German employee at this French company accesses the data, the customer names need to show up in the order that meets this employee's expectations — that is, in a German order — even though there will be many different accented characters that do not normally appear in German text.

For scripts and characters outside the use of a particular language, explicit rules may not exist. For example, Swedish and French have clear and different rules on sorting ä (either after z or as an accented character with a secondary difference from a), but neither defines the ordering of other characters such as Ж, ש, ♫, ∞, ◊, or ⌂.

1.1 Multi-Level Comparison

To address the complexities of language-sensitive sorting, a multilevel comparison algorithm is employed. In comparing two words, for example, the most important feature is the base character: such as the difference between an A and a B. Accent differences are typically ignored, if there are any differences in the base letters. Case differences (uppercase versus lowercase), are typically ignored, if there are any differences in the base or accents. Punctuation is variable. In some situations a punctuation character is treated like a base character. In other situations, it should be ignored if there are any base, accent, or case differences. There may also be a final, tie-breaking level, whereby if there are no other differences at all in the string, the (normalized) code point order is used.

These examples are in English; the levels may correspond to different features in other languages. Notice that in each example for levels L2 through Ln, the differences on that level (indicated by the underlined characters) are swamped by the stronger-level differences (indicated by the blue text). For example, the L2 example shows that difference between an o and an accented ô is swamped by an L1 difference (the presence or absence of an s). In the last example, the □ represents a format character, which is otherwise completely ignorable.

The core concept is that the primary level (L1) is for the basic sorting of the text, and the non-primary levels (L2..Ln) are for tweaking other linguistic elements in the writing system that are important to users in ordering, but less important than the order of the basic sorting. In practice, not all of these levels may be needed, depending on the user preferences or customizations.

Note: Many people see the Unicode code charts, and expect the characters in their language to be in the "correct" order in the code charts. Because collation varies by language — not just by script —, it is not possible to arrange code points for characters so that simple binary string comparison produces the desired collation order for all languages. Because multi-level sorting is a requirement, it is not even possible to arrange code points for characters so that simple binary string comparison produces the desired collation order for any particular language. Separate data tables are required for correct sorting order. For more information on tailorings for different languages, see [CLDR].

The sorting weight of characters is not provided by their position in the Unicode code charts.

1.2 Canonical Equivalence

There are a number of cases in Unicode where two sequences of characters are canonically equivalent; they are essentially the same character but can be represented in different ways. For more information on what this means, see [UAX15].

For collation, sequences that are canonically equivalent sort the same. In the table below are some examples. For example, the angstrom symbol was encoded for compatibility, and is canonically equivalent to an A-ring. The latter is also equivalent to the decomposed sequence of A plus the combining ring character. The order of certain combining marks in many cases is also irrelevant, so these must be sorted the same, as in the second example. In the third example, we have a composed character that can be decomposed in four different ways, all of which are canonically equivalent.

1.3 Contextual Sensitivity

Beyond the concept of levels, there are additional complications in certain languages, whereby the comparison is context sensitive: it depends on more than just single characters compared directly against one another.

First are contractions, where two (or more) characters sort as if they were a single base character. In the table below, CH acts like a character after C. Second are expansions, where a single character sorts as if it were two (or more) characters in sorting. In the table below, an Πligature sorts as if it were O + E. Both of these can be combined: that is, two (or more) characters may sort as if they were a different sequence of two (or more) characters. In the example below, for Japanese, a length mark sorts like the vowel of the previous syllable: as an A after KA and as an I after KI.

There are some further oddities in the ways that languages work. Normally, all differences in sorting are assessed going from the start to the end of the string. If all of the base characters are the same, the first accent difference determines the final order. In row 1 of the example below, the first accent difference is on the o, so that is what determines the order. In French and a few other languages, however, it is the last accent difference that determines the order, as in row 2.

1.4 Customization

In practice, there are additional features of collation that users need control over, which are expressed in user-interfaces and eventually in APIs. Other customizations or user preferences include (but are not limited to) the following:

• Language. As discussed above, this is the most important feature, because it is crucial that the collation match the expectations of users of the target language community.
• Strength. Next to that is the strength, the number of levels that are to be considered in comparison. For comparison, most of the time a three-level strength will need to be used. In some cases, a larger number of levels will be needed, while in others — especially in searching — fewer levels will be desired.
• Case Ordering. Some dictionaries and authors use uppercase before lowercase while others use the reverse, so that needs to be customizable. Sometimes the case ordering is mandated by the government, as in Denmark. But often it is simply a customization or user preference. Another common option is whether to treat punctuation (including spaces) as base characters or treat them as a level 4 difference.
• User-Defined Rules. Such rules provide specified results for given combinations of letters. For example, in an index, an author may wish to have symbols sorted as if they were spelled out, thus "?" may sort as if it were "question mark".
• Merging Tailorings. These allow the merging of sets of rules for different languages. For example, someone may want Latin characters sorted as in French, and Arabic characters sorted as in Iranian. In such an approach, generally one is the “master” in cases of conflicts.
• Script Order. This allows users to determine which scripts come first. For example, in an index an author may want the script of the text of the book to come first. For example:

  b < ב < β < б versus
  β < b < б < ב

  Attempting to achieve the same effect by introducing an extra strength level before the first (primary) level would give incorrect results for strings containing mixed scripts

• Numbers: This allows sorting numbers by numeric order. If numbers are sorted alphabetically, “A-10” comes before “A-2”, which is often not desired. This can be customized, but is much trickier than it sounds because of ambiguities with recognizing numbers within strings (because they may be formatted according to different language conventions). Once each number is recognized, it can be preprocessed in place it into a format that allows for correct numeric sorting, such as a textual version of the IEEE numeric format.

Note that phonetic sorting of Han characters requires use of either a lookup dictionary of words or, more typically, special construction of programs or databases to maintain an associated phonetic spelling for the words in the text.

1.5 Other Applications of Collation

The same collation behavior has application in other realms than sorting. In particular, searching should behave consistently with sorting. For example, if v and w are treated as identical base letters in Swedish sorting, then they should do so for searching. For searching, the ability to set the maximal strength level is very important.

Selection is the process of using the comparisons between the endpoints of a range, as when using a SELECT command in a database query. It is crucial that the correct range be returned, according to the users expectations. Consider the example of a German businessman making a database selection, such as to sum up revenue in each of of the cities from O... to P... for planning purposes. If behind his back all cities starting with Ö are excluded because the query selection is using a Swedish collation, there is going to be one very unhappy customer.

A sequence of characters considered to be a unit in collation, such as ch in Slovak, represents a tailored grapheme cluster. For applications of this, see UTS #18: Unicode Regular Expression Guidelines [UTS18]. For more information on grapheme clusters, see UAX #29: Text Boundaries [UAX29].

1.6 Interleaved Levels

Levels may also need to be interleaved. Take, for example, sorting a database according to two fields. The simplest way to sort is field by field, sequentially. This gives us the results in column one in the example below. First all the levels in Field 1 are compared, then all the levels in Field 2. The problem with this approach is that high level differences in the second field are swamped by minute differences in the first field. Thus we get unexpected ordering for the first names.

A second way to do this is to ignore all but base-level differences in the sorting of the first field. This gives us the results in column 2. The first names are then all in the right order, but the problem is now that the first field is not correctly ordered except on the base character level.

The correct way to sort is to merge the fields in sorting, as shown in the last column. Using this technique, all differences in the fields are taken into account, and the levels are considered uniformly: accents in all fields are ignored if there are any base character differences in any of the fields; case in all fields is ignored if there are accent or base character differences in any of the fields; and so on.

1.7 Performance

Collation is one of the most performance-critical features in a system. Consider the number of comparison operations that are involved in sorting or searching large databases, for example. Most production implementations will use a number of optimizations to speed up string comparison.

There is a common mechanism for preprocessing strings so that multiple comparisons operations are much faster. With this mechanism, each collation engine provides for the generation of a sort key from any given string. The binary comparison of any two sort keys will yield the same result (less, equal, or greater) as the collation engine would return for a comparison of the original strings. Thus for a given collation C and any two strings A and B:

A ≤ B according to C if and only if sortkey(C, A) ≤ sortkey(C, B)

Still, simple string comparison is faster for any individual comparison. This is easy to understand, because the generation of a sort key requires processing an entire string, while in most string comparisons differences are found before all the characters are processed. Typically there is a considerable difference in performance, with simple string comparison being about 5 to 10 times faster than generating sort keys and then using a binary comparison.

However, sort keys can be much faster for multiple comparisons. Because binary comparison is blindingly faster than string comparison, whenever there will be more than about 10 comparisons per string — and the system can afford the storage — it is faster to use sort keys.

1.8 Common Misperceptions

There are a number of common misperceptions about collation.

1. Collation is not aligned with character sets or repertoires of characters. Swedish and German share most of the same characters, for example, but have very different sorting orders.
2. Collation is not code point (binary) order. The simplest case of this is capital Z versus lowercase a. As noted above, beginners may complain about Unicode that a particular character is “not in the right place in the code chart”. That is a misunderstanding of the role of the character encoding in collation. While the Unicode Standard does not gratuitously place characters such that the binary ordering is odd, the only way to get the linguistically-correct order is to use a language-sensitive collation, not a binary ordering.
3. Collation is not a property of strings. Consider a list of cities, with each city correctly tagged with its language. Despite this, a German user will expect to see the cities all sorted according to German order, and not expect to see a word with ö appear after z, simply because the city has a Swedish name. As mentioned above it is of crucial importance that if a German businessman makes a database selection, such as to sum up revenue in each of of the cities from O... to P... for planning purposes, then cities starting with Ö must not be excluded.
4. Collation order is not preserved under concatenation or substring operations, in general. For example, the fact that x is less than y does not mean that x + z is less than y + z. This is because characters may form contractions across the substring or concatenation boundaries. In summary, the following shows which implications not to expect.

   x < y ↛ xz < yz
   x < y ↛ zx < zy
   xz < yz ↛ x < y
   zx < zy ↛ x < y
    

5. Collation order is not preserved when comparing sort keys generated from different collation sequences. Remember that sort keys are a preprocessing of strings according to a given set of collation features. From different features, you will get different binary sequences. For example, suppose we have two collations, F and G, where F is a French collation (with accents compared from the end), and G is a German phonebook ordering. Then:
   • A ≤ B according to F if and only if sortkey(F, A) ≤ sortkey(F, B), and
   • A ≤ B according to G if and only if sortkey(G, A) ≤ sortkey(G, B)
   • But the relation between sortkey(F, A) and sortkey(G, B) says nothing about whether A ≤ B according to F, or whether A ≤ B according to G.
6. Collation order is not a stable sort; that is a property of a sort algorithm, not a collation sequence. For more information, see Section 3.4 Stability.
7. Collation order is not fixed. Over time, collation order will vary: there may be fixes that are discovered as more information becomes available about languages; there may be new government or industry standards for the language that require changes; and finally, the new characters that are added to Unicode periodically will interleave with the previously-defined ones. Thus collations must be carefully versioned.

1.9 The Unicode Collation Algorithm

The Unicode Collation Algorithm (UCA) provides a specification for how to compare two Unicode strings while remaining conformant to the requirements of The Unicode Standard. The UCA also supplies the Default Unicode Collation Element Table (DUCET), which is data specifying the default collation order for all Unicode characters. This table is designed so that it can be tailored to meet the requirements of different languages and customizations.

Briefly stated, the Unicode Collation Algorithm takes an input Unicode string and a Collation Element Table, containing mapping data for characters. It produces a sort key, which is an array of unsigned 16-bit integers. Two or more sort keys so produced can then be binary-compared to give the correct comparison between the strings for which they were generated.

The Unicode Collation Algorithm assumes multiple-level key weighting, along the lines widely implemented in IBM technology, and as described in the Canadian sorting standard [CanStd] and the International String Ordering standard [ISO14651].

By default, the algorithm makes use of three fully-customizable levels. For the Latin script, these levels correspond roughly to:

1. alphabetic ordering
2. diacritic ordering
3. case ordering.

A final level for tie-breaking (semi-stability) may be used for tie-breaking between strings not otherwise distinguished.

This design allows implementations to produce culturally acceptable collation, while putting the least burden on implementations in terms of memory requirements and performance. In particular, Collation Element Tables only require storage of 32 bits of collation data per significant character.

However, implementations of the Unicode Collation Algorithm are not limited to supporting only three levels. They are free to support a fully customizable 4th level (or more levels), as long as they can produce the same results as the basic algorithm, given the right Collation Element Tables. For example, an application which uses the algorithm, but which must treat some collection of special characters as ignorable at the first three levels and must have those specials collate in non-Unicode order (as, for example to emulate an existing EBCDIC-based collation), may choose to have a fully customizable 4th level. The downside of this choice is that such an application will require more storage, both for the Collation Element Table and in constructed sort keys.

The Collation Element Table may be tailored to produce particular culturally required orderings for different languages or locales. As in the algorithm itself, the tailoring can provide full customization for three (or more) levels.

1.9.1 Goals

The algorithm is designed to satisfy the following goals:

1. A complete, unambiguous, specified ordering for all characters in Unicode.
2. A complete resolution of the handling of canonical and compatibility equivalences as relates to the default ordering.
3. A complete specification of the meaning and assignment of collation levels, including whether a character is ignorable by default in collation.
4. A complete specification of the rules for using the level weights to determine the default collation order of strings of arbitrary length.
5. Allowance for override mechanisms (tailoring) for creating language-specific orderings. Tailoring can be provided by any well-defined syntax that takes the default ordering and produces another well-formed ordering.
6. An algorithm that can be efficiently implemented, both in terms of performance and in terms of memory requirements.

Given the standard ordering and the tailoring for any particular language, any two companies or individuals — with their own proprietary implementations — can take any arbitrary Unicode input and produce exactly the same ordering of two strings. In addition, when given a tailoring specifying French accents this algorithm passes the Canadian and ISO 14651 benchmarks ([CanStd], [ISO14651]).

Note: The Default Unicode Collation Element Table does not explicitly list weights for all assigned Unicode characters. However, the algorithm is well defined over all Unicode code points. See Section 7.1.2 Legal Code Points.

1.9.2 Non-Goals

The Default Unicode Collation Element Table explicitly does not provide for the following features:

1. reversibility: from a Collation Element you are not guaranteed that you can recover the original character.
2. numeric formatting: numbers composed of a string of digits or other numerics will not necessarily sort in numerical order.
3. API: no particular API is specified or required for the algorithm.
4. title sorting: for example, removing articles such as a and the during bibliographic sorting is not provided.
5. Stability of binary sort key values between versions: For more information, see Section 3.4 Stability.
6. linguistic applicability: to meet most user expectations, a linguistic tailoring is needed. For more information, see Section 5 Tailoring.

2 Conformance

There are many different ways to compare strings, and the Unicode Standard does not restrict the ways in which implementations can do this. However, any Unicode-conformant implementation that purports to implement the Unicode Collation Algorithm must do so as described in this document.

Note: A conformance test for the UCA is available in [Test].

The algorithm is a logical specification, designed to be straightforward to describe. Actual implementations of the algorithm are free to change any part of the algorithm as long as any two strings compared by the implementation are ordered the same as they would be by the algorithm. They are also free to use a different format for the data in the Collation Element Table. The sort key is also a logical intermediate object: as long as an implementation produces the same results in comparison of strings, the sort keys can differ in format from what is specified here. (See Section 6 Implementation Notes.)

The requirements for conformance on implementations of the Unicode Collation Algorithm are as follows:

3 Collation Element Table

A Collation Element Table contains a mapping from one (or more) characters to one (or more) collation elements, where a collation element is an ordered list of three or more 16-bit weights. (All code points not explicitly mentioned in the mapping are given an implicit weight: see Section 7 Weight Derivation).

Note: Implementations can produce the same result without using 16-bit weights — see Section 6 Implementation Notes.

The first weight is called the Level 1 weight (or primary weight), the second is called the Level 2 weight (secondary weight), the third is called the Level 3 weight (tertiary weight), the fourth is called the Level 4 weight (quaternary weight), and so on. For a collation element X, these can be abbreviated as X₁, X₂, X₃, X₄, and so on. Given two collation elements X and Y, we will use the following notation:

Other operations are given their customary definitions in terms of the above. That is:

• X ≤_n Y if and only if X <_n Y or X =_n Y
• X >_n Y if and only if Y <_n X
• X ≥_n Y if and only if Y ≤_n X

The collation algorithm results in a similar ordering among characters and strings, so that for two strings A and B we can write A <₂ B, meaning that A is less than B and there is a primary or secondary difference between them. If A <₂ B but A=₁ B, we say that there is only a secondary difference between them. If two strings are equivalent (equal at all levels) according to a given Collation Element Table, we write A ≡ B. If they are bit-for-bit identical, we write A = B.

If a weight is 0000, then that collation element is ignorable at that level: the weight at that level is not taken into account in sorting. A Level N ignorable is a collation element that is ignorable at level N but not at level N+1. Thus:

• A Level 1 ignorable (or primary ignorable) is a collation element that is ignorable at Level 1, but not at Level 2;
• a Level 2 ignorable (or secondary ignorable) is ignorable at Levels 1 and 2, but not Level 3;
• a Level 3 ignorable (or tertiary ignorable) is ignorable at Levels 1, 2, and 3 but not Level 4;

In addition:

• A collation element that is not ignorable at any level is called a non-ignorable.
• A collation element with zeros at every level is called completely ignorable.

For a given Collation Element Table, MIN_n is the least weight in any collation element at level n, and MAX_n is the maximum weight in any collation element at level n.

The following are sample collation elements that are used in the examples illustrating the algorithm. Unless otherwise noted, all weights are in hexadecimal format.

Note: Weights in all examples are illustrative, and may not match what is in the latest Default Unicode Collation Element Table.

3.1 Linguistic Features

The following section describes the implications of the features discussed in Section 1 Introduction.

3.1.1 Multiple Mappings

The mapping from characters to collation elements may not be a simple mapping from one character to one collation element: in general, it may map from one to many, from many to one, or from many to many. The following sections illustrate this.

3.1.1.1 Expansions

The Latin letter æ is treated as an independent letter by default. Collations such as English, which may require treating it as equivalent to an <a e> sequence, can tailor the letter to map to a sequence of more than one collation elements, such as in the following example:

In this example, the collation element [06D9.0020.0002] gives the weight values for a, and the collation element [073A.0020.0002] gives the weight values for e.

3.1.1.2 Contractions

Similarly, where ch is treated as a single letter as in traditional Spanish, it is represented as a mapping from two characters to a single collation element, such as in the following example:

In this example, the collation element [0707.0020.0002] has a primary value one greater than the primary value for the letter c by itself, so that the sequence ch will collate after c and before d. The above example shows the result of a tailoring of collation elements to weight sequences of letters as a single unit.

Any character (such as soft hyphen) that is not completely ignorable between two characters of a contraction will cause them to sort as separate characters. Thus a soft hyphen can be used to separate and cause distinct weighting of sequences such as Slovak ch or Danish aa that would normally weight as units.

3.1.1.3 Other Multiple Mappings

Certain characters may both expand and contract: see Section 1.3 Contextual Sensitivity.

3.1.2 French Accents

In some languages (notably French), accents are sorted from the back of the string to the front of the string. This behavior is not marked in the Default Unicode Collation Element Table, but may occur in tailored tables. In such a case, the collation elements for the accents and their base characters are marked as being backwards at Level 2.

3.1.3 Rearrangement

Certain characters are not coded in logical order, such as the Thai vowels เ through ไ and the Lao vowels ເ through ໄ (this list is indicated by the Logical_Order_Exception property in the Unicode Character Database [UCD]). For collation, they are rearranged by swapping with the following character before further processing, because logically they belong afterwards. This is done by providing these sequences as contractions in the Collation Element Table.

3.1.4 Default Values

Both in the Default Unicode Collation Element Table and in typical tailorings, most unaccented letters differ in the primary weights, but have secondary weights (such as a₁) equal to MIN₂. The primary ignorables will have secondary weights greater than MIN₂. Characters that are compatibility or case variants will have equal primary and secondary weights (for example, a₁ = A₁ and a₂ = A₂), but have different tertiary weights (for example, a₃ < A₃). The unmarked characters will have tertiary weights (such as a₃) equal to MIN₃.

However, a well-formed Unicode Collation Element Table does not guarantee that the meaning of a secondary or tertiary weight is uniform across tables. For example, a capital A and katakana ta could both have a tertiary weight of 3.

3.1.5 Collation Graphemes

A collation ordering determines a collation grapheme cluster (also known as a collation grapheme or collation character), which is a sequence of characters that is treated as a primary unit by the ordering. For example, ch is a collation grapheme for a traditional Spanish ordering. These are generally contractions, but may include additional ignorable characters. To determine the boundaries for a collation grapheme starting at a given position, use the following process:

1. Set oldPosition to be equal to position.
2. If position is at the end of the string, return it.
3. Fetch the next collation element(s) mapped to by the character(s) at position.
4. If the collation element(s) contain a non-ignorable and position is not equal to oldPosition, return position.
5. Otherwise set position to be the end of the characters mapped.
6. Loop back to step 2.

For information on the use of collation graphemes, see [UTS18].

3.1.6 Combining Grapheme Joiner

The Unicode Collation Algorithm involves the normalization of Unicode text strings before collation weighting. The U+034F COMBINING GRAPHEME JOINER (CGJ) is ordinarily ignored in collation key weighting in the UCA, but it can be used to block the reordering of combining marks in a string as described in [Unicode]. In that case, its effect can be to invert the order of secondary key weights associated with those combining marks. Because of this, the two strings would have distinct keys, making it possible to treat them distinctly in searching and sorting without having to further tailor either the combining grapheme joiner or the combining marks themselves.

The CGJ can also be used to prevent the formation of contractions in the Unicode Collation Algorithm. Thus, for example, while ch is sorted as a single unit in a tailored Slovak collation, the sequence <c, CGJ, h> will sort as a c followed by an h. This can also be used in German, for example, to force ü to be sorted as u + umlaut (thus u <₂ ü), even where a dictionary sort is being used (which would sort ue <₃ ü). This happens without having to further tailor either the combining grapheme joiner or the sequence.

Note: As in a few other cases in Unicode, such as U+200B ZERO WIDTH SPACE (which is not a white space character), the name of the CGJ is misleading: the usage above is in some sense the inverse of "joining".

Sequences of characters which include the combining grapheme joiner or other completely ignorable characters may also be given tailored weights. Thus the sequence <c, CGJ, h> could be weighted completely differently from the either the contraction ch or how c and h would have sorted without the contraction. However, this application of CGJ is not recommended, because it would produce effects much different than the normal usage above, which is to simply interrupt contractions.

3.2 Default Unicode Collation Element Table

The Default Unicode Collation Element Table is provided in [AllKeys]. This table provides a mapping from characters to collation elements for all the explicitly weighted characters. The mapping lists characters in the order that they would be weighted. Any code points that are not explicitly mentioned in this table are given a derived collation element, as described in Section 7 Weight Derivation. There are three types of mappings:

• Normal. One Unicode character maps to one collation element.
• Expansions. One Unicode character maps to a sequence of collation elements.
• Contractions. A sequence of Unicode characters maps to a sequence of (one or more) collation elements.

Contractions are provided for those instances where a canonical decomposable character needed to be given a distinct primary weight in the main weight table, which implied that the canonically equivalent character sequences should also be given the same weights. These currently include Indic two-part vowels and with some Cyrillic accented characters, to match the expected collating behavior for those scripts. Contractions are also provided for Thai/Lao reordering.

This table is constructed to be consistent with the Unicode Canonical Equivalence algorithm, and to respect the Unicode character properties. It is not, however, merely algorithmically derivable from those data, because the assignment of levels does take into account characteristics of particular scripts. For example, in general the combining marks are Level 1 ignorables; however, the Indic combining vowels are given non-zero Level 1 weights, because they are as significant in sorting as the consonants.

Any character may have variant forms or applied accents which affect collation. Thus, for FULL STOP there are three compatibility variants, a fullwidth form, a compatibility form, and a small form. These get different tertiary weights, accordingly. For more information on how the table was constructed, see Section 7 Weight Derivation.

The following table shows the layout of the collation elements in the Default Unicode Collation Element Table, ordered by primary weight:

For most languages, some degree of tailoring is required to match user expectations. For more information, see Section 5 Tailoring.

3.2.1 File Format

Each of the files consists of a version line followed by an optional variable-weight line, optional backwards lines, and a series of entries, all separated by newlines. A '#' or '%' and any following characters on a line are comments. Whitespace between literals is ignored. The following is an extended BNF description of the format, where "x+" indicates one or more x's, "x*" indicates zero or more x's, "x?" indicates zero or one x, and <char> is a hexadecimal Unicode code value.

<collationElementTable> := <version> 
                           <variable>?
                           <backwards>*
                           <entry>+

The version line is of the form:

@<version> := <major>.<minor>.<variant> <eol>

The variable-weight line has three possible values that may change the weights of collation elements in processing (see Section 3.2.2 Variable Weighting). The default is shifted.

<variable>       := '@variable ' <variableChoice> <eol>
<variableChoice> := 'blanked' | 'non-ignorable' | 'shifted'

A backwards line lists a level that is to be processed in reverse order. A forwards line does the reverse. The default is for lines to be forwards.

<backwards> := ('@backwards ' | '@forwards ') <levelNumber> <eol>

Each entry is a mapping from character(s) to collation element(s), and is of the following form:

<entry>       := <charList> ';' <collElement>+ <eol>
<collElement> := "[" <alt> <char> "." <char> "." <char> ("." <char>)* "]"
<alt>         := "*" | "."

In the Default Unicode Collation Element Table, the comment may contain informative tags.

Here are some selected entries taken from a particular version of the data file. (It may not match the actual values in the current data file.)

0020 ; [*0209.0020.0002.0020] % SPACE
02DA ; [*0209.002B.0002.02DA] % RING ABOVE; COMPATSEQ
0041 ; [.06D9.0020.0008.0041] % LATIN CAPITAL LETTER A
3373 ; [.06D9.0020.0017.0041] [.08C0.0020.0017.0055] % SQUARE AU; COMPATSEQ
00C5 ; [.06D9.002B.0008.00C5] % LATIN CAPITAL LETTER A WITH RING ABOVE; CANONSEQ
212B ; [.06D9.002B.0008.212B] % ANGSTROM SIGN; CANONSEQ
0042 ; [.06EE.0020.0008.0042] % LATIN CAPITAL LETTER B
0043 ; [.0706.0020.0008.0043] % LATIN CAPITAL LETTER C
0106 ; [.0706.0022.0008.0106] % LATIN CAPITAL LETTER C WITH ACUTE; CANONSEQ
0044 ; [.0712.0020.0008.0044] % LATIN CAPITAL LETTER D

The entries in each file are ordered by collation element, not by character, using a SHIFTED comparison. This makes it easy to see the order in which characters would be collated. Although this document describes collation elements as three levels, the file contains a fourth level (as in [.0712.0020.0008.0044]) which is computable. For more information, see Section 3.4 Stability.

Implementations can also add more customizable levels, as discussed above under conformance. For example, an implementation might want to be capable not only of handling the standard Unicode Collation, but also capable of emulating an EBCDIC multi-level ordering (having a fourth-level EBCDIC binary order). 

3.2.2 Variable Weighting

Collation elements that are marked with an asterisk in a Unicode Collation Element Table are known as variable collation elements.

Based on the setting of the variable weighting tag, collation elements can be either treated as ignorables or not. When they are treated as ignorables, then any sequence of ignorable characters that immediately follows the variable collation element is also affected.

There are four possible options for variable weighted characters, with the default being Shifted:

• Blanked: Variable collation elements and any subsequent ignorables are reset so that their weights at levels one through three are zero. For example,
  • SPACE would have the value [.0000.0000.0000]
  • A combining grave accent after a space would have the value [.0000.0000.0000]
  • Capital A would be unchanged, with the value [.06D9.0020.0008]
  • A combining grave accent after a Capital A would be unchanged
• Non-ignorable: Variable collation elements are not reset to ignorable, and get the weights explicitly mentioned in the file.
  • SPACE would have the value [.0209.0020.0002]
  • Capital A would be unchanged, with the value [.06D9.0020.0008]
  • Ignorables are unchanged.
• Shifted: Variable collation elements are set to ignorable at levels one through three. In addition, a new final-level weight is appended, whose value depends on the type:
   

  Type	L4	Examples
  Completely Ignorable	0000	NULL [.0000.0000.0000.0000]
  Ignorable (L1, L2) after Variable	0000	COMBINING GRAVE [.0000.0000.0000.0000]
  Variable	old L1	SPACE [.0000.0000.0000.0209]
  None of the above	FFFF	Capital A [.06D9.0020.0008.FFFF]

  Any subsequent ignorables are reset so that their weights at levels one through four are zero.

  • A combining grave accent after a space would have the value [.0000.0000.0000.0000].
  • A combining grave accent after a Capital A would be unchanged.

  The shifted option provides for improved orderings when the variable collation elements are ignorable, while still only requiring three fields to be stored in memory for each collation element. It does result in somewhat longer sort keys, although they can be compressed (see Section 6.1, Reducing Sort Key Lengths and Section 6.3, Reducing Table Sizes).

• Shift-Trimmed: the same as Shifted, except that all trailing FFFFs are trimmed from the sort key. This option is designed to emulate POSIX behavior.

The following gives an example of the differences between orderings using the different options for variable collation elements. In this example, sample strings differ by the third character: a letter, space, '-' hyphen-minus (002D), or '-' hyphen (2010); followed by an uppercase/lowercase distinction. In the first column below, the words with hyphen-minus and hyphen are separated by deluge, because an l comes between them in Unicode code order. In the second column, they are grouped together but before all letters in the third position. This is because they are no longer ignorable, and have primary values that differ from the letters. In the third column, the hyphen-minus and hyphen are grouped together, and their differences are less significant than between the deluge. In this case, it is because they are ignorable, but their fourth level differences are according to the original primary order, which is more intuitive than Unicode order.

Primaries for variable collation elements are not interleaved with other primary weights. This allows for more compact storage of memory tables. Rather than using a bit per collation element to determine whether the collation element is variable, the implementation only needs to store the maximum primary value for all the variable elements. All collation elements with primary weights from 1 to that maximum are variables; all other collation elements are not.

3.3 Well-Formed Collation Element Tables

A well-formed Collation Element Table meets the following conditions:

1. Except in special cases detailed in Section 6.2, Large Weight Values, no collation element can have a zero weight at Level N and a non-zero weight at Level N-1.

   For example, the secondary can only be ignorable if the primary is ignorable. The reason for this will be explained under Step 4 of the main algorithm.

2. All Level N weights in Level N-1 ignorables must be strictly less than all weights in Level N-2 ignorables.

   For example, secondaries in non-ignorables must be strictly less than those in primary ignorables:

   • Given collation elements [C, D, E] and [0, A, B], where C ≠ 0 and A ≠ 0
   • Then D must be less than A.
3. No variable collation element has an ignorable primary.
4. For all variable collation elements U, V, if there is a collation element W such that U₁ ≤ W₁ and W₁ ≤ V₁, then W is also variable.

   This provision prevents interleaving, mentioned above.

3.4 Stability

The notion of stability in sorting often causes confusion when discussing collation.

A stable sort is one where two records with a field that compares as equal will retain their order if sorted according to that field. This is a property of the sorting algorithm, not the comparison mechanism. For example, a bubble sort is stable, while a quick sort is not. This is a useful property, but cannot be accomplished by modifications to the comparison mechanism or tailorings.

A semi-stable collation is different. It is a collation where strings that are not canonical equivalents will not be judged to be equal. This is a property of comparison, not the sorting algorithm. In general this is not a particularly useful property; its implementation also typically requires extra processing in string comparison or an extra level in sort keys, and thus may degrade performance to little purpose. However, if a semi-stable collation is required, the specified mechanism is to append the NFD form of the original string after the sort key, in Section 4.3, Form Sort Key. See also Appendix A: Deterministic_Sorting.

The fourth-level weights in the Default Collation Element Table can be used to provide an approximation of a semi-stable collation.

Neither one of the above refers to the stability of the Default Collation Element Table itself. For any particular version of the UCA, the contents of that table will remain unchanged. The contents may, however, change between successive versions of the UCA, as new characters are added, or as more information is obtained about existing characters.

Implementers should be aware that using different versions of the UCA, as well as different versions of the Unicode Standard, could result in different collation results of their data. There are numerous ways collation data could vary across versions, for example:

1. Code points that were unassigned in a previous version of the Unicode Standard are now assigned in the current version, and as such, will have a sorting semantic appropriate to the repertoire to which they belong. For example, the code points U+103D0..U+103DF were undefined in Unicode 3.1. Because they were assigned characters in Unicode 3.2, their sorting semantics and respective sorting weights will change.
2. Certain semantics of the Unicode standard could change between versions, such that code points are treated in a manner different than previous versions of the standard (for example, normalization errata).
3. More information is gathered about a particular script, and in order to provide a more linguistically accurate sort, the weight of a code point may need to be adjusted.

Any of these reasons could necessitate a change between versions with regards to sort weights for code points, and as such, it is important that the implementers specify the version of the UCA, as well as the version of the Unicode standard under which their data is sorted.

4 Main Algorithm

The main algorithm has four steps. First is to normalize each input string, second is to produce an array of collation elements for each string, and third is to produce a sort key for each string from the collation elements. Two sort keys can then be compared with a binary comparison; the result is the ordering for the original strings.

4.1 Normalize

Step 1. Produce a normalized form of each input string, applying S1.1.

S1.1 Use the Unicode canonical algorithm to decompose characters according to the canonical mappings. That is, put the string into Normalization Form D (see [UAX15]).

• Conformant implementations may skip this step in certain circumstances: see Section 7, Weight Derivation for more information.

4.2 Produce Array

Step 2. The collation element array is built by sequencing through the normalized form as follows:

Note: A non-starter in a string is called blocked if there is another non-starter of the same canonical combining class or zero between it and the last character of canonical combining class 0.

S2.1 Find the longest initial substring S at each point that has a match in the table.

S2.1.1 If there are any non-starters following S, process each non-starter C.

S2.1.2 If C is not blocked, find if S + C has a match in the table.

S2.1.3 If there is a match, replace S by S + C, and remove C.

S2.2 Fetch the corresponding collation element(s) from the table if there is a match. If there is no match, synthesize a weight as described in Section 7.1, Derived Collation Elements.

S2.3 Process collation elements according to the variable-weight setting, as described in Section 3.2.2, Variable Weighting.

S2.4 Append the collation element(s) to the collation element array.

S2.5 Proceed to the next point in the string (past S).

S2.6 Loop until the end of the string is reached.

Conformant implementations may skip steps 2.1.1 through 2.1.3 if their repertoire of supported character sequences does not require this level of processing.

Note: The reason for considering the extra non-starter C is that otherwise irrelevant characters could interfere with matches in the table. For example, suppose that the contraction <a, combining_ring> (= å) is ordered after z. If a string consists of the three characters <a, combining_ring, combining_cedilla>, then the normalized form is <a, combining_cedilla, combining_ring>, which separates the a from the combining_ring. If we did not have the step of considering the extra non-starter, this string would compare incorrectly as after a and not after z.

If the desired ordering treats <a, combining_cedilla> as a contraction which should take precedence over <a, combining_ring>, then an additional mapping for the combination <a, combining_ring, combining_cedilla> can be introduced to produce this effect.

Note: For conformance to Unicode canonical equivalence, only unblocked non-starters are matched. For example, <a, combining_macron, combining_ring> would compare as after a-macron, and not after z. As in the previous note, additional mappings can be added to customize behavior.

4.3 Form Sort Key

Step 3. The sort key is formed by successively appending weights from the collation element array. The weights are appended from each level in turn, from 1 to 3. (Backwards weights are inserted in reverse order.)

An implementation may allow the maximum level to be set to a smaller level than the available levels in the collation element array. For example, if the maximum level is set to 2, then level 3 and higher weights are not appended to the sort key. Thus any differences at levels 3 and higher will be ignored, leveling any such differences in string comparison.

Here is a more detailed statement of the algorithm:

S3.1 For each weight level L in the collation element array from 1 to the maximum level,

S3.2 If L is not 1, append a level separator*

S3.3 If the collation element table is forwards at level L,

S3.4 For each collation element CE in the array

S3.5 Append CE_L to the sort key if CE_L is non-zero.

S3.6 Else the collation table is backwards at level L, so

S3.7 Form a list of all the non-zero CE_L values.

S3.8 Reverse that list

S3.9 Append the CE_L values from that list to the sort key.

* The level separator is zero (0000), which is guaranteed to be lower than any weight in the resulting sort key. This guarantees that when two strings of unequal length are compared, where the shorter string is a prefix of the longer string, the longer string is always sorted after the shorter (in the absence of special features like contractions). For example:

"abc" < "abcX" where "X" can be any character(s)

S3.10 If a semi-stable sort is required, then after all the level weights have been added, append a copy of the NFD version of the original string. (See also Appendix A: Deterministic_Sorting.)

Example:

collation element array:	[0706.0020.0002], [06D9.0020.0002], [0000.0021.0002], [06EE.0020.0002]
sort key:	0706 06D9 06EE 0000 0020 0020 0021 0020 0000 0002 0002 0002 0002

4.4 Compare

Step 4. Compare the sort keys for each of the input strings, using a binary comparison. This means that:

• Level 3 differences are ignored if there are any Level 1 or 2 differences
• Level 2 differences are ignored if there are any Level 1 differences
• Level 1 differences are never ignored.

Example:

String	Sort Key
cab	0706 06D9 06EE 0000 0020 0020 0020 0000 0002 0002 0002
Cab	0706 06D9 06EE 0000 0020 0020 0020 0000 0008 0002 0002
cáb	0706 06D9 06EE 0000 0020 0020 0021 0020 0000 0002 0002 0002 0002
dab	0712 06D9 06EE 0000 0020 0020 0020 0000 0002 0002 0002

In this example, "cab" <₃ "Cab" <₂ "cáb" <₁ "dab". The differences that produce the ordering are shown by the bold underlined items:

• For the first two strings, the first difference is in 0002 versus 0008 (Level 3)
• For the middle two strings the first difference is in 0020 versus 0021 (Level 2)
• For the last two strings, the first difference is in 0706 versus 0712 (Level 1).

Note: At this point we can explain the reason for only allowing well-formed weights. If ill-formed weights were allowed, the ordering of elements can be incorrectly reflected in the sort key. For example, suppose the secondary weights of the Latin characters were zero (ignorable) and that (as normal) the primary weights of case-variants are equal: that is, a₁ = A₁. Then the following incorrect keys would be generated:

1. "áe" = <a, acute, e> => [a₁ e₁ 0000 acute₂ 0000 a₃ acute₃ e₃...]
2. "Aé" = <A, e, acute> => [a₁ e₁ 0000 acute₂ 0000 A₃ acute₃ e₃...]

Because the secondary weights for a, A, and e are lost in forming the sort key, the relative order of the acute is also lost, resulting in an incorrect ordering based solely on the case of A versus a. With well-formed weights, this does not happen, and you get the following correct ordering:

1. "Aé" = <A, e, acute> => [a₁ e₁ 0000 a₂ e₂ acute₂ 0000 a₃ acute₃ e₃...]
2. "áe" = <a, acute, e> => [a₁ e₁ 0000 a₂ acute₂ e₂ 0000 A₃ acute₃ e₃...]

However, there are circumstances--typically in expansions--where higher-level weights in collation elements can be zeroed (resulting in ill-formed collation elements) without consequence (see Section 6.2, Large Weight Values). Implementations are free to do this as long as they produce the same result as with well-formed tables.

5 Tailoring

Tailoring is any well-defined syntax that takes the Default Unicode Collation Element Table and produces another well-formed Unicode Collation Element Table. This syntax can provide linguistically-accurate collation, if desired. Such syntax will usually allow for the following capabilities:

1. Reordering any character (or contraction) with respect to others in the standard ordering. Such a reordering can represent a Level 1 difference, Level 2 difference, Level 3 difference, or identity (in levels 1 to 3). Because such reordering includes sequences, arbitrary multiple mappings can be specified.

2. Setting the secondary level to be backwards (French) or forwards (normal).

3. Set variable weighting options.

4. Customizing the exact list of variable collation elements.

For examples of tailoring syntax, see Section 6.9, Tailoring Example: Java.

5.1 Preprocessing

In addition to tailoring, some implementations may choose to preprocess the text for special purposes. Once such preprocessing is done, the standard algorithm can be applied.

Examples include:

• mapping "McBeth" to "MacBeth"

• mapping "St." to "Street" or "Saint", depending on the context

• padding digits with zeros to approximate numeric order

• dropping articles, such as a or the

• using extra information, such as pronunciation data for Han characters

Such preprocessing is outside of the scope of this document.

6 Implementation Notes

As noted above for efficiency, implementations may vary from this logical algorithm as long as they produce the same result. The following items discuss various techniques that can be used for reducing sort key length, reducing table sizes, customizing for additional environments, searching, and other topics.

6.1 Reducing Sort Key Lengths

The following discuss methods of reducing sort key lengths. If these methods are applied to all of the sort keys produced by an implementation, they can result in significantly shorter and more efficient sort keys while retaining the same ordering.

6.1.1 Eliminating Level Separators

Level separators are not needed between two levels in the sort key, if the weights are properly chosen. For example, if all L3 weights are less than all L2 weights, then no level separator is needed between them. If there is a fourth level, then the separator before it needs to be retained.

For example, here is a sort key with these level separators removed.

While this technique is relatively easy to implement, it can interfere with other compression methods.

6.1.2 L2/L3 in 8 Bits

The L2 and L3 weights commonly are small values. Where that condition occurs for all possible values, they can then be represented as single 8-bit quantities.

Here is the above example with both these changes (and grouping by bytes). Note that the separator has to remain after the primary weight when combining these techniques. If any separators are retained (such as before the fourth level), they need to have the same width as the previous level.

6.1.3 Machine Words

The sort key can be represented as an array of different quantities depending on the machine architecture. For example, comparisons as arrays of 32-bit quantities may be much faster on some machines. If this is done, the original is to be padded with trailing (not leading) zeros as necessary.

6.1.4 Run-Length Compression

Generally sort keys do not differ much in the secondary or tertiary weights, so you tend to end up with keys with a lot of repetition. This also occurs with quaternary weights generated with the shifted parameter. By the structure of the collation element tables, there are also many weights that are never assigned at a given level in the sort key. You can take advantage of these regularities in these sequences to compact the length — while retaining the same sort sequence — by using the following technique. (There are other techniques that can also be used.)

This is a logical statement of the process: the actual implementation can be much faster and performed as the sort key is being generated.

• For each level n, find the most common value COMMON produced at that level by the collation element table for typical strings. For example, for the Default Unicode Collation Element Table, this is:
  • 0020 for the secondaries (corresponding to unaccented characters)
  • 0002 for tertiaries (corresponding to lowercase or unmarked letters)
  • FFFF for quaternaries (corresponding to non-ignorables with the shifted parameter)
• Reassign the weights in the collation element table at level n to create a gap of size GAP above COMMON. Typically for secondaries or tertiaries this is done after the values have been reduced to a byte range by the above methods. Here is a mapping that moves weights up or down to create a gap in a byte range.
  w -> w + 01 - MIN, for MIN <= w < COMMON
  w -> w + FF - MAX, for COMMON < w <= MAX
• At this point, weights go from 1 to MINTOP, and from MAXBOTTOM to MAX. These new unassigned values are used to run-length encode sequences of COMMON weights.
• When generating a sort key, look for maximal sequences of m COMMON values in a row. Let W be the weight right after the sequence.
  • If W < COMMON (or there is no W), replace the sequence by a synthetic low weight equal to (MINTOP + m).
  • If W > COMMON, replace the sequence by a synthetic high weight equal to (MAXBOTTOM - m).

  In the following example, the low weights are 01, 02; the high weights are FE, FF; and the common weight is 77.

Examples

01
02
77 01
77 02
77 77 01
77 77 02
77 77 77 01
77 77 77 02
...
77 77 77 FE
77 77 77 FF
77 77 FE
77 77 FF
77 FE
77 FF
FE
FF

01
02
03 01
03 02
04 01
04 02
05 01
05 02
...
FB FE
FB FF
FC FE
FC FF
FD FE
FD FF
FE
FF

• The last step is a bit too simple, because we have to keep the synthetic weights from colliding with other values with long strings of COMMON weights. This is done by using a sequence of synthetic weights, absorbing as much length into each one as possible. This is done by defining a value BOUND between MINTOP and MAXBOTTOM. The exact value for BOUND can be chosen based on the expected frequency of synthetic low weights versus high weights for the particular collation element table.
  • If a synthetic low weight would not be less than BOUND, use a sequence of low weights of the form (BOUND-1)..(BOUND-1)(MINTOP + remainder) to express the length of the sequence.
  • Similarly, if a synthetic high weight would be less than BOUND, use a sequence of high weights of the form (BOUND)..(BOUND)(MAXBOTTOM - remainder).

This process results in keys that are never longer than the original, are generally much shorter, and result in the same comparisons.

6.2 Large Weight Values

If a collation sequence requires more than 65,535 weight values (or 65,024 values where zero bytes are avoided), this can still be accommodated by using multiple collation elements for a single character. For example, suppose that 50,000 UTF-16 supplementary characters are assigned in a particular implementation, and that these are to be sorted after X. Simply assign them all dual collation elements of the form

[(X1+1).0000.0000], [yyyy.zzzz.wwww]

They will then sort properly with respect to each other and to the rest of the characters. (The first collation element is one of the instances where ill-formed collation elements are allowed. Because the second collation element is well-formed and the first element will only occur in combination, ordering is preserved.)

6.3 Reducing Table Sizes

The data tables required for full Unicode sorting can be quite sizable. This section discusses ways to significantly reduce the table size in memory. These have very important implications for implementations.

6.3.1 Contiguous Weight Ranges

The Default Unicode Collation Element Table has secondary weights that are greater than 00FF. This is the result of the derivation described in Section 7, Weight Derivation. However, these values can be compacted to a range of values that do not exceed 00FF. Whenever collation elements have different primary weights, the ordering of their secondary weights is immaterial. Thus all of the secondaries that share a single primary can be renumbered to a contiguous range without affecting the resulting order. Composite characters still need to be handled correctly if normalization is avoided as discussed in Section 7, Weight Derivation.

For example, for the primary value 0820 (for the letter O), there are 31 distinct secondary values ranging from 0020 to 012D. These can be renumbered to the contiguous range from 0020 to 003F, which is less than 00FF.

6.3.2 Escape Hatch

Although the secondary and tertiary weights for the Default Unicode Collation Element Table can both fit within one byte, of course, any particular tailored table could conceivably end up with secondary or tertiary weights that exceed what can be contained in a single byte. However, the same technique used for large weight values can also be used for implementations that do not want to handle more than 00FF values for a particular weight.

For example, the Java collation implementation only stores 8-bit quantities in level 2 and level 3. However, characters can be given L2 or L3 weights with greater values by using a series of two collation elements. For example, with characters requiring 2,000 weights at L2, then 248 characters can be given single keys, while 1,792 are given two collation keys of the form [yyyy.00zz.00ww] [0000.00nn.0000]. (The 248 can be chosen to be the higher frequency characters!)

6.3.3 Leveraging Unicode Tables

Because all canonically decomposable characters are decomposed in Step 1.1, no collation elements need to be supplied for them. This includes a very large number of characters, not only a large number of Latin and Greek characters, but also the very large number of Hangul Syllables.

Because most compatibility decomposable characters in the default table can be algorithmically generated from the decomposition, no collation elements need to be stored for those decomposable characters: the collation elements can be generated on the fly with only a few exceptions entered in the table. The collation elements for the Han characters (unless tailored) are algorithmically derived; no collation elements need to be stored for them either. For more information, see Section 7, Weight Derivation.

This means that only a small fraction of the total number of Unicode characters need to have an explicit collation element. This can cut down the memory storage considerably.

6.3.4 Reducing the Repertoire

If characters are not fully supported by an implementation, then their code points can be treated as if they were unassigned. This allows them to be algorithmically constructed from code point values instead of including them in a table. This can significantly reduce the size of the required tables. See Section 7.1, Derived Collation Elements for more information.

6.3.5 Memory Table Size

Applying the above techniques, an implementation can thus safely pack all of the data for a collation element into a single 32-bit quantity: 16 for the primary, 8 for the secondary and 8 for the tertiary. Then applying techniques such as the Two-Stage table approach described in Section 5.7, Compression of [Unicode], the mapping table from characters to collation elements can both fast and small. For an example of how this can be done, see Section 6.10, Flat File Example.

6.4 Avoiding Zero Bytes

If the resulting sort key is to be a C-string, then zero bytes must be avoided. This can be done by:

• using the value 0101₁₆ for the level separator instead of 0000.
• preprocessing the weight values to avoid zero bytes, such as remapping as follows:
  • x => 0101₁₆ + (x / 255)*256 + (x % 255)
• Where the values are limited to 8-bit quantities (as discussed above), zero bytes are even more easily avoided by just using 01 as the level separator (where one is necessary), and mapping weights by
  • x => 01 + x.

6.5 Avoiding Normalization

Implementations that do not handle separate combining marks can map decomposable characters (such as "à") to single collation elements with different Level 2 weights for the different accents. For more information, see Section 7, Weight Derivation. However, this does require including the mappings for these characters in the collation table, which will increase the size substantially unless the collation elements for the Hangul Syllables are computed algorithmically.

6.6 Case Comparisons

In some languages, it is common to sort lowercase before uppercase; in other languages this is reversed. Often this is more dependent on the individual concerned, and is not standard across a single language. It is strongly recommended that implementations provide parameterization that allow uppercase to be sorted before lowercase, and provide information as to the standard (if any) for particular countries. This can easily be done to the Default Unicode Collation Element Table before tailoring by remapping the L3 weights (see Section 7, Weight Derivation). It can be done after tailoring by finding the case pairs and swapping the collation elements.

6.7 Incremental Comparison

Implementations do not actually have to produce full sort keys. Collation elements can be incrementally generated as needed from two strings, and compared with an algorithm that produces the same results as sort keys would have. The choice of which algorithm to use depends on the number of comparisons between the same strings.

• Generally incremental comparison is more efficient than producing full sort keys if strings are only to be compared once and if they are generally dissimilar, because differences are caught in the first few characters without having to process the entire string.
• Generally incremental comparison is less efficient than producing full sort keys if items are to be compared multiple times.

However, it is very tricky to produce an incremental comparison that produces correct results. For example, some implementations have not even been transitive! Be sure to test any code for incremental comparison thoroughly.

6.8 Catching Mismatches

Sort keys from two different tailored collations cannot be compared, because the weights may end up being rearranged arbitrarily. To catch this case, implementations can produce a hash value from the collation data, and prepend it to the sort key. Except in extremely rare circumstances, this will distinguish the sort keys. The implementation then has the opportunity to signal an error.

6.9 Tailoring Example: Java

Java 2 implements a number of the tailoring features described in this document. The following summarizes these features (for more information, see Collator on [JavaCollator]).

1. Java does not use a default table in the Unicode Collation Element format: instead it always uses a tailoring syntax. Here is a description of the entries:

Either x or y can be more than one character, to handle contractions and expansions. NULL is completely ignorable, so by using the above operations, various levels of ignorable characters can be specified.

2. Entries can be abbreviated in a number of ways:

• They do not need to be separated by newlines.
• Characters can be specified directly, instead of using their hexadecimal Unicode values.
• Wherever you have rules of the form "x < y & y < z", you can omit "& y", leaving just "x < y < z".

These can be done successively, so the following are equivalent in ordering.

0061 ; [.0001.0001.0001] % a
0040 ; [.0001.0001.0002] % A
00E0 ; [.0001.0002.0001] % à
00C0 ; [.0001.0002.0002] % à
0042 ; [.0002.0001.0001] % b
0062 ; [.0002.0001.0002] % B

For a discussion of more powerful tailoring features, see [ICUCollator]. For details on a common XML format for tailorings, see [LDML].

6.10 Flat File Example

The following is a sample flat-file binary layout and sample code for collation data. It is included only for illustration. The table is used to generate collation elements from characters, either going forwards or backwards, and detect the start of a contraction. The backwards generation is for searching backwards or Boyer-Moore-style searching; the contraction detection is for random access.

In the file representation, ints are 32 bit values, shorts are 16, bytes are 8 bits. Negatives are two's-complement. For alignment, the ends of all arrays are padded out to multiples of 32 bits. The signature determines endianness. The locale uses an ASCII representation for the Java locale: a 2 byte ISO language code, optionally followed by '_' and 2 byte ISO country code, followed optionally by a series of variant tags separated by '_'; any unused bytes are zero.

6.10.1 Collation Element Format

• 'real' collationElement
  • 16 bits primary (FFE0..FFFF not allowed)
  • 8 bits secondary
  • 8 bits tertiary
• expansionsOffset
  • 12 bits = FFF
  • 20 bits = offset (allows for 1,048,576 items)
• contractionsOffset
  • 12 bits = FFE
  • 20 bits = offset (allows for 1,048,576 items)

An alternative structure would have the offsets be byte offsets from the start of the table, instead of indexes into the arrays. That would limit the size of the table, but use fewer machine instructions.

6.10.2 Sample Code

The following is a pseudo code using this table for the required operations. Although using Java syntax in general, the code example uses arrays so as to be more familiar to users of C and C++. The code is presented for illustration only; it is not a complete statement of the algorithm. 

char[] input;   // input buffer (i)
int inputPos;   // position in input buffer (io)
int[] output;   // output buffer (o)
int outputPos;  // position in output buffer (io)
boolean forwards;   // 0 for forwards, 1 for backwards (i)
    
/**
* Reads characters from input, writes collation elements in output
*/
void getCollationElements() {
    char c = input[inputPos++];
    int ce = collationElements[index[c>>8] + c&0xFF];
    processCE(ce);
}
    
/**
* Normally just returns ce. However, special forms indicate that
* the ce is actually an expansion, or that we have to search
* to see if the character was part of a contraction.
* Expansions use 
*/
void processCE(int ce) {
    if (ce < 0xFFF00000) {
        output[outputPos++] = ce;
    } else if (ce >= 0xFFE00000) {
        copyExpansions(ce & 0x7FFFFF);
    } else {
        searchContractions(ce & 0x7FFFFF);
    }
}
    
/**
* Search through a contraction sublist to see if there is a match.
* Because the list is sorted, we can exit if our value is too high.<p>
* Because we have a length, we could implement this as a
* binary search, although we do not right now.<p>
* If we do find a match, we need to recurse. That's how "abc" would
* be handled.<p>
* If we fail, we return the non-matching case. That can be an expansion
* itself (it would never be a contraction).
*/
void searchContractions(int offset) {
    if (forwards) inputPos++;
    else offset += input[inputPos++];
    short goal = (short)input[inputPos++];
    int limit = offset + contractionMatches[offset];
    for (int i = offset; i < limit; ++i) {
        short cc = contractionMatches[i];
        if (cc > goal) { // definitely failed
            processCE(contractionCEs[offset]);
            break;
        } else if (cc == goal) { // found match
            processCE(contractionCEs[i]);
            break;
        }
    }
}
    
/**
* Copy the expansion collation elements up to the terminator.
* Do not use 00000000 as a terminator, because that may be a valid CE.
* These elements do not recurse.
*/
void copyExpansions (int offset) {
    int ce = expansions[offset++];
    while (ce != 0xFFFFFFFF) {
        output[outputPos++] = ce;
        ce = expansions[offset++];
    }
}
    
/**
* For random access, gets the start of a collation element.
* Any non-initial characters are in a sorted list, so
* we just check that list.<p>
* Because we have a length, we could implement this as a
* binary search, although we do not right now.
*/
int getCollationElementStart(char[] buffer, int offset) {
    int i;
    main:
    for (i = offset; i > 0; --i) {
        char c = buffer[i];
        for (int j = 0; j < nonInitialsLength; ++j) {
            char n = nonInitials[j];
            if (c == n) continue main;
            if (c > n) break main;
        }
        break;
    }
    return i;
}

7 Weight Derivation

This section describes the generation of the Unicode Default Unicode Collation Element Table, and the assignment of weights to code points that are not explicitly mentioned in a Collation Element Table. This uses information from the Unicode Character Database [UCD].

7.1 Derived Collation Elements

CJK Ideographs and Hangul Syllables are not explicitly mentioned in the default table. CJK ideographs are mapped to collation elements that are derived from their Unicode code point value as described in Section 7.1.3, Implicit Weights.

The collation algorithm requires that Hangul Syllables be decomposed. However, if the table is tailored so that the primary weights for Hangul Jamo (and all related characters) are adjusted, then the Hangul Syllables can be left as single code points and treated in the same way as CJK ideographs. That will provide a collation which is approximately the same as UCA, and may be sufficient in environments where individual jamo are not expected.

The adjustment is to move each initial jamo (and related characters) to have a primary weight corresponding to the first syllables starting with that jamo, and make all non-initial jamo (and related characters) be ignorable at a primary level.

7.1.1 Illegal Code Points

Certain code points are illegal in a data stream. These include noncharacters (code points with the Noncharacter_Code_Point property in the Unicode Character Database [UCD]), unpaired surrogates (code points with the General_Category property Cs), and out-of-range values (< 0 or > 10FFFF). Implementations may also choose to treat these as error conditions and respond appropriately, such as by throwing an exception.

If they are not treated as an error condition, they must be mapped to [.0000.0000.0000.], and thus ignored.

7.1.2 Legal Code Coints

Any other legal code point that is not explicitly mentioned in the table is mapped a sequence of two collation elements as described in Section 7.1.3, Implicit Weights.

7.1.3 Implicit Weights

A character is mapped to an implicit weight in the following way. The result of this process consists of collation elements that are sorted in code point order, that do not collide with any explicit values in the table, and that can be placed anywhere (for example, at BASE) with respect to the explicit collation element mappings (by default, they go after all explicit collation elements).

To derive the collation elements, the code point CP is separated into two parts, chosen for the correct numerical properties. First, separate off the top 6 bits of the code point. Because code points can go from 0 to 10FFFF, this will have values from 0 to 21₁₆ (= 33₁₀). Add this to the special value BASE.

AAAA = BASE + (CP >> 15);

Now take the bottom 15 bits of the code point. Turn the top bit on, so that the value is non-zero.

BBBB = (CP & 0x7FFF) | 0x8000;

The mapping given to CP is then given by:

CP => [.AAAA.0020.0002.][.BBBB.0000.0000.]

If a fourth or higher weights are used, then the same pattern is used: they are set to a non-zero value, and so on in the first collation element and zero in the second. (Because all distinct code points have different AAAA/BBBB combination, the exact non-zero value does not matter.)

The value for BASE depends on the type of character:

These results make AAAA (in each case) larger than any explicit primary weight; thus the implicit weights will not collide with explicit weights. It is not generally necessary to tailor these values to be within the range of explicit weights. However if this is done, the explicit primary weights must be shifted so that none are between each of the BASE values and BASE + 34.

7.1.4 Trailing Weights

The range of primary weights from FC00 to FFFF is available for use as trailing weights especially for the case of Hangul Syllables. These syllables can be of the form LL*VV*T*: that is, one or more Lead jamo, followed by one or more Vowel jamo, followed optional by any number of Trail jamos. For more information, see Section 3.12 Conjoining Jamo Behavior in [Unicode].

Trailing weights are for characters that are given primary weights, but grouped as a unit together with a previous character, such as U+1160 HANGUL JUNGSEONG FILLER  through U+11F9 HANGUL JONGSEONG YEORINHIEUH. By tailoring these characters in this range, the units are ordered independently of subsequent characters with higher weights. Otherwise problems may occur, such as in the following example.

In this example, the symbols {G}, {A}, and {K} represent letters in a script where syllables (or other sequences of characters) are sorted as units. By proper choice of weights for the individual letters, the syllables can be ordered correctly. But the weights of the following letters may cause syllables of different lengths to change order. Thus {G}{A}{K} comes after GA in Case 1. But in Case 2, it comes before. That is, the order of these two syllables would be reversed when each is followed by a CJK character: in this case, U+56D7 (囗).

7.1.4.1 Hangul Trailing Weights

Hangul is in a rather unique position, because of the large number of the precomposed characters, and because those precomposed characters are the normal (NFC) form of interchanged text. For Hangul syllables to sort correctly, either the UCA data must be tailored or the UCA algorithm (and data) must be tailored. The following are possible solutions:

Data Method

1. Tailor the Vs and Ts to be Trailing Weights, with the ordering T < V
2. Tailor each sequence of multiple L's that occurs in the repertoire as a contraction, with an independent primary weight after any prefix's weight
   • This means that if L₁ has a primary weight of 555, and L₂ has 559, then L₁L₁ would have to be given a weight from 556 to 558.

Terminator Method

1. Add an internal terminator primary weight (Ⓣ).
2. Tailor all Jamo so that Ⓣ < T < V < L
3. Algorithmically add the terminator primary weight (Ⓣ) to the end of every standard Hangul syllable.
   • This is done by adding the terminator between any pairs of characters that are not kept together according to the rules of Section 3.12 Conjoining Jamo Behavior of [Unicode]

Interleaving Method

1. Generate a modified weight table:
   1. Assign a weight to each precomposed Hangul Syllable character, with a 1-weight gap between each one. (see Section 6.2, Large Weight Values)
   2. Give each Jamo a 1-byte internal weight. Also add an internal terminator 1-byte weight (Ⓣ). These are assigned so that all Ⓣ < T <  V < L.
      • These weights are separate from the default weights, and are just used internally.
2. When any string of Jamo and/or Hangul Syllables is encountered, break it into syllables according to the rules of Section 3.12 Conjoining Jamo Behavior of [Unicode]. Process each syllable separately:
   1. If a syllable is canonically equivalent to one of the precomposed Hangul Syllables, then just assign the weight as above
   2. If not, then find the greatest syllable that it is greater than; call that the base syllable. Generate a weight sequence corresponding to the following gap weight, followed by all the Jamo weight bytes, followed by the terminator byte.

Each of these methods can correctly represent the ordering of all modern and ancient Hangul Syllables, but there are implementation trade-offs between them. These trade-offs can have a significant impact on the acceptability of the implementation, because substantially longer sort keys will cause significant performance degradations and database index bloat.

Note: If the repertoire of supported Hangul syllables is limited to modern syllables (those of the form LV or LVT), then all of these become simpler.

The Data method provides for the following order of weights, where the X_b are all the scripts sorted before Hangul, and the X_a are all those sorted after.

Xb

L

Xa

T

V

This ordering gives the right results among the following:

Chars	Weights				Comments
L1V1Xa	WL1	WV1	WXa
L1V1L...	WL1	WV1	WLn	...
L1V1Xb	WL1	WV1	WXb
L1V1T1	WL1	WV1	WT1		Works because WT > all WX and WL
L1V1V2	WL1	WV1	WV2		Works because WV > all WT
L1L2V1	WL1L2	WV1			Works if L1L2 is a contraction.

The disadvantages of the Data method are that the weights for T and V are separated from those of L, which can cause problems for sort-key compression, and that a combination of LL that is outside the contraction table will not sort properly.

The Terminator method would assign the following weights:

Ⓣ

Xb

T

V

L

Xa

This ordering gives the right results among the following:

Chars	Weights					Comments
L1V1Xa	WL1	WV1	Ⓣ	WXa
L1V1Ln...	WL1	WV1	Ⓣ	WLn	...
L1V1Xb	WL1	WV1	Ⓣ	WXb
L1V1T1	WL1	WV1	WT1	Ⓣ		Works because WT > all WX and Ⓣ
L1V1V2	WL1	WV1	WV2	Ⓣ		Works because WV > all WT
L1L2V1	WL1	WL2	WV1	Ⓣ		Works because WL > all WV

The disadvantages of the Terminator method are that an extra weight is added to all Hangul syllables, increasing the length of sort keys by roughly 40%, and the fact that the terminator weight is non-contiguous can disable sort-key compression.

The Interleaving method provides for the following assignment of weights. W_n represents the weight of a Hangul Syllable, and W_n' is the weight of the gap right after it. The L, V, T weights will only occur after a W, and thus can be considered part of an entire weight.

Xb

W

Xa

byte weights:

Ⓣ

T

V

L

This ordering gives the right results among the following:

Chars	Weights			Comments
L1V1Xa	Wn	Xa
L1V1Ln...	Wn	Wk	...	The Ln will start another syllable
L1V1Xb	Wn	Xb
L1V1T1	Wm			Works because Wm > Wn
L1V1V2	Wm'L1V1V2Ⓣ			Works because Wm'>Wm
L1L2V1	Wm'L1L2V1Ⓣ			Works because the byte weight for L2 > all V

The Interleaving method is somewhat more complex than the others, but produces the shortest sort keys for all of the precomposed Hangul Syllables, so for normal text it will have the shortest sort keys. If there were a large percentage of ancient Hangul Syllables, the sort keys would be longer than other methods.

Note: The Unicode Consortium recognizes that one of these solutions should be implemented in the standard UCA algorithm and tables, but is attempting to work out a common approach to the problem with the ISO SC22 WG20 group, which takes considerable time. In the meantime, one of these approaches can be used for correct ordering.

7.2 Canonical Decompositions

Characters with canonical decompositions do not require mappings to collation elements, because Step 1.1 maps them to collation elements based upon their decompositions. However, they may be given mappings to collation elements anyway. The weights in those collation elements must be computed in such a way they will sort in the same relative location as if the characters were decomposed using Normalization Form D. By including these mappings, this allows an implementation handling a restricted repertoire of supported characters to compare strings correctly without performing the normalization in Step 1.1 of the algorithm.

A combining character sequence is called impeding if it contains any conjoining Jamo, or if it contains an L1-ignorable combining mark and there is some character that canonically decomposes to a sequence containing the same base character. For example, the sequence <a, cedilla> is an impediment, because cedilla is an L1-ignorable character, and there is some character (for example, a-grave) that decomposes to a sequence containing the same base letter a. Note that although strings in Normalization Form C generally do not contain impeding sequences, there is nothing prohibiting them from containing them.

Note: Conformant implementations that do not support impeding character sequences as part of their repertoire can avoid performing Normalization Form D processing as part of collation.

7.3 Compatibility Decompositions

As remarked above, most characters with compatibility decompositions can have collation elements computed at runtime to save space, duplicating the work that was done to compute the Default Unicode Collation Element Table. This can be an important savings in memory space. The process works as follows.

1. Derive the decomposition. For example,

2475 PARENTHESIZED DIGIT TWO => 0028, 0032, 0029

2. Get the CE for each character in the decomposition. For example,

0028 [*023D.0020.0002] % LEFT PARENTHESIS
0032 [.06C8.0020.0002] % DIGIT TWO
0029 [*023E.0020.0002] % RIGHT PARENTHESIS

3. Set the first two L3 values to be lookup (L3), where the lookup uses the table in Section 7.3.1, Tertiary Weight Table. Set the remaining L3 values to MAX (which in the default table is 001F). For example,

0028 [*023D.0020.0004] % LEFT PARENTHESIS
0032 [.06C8.0020.0004] % DIGIT TWO
0029 [*023E.0020.001F] % RIGHT PARENTHESIS

4. Concatenate the result to produce the sequence of collation elements that the character maps to. For example,

2475 [*023D.0020.0004] [.06C8.0020.0004] [*023E.0020.0004] 

Some characters cannot be computed in this way. They must be filtered out of the default table and given specific values. For example,

017F [.085D.00FD.0004.017F] % LATIN SMALL LETTER LONG S; COMPAT

7.3.1 Tertiary Weight Table

Characters are given tertiary weights according to the following table. The Decomposition Type is from the Unicode Character Database [UCD]. The Condition is either based on the General Category or on a specific list of characters. The weights are from MIN = 2 to MAX = 1F₁₆, excluding 7, which is not used for historical reasons. The Samples show some minimal values that are distinguished by the different weights. All values are distinguished from MIN except for the Katakana/Hiragana values.

8 Searching and Matching

The collation elements can also be used for matching string and for searching for strings, so that a proper native-language match is produced. For example, "ß" will properly match against "ss". Users of search algorithms should be allowed to modify the comparison strength, thus excluding differences at less significant levels. This is especially useful for searching, but can also apply to comparison.

Excluding differences at Level 3 has the effect of ignoring case and compatibility format distinctions between letters when searching. Excluding differences at Level 2 has the effect of ignoring accentual distinctions when searching.

Conceptually, a string matches some target where a substring of the target has the same sort key. But there are a number of complications:

1. The lengths of matching strings may differ: "aa" and "å" would match in Danish.
2. Because of ignorables (at different levels), there are different possible positions where a string matches, depending on the attribute settings of the collation. For example, if hyphens are ignorable for a certain collation, then "abc" will match "abc", "abc-", "-abc-", and so on.
3. Suppose that the collator has contractions, and that a contraction spans the boundary of the match. Whether or not it is considered a match may depend on user settings, just as users are given a "Whole Words" option in searching. So in a language where "ch" is a contraction, "bac" would not match in "bach" (given the proper user setting).
4. Similarly, combining character sequences may need to be taken into account. Users may not want a search for "abc" to match in "...abç..." (with a cedilla on the c). However, this may also depend on language and user customization.
5. The above two conditions can be considered part of a general condition: "Whole Characters Only"; very similar to the common "Whole Words Only" checkbox that is included in most search dialog boxes. (For more information on grapheme clusters, see [UTS18].
6. If the matching does not check for "Whole Grapheme Clusters Only", then some other complications may occur. For example, suppose that P is "x^", and Q is "x ^¸". Because the cedilla and circumflex can be written in arbitrary order and still be equivalent, one would expect to find a match for P in Q. A canonically-equivalent matching process requires special processing at the boundaries to check for situations like this. (It does not require such special processing within the P or the substring of Q because collation is defined to observe canonical equivalence.)

The following are used to provide a clear definition of searching and matching that deal with the above complications:

DS1. Define S[start,end] to be the substring of S that includes the character after the offset start up to the character before offset end. For example, if S is "abcd", then S[1,3] is "bc".

DS1a. A boundary condition is a test imposed on an offset within a string. Examples include Whole Grapheme Cluster Search and Whole Word Search, as defined in UAX #29. See [UAX29]).

By using grapheme-complete conditions, contractions and combining sequences are not interrupted. This also avoids the need to present visually discontiguous selections to the user (except for BIDI text).

Suppose there is a collation C, a pattern string P and a target string Q, and a boundary condition B. C has some particular set of attributes, such as a strength setting, and choice of variable weighting.

DS2. There is a match according to C for P within Q[s,e] if and only if C generates the same sort key for P as for Q[s,e], and the offsets s and e meet the condition B.

DS2a. A match is grapheme-complete if B requires that the offset be at a grapheme cluster boundary. Note that Whole Word Search as defined in UAX #29 is grapheme complete. See [UAX29]).

DS3. There is a canonical match according to C for P within Q[s,e] if and only if there is some Q', canonically equivalent to Q[s,e], and some s' and e' such that P matches within Q[s',e'].

DS4. The match is minimal if for all positive i and j, there is no match at Q[s+i,e-j]. In such a case, we also say that P minimal matchs at Q[s,e].

DS4a. The match is medial when it contains the minimal match, and is extended beyond whenever there is a successive binary match between the extra characters in pattern and target.

DS4b. The match is maximal if for all positive i and j, there is no match at Q[s-i,e+j]. In such a case, we also say that P maximal matchs at Q[s,e].

As an example of the differences between these, consider the following case, where the collation strength is set to ignore punctuation and case:

By using minimal, maximal, or medial matches, the issue with ignorables is avoided. Medial matches tend to match user expectations the best.

When an additional condition is set on the match, the types (minimal, maximal, medial) are based on the matches that meet that condition. Consider the following.

Thus if the condition is Whole Grapheme, then the matches are restricted to "abc¸|-°|d", thus discarding match positions that would not be on a grapheme cluster boundary. Thus the minimal match would be "abc¸|-°d"

DS6. The first forward match for P in Q starting at b is the least offset s greater than or equal to b such that for some e, P matches within Q[s,e].

DS7. The first backward match for P in Q starting at b is the greatest offset e less than or equal to b such that for some s, P matches within Q[s,e].

In DS6 and DS7, matches can be minimal, medial, or maximal; the only requirement is that the combination in use in DS6 and DS7 be specified. Of course, a possible match can also be rejected on the basis of other conditions, such as being grapheme-complete or applying Whole Word Search, as described in [UAX29]).

Appendix A: Deterministic Sorting

There is often a good deal of confusion about what is meant by the terms "stable" or "deterministic" when applied to sorting or comparison. This confusion in terms often leads people to make mistakes in their software architecture, or make choices of language-sensitive comparison options that have significant impact in terms of performance and footprint, and yet do not give the results that users expect.

A.1 Stable Sort

A stable sort is one where two records will retain their order when sorted according to a particular field, even when the two fields have the same contents. Thus those two records come out in the same relative order that they were in before sorting, although their positions relative to other records may change. Importantly, this is a property of the sorting algorithm, not the comparison mechanism.

Two examples of differing sorting algorithms are Quick Sort and Merge. Quick Sort is not stable while Merge Sort is stable. (A Bubble Sort, as typically implemented, is also stable.)

• For background on the names and characteristics of different sorting methods, see [SortAlg]
• For a definition of stable sorting, see [Unstable]

 Suppose that you have the following records and you sort on the Last_Name field only:

As you see from the above, the Quicksort algorithm is not stable; the records 1 and 2 are not in the same order they were in before sorting.

A stable sort is often desired; for one thing, it allows records to be successively sorting according to different fields, and retain the correct lexigraphic order. Thus with a stable sort, one could all the records by First_Name, then sort all the records by Last_Name, giving the desired results: that all records would be sorted by Last_Name, and where the Last_Names are the same, sorted by First_Name.

A.2 Deterministic Sort

A deterministic sort is a very different beast. This is a sort algorithm that returns the same results each time. On the face of it, it would seem odd for any sort algorithm to not be deterministic, but there are examples of real-world sort algorithms that aren't.

The key concept is that these sort algorithms are deterministic when two records have unequal fields, but they may return different results at different times when two records have equal fields.

For example, a classic Quick Sort algorithm works recursively on ranges of records. For any given range of records, it takes the first element as the pivot element. We're not going to explain the details here, but that algorithm performs badly with input data that happens to be sorted (or mostly sorted). A randomized Quick Sort, which picks a random element as the pivot, can on average be faster. The results it gets are not deterministic; from exactly the same input, different results can be output:

As another example, multiprocessor sorting algorithms can be non-deterministic. The work of sorting different blocks of data are farmed out to different processors and then merged back together. The ordering of records with equal fields might be different according to when different processors finish different tasks.

Note that a deterministic sort is weaker than a stable sort. A stable sort is always deterministic, but not vice versa. And typically when people say they want a deterministic sort, they really mean that they want a stable sort.

A.3 Deterministic Comparison

A deterministic comparison is different than either of the above; it is a property of a comparison function, not a sorting algorithm. This is a comparison where strings that do not have identical binary contents (optionally, after some process of normalization) will compare as unequal. A deterministic comparison is sometimes called a stable (or semi-stable) comparison.

There are many people who confuse a deterministic comparison with a deterministic (or stable) sort, but once again, these are very different creatures. A comparison is used by a sorting algorithm to determine the relative ordering of two fields, such as strings. Using a deterministic comparison cannot cause a sort to be deterministic, nor to be stable. Whether a sort is deterministic or stable is a property of the sort algorithm, not the comparison function. If you look at the examples above, this is clear.

A.3.1 Forcing Deterministic Comparisons

One can produce a deterministic comparison function from a non-deterministic one, in the following way (in pseudo-code):

int new_compare (String a, String b) {
  int result = old_compare(a, b);
  if (result == 0) {
    result = binary_compare(a, b);
  }
  return result;
}

Programs typically also provide the facility to generate a sort key, which is a sequences of bytes generated from a string in alignment with a comparison function. Two sort keys will binary-compare in the same order as their original strings.  To create a deterministic sort key that aligns with the above new_compare, the simplest means is to append a copy of the original string to the sort key. This will force the comparison to be deterministic.

byteSequence new_sort_key (String a) {
  return old_sort_key(a) + SEPARATOR + toByteSequence(a);
}

Because sort keys and comparisons must be aligned, a sort key generator is deterministic if and only if a comparison is.

A.3.2 Best Practice

However, a deterministic comparison is generally not best practice. First, it has a certain performance cost in comparison, and a quite substantial impact on sort key size. (For example, ICU language-sensitive sort keys are generally about the size of the original string, so appending a copy of the original string generally doubles the size of the sort key.)  A database using these sort keys can have substantially increased disk footprint and memory footprint, and consequently reduced performance.

More importantly, a deterministic comparison function does not actually achieve the effect people think it will have. Look at the sorted examples above. Whether a deterministic comparison is use or not, there will be no effect on Quick Sort example, since the two records in question have identical last name fields. It does not make a non-deterministic sort into a deterministic one, nor does it make a non-stable sort into a stable one.

Thirdly, a deterministic comparison is often not what is wanted, when people look closely at the implications. Look at our above example, and suppose that this time the user is sorting first by last name, then by first name.

The desired results are the following, which should result whether the sorting algorithm is stable or not, since we are using both fields.

Now suppose that in record 2, the source for the data caused the last name to contain a control character, such as a ZWJ (used to request ligatures on display). There is in this case no visible distinction in the forms, since the font doesn't have any ligatures for these values. The standard UCA collation sequence causes that character to be—correctly—ignored in comparison, since it should only affect rendering. However, if that comparison is changed to be deterministic (by appending the binary original string, then unexpected results will occur.

A.3.3 Forcing Stable Sorts

Typically, what people really want when they say they want a deterministic comparison is actually a stable sort.

One can force non-stable sorting algorithm to produce stable results by how one does the comparison. However, it has literally nothing to do with making the comparison be deterministic or not. Instead, it can be done by appending the current record number to the strings to be compared. (The implementation may not actually append the number; it may use some other mechanism, but the effect would be the same.)

If such a modified sort comparison is used, for example, then it forces Quick Sort to get the same results as Merge Sort. And in that case, the irrelevant character ZWJ does not affect the outcome, as illustrated below, and the correct results occur.

If anything, this then is what users want when they say they want a deterministic comparison. See also Section 1.6 Interleaved Levels.

A.4 Stable Comparison

There are a few other terms worth mentioning, simply because they are also subject to considerable confusion. Any or all of the following may be easily confused with above.

A stable comparison is one that does not change over successive software versions. That is, as one uses successive versions of an API, with the same "settings" (such as locale), one gets the same results.

A stable sort key generator is one that generates the same binary sequence over successive software versions.

Warning: if the sort key generator is stable, then the associated comparison will perforce be. However, the reverse is not guaranteed. To take a trivial example, suppose the new version of the software always adds an 0xFF byte at the front of every sort key. The results of any comparison of any two new keys would be identical to the results of the comparison of any two corresponding old keys. But the bytes have changed, and the comparison of old and new keys would give different results. Thus one can have a stable comparison, yet an associated non-stable sort key generator.

A portable comparison is where corresponding APIs for comparison produce the same results across different platforms. That is, if one uses the same "settings" (such as locale), one gets the same results.

A portable sort key generator is where corresponding sort key APIs produce exactly the same sequence of bytes across different platforms.

Warning: as above, a comparison may be portable without the associated sort key generator being portable.

Ideally, all products would have the same string comparison and sort key generation for, say Swedish, and thus be portable. For historical reasons, this is not the case. Even if the main letters sort the same, there will be differences in the handling of other letters, or symbols, punctuation, and other characters. There are some libraries that offer portable comparison, such as [ICU], but in general the results of comparison or sort key generation may vary significantly between different platforms.

In a closed system, or in simple scenarios, portability may not matter. Where someone has a given set of data to present to a user, and just wants the output to be reasonably appropriate for Swedish, then the exact order on the screen may not matter.

In other circumstances, it can lead to data corruption. For example, suppose that two implementations do a database SELECT for records between a pair of strings. If the collation is different in the least way, they can get different data results. Financial data might be different, for example, if a city is included in one SELECT on one platform and excluded from the same SELECT on another platform.

Acknowledgements

Thanks to Bernard Desgraupes, Richard Gillam, Kent Karlsson, Åke Persson, Roozbeh Pournader, Markus Scherer, Javier Sola, Otto Stolz, and Vladimir Weinstein for their feedback on previous versions of this document, to Jianping Yang and Claire Ho for their contributions on matching, and to Cathy Wissink for her many contributions to the text.

References

Modifications

The following summarizes modifications from the previous revisions of this document.

Copyright © 1998-2006 Unicode, Inc. All Rights Reserved. The Unicode Consortium makes no expressed or implied warranty of any kind, and assumes no liability for errors or omissions. No liability is assumed for incidental and consequential damages in connection with or arising out of the use of the information or programs contained or accompanying this technical report. The Unicode Terms of Use apply.

Unicode and the Unicode logo are trademarks of Unicode, Inc., and are registered in some jurisdictions.