XML Schema 1.1 Part 2: Datatypes

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wd-20050224

W3C Working Draft

24 February 2005 http://www.w3.org/TR/2005/WD-xmlschema11-2-20050224/ XML XHTML with changes since version 1.0 marked XHTML with changes since previous Working Draft marked Independent copy of the schema for schema documents A schema for built-in datatypes only, in a separate namespace Independent copy of the DTD for schema documents List of translations http://www.w3.org/TR/xmlschema11-2/ http://www.w3.org/TR/2004/WD-xmlschema11-2-20040716/ David Peterson invited expert (SGMLWorks!) davep@iit.edu Paul V. Biron Kaiser Permanente, for Health Level Seven Paul.V.Biron@kp.org Ashok Malhotra Oracle Corporation ashokmalhotra@alum.mit.edu C. M. Sperberg-McQueen World Wide Web Consortium cmsmcq@w3.org

This section describes the status of this document at the time of its publication. Other documents may supersede this document. A list of current W3C publications and the latest revision of this technical report can be found in the W3C technical reports index at http://www.w3.org/TR/.

This is a Public Working Draft of XML Schema 1.1. It is here made available for review by W3C members and the public. It is intended to give an indication of the W3C XML Schema Working Group's intentions for this new version of the XML Schema language and our progress in achieving them. It attempts to be complete in indicating what will change from version 1.0, but does not specify in all cases how things will change.

For those primarily interested in the changes since version 1.0, the appendix, which summarizes both changes already made and also those in prospect, with links to the relevant sections of this draft, is the recommended starting point. Accompanying versions of this document display in color all changes to normative text since version 1.0 and since the previous Working Draft.

This draft was published on 24 February 2005. The major changes are:

A new primitive decimal type has been defined, which retains information about the precision of the value. This type is aligned with the floating-point decimal types which will be part of the next edition of IEEE 754.

In order to align this specification with those being prepared by the XSL and XML Query Working Groups, a new datatype named has been introduced.

The conceptual model of the date- and time-related types has been defined more formally.

Two subtypes of ( and ) have been introduced, each of which is totally ordered.

A more formal treatment of the fundamental facets of the primitive datatypes has been adopted.

More formal definitions of the lexical space of most types have been provided, with detailed descriptions of the mappings from lexical representation to value and from value to canonical representation.

Please send comments on this Working Draft to www-xml-schema-comments@w3.org (archive).

Publication as a Working Draft does not imply endorsement by the W3C Membership. This is a draft document and may be updated, replaced or obsoleted by other documents at any time. It is inappropriate to cite this document as other than work in progress.

This document has been produced by the W3C XML Schema Working Group as part of the W3C XML Activity. The goals of the XML Schema language version 1.1 are discussed in the Requirements for XML Schema 1.1 document. The authors of this document are the members of the XML Schema Working Group. Different parts of this specification have different editors.

Patent disclosures relevant to this specification may be found on the Working Group's Patent disclosure page in conformance with the W3C Patent Policy of 5 February 2004. An individual who has actual knowledge of a patent which the individual believes contains Essential Claim(s) with respect to this specification should disclose the information in accordance with section 6 of the W3C Patent Policy.

The English version of this specification is the only normative version. Information about translations of this document is available at http://www.w3.org/2003/03/Translations/byTechnology?technology=xmlschema.

XML Schema: Datatypes is part 2 of the specification of the XML Schema language. It defines facilities for defining datatypes to be used in XML Schemas as well as other XML specifications. The datatype language, which is itself represented in XML 1.0, provides a superset of the capabilities found in XML 1.0 document type definitions (DTDs) for specifying datatypes on elements and attributes.

RQ-152 (xml1.1)

How should this specification be aligned with XML 1.1? The changes in character set and name characters, and the question of what determines which ones to use, must be addressed.

English Extended Backus-Naur Form (formal grammar) diff group junk: a few homeless targets; should probably ALWAYS BE SHOW unless nothing is, or it is empty diff group fa1: RQ-24 facets proposal, changes made BEFORE the publication of the first public working draft. APPROVED SOME TELECON 2004-10 diff group fa1: RQ-24 facets proposal, changes made AFTER the publication of the first public working draft. APPROVED SOME TELECON 2004-10 diff group cvs1: Constructed Values Appendix (div1) diff group cvs1_pwd: Constructed Values Appendix as a whole (to avoid nested like-named diffs) diff group num1: Numerical Values Appendix (div2); requires cvs1 diff group numap1: in-text productions, etc., first cut; requires funbase, nu1, num1 diff group funbase: The functions appendix in its entirety. ALWAYS ACCEPT OR SHOW diff group nu1: basic numerical functions; requires funbase, num1, cvs1 diff group du0: first Ph 2 for duration; requires numap, nu1, num1, funbase. NOT YET MARKED; APPROVED pre-FPWD diff group du1: second set of revs for duration (compare du2) diff group du2: second set of revs for dayTimeDuration and yearMonthDuration (compare du1) diff group dt1: RQ-13 date/time rewrite, first part Ph 2 (d/t app and gDay); requires funbase, nu1, num1; APPROVED 2004-08-27 FTF diff group dt2: RQ-13 date/time rewrite, second part Ph 2 (time and others); requires dt1, funbase, nu1, num1 diff group dtr: date/time nonnormative description (INCLUDES 2 NORMATIVE TABLES); requires dt1 diff group dt3: RQ-13 date/time rewrite, third part Ph 2 (time and others); requires dt1, dt2, funbase, nu1, num1 diff group dt2-3: RQ-13 date/time rewrite, third part Ph 2 (time and others); marks an item added indt2 and then delled in dt3 as del. Accept ("post"), except reject ("pre") if dt2 is accept and dt3 is reject, and show ("colour") if dt2 is accept and dt3 is show. diff group dt4: RQ-13 date/time rewrite, fourth part Ph 2 (time and others); requires dt1, dt2, dt3, funbase, nu1, num1 diff group pd1: RQ-31 precisionDecimal first cut for approval; co-requires pre, pd2, pd3; requires pdf diff group pdo: RQ-31 precisionDecimal first cut, deletion of old decimal; co-requires pre, pd1 ,pd3; requires pdf. 2005-01-20: WG chooses two-primitive approach, rejects this change. 2005-01-26: MSM removes this diff group to reduce cruft in the document. diff group pd2: RQ-31 precisionDecimal first cut, addition of new aPDedimal; co-requires pre, pd1, pd2; requires pdf. 2005-01-20: WG chooses two-primitive approach, rejects this change. 2005-01-26: MSM removes this diff group to reduce cruft in the document. diff group pre: Precision Appendix; co-requires pd1, requires num1 and cvs1. Final wording approved (with changes) 2005-02-04. diff group pdf: numerical functions just for precisionDecimal (RQ-31); requires num1 (??). Final wording approved (with changes) 2005-02-04. diff group pdf: numerical functions for precisionDecimal (RQ-31) in two-primitive form. Final wording approved (with changes) 2005-02-04. diff group pdf: numerical functions for precisionDecimal (RQ-31) in single-primitive form. Removed 2005-01-26 after WG chose two-primitive form. diff group aat: anyAtomicType (RQ-???); may require fa1 ?? APPROVED with changes FTF 2004-11-10. Changes decided by WG entered (as aatf), 2005-01-25. Draft final wording approved (with changes) 2005-02-04. diff group aat1: anyAtomicType (RQ-???); requires aat diff group trm1: terminological cleanup begun with tightening meaning of derived (RQ-120); diff group rq31facets: with MSM's proposed changes related to facets of precision decimal. This takes a single-primitive ('unitarian') view of precision decimal and legacy decimal (here under the name aPdecimal). Compatible with both rq31m and rq31u. diff group rq31u: with changes for a one-primitive ('unitarian') version of precision decimal. Incompatible with: rq31m, which takes the manichean view, Assumes: pd1, pd2, pre, pdf, num1, pdo(which deletes old decimal), pd2 (which inserts new aPDecimal). The WG chose the Manichean decimal proposal over the Unitarian one, 2005-01-20. Diffs for group rq31u were removed 2005-01-26. diff group rq31m: with changes for a two-primitive ('manichean') version of precision decimal. Incompatible with: rq31u, which takes the unitarian view, pdo, which deletes old decimal, pd2, which inserts new aPDecimal. Assumes: pd1, pre, pdf, num1. Final wording approved (with changes) 2005-02-04. diff group fa1-fix: MSM's proposed changes for fixing problems (missing term definitions, in particular) caused by the fact that fa1 was incomplete and left the document in an unstable state. diff group iff: with an editorial proposal (2005-01-01) for being more consistent about the use of conditionals and biconditionals. When terms are being defined (whether or not marked as termdefs) or necessary and sufficient conditions for some state are being given (e.g. in constraint notes, which define terms like 'facet valid with respect to X'), this diff group proposes to use 'if' only for conditions which are sufficient but not necessary; if the conditions are both sufficient and necessary, then use 'if and only if'. diff group pdf_tweak: for proposed improvements to diff group pdf (all gone away now, and then come back again). Final wording approved (with changes) 2005-02-04. diff group review: for marking stuff that is really intended only for editorial review (usually to be used on ednotes). diff group wdd: for working-draft deviations: changes between the publication of the first public WD in July and the advent of thorough and permanent change markup. (Diff group wdd begun 9 January 2005, but diff not completed. It was looking like another three hours work.) I.e. wdd should mark all and only those differences between TR/2004/WD-xmlschema11-2-20040716/datatypes.xml and xse/datatypes/datatypes.xml which are not already marked. When we run the result through the dg.xsl filter with wdd set to reject, the result should be (modulo whitespace and other non-significant differences) substantively the same as the public WD. diff group dpno: change proposals transferred into this file from the experimental fork datatypes.newOrg.xml. At the moment, the quasi-systematic changes of ID have not been reproduced. diff group fpwd-rescinded-add: marks some paragraphs added in the first public working draft but since deleted again. diff group fpwd-rescinded-del: marks some paragraphs marked as deleted in the first public working draft but since restored. diff group aatf: anyAtomicType (RQ-141). Changes decided on by WG at Redwood Shores ftf 2004-11-10. Draft final wording approved (with changes) 2005-02-04. diff group aatj: anyAtomicType (RQ-141). Proposal for change, submitted to WG at Brisbane, January 2005 (hence the 'j'). Final wording approved (with changes) 2005-02-04. diff group aatg: anyAtomicType (RQ-141). Changes to correct errors found in review of aatf, including changes agreed by WG in telcon of 2005-02-04 when the RQ-141 proposal was approved. diff group vrd: make validation rules declarative. Not yet complete. Stems from rq31m edits: first cut at editing the upper and lower bounds facets included reformulation of the validation rules to talk about numeric value. When the order relation for numeric values and pDecimal values was defined, however, it became clear that the validation rules didn't need that change, and the remaining change (making them declarative) didn't really have anything to do with anyAtomicType. diff group fpwd: used to mark things that changed between 1.0 2E and the first public working draft of July 2004. (N.B. issues elements and editorial notes are not consistently marked as added. They may consistently be unmarked.) diff group rq001: marks a phase-2 proposal to resolve requirement RQ-001, adopted by the WG on 2 March 2004. diff group rq31fix: marks some wording changes intended to address problems identified by Dave Peterson, Sandy Gao, and Noah Mendelsohn after the draft final wording for RQ-31 went to the WG. Micro-component-related changes Last-minute hacks to make the Working Draft of February 2005 be valid and produce valid clean HTML.

Introduction

RQ-21 (regex/BNF for all primitive types)

Current plan is that all datatypes defined herein will have EBNF productions at least approximately defining their lexical space, and will include a nonnormative regex derived from the EBNF if a user wishes to copy it directly.

RQ-24 (systematic facets: canonical representations for all datatypes)

It is not possible for all datatypes to have canonical representations of all values without violating the rules of derivation or adding special-purpose &cfacet;s which the WG does not deem appropriate. The WG has not yet decided how to deal with datatypes whose lexical and/or canonical mappings are context sensitive.

RQ-148 (clarify use of "truncation)

The word will probably be removed.

RQ-120 (consistent use of "derived)

"Derivations" other than "derivations by restriction" will be renamed "constructions".

RQ-24 (systematic facets: assignment of datatype to nodes without components)

Introduction to Version 1.1

The Working Group has two main goals for this version of W3C XML Schema:

Significant improvements in simplicity of design and clarity of exposition without loss of backward or forward compatibility;

Provision of support for versioning of XML languages defined using the XML Schema specification, including the XML transfer syntax for schemas itself.

These goals are slightly in tension with one another -- the following summarizes the Working Group's strategic guidelines for changes between versions 1.0 and 1.1:

Add support for versioning (acknowledging that this may be slightly disruptive to the XML transfer syntax at the margins)

Allow bug fixes (unless in specific cases we decide that the fix is too disruptive for a point release)

Allow editorial changes

Allow design cleanup to change behavior in edge cases

Allow relatively non-disruptive changes to type hierarchy (to better support current and forthcoming international standards and W3C recommendations)

Allow design cleanup to change component structure (changes to functionality restricted to edge cases)

Do not allow any significant changes in functionality

Do not allow any changes to XML transfer syntax except those required by version control hooks and bug fixes

The overall aim as regards compatibility is that

All schema documents conformant to version 1.0 of this specification should also conform to version 1.1, and should have the same validation behaviour across 1.0 and 1.1 implementations (except possibly in edge cases and in the details of the resulting PSVI);

The vast majority of schema documents conformant to version 1.1 of this specification should also conform to version 1.0, leaving aside any incompatibilities arising from support for versioning, and when they are conformant to version 1.0 (or are made conformant by the removal of versioning information), should have the same validation behaviour across 1.0 and 1.1 implementations (again except possibly in edge cases and in the details of the resulting PSVI);

Purpose

The specification defines limited facilities for applying datatypes to document content in that documents may contain or refer to DTDs that assign types to elements and attributes. However, document authors, including authors of traditional documents and those transporting data in XML, often require a higher degree of type checking to ensure robustness in document understanding and data interchange.

The table below offers two typical examples of XML instances in which datatypes are implicit: the instance on the left represents a billing invoice, the instance on the right a memo or perhaps an email message in XML.

Data oriented	Document oriented
1999-01-21 1999-01-25 Ashok Malhotra 123 Microsoft Ave. Hawthorne NY 10532-0000 555-1234 555-4321 ]]>	Paul V. Biron Ashok Malhotra Latest draft We need to discuss the latest draft immediately. Either email me at mailto:paul.v.biron@kp.org or call 555-9876 ]]>

The invoice contains several dates and telephone numbers, the postal abbreviation for a state (which comes from an enumerated list of sanctioned values), and a ZIP code (which takes a definable regular form). The memo contains many of the same types of information: a date, telephone number, email address and an "importance" value (from an enumerated list, such as "low", "medium" or "high"). Applications which process invoices and memos need to raise exceptions if something that was supposed to be a date or telephone number does not conform to the rules for valid dates or telephone numbers.

In both cases, validity constraints exist on the content of the instances that are not expressible in XML DTDs. The limited datatyping facilities in XML have prevented validating XML processors from supplying the rigorous type checking required in these situations. The result has been that individual applications writers have had to implement type checking in an ad hoc manner. This specification addresses the need of both document authors and applications writers for a robust, extensible datatype system for XML which could be incorporated into XML processors. As discussed below, these datatypes could be used in other XML-related standards as well.

Requirements

The document spells out concrete requirements to be fulfilled by this specification, which state that the XML Schema Language must:

provide for primitive data typing, including byte, date, integer, sequence, SQL and Java primitive datatypes, etc.;

define a type system that is adequate for import/export from database systems (e.g., relational, object, OLAP);

distinguish requirements relating to lexical data representation vs. those governing an underlying information set;

allow creation of user-defined datatypes, such as datatypes that are derived from existing datatypes and which may constrain certain of its properties (e.g., range, precision, length, format).

Scope

This portion of the XML Schema Language discusses datatypes that can be used in an XML Schema. These datatypes can be specified for element content that would be specified as #PCDATA and attribute values of various types in a DTD. It is the intention of this specification that it be usable outside of the context of XML Schemas for a wide range of other XML-related activities such as and .

Terminology

The terminology used to describe XML Schema Datatypes is defined in the body of this specification. The terms defined in the following list are used in building those definitions and in describing the actions of a datatype processor:

for compatibility

A feature of this specification included solely to ensure that schemas which use this feature remain compatible with

may

Conforming documents and processors are permitted to but need not behave as described.

match

(Of strings or names:) Two strings or names being compared must be identical. Characters with multiple possible representations in ISO/IEC 10646 (e.g. characters with both precomposed and base+diacritic forms) match only if they have the same representation in both strings. No case folding is performed. (Of strings and rules in the grammar:) A string matches a grammatical production if and only if it belongs to the language generated by that production.

must

Conforming documents and processors are required to behave as described; otherwise they are in error.

error

A violation of the rules of this specification; results are undefined. Conforming software detect and report an error and recover from it.

Constraints and Contributions

This specification provides three different kinds of normative statements about schema components, their representations in XML and their contribution to the schema-validation of information items:

Constraint on Schemas

Constraints on the schema components themselves, i.e. conditions components satisfy to be components at all. Largely to be found in .

Schema Representation Constraint

Constraints on the representation of schema components in XML. Some but not all of these are expressed in and .

Validation Rule

Constraints expressed by schema components which information items satisfy to be schema-valid. Largely to be found in .

TypeDatatype System

This section describes the conceptual framework behind the datatype system defined in this specification. The framework has been influenced by the standard on language-independent datatypes as well as the datatypes for and for programming languages such as Java.

The datatypes discussed in this specification are computer representations offor the most part well known abstract concepts such as integer and date. It is not the place of this specification to thoroughly define these abstract concepts; many other publications provide excellent definitions. However, this specification will attempt to describe the abstract concepts well enough that they can be readily recognized and distinguished from other abstractions with which they may be confused.

Only those operations and relations needed for schema processing are defined in this specification. Applications using these datatypes are generally expected to implement appropriate additional functions and/or relations to make the datatype generally useful. For example, the description herein of the datatype does not define addition or multiplication, much less all of the operations defined for that datatype in on which it is based.

Datatype

In this specification, a datatype is a 3-tuple, consisting of a) a set of distinct values, called its , b) a set of lexical representations, called its , and c) a set of s that characterize properties of the , individual values or lexical items.

In this specification, a datatype is a thing with fourhas three properties:

A , which is simply a set of values. What the members of this set are called (beyond being generically called values) is influenced by the set of value-space operations and relations used therewith.

A , which is the domain of the . Some lexical mappings are context sensitive, so that the depends on the context in which the lexical representation occurs.a set of &string;s used to denote the values.

A small collection of functions, relations, and procedures associated with the datatype. Included are equality and order relations on the , and a , which is a function on the onto the .

A , which serves to define and/or identify the datatype.

This specification only defines the operations and relations needed for schema processing. The choice of terminology for describing/naming the datatypes is selected to guide users and implementers in how to expand the datatype to be generally useful—i.e., how to recognize the real world datatypes and their variants for which the datatypes defined herein are meant to be used for data interchange.

Along with the it is often useful to have an inverse which provides a standard for each value. Such a is not required for schema processing, but is described herein for the benefit of users of this specification, and other specifications which might find it useful to reference these descriptions normatively.

Value space

A value space is the set of values for a given datatype. Each value in the value space of a datatype is denoted by one or more literals in its .

The value space of a datatype is the set of values for that datatype. Associated with each value space are selected operations and relations necessary to permit proper schema processing. Each value in the value space of a datatype is denoted by one or more character strings in its , according to the lexical mapping. (If the mapping is restricted during a derivation in such a way that a value has no denotation, that value is dropped from the value space.)

The value spaces of datatypes are abstractions, and are defined in to the extent needed to clarify them for readers. For example, in defining the numerical datatypes, we assume some general numerical concepts such as number and integer are known. In many cases we provide references to other documents providing more complete definitions.

The value spaces and the values therein are abstractions. This specification does not prescribe any particular internal representations that must be used when implementing these datatypes. In some cases, there are references to other specifications which do prescribe specific internal representations; these specific internal representations must be used to comply with those other specifications, but need not be used to comply with this specification.

In addition, other applications are expected to define additional appropriate operations and/or relations on these value spaces (e.g., addition and multiplication on the various numerical datatypes' value spaces), and are permitted where appropriate to even redefine the operations and relations defined within this specification, provided that for schema processing the relations and operations used are those defined herein.

The of a given datatype can be defined in one of the following ways:

defined elsewhere axiomatically from fundamental notions (intensional definition) [see ]

enumerated outright from values of an already defined datatype (extensional definition) [see ]

defined by restricting the of an already defined datatype to a particular subset with a given set of properties [see ]

defined as a combination of values from one or more already defined (s) by a specific construction procedure [see and ]

s have certain properties. For example, they always have the property of , some definition of equality and might be , by which individual values within the can be compared to one another. The properties of s that are recognized by this specification are defined in .

The relations of identity, equality, and order are required for each value space. A very few datatypes have other relations or operations prescribed for the purposes of this specification.

Identity

The identity relation is always defined. Every value space inherently has an identity relation. Two things are identical if and only if they are actually the same thing: i.e., if there is no way whatever to tell them apart. The identity relation is used when making restrictions by enumeration, and when checking identity constraints. These are the only uses of identity for schema processing.

This does not preclude implementing datatypes by using more than one internal representation for a given value, provided no mechanism inherent in the datatype implementation (i.e., other than bit-string-preserving "casting" of the datum to a different datatype) will distinguish between the two representations.

In the identity relation defined herein, values from different datatypes' value spaces are made artificially distinct if they might otherwise be considered identical. For example, there is a number two in the datatype and a number two in the datatype. In the identity relation defined herein, these two values are considered distinct. Other applications making use of these datatypes may choose to consider values such as these identical, but for the view of datatypes' value spaces used herein, they are distinct.

WARNING: Care must be taken when identifying values across distinct primitive datatypes. It turns out that, for example, 0.1 and 0.10000000009 are effectively identical in but not in . (Neither 0.1 nor 0.10000000009 are in the value space, but the lexical mapping of maps both 0.1 and 0.10000000009 to the same number (0.100000001490116119384765625) that is in the value space.)

Equality

Each datatype has prescribed an equality relation for its value space. The equality relation for most datatypes is the identity relation. In the few cases where it is not, it has been carefully defined so as to be a congruence relation for most other operations of interest to the datatype. (This means simply that if two values are equal and one is substituted for the other as an argument to any of the operations, the results will always also be equal. For example, identity is by definition a congruence relation for all other operations of interest.) Equality is always a congruence for the order relation.

On the other hand, equality need not cover the entire value space of the datatype (though it usually does).

The equality relation is used in conjunction with order when making restrictions involving order. This is the only use of equality for schema processing.

In the prior version of this specification (1.0), equality was always identity. This has been changed to permit the datatypes defined herein to more closely match the real world datatypes for which they are intended to be used as transmission formats.

For example, the datatype has an equality which is not the identity ( −0 = +0 , but they are not identical—although they were identical in the 1.0 version of this specification), and whose domain excludes one value, NaN, so that NaN ≠ NaN .

For another example, the datatype previously lost any timezone information in the as the value was converted to timezone Z; now the timezone is retained and two values representing the same moment in time but with different remembered timezones are now equal but not identical.

In the equality relation defined herein, values from different primitive data spaces are made artificially unequal even if they might otherwise be considered equal. For example, there is a number two in the datatype and a number two in the datatype. In the equality relation defined herein, these two values are considered unequal. Other applications making use of these datatypes may choose to consider values such as these equal (and must do so if they choose to consider them identical); nonetheless, in the equality relation defined herein, they are unequal.

For the purposes of this specification, there is one equality relation for all values of all datatypes (the union of the various datatype's individual equalities, if one consider relations to be sets of ordered pairs). The equality relation is denoted by = and its negation by ≠, each used as an binary infix predicate: x = y and x ≠ y . On the other hand, identity relationships are always described in words.

Order

Each datatype has an order relation prescribed. This order may be a partial order, which means that there may be values in the which are neither equal, less-than, nor greater-than. Such value pairs are incomparable. In many cases, the prescribed order is the null order: the ultimate partial order, in which no pairs are less-than or greater-than; they are all equal or . Two values that are neither equal, less-than, nor greater-than are incomparable. Two values that are not are comparable. The order relation is used in conjunction with equality when making restrictions involving order. This is the only use of order for schema processing.

In this specification, this less-than order relation is denoted by < (and its inverse by >), the weak order by ≤ (and its inverse by ≥), and the resulting relation by <>, each used as an binary infix predicate: x < y , x ≤ y , x > y , x ≥ y , and x &inc; y .

The weak order less-than-or-equal means less-than or equal and one can tell which. For example, the P1M (one month) is not less-than-or-equal P31D (thirty-one days) because P1M is not less than P31D, nor is P1M equal to P31D. Instead, P1M is with P31D.) The formal definition of order for () insures that this is true.

The value spaces of primitive datatypes are abstractions, which may have values in common. In the order relation defined herein, these value spaces are made artificially . For example, the numbers two and three are values in both the decimal&pD; datatype and the float datatype. In the order relation defined herein, two in the decimal datatype and three in the float datatype are incomparable values. Other applications making use of these datatypes may choose to consider values such as these comparable.

While it is not an error to attempt to compare values from the value spaces of two different primitive datatypes, they will alway be and therefore unequal: If x and y are in the value spaces of different primitive datatypes then x &inc; y (and hence x ≠ y ).

Lexical space

In addition to its , each datatype also has a lexical space.

A lexical space is the set of valid literals for a datatype.

For example, "100" and "1.0E2" are two different literals from the of which both denote the same value. The type system defined in this specification provides a mechanism for schema designers to control the set of values and the corresponding set of acceptable literals of those values for a datatype.

The literals in the s defined in this specification have the following characteristics:

Interoperability:

The number of literals for each value has been kept small; for many datatypes there is a one-to-one mapping between literals and values. This makes it easy to exchange the values between different systems. In many cases, conversion from locale-dependent representations will be required on both the originator and the recipient side, both for computer processing and for interaction with humans.

Basic readability:

Textual, rather than binary, literals are used. This makes hand editing, debugging, and similar activities possible.

Ease of parsing and serializing:

Where possible, literals correspond to those found in common programming languages and libraries.

Canonical Lexical Representation

While the datatypes defined in this specification have, for the most part, a single lexical representation i.e. each value in the datatype's is denoted by a single literal in its , this is not always the case. The example in the previous section showed two literals for the datatype which denote the same value. Similarly, there be several literals for one of the date or time datatypes that denote the same value using different timezone indicators.

A canonical lexical representation is a set of literals from among the valid set of literals for a datatype such that there is a one-to-one mapping between literals in the canonical lexical representation and values in the .

The Lexical Space and Lexical Mapping

The lexical mapping for a datatype is a prescribed function whose domain is a prescribed set of character strings (the ) and whose range is the of that datatype.

The lexical space of a datatype is the prescribed domain of the lexical mapping for that datatype.

The members of the are lexical representations of the values to which they are mapped.

Should a derivation be made using a derivation mechanism that removes lexical representations from the to the extent that one or more values cease to have any , then those values are dropped from the .

This could happen by means of a facet.

Conversely, should a derivation remove values then their lexical representations are dropped from the unless there is a facet value whose impact is defined to cause the otherwise-dropped to be mapped to another value instead.

There are currently no facets with such an impact. There may be in the future.

For example, '100' and '1.0E2' are two different lexical representations from the datatype which both denote the same value. The datatype system defined in this specification provides mechanisms for schema designers to control the and the corresponding set of acceptable lexical representations of those values for a datatype.

Canonical Mapping

RQ-129 (remove dependency on canonical representations)

The dependencies are in Part 1; they will be resolved there. Text in this Part will reflect that canonical representation are provided for the benefit of other users, including other specifications that might want to reference these datatypes.

RQ-126 (restricting away canonical representations)

Given the "pattern" &cfacet;, restricting away canonical representations cannot be prohibited without undue processing expense. A warning will be inserted, and RQ-129 will insure that loss of canonical representations will not affect schema processing.

While the datatypes defined in this specification generally have a single for each value (i.e., each value in the datatype's is denoted by a single representation in its ), this is not always the case. The example in the previous section shows two lexical representations from the datatype which denote the same value.

The canonical mapping is a prescribed subset of the inverse of a which is one-to-one and whose domain (where possible) is the entire range of the (the ). Thus a selects one for each value in the .

The canonical representation of a value in the of a datatype is the associated with that value by the datatype's .

Canonical mappings are not available for datatypes whose lexical mappings are context dependent (i.e., mappings for which the value of a depends on the context in which it occurs, or for which a character string may or may not be a valid similarly depending on its context)

Canonical representations are provided where feasible for the use of other appilications; they are not required for schema processing itself. A conforming schema processor implementation is not required to implement canonical mappings.

Datatype dichotomies

It is useful to categorize the datatypes defined in this specification along various dimensions, forming a set of characterization dichotomies.

Atomic vs. list vs. union datatypes

The first distinction to be made is that between , and datatypes.

Atomic datatypes are those having values which are regarded by this specification as being indivisible. Atomic datatypes are and all datatypes derived from it.

List datatypes are those having values each of which consists of a finite-length (possibly empty) sequence of values of an datatype. List datatypes are those which are explicitly constructed as lists, or are derived from another list datatype.

Union datatypes are those whose s and s are the union of the s and s of one or more other datatypes. Union datatypes are those which are explicitly constructed as lists, or are derived from another union datatype.

For example, a single token which matches Nmtoken from could be the value of an datatype (); while a sequence of such tokens could be the value of a datatype ().

Atomic datatypes

datatypes can be either or . The of an datatype is a set of "atomic" values, which for the purposes of this specification, are not further decomposable. An datatype has a consisting of a set of atomic values which for purposes of this specification are not further decomposable. The of an datatype is a set of literals whose internal structure is specific to the datatype in question. There is one special atomic type () and a number of atomic types, which have as their base type. All other atomic types are derived by restriction either from one of the primitive atomic types or from another ordinary atomic type. No user-defined type may have as its base type.

List datatypes

Several type systems (such as the one described in ) treat datatypes as special cases of the more general notions of aggregate or collection datatypes.

datatypes are always . The of a datatype is a set of finite-length sequences of values. The of a datatype is a set of literals whose internal structure is a space-separated sequence of literals of the datatype of the items in the .

The or datatype that participates in the definition of a datatype is known as the itemType of that datatype.

]]> 8 10.5 12 ]]>

A datatype can be from an ordinary datatype whose allows space (such as or ) or a datatype any of whose 's allows space. In such a case, regardless of the input, list items will be separated at space boundaries.

]]> <someElement xsi:type='listOfString'> this is not list item 1 this is not list item 2 this is not list item 3 </someElement>

In the above example, the value of the someElement element is not a of 3; rather, it is a of 18.

When a datatype is from a datatype, the following s apply:

For each of , and , the unit of length is measured in number of list items. The value of is fixed to the value collapse.

For datatypes the is composed of space-separated literals of its . Hence, any specified when a new datatype is from a datatype is matched against each literal of the datatype and not against the literals of the datatype that serves as its .

123 456 123 987 456 123 987 567 456 ]]>

The for the datatype is defined as the lexical form in which each item in the has the canonical lexical representation of its .

Union datatypes

The and of a datatype are the union of the s and s of its . datatypes are always . Currently, there are no datatypes.

A prototypical example of a type is the maxOccurs attribute on the element element in XML Schema itself: it is a union of nonNegativeInteger and an enumeration with the single member, the string "unbounded", as shown below.

use="optional" use="optional" default="1" ]]>

Any number (greater than 1) of ordinary or s can participate in a type.

The datatypes that participate in the definition of a datatype are known as the memberTypes of that datatype.

The order in which the are specified in the definition (that is, the order of the <simpleType> children of the <union> element, or the order of the s in the memberTypes attribute) is significant. During validation, an element or attribute's value is validated against the in the order in which they appear in the definition until a match is found. The evaluation order can be overridden with the use of xsi:type.

For example, given the definition below, the first instance of the <size> element validates correctly as an , the second and third as .

]]> 1 large 1 ]]>

The for a datatype is defined as the lexical form in which the values have the canonical lexical representation of the appropriate .

A datatype which is in this specification need not be an atomic datatype in any programming language used to implement this specification. Likewise, a datatype which is a in this specification need not be a "list" datatype in any programming language used to implement this specification. Furthermore, a datatype which is a in this specification need not be a "union" datatype in any programming language used to implement this specification.

Primitive vs. derived datatypesConstructed Datatypes

Next, we distinguish between , , and datatypes.

Primitive datatypes are those that are not defined in terms of other datatypes; they exist ab initio.

Derived datatypes are those that are defined in terms of other datatypes.

Constructed datatypes are those that are defined in terms of other datatypes.

For example, in this specification, is a well-defined mathematical concept that cannot be defined in terms of other datatypes, while a is a special case of the more general datatype .

RQ-141 (add abstract anyAtomicType) RQ-24 (systematic facets: status and value space of anySimpleType)

A new special datatype will be introduced as a child of anySimpleType and the base type of all primitive atomic datatypes.

The simple ur-type definitiondefinition of is a special restriction of the ur-type definition whose name is anySimpleType in the XML Schema namespace. anySimpleType can be considered as the of all datatypes. anySimpleType is considered to have an unconstrained lexical space and a consisting of the union of the s of all the datatypes and the set of all lists of all members of the s of all the datatypes.

The datatypes defined by this specification fall into both the and categories. It is felt that a judiciously chosen set of datatypes will serve the widest possible audience by providing a set of convenient datatypes that can be used as is, as well as providing a rich enough base from which the variety of datatypes needed by schema designers can be .

In the example above, is from .

A datatype which is in this specification need not be a "primitive" datatype in any programming language used to implement this specification. Likewise, a datatype which is in this specification need not be a "derived" datatype in any programming language used to implement this specification.

As described in more detail in , each datatype be defined in terms of another datatype in one of three ways: 1) by assigning s which serve to restrict the of the datatype to a subset of that of the ; 2) by creating a datatype whose consists of finite-length sequences of values of its ; or 3) by creating a datatype whose consists of the union of the s of its .

Derived by restriction

A datatype is said to be by restriction from another datatype when values for zero or more s are specified that serve to constrain its and/or its to a subset of those of its .

Every datatype that is by is defined in terms of an existing datatype, referred to as its base type. base types can be either or .

Derived by list

A datatype can be from another datatype (its ) by creating a that consists of a finite-length sequence of values of its .

Derived by union

One datatype can be from one or more datatypes by ing their s and, consequently, their s.

Built-in vs. user-derived datatypes

Built-in datatypes are those which are defined in this specification, and can be either or ;

User-derived datatypes are those datatypes that are defined by individual schema designers.

Conceptually there is no difference between the datatypes included in this specification and the datatypes which will be created by individual schema designers. The datatypes are those which are believed to be so common that if they were not defined in this specification many schema designers would end up "reinventing" them. Furthermore, including these datatypes in this specification serves to demonstrate the mechanics and utility of the datatype generation facilities of this specification.

A datatype which is in this specification need not be a "built-in" datatype in any programming language used to implement this specification. Likewise, a datatype which is in this specification need not be a "user-derived" datatype in any programming language used to implement this specification.

Datatypes and Schemas

Datatypes as defined above exist, in the abstract, independently of whether they have any relation to schemas as defined in this specification. Datatypes are tied to schemas either by explicit description in this specification, or by user mechanisms prescribed in this specdification for use in user-created schemas.

The user-usable mechanism prescribed by this specification is the ability to add additional s to schemas. s and their use within schemas are described in . A selects a particular datatype and gives it a name and a place in the schema's datatype hierarchy, which is a structuring of all the datatypes associated with a schema.

The Datatype Derivation Hierarchy

Datatypes associated with a schema are organized in a hierarchy that exactly parallels the datatypes' defining (or selecting) s in the schema's corresponding schema type hierarchy, as described in . A datatype is immediately derived from another if and only if it is immediately below the other (i.e., away from the root) in the derivation hierarchy. A datatype is the base type of another if and only if the other is immediately derived from it. A datatype is derived from another if and only if there is a chain of datatypes beginning with it and ending with the other. It is often easiest to determine a datatype's location in the hierarchy by examining the corresponding in the schema type hierarchy.

At the root of the hierarchy are two special datatypes, and . is the real root; is from .

All other (ordinary) datatypes are from these two special datatypes. The most important class of datatypes from these two are the primitive datatypes, all of which are described in . Starting with the primitive datatypes, all other schema-usable datatypes are either facet-derived, constructed as lists, or constructed as unions.

Atomic, List, and Union Datatypes

Ordinary datatypes may be characterized as atomic, list, or union datatypes.

An atomic datatype is one which is from . Since only (and all) primitive datatypes are from , all other atomic datatypes are from primitives.

A list datatype is one that is constructed to have lists of values from some other datatype, or any datatype subsequently from a list datatype The other datatype from which a list datatype is constructed is the list datatype's item type. Datatypes that are constructed as lists are from , so all list datatypes are from .

A union datatype is one that is constructed to have the of values from some other datatypes, or any datatype subsequently from a union datatype The other datatypes from which a union datatype is constructed are the union datatype's member types. Datatypes that are constructed as unions are from , so all union datatypes are from .

All datatypes in the datatype hierarchy of a schema that are not from or are facet-derived from their base types. The mechanisms of construction and facet-derivation are described in .

Placing a Datatype in the Hierarchy

Special and primitive datatypes are placed in the hierarchy by explicit rules in this specification. As mentioned above, is at the root of the hierarchy, is from , and all primitive datatypes—and only primitive datatypes—are from .

A constructed datatype ( or ) is always from . A facet-derived datatype is always from its . These are the only ways a datatype not special or primitive can be placed in a schema's datatype hierarchy.

The special, primitive, and other ordinary datatypes described in this specification are present in every schema's datatype hierarchy. Any others depend on the schema.

YYY

Built-in datatypesBuilt-in s and their Datatypes

Each built-in datatype in this specification (both and ) can be uniquely addressed via a URI Reference constructed as follows:

the base URI is the URI of the XML Schema namespace

the fragment identifier is the name of the datatype

For example, to address the datatype, the URI is:

http://www.w3.org/2001/XMLSchema#int

Additionally, each facet definition element can be uniquely addressed via a URI constructed as follows:

the base URI is the URI of the XML Schema namespace

the fragment identifier is the name of the facet

For example, to address the maxInclusive facet, the URI is:

http://www.w3.org/2001/XMLSchema#maxInclusive

Additionally, each facet usage in a built-in datatype definition can be uniquely addressed via a URI constructed as follows:

the base URI is the URI of the XML Schema namespace

the fragment identifier is the name of the datatype, followed by a period (".") followed by the name of the facet

For example, to address the usage of the maxInclusive facet in the definition of int, the URI is:

http://www.w3.org/2001/XMLSchema#int.maxInclusive

Namespace considerations

The datatypes defined by this specification are designed to be used with the &schema-language; as well as other XML specifications. To facilitate usage within the &schema-language;, the datatypes in this specification have the namespace name:

http://www.w3.org/2001/XMLSchema

To facilitate usage in specifications other than the &schema-language;, such as those that do not want to know anything about aspects of the &schema-language; other than the datatypes, each datatype is also defined in the namespace whose URI is:

http://www.w3.org/2001/XMLSchema-datatypes

This applies to both and datatypes.

Each datatype is also associated with a unique namespace. However, datatypes do not come from the namespace defined by this specification; rather, they come from the namespace of the schema in which they are defined (see XML Representation of Schemas in ).

Special DatatypesSimple Type Definitions

Special datatypes

There are two special s. (All others are ordinary.) The special s are, unlike the ordinary ones, more important as s than as datatypes.

anySimpleType

xxx

anyAtomicType

xxx

Primitive s and Ddatatypes

The datatypes defined by this specification are described below. For each datatype, the and are defined, s which apply to the datatype are listed and any datatypes from this datatype are specified.

datatypes can only be added by revisions to this specification.

string

The string datatype represents character strings in XML. The of string is the set of finite-length sequences of characters (as defined in ) that the Char production from . A character is an atomic unit of communication; it is not further specified except to note that every character has a corresponding Universal Character Set code point, which is an integer.

Many human languages have writing systems that require child elements for control of aspects such as bidirectional formating or ruby annotation (see and Section 8.2.4 Overriding the bidirectional algorithm: the BDO element of ). Thus, string, as a simple type that can contain only characters but not child elements, is often not suitable for representing text. In such situations, a complex type that allows mixed content should be considered. For more information, see Section 5.5 Any Element, Any Attribute of .

As noted in , the fact that this specification does not specify an order relation for order for does not preclude other applications from treating strings as being ordered.

Derived datatypesConstructed and Immediately Derived s boolean

boolean has the required to support the mathematical concept of binary-valued logic: {true, false}.

Lexical representation

An instance of a datatype that is defined as can have the following legal literals {true, false, 1, 0}.

Canonical representation

The canonical representation for boolean is the set of literals {true, false}.

&Odec;

RQ-150 (minimum number of digits for decimal)

The minimum number of digits implementations are required to support will be lowered to 16 digits; a health warning will be added to note that implementations of derived datatypes may support more digits of precision than the base decimal type does, but that they are not required to do so.

&odec; represents a subset of the real numbers, which can be represented by decimal numerals. The of &odec; is the set of numbers that can be obtained by multiplyingdividing an integer by a non-positivenegative power of ten, i.e., expressible as i × 10^-ni / 10ⁿ where i and n are integers and n >= 0n ≥ 0. Precision is not reflected in this value space; the number 2.0 is not distinct from the number 2.00. (The datatype may be used for values in which precision is significant.) The order relation on &odec; is the order relation on real numbers, restricted to this subset.

All processors support &odec; numbers with a minimum of 1816 decimal digits (i.e., with a of 18they must support all values which would be allowed by a simple type definition which set to 16). However, processors set an application-defined limit on the maximum number of decimal digits they are prepared to support, in which case that application-defined maximum number be clearly documented.

Lexical representation

&odec; has a lexical representation consisting of a finite-length sequence of decimal digits (#x30-#x39) separated by a period as a decimal indicator. An optional leading sign is allowed. If the sign is omitted, "+" is assumed. Leading and trailing zeroes are optional. If the fractional part is zero, the period and following zero(es) can be omitted. For example: -1.23, 12678967.543233, +100000.00, 210.

The Lexical Representation &odec;LexicalRep |

The lexical space of &odec; is the set of lexical representations which match the grammar given above, or (equivalently) the regular expression -?(([0-9]+(.[0-9]*)?)|(.[0-9]+)).

The mapping from lexical representations to values is the usual one for decimal numerals; it is given formally in:

Canonical representation

The canonical representation for &odec; is defined by prohibiting certain options from the . Specifically, the preceding optional "+" sign is prohibited. The decimal point is required. Leading and trailing zeroes are prohibited subject to the following: there must be at least one digit to the right and to the left of the decimal point which may be a zero.

The mapping from values to canonical representations is given formally in:

Derived datatypesDatatypes based on &odec; &pD;

The &pD; datatype represents decimal numbers, together with their (arithmetic) precisionthe numeric value and (arithmetic) precision of decimal numbers which retain precision; it also includes special values for positive and negative infinity and not a number, and it differentiates between positive zero and negative zero. The special values are introduced to make the datatype correspond closely to decimal datatypes whose definition is planned for the next revision of IEEE/ANSI 754the floating-point decimal datatypes described by the forthcoming revision of IEEE/ANSI 754.

Precision is sometimes given in absolute, sometimes in relative terms. The arithmetic precision of a value is expressed in absolute quantitative terms, by indicating how many digits to the right of the decimal point are significant. 5 has an arithmetic precision of 0, and 5.01 an arithmetic precision of 2.

Value Space Properties of Values numericalValue a &decimal;, positiveInfinity, negativeInfinity or notANumber arithmeticPrecision an &integer; or absent; absent if and only if is a . sign positive, negative, or absent; must be positive if is positive or positiveInfinity, must be negative if is negative or negativeInfinity, must be absent if and only if is notANumber

The property is redundant except when is zero; in other cases, the value is fully determined by the value. Code optimization may well make it desirable to separate out the and the absolute value of the , which will make implementation easier, but the verbal descriptions of such things as equality and order somewhat more complicated.

As explained below, the lexical representation of the value object whose is notANumber is NaN. Accordingly, in English text we use NaN to refer to that value. Similarly we use INF and −INF to refer to the two value objects whose is positiveInfinity and negativeInfinity. These three value objects are also informally called not-a-number, positive infinity, and negative infinity. The latter two together are called the infinities.

Equality and order for are defined as follows:

Two numerical values are ordered (or equal) as their values are ordered (or equal). (This means thethat two zeros with a given but different s are equal; negative zeros are not ordered less than positive zeros.)

A numerical value n is less than, equal to, or greater than and a value v other than INF, -INF, or NaN as n is less than, equal to, or greater than the of v. (This comparison is necessary when comparing values to upper and lower bounds.)

INF is equal only to itself, and is greater than −INF and all numerical values.

−INF is equal only to itself, and is less than INF and all numerical values.

NaN is incomparable with all values, including itself.

Lexical Mapping

's lexical space is the set of all decimal numerals with or without a decimal point, numerals in scientific (exponential) notation, and the character strings INF, +INF, -INF, and NaN. The facet can remove any one or two of the three subsets of numerals, with corresponding reductions in the value space. Using this facet rather than will change the canonical mapping to insure that the resulting datatype will still have canonical representations of all its values. Lexical Space precisionDecimalRep | | |

The lexical mapping and canonical mapping for are the following functions:

Simple Type Definition for &pD;

The of is present in every schema. It has the following properties:

of &pD; http://www.w3.org/2001/XMLSchema The The empty set atomic {

a facet with = collapse and = true

a facet with the value {nodecimal, decimal, scientific}

}

{

an facet with = total

a facet with = false

a facet with = countable

a facet with = true

}

global absent absent The empty sequence &CFacet;s float

RQ-1 (canonical representation of float, double)

The description of canonical representations for float and double needs to be cleaned up.

RQ-140 (positive and negative zero in float and double)

Two zeros will be provided similar to those in precisionDecimal

float is patterned after the IEEE single-precision 32-bit floating point type . The basic of float consists of the values m × 2^e, where m is an integer whose absolute value is less than 2^24, and e is an integer between -149 and 104, inclusive. In addition to the basic described above, the of float also contains the following three special values: positive and negative infinity and not-a-number (NaN). The order relation on float is: x < y iff y - x is positive for x and y in the value space. Positive infinity is greater than all other non-NaN values. NaN equals itself but is incomparable with (neither greater than nor less than) any other value in the .

"Equality" in this Recommendation is defined to be "identity" (i.e., values that are identical in the are equal and vice versa). Identity must be used for the few operations that are defined in this Recommendation. Applications using any of the datatypes defined in this Recommendation may use different definitions of equality for computational purposes; -based computation systems are examples. Nothing in this Recommendation should be construed as requiring that such applications use identity as their equality relationship when computing.

Any value incomparable with the value used for the four bounding facets (, , , and ) will be excluded from the resulting restricted . In particular, when "NaN" is used as a facet value for a bounding facet, since no other float values are comparable with it, the result is a either having NaN as its only member (the inclusive cases) or that is empty (the exclusive cases). If any other value is used for a bounding facet, NaN will be excluded from the resulting restricted ; to add NaN back in requires union with the NaN-only space.

This datatype differs from that of in that there is only one NaN and only one zero. This makes the equality and ordering of values in the data space differ from that of only in that for schema purposes NaN = NaN.

A literal in the representing a decimal number d maps to the normalized value in the of float that is closest to d in the sense defined by ; if d is exactly halfway between two such values then the even value is chosen.

Lexical representation

float values have a lexical representation consisting of a mantissa followed, optionally, by the character E or e, followed by an exponent. The exponent be an . The mantissa must be a number. The representations for exponent and mantissa must follow the lexical rules for and . If the E or e and the following exponent are omitted, an exponent value of 0 is assumed.

The special values positive and negative infinity and not-a-number have lexical representations INF, -INF and NaN, respectively. Lexical representations for zero may take a positive or negative sign.

For example, -1E4, 1267.43233E12, 12.78e-2, 12 , -0, 0 and INF are all legal literals for float.

Canonical representation

The canonical representation for float is defined by prohibiting certain options from the . Specifically, the exponent must be indicated by "E". Leading zeroes and the preceding optional "+" sign are prohibited in the exponent. If the exponent is zero, it must be indicated by "E0". For the mantissa, the preceding optional "+" sign is prohibited and the decimal point is required. Leading and trailing zeroes are prohibited subject to the following: number representations must be normalized such that there is a single digit which is non-zero to the left of the decimal point and at least a single digit to the right of the decimal point unless the value being represented is zero. The canonical representation for zero is 0.0E0.

NaN has the canonical form NaN. Infinity and negative infinity have the canonical forms INF and -INF respectively. Besides these special values, the general form of the canonical form for float is a mantissa, which is a decimal, followed by E followed by an exponent which is an integer. Leading zeroes and the preceding optional + sign are prohibited in the exponent. If the exponent is zero it must be indicated by E0. For the mantissa, the preceding optional + sign is prohibited and the decimal point is required. Leading and trailing zeroes are prohibited subject to the following: number representations must be normalized such that there is a single digit which is non-zero to the left of the decimal point and at least a single digit to the right of the decimal point unless the value being represented is zero. The canonical form of positive zero is 0.0E0. The canonical form for negative zero is -0.0E0. Beyond the one required digit after the decimal point in the mantissa, there must be as many, but only as many, additional digits as are needed to uniquely distinguish the value from all other values for the datatype after rounding.

double

The double datatype is patterned after the IEEE double-precision 64-bit floating point type . The basic of double consists of the values m × 2^e, where m is an integer whose absolute value is less than 2^53, and e is an integer between -1075 and 970, inclusive. In addition to the basic described above, the of double also contains the following three special values: positive and negative infinity and not-a-number (NaN). The order relation on double is: x < y iff y - x is positive for x and y in the value space. Positive infinity is greater than all other non-NaN values. NaN equals itself but is incomparable with (neither greater than nor less than) any other value in the .

Any value incomparable with the value used for the four bounding facets (, , , and ) will be excluded from the resulting restricted