XPath and XQuery Functions and Operators 4.0

4 Functions and operators on numerics

This section specifies arithmetic operators on the numeric datatypes defined in [XML Schema Part 2: Datatypes Second Edition].

4.4 Functions on numeric values

The following functions are defined on numeric types. Each function returns a value of the same type as the type of its argument.

If the argument is the empty sequence, the empty sequence is returned.
For xs:float and xs:double arguments, if the argument is NaN, NaN is returned.
With the exception of fn:abs, functions with arguments of type xs:float and xs:double that are positive or negative infinity return positive or negative infinity.

Function	Meaning
`fn:abs`	Returns the absolute value of `$value`.
`fn:ceiling`	Rounds `$value` upwards to a whole number.
`fn:floor`	Rounds `$value` downwards to a whole number.
`fn:round`	Rounds a value to a specified number of decimal places, with control over how the rounding takes place.
`fn:round-half-to-even`	Rounds a value to a specified number of decimal places, rounding to make the last digit even if two such values are equally near.
`fn:divide-decimals`	Divides one `xs:decimal` by another to a defined precision, returning both the quotient and the remainder.
`fn:is-NaN`	Returns `true` if the argument is the `xs:float` or `xs:double` value `NaN`.

Note:

The fn:round function has been extended with a third argument in version 4.0 of this specification; this means that the fn:ceiling, fn:floor, and fn:round-half-to-even functions are now technically redundant. They are retained, however, both for backwards compatibility and for convenience.

4.4.4 fn:round

Changes in 4.0 ⬇ ⬆

A third argument has been added, providing control over the rounding mode. [Issues 1187 1274 PRs 1260 1275 11 June 2024]
It is explicitly stated that the limits for $precision are implementation-defined. [Issue 1705 1 January 2025]
It is explicitly stated that the limits for $precision are implementation-defined. [Issue 1705 1 January 2025]

Summary

Rounds a value to a specified number of decimal places, with control over how the rounding takes place.

Signature

`fn:round`(
`$value`	`as` `xs:numeric?`,
`$precision`	`as` `xs:integer?`	`:=` `0`,
`$mode`	`as` `enum('floor', 'ceiling', 'toward-zero', 'away-from-zero', 'half-to-floor', 'half-to-ceiling', 'half-toward-zero', 'half-away-from-zero', 'half-to-even')?`	`:=` `'half-to-ceiling'`
) `as` `xs:numeric?`

Properties

This function is ·deterministic·, ·context-independent·, and ·focus-independent·.

Rules

General rules: see 4.4 Functions on numeric values.

The function returns a value that is close to $value and that is a multiple of ten to the power of minus $precision. The default value of $precision is zero, in which case the function returns a whole number (but not necessarily an xs:integer).

The detailed way in which rounding is performed depends on the value of $mode, as follows. Here L means the highest multiple of ten to the power of minus $precision that is less than or equal to $value, U means the lowest multiple of ten to the power of minus $precision that is greater than or equal to $value, N means the multiple of ten to the power of minus $precision that is numerically closest to $value, and midway means that $value is equal to the arithmetic mean of L and U.

Rounding Modes
Rounding Mode	Meaning
`'floor'`	Returns `L`.
`'ceiling'`	Returns `U`.
`'toward-zero'`	Returns `L` if `$value` is positive, otherwise `U`.
`'away-from-zero'`	Returns `U` if `$value` is positive, otherwise `L`
`'half-to-floor'`	Returns `N`, unless midway, in which case `L`.
`'half-to-ceiling'`	Returns `N`, unless midway, in which case `U`. This is the default.
`'half-toward-zero'`	Returns `N`, unless midway, in which case it returns `L` if `$value` is positive, otherwise `U`.
`'half-away-from-zero'`	Returns `N`, unless midway, in which case it returns `U` if `$value` is positive, otherwise `L`.
`'half-to-even'`	Returns `N`, unless midway, in which case it returns whichever of `L` and `U` has a last significant digit that is even.

For the four types xs:float, xs:double, xs:decimal and xs:integer, it is guaranteed that if the type of $value is an instance of type T then the result will also be an instance of T. The result may also be an instance of a type derived from one of these four by restriction. For example, if $value is an instance of xs:decimal and $precision is less than one, then the result may be an instance of xs:integer.

If the second argument is omitted or is an empty sequence, the function produces the same result as when $precision = 0 (that is, it rounds to a whole number).

When $value is of type xs:float and xs:double:

If $value is NaN, positive or negative zero, or positive or negative infinity, then the result is the same as the argument.
For other values, the argument is cast to xs:decimal using an implementation of xs:decimal that imposes no limits on the number of digits that can be represented. The function is applied to this xs:decimal value, and the resulting xs:decimal is cast back to xs:float or xs:double as appropriate to form the function result. If the resulting xs:decimal value is zero, then positive or negative zero is returned according to the sign of $value.

There may be ·implementation-defined· limits on the precision available. If the requested $precision is outside this range, it should be adjusted to the nearest value supported by the implementation.

Notes

This function is typically used with a non-zero $precision in financial applications where the argument is of type xs:decimal. For arguments of type xs:float and xs:double the results may be counter-intuitive. For example, consider round(35.425e0, 2). The result is not 35.43, as might be expected, but 35.42. This is because the xs:double written as 35.425e0 has an exact value equal to 35.42499999999..., which is closer to 35.42 than to 35.43.

The call round($v, 0, "floor") is equivalent to floor($v).

The call round($v, 0, "ceiling") is equivalent to ceiling($v).

The call round($v, $p, "half-to-even") is equivalent to round-half-to-even($v, $p).

Examples

Expression	Result
`round(2.5)`	3.0
`round(2.4999)`	2.0
`round(-2.5)`	-2.0
`round(1.125, 2)`	1.13
`round(8452, -2)`	8500
`round(3.1415e0, 2)`	3.14e0
`math:log(0) => round()`	-xs:double('INF')
`round(1.7, 0, "floor")`	1
`round(-1.7, 0, "floor")`	-2
`round(1.7, 0, "ceiling")`	2
`round(-1.7, 0, "ceiling")`	-1
`round(1.7, 0, "toward-zero")`	1
`round(-1.7, 0, "toward-zero")`	-1
`round(1.7, 0, "away-from-zero")`	2
`round(-1.7, 0, "away-from-zero")`	-2
`round(1.125, 2, "half-to-floor")`	1.12
`round(-1.125, 2, "half-to-floor")`	-1.13
`round(1.125, 2, "half-to-ceiling")`	1.13
`round(-1.125, 2, "half-to-ceiling")`	-1.12
`round(1.125, 2, "half-toward-zero")`	1.12
`round(-1.125, 2, "half-toward-zero")`	-1.12
`round(1.125, 2, "half-away-from-zero")`	1.13
`round(-1.125, 2, "half-away-from-zero")`	-1.13
`round(1.125, 2, "half-to-even")`	1.12
`round(-1.125, 2, "half-to-even")`	-1.12

4.4.5 fn:round-half-to-even

Changes in 4.0 ⬇ ⬆

It is explicitly stated that the limits for $precision are implementation-defined. [Issue 1705 1 January 2025]

Summary

Rounds a value to a specified number of decimal places, rounding to make the last digit even if two such values are equally near.

Signature

`fn:round-half-to-even`(
`$value`	`as` `xs:numeric?`,
`$precision`	`as` `xs:integer?`	`:=` `0`
) `as` `xs:numeric?`

Properties

This function is ·deterministic·, ·context-independent·, and ·focus-independent·.

Rules

General rules: see 4.4 Functions on numeric values.

The function returns the nearest (that is, numerically closest) value to $value that is a multiple of ten to the power of minus $precision. If two such values are equally near (e.g. if the fractional part in $value is exactly .500...), the function returns the one whose least significant digit is even.

If the second argument is omitted or an empty sequence, the function produces the same result as the two-argument version with $precision = 0.

For arguments of type xs:float and xs:double:

If the argument is NaN, positive or negative zero, or positive or negative infinity, then the result is the same as the argument.
In all other cases, the argument is cast to xs:decimal using an implementation of xs:decimal that imposes no limits on the number of digits that can be represented. The function is applied to this xs:decimal value, and the resulting xs:decimal is cast back to xs:float or xs:double as appropriate to form the function result. If the resulting xs:decimal value is zero, then positive or negative zero is returned according to the sign of the original argument.

Notes

This function is typically used in financial applications where the argument is of type xs:decimal. For arguments of type xs:float and xs:double the results may be counter-intuitive. For example, consider round-half-to-even(xs:float(150.015), 2). The result is not 150.02 as might be expected, but 150.01. This is because the conversion of the xs:float value represented by the literal 150.015 to an xs:decimal produces the xs:decimal value 150.014999389..., which is closer to 150.01 than to 150.02.

From 4.0, the effect of this function can also be achieved by calling fn:round with the third argument set to "half-to-even".

Examples

Expression	Result
`round-half-to-even(0.5)`	0.0
`round-half-to-even(1.5)`	2.0
`round-half-to-even(2.5)`	2.0
`round-half-to-even(3.567812e+3, 2)`	3567.81e0
`round-half-to-even(4.7564e-3, 2)`	0.0e0
`round-half-to-even(35612.25, -2)`	35600
`math:log(0) => round-half-to-even()`	-xs:double('INF')

4.4.6 fn:divide-decimals

Changes in 4.0 ⬇ ⬆

New in 4.0. [Issue 1261 1 January 2025]

Summary

Divides one xs:decimal by another to a defined precision, returning both the quotient and the remainder.

Signature

`fn:divide-decimals`(
`$value`	`as` `xs:decimal`,
`$divisor`	`as` `xs:decimal`,
`$precision`	`as` `xs:integer?`	`:=` `0`
) `as` `record(quotient as xs:decimal, remainder as xs:decimal)`

Properties

This function is ·deterministic·, ·context-independent·, and ·focus-independent·.

Rules

The function returns a record with two fields:

quotient is the xs:decimal value furthest from zero such that:
1. quotient is an exact multiple of ten to the power of minus $precision;
2. the absolute value of quotient multipled by $divisor is less than or equal to the absolute value of $value;
3. the sign of quotient is the same as the sign of op:numeric-divide($value, $divisor).
remainder is the exact result of subtracting quotient multiplied by $divisor from $value.

If $precision exceeds the maximum precision for xs:decimal values supported by the implementation, then the maximum available precision is used in its place.

Error Conditions

A dynamic error is raised [err:FOAR0001] if $divisor is zero.

Examples

Expression	Result
`divide-decimals(120.6, 60.3, 4)`	{ "quotient": 2, "remainder": 0 }
`divide-decimals(10, 3)`	{ "quotient": 3, "remainder": 1 }
`divide-decimals(10, -3)`	{ "quotient": -3, "remainder": 1 }
`divide-decimals(-10, 3)`	{ "quotient": -3, "remainder": -1 }
`divide-decimals(-10, -3)`	{ "quotient": 3, "remainder": -1 }
`divide-decimals(10, 3, 6)`	{ "quotient": 3.333333, "remainder": 0.000001 }
`divide-decimals(100, 30)`	{ "quotient": 3, "remainder": 10 }
`divide-decimals(150_862, 7, -3)`	{ "quotient": 21_000, "remainder": 3_862 }

F Checklist of implementation-defined features (Non-Normative)

It is ·implementation-defined· which version of Unicode is supported, but it is recommended that the most recent version of Unicode be used. (See Conformance.)
It is ·implementation-defined· whether the type system is based on XML Schema 1.0 or XML Schema 1.1. (See Conformance.)
It is ·implementation-defined· whether definitions that rely on XML (for example, the set of valid XML characters) should use the definitions in XML 1.0 or XML 1.1. (See Conformance.)
Implementations may attach an ·implementation-defined· meaning to options in the map that are not described in this specification. These options should use values of type xs:QName as the option names, using an appropriate namespace. (See Options.)
It is ·implementation-defined· which version of [The Unicode Standard] is supported, but it is recommended that the most recent version of Unicode be used. (See Strings, characters, and codepoints.)
[Definition] Some functions (such as fn:distinct-values, fn:unordered, map:keys, and map:for-each) produce results in an ·implementation-defined· or ·implementation-dependent· order. In such cases two calls with the same arguments are not guaranteed to produce the results in the same order. These functions are said to be nondeterministic with respect to ordering. (See Properties of functions.)
Where the results of a function are described as being (to a greater or lesser extent) ·implementation-defined· or ·implementation-dependent·, this does not by itself remove the requirement that the results should be deterministic: that is, that repeated calls with the same explicit and implicit arguments must return identical results. (See Properties of functions.)
In addition, the values of $input, typically serialized and converted to an xs:string, and $label (if supplied and non-empty) may be output to an ·implementation-defined· destination. (See fn:trace.)
Consider a situation in which a user wants to investigate the actual value passed to a function. Assume that in a particular execution, $v is an xs:decimal with value 124.84. Writing fn:trace($v, 'the value of $v is:') will return $v. The processor may output "124.84" and "the value of $v is:" to an ·implementation-defined· destination. (See fn:trace.)
Similar to fn:trace, the values of $input, typically serialized and converted to an xs:string, and $label (if supplied and non-empty) may be output to an ·implementation-defined· destination. (See fn:message.)
They may provide an ·implementation-defined· mechanism that allows users to choose between raising an error and returning a result that is modulo the largest representable integer value. See [ISO 10967]. (See Arithmetic operators on numeric values.)
For xs:decimal values, let N be the number of digits of precision supported by the implementation, and let M (M <= N) be the minimum limit on the number of digits required for conformance (18 digits for XSD 1.0, 16 digits for XSD 1.1). Then for addition, subtraction, and multiplication operations, the returned result should be accurate to N digits of precision, and for division and modulus operations, the returned result should be accurate to at least M digits of precision. The actual precision is ·implementation-defined·. If the number of digits in the mathematical result exceeds the number of digits that the implementation retains for that operation, the result is truncated or rounded in an ·implementation-defined· manner. (See Arithmetic operators on numeric values.)
The [IEEE 754-2019] specification also describes handling of two exception conditions called divideByZero and invalidOperation. The IEEE divideByZero exception is raised not only by a direct attempt to divide by zero, but also by operations such as log(0). The IEEE invalidOperation exception is raised by attempts to call a function with an argument that is outside the function’s domain (for example, sqrt(-1) or log(-1)). Although IEEE defines these as exceptions, it also defines “default non-stop exception handling” in which the operation returns a defined result, typically positive or negative infinity, or NaN. With this function library, these IEEE exceptions do not cause a dynamic error at the application level; rather they result in the relevant function or operator returning the defined non-error result. The underlying IEEE exception may be notified to the application or to the user by some ·implementation-defined· warning condition, but the observable effect on an application using the functions and operators defined in this specification is simply to return the defined result (typically -INF, +INF, or NaN) with no error. (See Arithmetic operators on numeric values.)
The [IEEE 754-2019] specification distinguishes two NaN values: a quiet NaN and a signaling NaN. These two values are not distinguishable in the XDM model: the value spaces of xs:float and xs:double each include only a single NaN value. This does not prevent the implementation distinguishing them internally, and triggering different ·implementation-defined· warning conditions, but such distinctions do not affect the observable behavior of an application using the functions and operators defined in this specification. (See Arithmetic operators on numeric values.)
The implementation may adopt a different algorithm provided that it is equivalent to this formulation in all cases where ·implementation-dependent· or ·implementation-defined· behavior does not affect the outcome, for example, the implementation-defined precision of the result of xs:decimal division. (See op:numeric-integer-divide.)
There may be ·implementation-defined· limits on the precision available. If the requested $precision is outside this range, it should be adjusted to the nearest value supported by the implementation. (See fn:round.)
There may be ·implementation-defined· limits on the precision available. If the requested $precision is outside this range, it should be adjusted to the nearest value supported by the implementation. (See fn:round.)
There may be ·implementation-defined· limits on the precision available. If the requested $precision is outside this range, it should be adjusted to the nearest value supported by the implementation. (See fn:round-half-to-even.)
There may be ·implementation-defined· limits on the precision available. If the requested $precision is outside this range, it should be adjusted to the nearest value supported by the implementation. (See fn:round-half-to-even.)
There may be ·implementation-defined· limits on the precision available. If the requested $precision is outside this range, it should be adjusted to the nearest value supported by the implementation. (See fn:divide-decimals.)
There may be ·implementation-defined· limits on the precision available. If the requested $precision is outside this range, it should be adjusted to the nearest value supported by the implementation. (See fn:divide-decimals.)
XSD 1.1 allows the string +INF as a representation of positive infinity; XSD 1.0 does not. It is ·implementation-defined· whether XSD 1.1 is supported. (See fn:number.)
Any other format token, which indicates a numbering sequence in which that token represents the number 1 (one) (but see the note below). It is ·implementation-defined· which numbering sequences, additional to those listed above, are supported. If an implementation does not support a numbering sequence represented by the given token, it must use a format token of 1. (See fn:format-integer.)
For all format tokens other than a digit-pattern, there may be ·implementation-defined· lower and upper bounds on the range of numbers that can be formatted using this format token; indeed, for some numbering sequences there may be intrinsic limits. For example, the format token U+2460 (CIRCLED DIGIT ONE, ①) has a range imposed by the Unicode character repertoire — zero to 20 in Unicode versions prior to 3.2, or zero to 50 in subsequent versions. For the numbering sequences described above any upper bound imposed by the implementation must not be less than 1000 (one thousand) and any lower bound must not be greater than 1. Numbers that fall outside this range must be formatted using the format token 1. (See fn:format-integer.)
The set of languages for which numbering is supported is ·implementation-defined·. If the $language argument is absent, or is set to an empty sequence, or is invalid, or is not a language supported by the implementation, then the number is formatted using the default language from the dynamic context. (See fn:format-integer.)
...either a or t, to indicate alphabetic or traditional numbering respectively, the default being ·implementation-defined·. (See fn:format-integer.)
The string of characters between the parentheses, if present, is used to select between other possible variations of cardinal or ordinal numbering sequences. The interpretation of this string is ·implementation-defined·. No error occurs if the implementation does not define any interpretation for the defined string. (See fn:format-integer.)
It is ·implementation-defined· what combinations of values of the format token, the language, and the cardinal/ordinal modifier are supported. If ordinal numbering is not supported for the combination of the format token, the language, and the string appearing in parentheses, the request is ignored and cardinal numbers are generated instead. (See fn:format-integer.)
The use of the a or t modifier disambiguates between numbering sequences that use letters. In many languages there are two commonly used numbering sequences that use letters. One numbering sequence assigns numeric values to letters in alphabetic sequence, and the other assigns numeric values to each letter in some other manner traditional in that language. In English, these would correspond to the numbering sequences specified by the format tokens a and i. In some languages, the first member of each sequence is the same, and so the format token alone would be ambiguous. In the absence of the a or t modifier, the default is ·implementation-defined·. (See fn:format-integer.)
The static context provides a set of decimal formats. One of the decimal formats is unnamed, the others (if any) are identified by a QName. There is always an unnamed decimal format available, but its contents are ·implementation-defined·. (See Defining a decimal format.)
IEEE states that the preferred quantum is language-defined. In this specification, it is ·implementation-defined·. (See Trigonometric and exponential functions.)
IEEE defines various rounding algorithms for inexact results, and states that the choice of rounding direction, and the mechanisms for influencing this choice, are language-defined. In this specification, the rounding direction and any mechanisms for influencing it are ·implementation-defined·. (See Trigonometric and exponential functions.)
The map returned by the fn:random-number-generator function may contain additional entries beyond those specified here, but it must match the record type defined above. The meaning of any additional entries is ·implementation-defined·. To avoid conflict with any future version of this specification, the keys of any such entries should start with an underscore character. (See fn:random-number-generator.)
If two query parameters use the same keyword then the last one wins. If a query parameter uses a keyword or value which is not defined in this specification then the meaning is ·implementation-defined·. If the implementation recognizes the meaning of the keyword and value then it should interpret it accordingly; if it does not recognize the keyword or value then if the fallback parameter is present with the value no it should reject the collation as unsupported, otherwise it should ignore the unrecognized parameter. (See The Unicode Collation Algorithm.)
The following query parameters are defined. If any parameter is absent, the default is ·implementation-defined· except where otherwise stated. The meaning given for each parameter is non-normative; the normative specification is found in [UTS #35]. (See The Unicode Collation Algorithm.)
Because the set of collations that are supported is ·implementation-defined·, an implementation has the option to support all collation URIs, in which case it will never raise this error. (See Choosing a collation.)
The properties available are as defined for the Unicode Collation Algorithm (see 5.3.4 The Unicode Collation Algorithm). Additional ·implementation-defined· properties may be specified as described in the rules for UCA collation URIs. (See fn:collation.)
It is possible to define collations that do not have the ability to generate collation keys. Supplying such a collation will cause the function to fail. The ability to generate collation keys is an ·implementation-defined· property of the collation. (See fn:collation-key.)
Conforming implementations must support normalization form NFC and may support normalization forms NFD, NFKC, NFKD, and FULLY-NORMALIZED. They may also support other normalization forms with ·implementation-defined· semantics. (See fn:normalize-unicode.)
It is ·implementation-defined· which version of Unicode (and therefore, of the normalization algorithms and their underlying data) is supported by the implementation. See [UAX #15] for details of the stability policy regarding changes to the normalization rules in future versions of Unicode. If the input string contains codepoints that are unassigned in the relevant version of Unicode, or for which no normalization rules are defined, the fn:normalize-unicode function leaves such codepoints unchanged. If the implementation supports the requested normalization form then it must be able to handle every input string without raising an error. (See fn:normalize-unicode.)
It is possible to define collations that do not have the ability to decompose a string into units suitable for substring matching. An argument to a function defined in this section may be a URI that identifies a collation that is able to compare two strings, but that does not have the capability to split the string into collation units. Such a collation may cause the function to fail, or to give unexpected results, or it may be rejected as an unsuitable argument. The ability to decompose strings into collation units is an ·implementation-defined· property of the collation. The fn:collation-available function can be used to ask whether a particular collation has this property. (See Functions based on substring matching.)
The result of the function will always be such that validation against this schema would succeed. However, it is ·implementation-defined· whether the result is typed or untyped, that is, whether the elements and attributes in the returned tree have type annotations that reflect the result of validating against this schema. (See fn:analyze-string.)
Some URI schemes are hierarchical and some are non-hierarchical. Implementations must treat the following schemes as non-hierarchical: jar, mailto, news, tag, tel, and urn. Whether additional schemes are known to be non-hierarchical ·implementation-defined·. If a scheme is not known to be non-hierarchical, it must be treated as hierarchical. (See Parsing and building URIs.)
If the omit-default-ports option is true, the port is discarded and set to the empty sequence if the port number is the same as the default port for the given scheme. Implementations should recognize the default ports for http (80), https (443), ftp (21), and ssh (22). Exactly which ports are recognized is ·implementation-defined·. (See fn:parse-uri.)
If the omit-default-ports option is true then the $port is set to the empty sequence if the port number is the same as the default port for the given scheme. Implementations should recognize the default ports for http (80), https (443), ftp (21), and ssh (22). Exactly which ports are recognized is ·implementation-defined·. (See fn:build-uri.)
Processors may support a greater range and/or precision. The limits are ·implementation-defined·. (See Limits and precision.)
Similarly, a processor may be unable accurately to represent the result of dividing a duration by 2, or multiplying a duration by 0.5. A processor that limits the precision of the seconds component of duration values must deliver a result that is as close as possible to the mathematically precise result, given these limits; if two values are equally close, the one that is chosen is ·implementation-defined·. (See Limits and precision.)
All conforming processors must support year values in the range 1 to 9999, and a minimum fractional second precision of 1 millisecond or three digits (i.e., s.sss). However, processors may set larger ·implementation-defined· limits on the maximum number of digits they support in these two situations. Processors may also choose to support the year 0 and years with negative values. The results of operations on dates that cross the year 0 are ·implementation-defined·. (See Limits and precision.)
Similarly, a processor that limits the precision of the seconds component of date and time or duration values may need to deliver a rounded result for arithmetic operations. Such a processor must deliver a result that is as close as possible to the mathematically precise result, given these limits: if two values are equally close, the one that is chosen is ·implementation-defined·. (See Limits and precision.)
...the format token n, N, or Nn, indicating that the value of the component is to be output by name, in lower-case, upper-case, or title-case respectively. Components that can be output by name include (but are not limited to) months, days of the week, timezones, and eras. If the processor cannot output these components by name for the chosen calendar and language then it must use an ·implementation-defined· fallback representation. (See The picture string.)
...indicates alphabetic or traditional numbering respectively, the default being ·implementation-defined·. This has the same meaning as in the second argument of fn:format-integer. (See The picture string.)
The sequence of characters in the (adjusted) first presentation modifier is reversed (for example, 999'### becomes ###'999). If the result is not a valid decimal digit pattern, then the output is ·implementation-defined·. (See Formatting Fractional Seconds.)
The output for these components is entirely ·implementation-defined·. The default presentation modifier for these components is n, indicating that they are output as names (or conventional abbreviations), and the chosen names will in many cases depend on the chosen language: see 9.8.4.8 The language, calendar, and place arguments. (See Formatting Other Components.)
The set of languages, calendars, and places that are supported in the ·date formatting functions· is ·implementation-defined·. When any of these arguments is omitted or is an empty sequence, an ·implementation-defined· default value is used. (See The language, calendar, and place arguments.)
The choice of the names and abbreviations used in any given language is ·implementation-defined·. For example, one implementation might abbreviate July as Jul while another uses Jly. In German, one implementation might represent Saturday as Samstag while another uses Sonnabend. Implementations may provide mechanisms allowing users to control such choices. (See The language, calendar, and place arguments.)
The choice of the names and abbreviations used in any given language for calendar units such as days of the week and months of the year is ·implementation-defined·. (See The language, calendar, and place arguments.)
The calendar value if present must be a valid EQName (dynamic error: [err:FOFD1340]). If it is a lexical QName then it is expanded into an expanded QName using the statically known namespaces; if it has no prefix then it represents an expanded-QName in no namespace. If the expanded QName is in no namespace, then it must identify a calendar with a designator specified below (dynamic error: [err:FOFD1340]). If the expanded QName is in a namespace then it identifies the calendar in an ·implementation-defined· way. (See The language, calendar, and place arguments.)
At least one of the above calendars must be supported. It is ·implementation-defined· which calendars are supported. (See The language, calendar, and place arguments.)
The requirement to deliver a deterministic result has performance implications, and for this reason implementations may provide a user option to evaluate the function without a guarantee of determinism. The manner in which any such option is provided is ·implementation-defined·. If the user has not selected such an option, a call of the function must either return a deterministic result or must raise a dynamic error [err:FODC0003]. (See fn:doc.)
Various aspects of this processing are ·implementation-defined·. Implementations may provide external configuration options that allow any aspect of the processing to be controlled by the user. In particular:... (See fn:doc.)
It is ·implementation-defined· whether DTD validation and/or schema validation is applied to the source document. (See fn:doc.)
The effect of a fragment identifier in the supplied URI is ·implementation-defined·. One possible interpretation is to treat the fragment identifier as an ID attribute value, and to return a document node having the element with the selected ID value as its only child. (See fn:doc.)
By default, this function is ·deterministic·. This means that repeated calls on the function with the same argument will return the same result. However, for performance reasons, implementations may provide a user option to evaluate the function without a guarantee of determinism. The manner in which any such option is provided is ·implementation-defined·. If the user has not selected such an option, a call to this function must either return a deterministic result or must raise a dynamic error [err:FODC0003]. (See fn:collection.)
By default, this function is ·deterministic·. This means that repeated calls on the function with the same argument will return the same result. However, for performance reasons, implementations may provide a user option to evaluate the function without a guarantee of determinism. The manner in which any such option is provided is ·implementation-defined·. If the user has not selected such an option, a call to this function must either return a deterministic result or must raise a dynamic error [err:FODC0003]. (See fn:uri-collection.)
...the processor may use ·implementation-defined· heuristics to determine the likely encoding, otherwise... (See fn:unparsed-text.)
The fact that the resolution of URIs is defined by a mapping in the dynamic context means that in effect, various aspects of the behavior of this function are ·implementation-defined·. Implementations may provide external configuration options that allow any aspect of the processing to be controlled by the user. In particular:... (See fn:unparsed-text.)
The collation used for matching names is ·implementation-defined·, but must be the same as the collation used to ensure that the names of all environment variables are unique. (See fn:environment-variable.)
Except to the extent defined by these options, the precise process used to construct the XDM instance is ·implementation-defined·. In particular, it is implementation-defined whether an XML 1.0 or XML 1.1 parser is used. (See fn:parse-xml.)
Except as explicitly defined, the precise process used to construct the XDM instance is ·implementation-defined·. In particular, it is implementation-defined whether an XML 1.0 or XML 1.1 parser is used. (See fn:parse-xml-fragment.)
If the second argument is omitted, or is supplied in the form of an output:serialization-parameters element, then the values of any serialization parameters that are not explicitly specified is ·implementation-defined·, and may depend on the context. (See fn:serialize.)
Because the [DOM: Living Standard] and [HTML: Living Standard] are not fixed, it is ·implementation-defined· which versions are used. (See XDM Mapping from HTML DOM Nodes.)
If an implementation allows these nodes to be passed in via an API or similar mechanism, their behaviour is ·implementation-defined·. (See XDM Mapping from HTML DOM Nodes.)
If the local name contains a character that is not a valid XML NameStartChar or NameChar, then an ·implementation-defined· replacement string is used. The result must be a valid NCName. (See node-name Accessor.)
If the local name contains a character that is not a valid XML NameStartChar or NameChar, then an ·implementation-defined· replacement string is used. The result must be a valid NCName. (See node-name Accessor.)
Additional ·implementation-defined· parser options are allowed. (See HTML parser options.)
Any other method and html-version combinations are ·implementation-defined·. (See fn:parse-html.)
The default behaviour is ·implementation-defined·. (See fn:parse-html.)
An ·implementation-defined· parsing algorithm, tree construction, and validation consistent with the specified HTML version. (See fn:parse-html.)
The input may contain deviations from the grammar of [RFC 7159], which are handled in an ·implementation-defined· way. (Note: some popular extensions include allowing quotes on keys to be omitted, allowing a comma to appear after the last item in an array, allowing leading zeroes in numbers, and allowing control characters such as tab and newline to be present in unescaped form.) Since the extensions accepted are implementation-defined, an error may be raised [err:FOJS0001] if the input does not conform to the grammar. (See fn:parse-json.)
The supplied function is called to process the string value of any JSON number in the input. By default, numbers are processed by converting to xs:double using the XPath casting rules. Supplying the value xs:decimal#1 will instead convert to xs:decimal (which potentially retains more precision, but disallows exponential notation), while supplying a function that casts to (xs:decimal | xs:double) will treat the value as xs:decimal if there is no exponent, or as xs:double otherwise. Supplying the value fn:identity#1 causes the value to be retained unchanged as an xs:untypedAtomic. If the liberal option is false (the default), then the supplied number-parser is called if and only if the value conforms to the JSON grammar for numbers (for example, a leading plus sign and redundant leading zeroes are not allowed). If the liberal option is true then it is also called if the value conforms to an ·implementation-defined· extension of this grammar. (See fn:parse-json.)
The input may contain deviations from the grammar of [RFC 7159], which are handled in an ·implementation-defined· way. (Note: some popular extensions include allowing quotes on keys to be omitted, allowing a comma to appear after the last item in an array, allowing leading zeroes in numbers, and allowing control characters such as tab and newline to be present in unescaped form.) Since the extensions accepted are implementation-defined, an error may be raised (see below) if the input does not conform to the grammar. (See fn:json-to-xml.)
Default: ·Implementation-defined·. (See fn:json-to-xml.)
Indicates that the resulting XDM instance must be typed; that is, the element and attribute nodes must carry the type annotations that result from validation against the schema given at C.2 Schema for the result of fn:json-to-xml, or against an ·implementation-defined· schema if the liberal option has the value true. (See fn:json-to-xml.)
The result of the function will always be such that validation against this schema would succeed. However, it is ·implementation-defined· whether the result is typed or untyped, that is, whether the elements and attributes in the returned tree have type annotations that reflect the result of validating against this schema. (See fn:csv-to-xml.)
Additional, ·implementation-defined· options may be available, for example, to control aspects of the XML serialization, to specify the grammar start symbol, or to produce output formats other than XML. (See fn:invisible-xml.)
If the arguments to fn:function-lookup identify a function that is present in the static context of the function call, the function will always return the same function that a static reference to this function would bind to. If there is no such function in the static context, then the results depend on what is present in the dynamic context, which is ·implementation-defined·. (See fn:function-lookup.)
Default: The version given in the prolog of the library module; or ·implementation-defined· if this is absent. (See fn:load-xquery-module.)
A sequence of URIs (in the form of xs:string values) which may be used or ignored in an ·implementation-defined· way.... (See fn:load-xquery-module.)
Values for vendor-defined configuration options for the XQuery processor used to process the request. The key is the name of an option, expressed as a QName: the namespace URI of the QName should be a URI controlled by the vendor of the XQuery processor. The meaning of the associated value is ·implementation-defined·. Implementations should ignore options whose names are in an unrecognized namespace. The ·option parameter conventions· do not apply to this contained map.... (See fn:load-xquery-module.)
It is ·implementation-defined· whether constructs in the library module are evaluated in the same ·execution scope· as the calling module. (See fn:load-xquery-module.)
The library module that is loaded may import schema declarations using an import schema declaration. It is ·implementation-defined· whether schema components in the in-scope schema definitions of the calling module are automatically added to the in-scope schema definitions of the dynamically loaded module. The in-scope schema definitions of the calling and called modules must be consistent, according to the rules defined in Section 2.2.5 Consistency Constraints ^XQ31. (See fn:load-xquery-module.)
Default: ·Implementation-defined·. (See fn:transform.)
Default: ·Implementation-defined·. (See fn:transform.)
If the implementation provides a way of writing or invoking functions with side-effects, this post-processing function might be used to save a copy of the result document to persistent storage. For example, if the implementation provides access to the EXPath File library [EXPath], then a serialized document might be written to filestore by calling the file:write function. Similar mechanisms might be used to issue an HTTP POST request that posts the result to an HTTP server, or to send the document to an email recipient. The semantics of calling functions with side-effects are entirely ·implementation-defined·. (See fn:transform.)
Calls to fn:transform can potentially have side-effects even in the absence of the post-processing option, because the XSLT specification allows a stylesheet to invoke extension functions that have side-effects. The semantics in this case are ·implementation-defined·. (See fn:transform.)
A string intended to be used as the static base URI of the principal stylesheet module. This value must be used if no other static base URI is available. If the supplied stylesheet already has a base URI (which will generally be the case if the stylesheet is supplied using stylesheet-node or stylesheet-location) then it is ·implementation-defined· whether this parameter has any effect. If the value is a relative reference, it is resolved against the static base URI of the fn:transform function call.... (See fn:transform.)
Values for vendor-defined configuration options for the XSLT processor used to process the request. The key is the name of an option, expressed as a QName: the namespace URI of the QName should be a URI controlled by the vendor of the XSLT processor. The meaning of the associated value is ·implementation-defined·. Implementations should ignore options whose names are in an unrecognized namespace. Default is an empty map.... (See fn:transform.)
It is ·implementation-defined· whether the XSLT transformation is executed within the same ·execution scope· as the calling code. (See fn:transform.)
XSLT 1.0 does not define any error codes, so this is the likely outcome with an XSLT 1.0 processor. XSLT 2.0 and 3.0 do define error codes, but some APIs do not expose them. If multiple errors are signaled by the transformation (which is most likely to happen with static errors) then the error code should where possible be that of one of these errors, chosen arbitrarily; the processor may make details of additional errors available to the application in an ·implementation-defined· way. (See fn:transform.)
If ST is xs:float or xs:double, then TV is the xs:decimal value, within the set of xs:decimal values that the implementation is capable of representing, that is numerically closest to SV. If two values are equally close, then the one that is closest to zero is chosen. If SV is too large to be accommodated as an xs:decimal, (see [XML Schema Part 2: Datatypes Second Edition] for ·implementation-defined· limits on numeric values) a dynamic error is raised [err:FOCA0001]. If SV is one of the special xs:float or xs:double values NaN, INF, or -INF, a dynamic error is raised [err:FOCA0002]. (See Casting to xs:decimal.)
In casting to xs:decimal or to a type derived from xs:decimal, if the value is not too large or too small but nevertheless cannot be represented accurately with the number of decimal digits available to the implementation, the implementation may round to the nearest representable value or may raise a dynamic error [err:FOCA0006]. The choice of rounding algorithm and the choice between rounding and error behavior is ·implementation-defined·. (See Casting from xs:string and xs:untypedAtomic.)
If ST is xs:decimal, xs:float or xs:double, then TV is SV with the fractional part discarded and the value converted to xs:integer. Thus, casting 3.1456 returns 3 while -17.89 returns -17. Casting 3.124E1 returns 31. If SV is too large to be accommodated as an integer, (see [XML Schema Part 2: Datatypes Second Edition] for ·implementation-defined· limits on numeric values) a dynamic error is raised [err:FOCA0003]. If SV is one of the special xs:float or xs:double values NaN, INF, or -INF, a dynamic error is raised [err:FOCA0002]. (See Casting to xs:integer.)
The tz timezone database, available at http://www.iana.org/time-zones. It is ·implementation-defined· which version of the database is used. (See IANA Timezone Database.)
Unicode Standard Annex #15: Unicode Normalization Forms. Ed. Mark Davis and Ken Whistler, Unicode Consortium. The current version is 9.0.0, dated 2016-02-24. As with [The Unicode Standard], the version to be used is ·implementation-defined·. Available at: http://www.unicode.org/reports/tr15/. (See UAX #15.)
Unicode Standard Annex #29: Unicode Text Segmentation. Ed. Josh Hadley, Unicode Consortium. The current version is 15.1.0, dated 2023-08-16. As with [The Unicode Standard], the version to be used is ·implementation-defined·. Available at: http://www.unicode.org/reports/tr29/. (See UAX #29.)
The Unicode Consortium, Reading, MA, Addison-Wesley, 2016. The Unicode Standard as updated from time to time by the publication of new versions. See http://www.unicode.org/standard/versions/ for the latest version and additional information on versions of the standard and of the Unicode Character Database. The version of Unicode to be used is ·implementation-defined·, but implementations are recommended to use the latest Unicode version; currently, Version 9.0.0. (See The Unicode Standard.)
Unicode Technical Standard #10: Unicode Collation Algorithm. Ed. Mark Davis and Ken Whistler, Unicode Consortium. The current version is 9.0.0, dated 2016-05-18. As with [The Unicode Standard], the version to be used is ·implementation-defined·. Available at: http://www.unicode.org/reports/tr10/. (See UTS #10.)
Unicode Technical Standard #35: Unicode Locale Data Markup Language. Ed Mark Davis et al, Unicode Consortium. The current version is 29, dated 2016-03-15. As with [The Unicode Standard], the version to be used is ·implementation-defined·. Available at: http://www.unicode.org/reports/tr35/. (See UTS #35.)

G Changes since version 3.1 (Non-Normative)

G.1 Summary of Changes

Use the arrows to browse significant changes since the 3.1 version of this specification.
See 1 Introduction
Sections with significant changes are marked Δ in the table of contents. New functions introduced in this version are marked ➕ in the table of contents.
See 1 Introduction
PR 1547 1551
New in 4.0
See 2.2.8 fn:siblings
PR 629 803
New in 4.0
See 3.2.2 fn:message
PR 1260 1275
A third argument has been added, providing control over the rounding mode.
See 4.4.4 fn:round
New in 4.0
See 4.4.7 fn:is-NaN
PR 1049 1151
Decimal format parameters can now be supplied directly as a map in the third argument, rather than referencing a format defined in the static context.
See 4.7.2 fn:format-number
PR 1205 1230
New in 4.0
See 4.8.2 math:e
See 4.8.16 math:sinh
See 4.8.17 math:cosh
See 4.8.18 math:tanh
The 3.1 specification suggested that every value in the result range should have the same chance of being chosen. This has been corrected to say that the distribution should be arithmetically uniform (because there are as many xs:double values between 0.01 and 0.1 as there are between 0.1 and 1.0).
See 4.9.2 fn:random-number-generator
PR 261 306 993
New in 4.0
See 5.4.1 fn:char
New in 4.0
See 5.4.2 fn:characters
PR 937 995 1190
New in 4.0
See 5.4.13 fn:hash
The $action argument is new in 4.0.
See 5.6.4 fn:replace
New in 4.0
See 6.6.2 fn:parse-uri
PR 1423 1413
New in 4.0
See 6.6.3 fn:build-uri
New in 4.0
See 10.2.6 fn:in-scope-namespaces
Reformulated in 4.0 in terms of the new fn:in-scope-namespaces function; the semantics are unchanged.
See 10.2.7 fn:in-scope-prefixes
Reformulated in 4.0 in terms of the new fn:in-scope-namespaces function; the semantics are unchanged.
See 10.2.8 fn:namespace-uri-for-prefix
New in 4.0
See 13.1.9 fn:replicate
New in 4.0
See 13.1.12 fn:slice
New in 4.0. The function is identical to the internal op:same-key function in 3.1
See 13.2.1 fn:atomic-equal
PR 1120 1150
A callback function can be supplied for comparing individual items.
See 13.2.2 fn:deep-equal
Changed in 4.0 to use transitive equality comparisons for numeric values.
See 13.2.4 fn:distinct-values
New in 4.0. Originally proposed under the name fn:uniform
See 13.4.6 fn:all-equal
New in 4.0. Originally proposed under the name fn:unique
See 13.4.7 fn:all-different
PR 1117 1279
The $options parameter has been added.
See 13.6.6 fn:unparsed-text-lines
A new function is available for processing input data in HTML format.
See 14.2 Functions on HTML Data
PR 259 956
New in 4.0
See 14.2.3 fn:parse-html
PR 975 1058 1246
An option is provided to control how JSON numbers should be formatted.
See 14.3.4 fn:parse-json
Additional options are available, as defined by fn:parse-json.
See 14.3.5 fn:json-doc
PR 533 719 834 1066
New in 4.0
See 14.4.4 fn:csv-to-arrays
See 14.4.7 fn:parse-csv
PR 533 719 834 1066 1605
New in 4.0
See 14.4.9 fn:csv-to-xml
PR 791 1256 1282 1405
New in 4.0
See 14.5.1 fn:invisible-xml
New in 4.0
See 16.2.4 fn:every
New in 4.0
See 16.2.10 fn:highest
New in 4.0
See 16.2.11 fn:index-where
New in 4.0
See 16.2.12 fn:lowest
New in 4.0
See 16.2.15 fn:scan-right
New in 4.0
See 16.2.16 fn:some
PR 521 761
New in 4.0
See 16.2.21 fn:transitive-closure
New in 4.0
See 17.3.6 map:filter
A third argument is added, allowing user control of how absent keys should be handled.
See 17.3.9 map:get
New in 4.0
See 17.3.10 map:items
PR 478 515
New in 4.0
See 17.3.12 map:keys-where
New in 4.0
See 17.3.14 map:of-pairs
New in 4.0
See 17.3.15 map:pair
New in 4.0
See 17.3.16 map:pairs
New in 4.0
See 17.3.19 map:replace
New in 4.0.
See 17.4.7 fn:elements-to-maps
New in 4.0
See 18.2.3 array:empty
A third argument is added, allowing user control of how index-out-of-bounds conditions should be handled.
See 18.2.11 array:get
PR 968 1295
New in 4.0
See 18.2.13 array:index-of
PR 476 1087
New in 4.0
See 18.2.16 array:items
PR 360 476
New in 4.0
See 18.2.18 array:members
See 18.2.19 array:of-members
New in 4.0
See 18.2.22 array:replace
New in 4.0
See 18.2.25 array:slice
New in 4.0
See 18.2.26 array:sort
New in 4.0
See 18.2.27 array:split
Supplying an empty sequence as the value of an optional argument is equivalent to omitting the argument.
See 18.2.28 array:subarray
New functions are provided to obtain information about built-in types and types defined in an imported schema.
See 19 Functions on types
Options are added to customize the form of the output.
See 2.2.6 fn:path
PR 533 719 834
New functions are available for processing input data in CSV (comma separated values) format.
See 14.4 Functions on CSV Data
PR 734 1233
New in 4.0
See 16.2.2 fn:chain
A new function fn:elements-to-maps is provided for converting XDM trees to maps suitable for serialization as JSON. Unlike the fn:xml-to-json function retained from 3.1, this can handle arbitrary XML as input.
See 17.4 Converting Elements to Maps
New in 4.0
See 13.1.5 fn:identity
New in 4.0.
See 4.4.6 fn:divide-decimals
The default for the escape option has been changed to false. The 3.1 specification gave the default value as true, but this appears to have been an error, since it was inconsistent with examples given in the specification and with tests in the test suite.
See 14.3.4 fn:parse-json
The spec has been corrected to note that the function depends on the implicit timezone.
See 13.2.3 fn:compare
It is explicitly stated that the limits for $precision are implementation-defined.
See 4.4.4 fn:round
See 4.4.5 fn:round-half-to-even
It is explicitly stated that the limits for $precision are implementation-defined.
See 4.4.4 fn:round
See 4.4.5 fn:round-half-to-even
PR 173
New in 4.0
See 16.3.4 fn:op
PR 203
New in 4.0
See 17.3.1 map:build
PR 207
New in 4.0
See 10.1.2 fn:parse-QName
See 10.2.5 fn:expanded-QName
PR 222
New in 4.0
See 13.2.7 fn:starts-with-subsequence
See 13.2.8 fn:ends-with-subsequence
See 13.2.9 fn:contains-subsequence
PR 250
New in 4.0
See 13.1.3 fn:foot
See 13.1.15 fn:trunk
See 18.2.2 array:build
See 18.2.8 array:foot
See 18.2.30 array:trunk
PR 258
New in 4.0
See 18.2.14 array:index-where
PR 313
The second argument can now be a sequence of integers.
See 13.1.8 fn:remove
PR 314
New in 4.0
See 17.3.4 map:entries
PR 326
Higher-order functions are no longer an optional feature.
See 1.2 Conformance
PR 419
New in 4.0
See 13.1.7 fn:items-at
PR 434
New in 4.0
See 4.5.2 fn:parse-integer
The function has been extended to allow output in a radix other than 10, for example in hexadecimal.
See 4.6.1 fn:format-integer
PR 482
Deleted an inaccurate statement concerning the behavior of NaN.
See 4.3 Comparison operators on numeric values
PR 507
New in 4.0
See 16.2.13 fn:partition
PR 546
The rules regarding use of non-XML characters in JSON texts have been relaxed.
See 14.3.3 JSON character repertoire
See 14.3.4 fn:parse-json
PR 614
New in 4.0
See 13.2.5 fn:duplicate-values
PR 623
Substantially revised to allow multiple sort key definitions.
See 16.2.17 fn:sort
PR 631
New in 4.0
See 6.3 fn:decode-from-uri
PR 662
Constructor functions now have a zero-arity form; the first argument defaults to the context item.
See 20 Constructor functions
PR 680
The case-insensitive collation is now defined normatively within this specification, rather than by reference to the HTML "living specification", which is subject to change. The collation can now be used for ordering comparisons as well as equality comparisons.
See 5.3.5 The HTML ASCII Case-Insensitive Collation
PR 702
The function can now take any number of arguments (previously it had to be two or more), and the arguments can be sequences of strings rather than single strings.
See 5.4.4 fn:concat
PR 710
Changes the function to return a sequence of key-value pairs rather than a map.
See 16.1.4 fn:function-annotations
PR 727
It has been clarified that loading a module has no effect on the static or dynamic context of the caller.
See 16.3.2 fn:load-xquery-module
PR 795
New in 4.0
See 16.2.18 fn:sort-with
PR 828
The $predicate callback function accepts an optional position argument.
See 16.2.5 fn:filter
See 16.2.6 fn:fold-left
The $action callback function accepts an optional position argument.
See 16.2.7 fn:fold-right
See 16.2.8 fn:for-each
See 16.2.9 fn:for-each-pair
The $predicate callback function now accepts an optional position argument.
See 18.2.4 array:filter
The $action callback function now accepts an optional position argument.
See 18.2.6 array:fold-left
See 18.2.7 array:fold-right
See 18.2.9 array:for-each
See 18.2.10 array:for-each-pair
PR 881
The way that fn:min and fn:max compare numeric values of different types has changed. The most noticeable effect is that when these functions are applied to a sequence of xs:integer or xs:decimal values, the result is an xs:integer or xs:decimal, rather than the result of converting this to an xs:double
See 13.4.3 fn:max
See 13.4.4 fn:min
PR 901
All three arguments are now optional, and each argument can be set to an empty sequence. Previously if $description was supplied, it could not be empty.
See 3.1.1 fn:error
The $label argument can now be set to an empty sequence. Previously if $label was supplied, it could not be empty.
See 3.2.1 fn:trace
The third argument can now be supplied as an empty sequence.
See 5.4.6 fn:substring
The second argument can now be an empty sequence.
See 5.6.5 fn:tokenize
The optional second argument can now be supplied as an empty sequence.
See 6.1 fn:resolve-uri
The 3rd, 4th, and 5th arguments are now optional; previously the function required either 2 or 5 arguments.
See 9.8.1 fn:format-dateTime
See 9.8.2 fn:format-date
See 9.8.3 fn:format-time
The optional third argument can now be supplied as an empty sequence.
See 13.1.13 fn:subsequence
PR 905
The rule that multiple calls on fn:doc supplying the same absolute URI must return the same document node has been clarified; in particular the rule does not apply if the dynamic context for the two calls requires different processing of the documents (such as schema validation or whitespace stripping).
See 13.6.1 fn:doc
PR 909
The function has been expanded in scope to handle comparison of values other than strings.
See 13.2.3 fn:compare
PR 924
Rules have been added clarifying that users should not be allowed to change the schema for the fn namespace.
See C Schemas
PR 925
The decimal format name can now be supplied as a value of type xs:QName, as an alternative to supplying a lexical QName as an instance of xs:string.
See 4.7.2 fn:format-number
PR 932
The specification now prescribes a minimum precision and range for durations.
See 8.1.2 Limits and precision
PR 933
When comments and processing instructions are ignored, any text nodes either side of the comment or processing instruction are now merged prior to comparison.
See 13.2.2 fn:deep-equal
PR 940
New in 4.0
See 16.2.19 fn:subsequence-where
PR 953
Constructor functions for named record types have been introduced.
See 20.6 Constructor functions for named record types
PR 962
New in 4.0
See 16.2.3 fn:do-until
See 16.2.22 fn:while-do
PR 969
New in 4.0
See 17.3.3 map:empty
PR 984
New in 4.0
See 8.4.1 fn:seconds
PR 987
The order of results is now prescribed; it was previously implementation-dependent.
See 13.2.4 fn:distinct-values
See 13.2.5 fn:duplicate-values
PR 988
New in 4.0
See 14.3.8 fn:pin
See 14.3.9 fn:label
PR 1022
Regular expressions can include comments (starting and ending with #) if the c flag is set.
See 5.6.1 Regular expression syntax
See 5.6.2 Flags
PR 1028
An option is provided to control how the JSON null value should be handled.
See 14.3.4 fn:parse-json
PR 1032
New in 4.0
See 13.1.17 fn:void
PR 1046
New in 4.0
See 16.2.20 fn:take-while
PR 1059
Use of an option keyword that is not defined in the specification and is not known to the implementation now results in a dynamic error; previously it was ignored.
See 1.7 Options
PR 1068
New in 4.0
See 5.4.3 fn:graphemes
PR 1072
The return type is now specified more precisely.
See 16.3.2 fn:load-xquery-module
PR 1090
When casting from a string to a duration or time or dateTime, it is now specified that when there are more digits in the fractional seconds than the implementation is able to retain, excess digits are truncated. Rounding upwards (which could affect the number of minutes or hours in the value) is not permitted.
See 21.2 Casting from xs:string and xs:untypedAtomic
PR 1093
New in 4.0
See 5.3.8 fn:collation
PR 1117
The $options parameter has been added.
See 13.6.5 fn:unparsed-text
See 13.6.7 fn:unparsed-text-available
PR 1182
The $predicate callback function may return an empty sequence (meaning false).
See 16.2.3 fn:do-until
See 16.2.4 fn:every
See 16.2.5 fn:filter
See 16.2.6 fn:fold-left
See 16.2.11 fn:index-where
See 16.2.16 fn:some
See 16.2.20 fn:take-while
See 16.2.22 fn:while-do
See 17.3.6 map:filter
See 17.3.12 map:keys-where
See 18.2.4 array:filter
See 18.2.14 array:index-where
PR 1191
New in 4.0
See 2.3.1 fn:distinct-ordered-nodes
The $options parameter has been added, absorbing the $collation parameter.
See 13.2.2 fn:deep-equal
PR 1250
For selected properties including percent and exponent-separator, it is now possible to specify a single-character marker to be used in the picture string, together with a multi-character rendition to be used in the formatted output.
See 4.7.2 fn:format-number
PR 1257
The $options parameter has been added.
See 14.1.1 fn:parse-xml
See 14.1.2 fn:parse-xml-fragment
PR 1262
New in 4.0
See 5.3.9 fn:collation-available
PR 1265
The constraints on the result of the function have been relaxed.
See 2.1.6 fn:document-uri
PR 1280
As a result of changes to the coercion rules, the number of supplied arguments can be greater than the number required: extra arguments are ignored.
See 16.2.1 fn:apply
PR 1288
Additional error conditions have been defined.
See 14.1.1 fn:parse-xml
PR 1296
New in 4.0
See 16.2.14 fn:scan-left
PR 1333
A new option is provided to allow the content of the loaded module to be supplied as a string.
See 16.3.2 fn:load-xquery-module
PR 1353
An option has been added to suppress the escaping of the solidus (forwards slash) character.
See 14.3.7 fn:xml-to-json
PR 1358
New in 4.0
See 9.3.2 fn:unix-dateTime
PR 1361
The term atomic value has been replaced by atomic item.
See 1.9 Terminology
PR 1393
Changes the function to return a sequence of key-value pairs rather than a map.
See 16.1.4 fn:function-annotations
PR 1409
This section now uses the term primitive type strictly to refer to the 20 atomic types that are not derived by restriction from another atomic type: that is, the 19 primitive atomic types defined in XSD, plus xs:untypedAtomic. The three types xs:integer, xs:dayTimeDuration, and xs:yearMonthDuration, which have custom casting rules but are not strictly-speaking primitive, are now handled in other subsections.
See 21.1 Casting from primitive types to primitive types
The rules for conversion of dates and times to strings are now defined entirely in terms of XSD 1.1 canonical mappings, since these deliver exactly the same result as the XPath 3.1 rules.
See 21.1.2.2 Casting date/time values to xs:string
The rules for conversion of durations to strings are now defined entirely in terms of XSD 1.1 canonical mappings, since the XSD 1.1 rules deliver exactly the same result as the XPath 3.1 rules.
See 21.1.2.3 Casting xs:duration values to xs:string
PR 1455
Numbers now retain their original lexical form, except for any changes needed to satisfy JSON syntax rules (for example, stripping leading zero digits).
See 14.3.7 fn:xml-to-json
PR 1481
The function has been extended to handle other Gregorian types such as xs:gYearMonth.
See 9.5.1 fn:year-from-dateTime
See 9.5.2 fn:month-from-dateTime
The function has been extended to handle other Gregorian types such as xs:gMonthDay.
See 9.5.3 fn:day-from-dateTime
The function has been extended to handle other types including xs:time.
See 9.5.4 fn:hours-from-dateTime
See 9.5.5 fn:minutes-from-dateTime
The function has been extended to handle other types such as xs:gYearMonth.
See 9.5.7 fn:timezone-from-dateTime
PR 1504
New in 4.0
See 13.1.11 fn:sequence-join
Optional $separator added.
See 18.2.17 array:join
PR 1523
New in 4.0
See 19.1.2 fn:schema-type
See 19.1.4 fn:atomic-type-annotation
See 19.1.5 fn:node-type-annotation
PR 1545
New in 4.0
See 9.6.4 fn:civil-timezone
PR 1570
New in 4.0
See 19.1.3 fn:type-of

XPath and XQuery Functions and Operators 4.0

W3C Editor's Draft 23 February 2026

Abstract

Status of this Document

4 Functions and operators on numerics

4.4 Functions on numeric values

4.4.4 fn:round

4.4.5 fn:round-half-to-even

4.4.6 fn:divide-decimals

F Checklist of implementation-defined features (Non-Normative)

G Changes since version 3.1 (Non-Normative)

G.1 Summary of Changes