Difference between revisions of "Math Module"

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−
The math [[Module Library|XQuery Module]] defines functions to perform mathematical operations, such as {{Code|pi}}, {{Code|asin}} and {{Code|acos}}. Most functions are specified in the [http://www.w3.org/TR/xpath-functions-30/ Functions and Operators Specification] of the upcoming XQuery 3.0 Recommendation, and some additional ones have been added in this module.
+
The math [[Module Library|XQuery Module]] defines functions to perform mathematical operations, such as {{Code|pi}}, {{Code|asin}} and {{Code|acos}}. Most functions are specified in the [https://www.w3.org/TR/xpath-functions-31/ Functions and Operators Specification] of the upcoming XQuery 3.0 Recommendation, and some additional ones have been added in this module.
  
 
=Conventions=
 
=Conventions=
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{| width='100%'
 
{| width='100%'
 
|-
 
|-
−
| width='120' | '''Signatures'''
+
| width='120' | '''Signature'''
−
|{{Func|math:pi||xs:double}}
+
|<pre>math:pi() as xs:double</pre>
 
|-
 
|-
 
| '''Summary'''
 
| '''Summary'''
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{| width='100%'
 
{| width='100%'
 
|-
 
|-
−
| width='120' | '''Signatures'''
+
| width='120' | '''Signature'''
−
|{{Func|math:sqrt|$arg as xs:double?|xs:double?}}
+
|<pre>math:sqrt(
 +
  $arg as xs:double?
 +
) as xs:double?</pre>
 
|-
 
|-
 
| '''Summary'''
 
| '''Summary'''
−
|Returns the square root of {{Code|$arg}}.<br/>If {{Code|$arg}} is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the {{Code|xs:double}} value of the mathematical square root of {{Code|$arg}}.
+
|Returns the square root of {{Code|$arg}}.<br/>If {{Code|$arg}} is the empty sequence, the empty sequence is returned.<br/>Otherwise the result is the {{Code|xs:double}} value of the mathematical square root of {{Code|$arg}}.
 
|}
 
|}
  
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{| width='100%'
 
{| width='100%'
 
|-
 
|-
−
| width='120' | '''Signatures'''
+
| width='120' | '''Signature'''
−
|{{Func|math:sin|$arg as xs:double?|xs:double?}}
+
|<pre>math:sin(
 +
  $arg as xs:double?
 +
) as xs:double?</pre>
 
|-
 
|-
 
| '''Summary'''
 
| '''Summary'''
−
|Returns the sine of the {{Code|$arg}}, expressed in radians.<br/>If {{Code|$arg}} is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the sine of {{Code|$arg}}, treated as an angle in radians.
+
|Returns the sine of the {{Code|$arg}}, expressed in radians.<br/>If {{Code|$arg}} is the empty sequence, the empty sequence is returned.<br/>Otherwise the result is the sine of {{Code|$arg}}, treated as an angle in radians.
 
|}
 
|}
  
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{| width='100%'
 
{| width='100%'
 
|-
 
|-
−
| width='120' | '''Signatures'''
+
| width='120' | '''Signature'''
−
|{{Func|math:cos|$arg as xs:double?|xs:double?}}
+
|<pre>math:cos(
 +
  $arg as xs:double?
 +
) as xs:double?</pre>
 
|-
 
|-
 
| '''Summary'''
 
| '''Summary'''
−
|Returns the cosine of {{Code|$arg}}, expressed in radians.<br/>If {{Code|$arg}} is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the cosine of {{Code|$arg}}, treated as an angle in radians.
+
|Returns the cosine of {{Code|$arg}}, expressed in radians.<br/>If {{Code|$arg}} is the empty sequence, the empty sequence is returned.<br/>Otherwise the result is the cosine of {{Code|$arg}}, treated as an angle in radians.
 
|}
 
|}
  
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{| width='100%'
 
{| width='100%'
 
|-
 
|-
−
| width='120' | '''Signatures'''
+
| width='120' | '''Signature'''
−
|{{Func|math:tan|$arg as xs:double?|xs:double?}}
+
|<pre>math:tan(
 +
  $arg as xs:double?
 +
) as xs:double?</pre>
 
|-
 
|-
 
| '''Summary'''
 
| '''Summary'''
−
|Returns the tangent of {{Code|$arg}}, expressed in radians.<br/>If {{Code|$arg}} is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the tangent of {{Code|$arg}}, treated as an angle in radians.
+
|Returns the tangent of {{Code|$arg}}, expressed in radians.<br/>If {{Code|$arg}} is the empty sequence, the empty sequence is returned.<br/>Otherwise the result is the tangent of {{Code|$arg}}, treated as an angle in radians.
 
|}
 
|}
  
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{| width='100%'
 
{| width='100%'
 
|-
 
|-
−
| width='120' | '''Signatures'''
+
| width='120' | '''Signature'''
−
|{{Func|math:asin|$arg as xs:double?|xs:double?}}
+
|<pre>math:asin(
 +
  $arg as xs:double?
 +
) as xs:double?</pre>
 
|-
 
|-
 
| '''Summary'''
 
| '''Summary'''
−
|Returns the arc sine of {{Code|$arg}}.<br/>If {{Code|$arg}} is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the arc sine of {{Code|$arg}}, returned as an angle in radians in the range -π/2 to +π/2.
+
|Returns the arc sine of {{Code|$arg}}.<br/>If {{Code|$arg}} is the empty sequence, the empty sequence is returned.<br/>Otherwise the result is the arc sine of {{Code|$arg}}, returned as an angle in radians in the range -π/2 to +π/2.
 
|}
 
|}
  
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{| width='100%'
 
{| width='100%'
 
|-
 
|-
−
| width='120' | '''Signatures'''
+
| width='120' | '''Signature'''
−
|{{Func|math:acos|$arg as xs:double?|xs:double?}}
+
|<pre>math:acos(
 +
  $arg as xs:double?
 +
) as xs:double?</pre>
 
|-
 
|-
 
| '''Summary'''
 
| '''Summary'''
−
|Returns the arc cosine of {{Code|$arg}}.<br/>If {{Code|$arg}} is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the arc cosine of {{Code|$arg}}, returned as an angle in radians in the range 0 to +π.
+
|Returns the arc cosine of {{Code|$arg}}.<br/>If {{Code|$arg}} is the empty sequence, the empty sequence is returned.<br/>Otherwise the result is the arc cosine of {{Code|$arg}}, returned as an angle in radians in the range 0 to +π.
 
|}
 
|}
  
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{| width='100%'
 
{| width='100%'
 
|-
 
|-
−
| width='120' | '''Signatures'''
+
| width='120' | '''Signature'''
−
|{{Func|math:atan|$arg as xs:double?|xs:double?}}
+
|<pre>math:atan(
 +
  $arg as xs:double?
 +
) as xs:double?</pre>
 
|-
 
|-
 
| '''Summary'''
 
| '''Summary'''
−
|Returns the arc tangent of {{Code|$arg}}.<br/>If {{Code|$arg}} is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the arc tangent of {{Code|$arg}}, returned as an angle in radians in the range -π/2 to +π/2.
+
|Returns the arc tangent of {{Code|$arg}}.<br/>If {{Code|$arg}} is the empty sequence, the empty sequence is returned.<br/>Otherwise the result is the arc tangent of {{Code|$arg}}, returned as an angle in radians in the range -π/2 to +π/2.
 
|}
 
|}
  
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{| width='100%'
 
{| width='100%'
 
|-
 
|-
−
| width='120' | '''Signatures'''
+
| width='120' | '''Signature'''
−
|{{Func|math:atan2|$arg1 as xs:double?, $arg2 as xs:double|xs:double?}}
+
|<pre>math:atan2(
 +
  $arg1 as xs:double?,
 +
  $arg2 as xs:double
 +
) as xs:double?</pre>
 
|-
 
|-
 
| '''Summary'''
 
| '''Summary'''
−
|Returns the arc tangent of {{Code|$arg1}} divided by {{Code|$arg2}}, the result being in the range -π/2 to +π/2 radians.<br/>If {{Code|$arg1}} is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the arc tangent of {{Code|$arg1}} divided by {{Code|$arg2}}, returned as an angle in radians in the range -π to +π.
+
|Returns the arc tangent of {{Code|$arg1}} divided by {{Code|$arg2}}, the result being in the range -π/2 to +π/2 radians.<br/>If {{Code|$arg1}} is the empty sequence, the empty sequence is returned.<br/>Otherwise the result is the arc tangent of {{Code|$arg1}} divided by {{Code|$arg2}}, returned as an angle in radians in the range -π to +π.
 
|}
 
|}
  
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{| width='100%'
 
{| width='100%'
 
|-
 
|-
−
| width='120' | '''Signatures'''
+
| width='120' | '''Signature'''
−
|{{Func|math:pow|$arg1 as xs:double?, $arg2 as xs:double|xs:double?}}
+
|<pre>math:pow(
 +
  $arg1 as xs:double?,
 +
  $arg2 as xs:double
 +
) as xs:double?</pre>
 
|-
 
|-
 
| '''Summary'''
 
| '''Summary'''
−
|Returns {{Code|$arg1}} raised to the power of {{Code|$arg2}}.<br/>If {{Code|$arg1}} is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the {{Code|$arg1}} raised to the power of {{Code|$arg2}}.
+
|Returns {{Code|$arg1}} raised to the power of {{Code|$arg2}}.<br/>If {{Code|$arg1}} is the empty sequence, the empty sequence is returned.<br/>Otherwise the result is the {{Code|$arg1}} raised to the power of {{Code|$arg2}}.
 
|-
 
|-
 
| '''Examples'''
 
| '''Examples'''
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{| width='100%'
 
{| width='100%'
 
|-
 
|-
−
| width='120' | '''Signatures'''
+
| width='120' | '''Signature'''
−
|{{Func|math:exp|$arg as xs:double?|xs:double?}}
+
|<pre>math:exp(
 +
  $arg as xs:double?
 +
) as xs:double?</pre>
 
|-
 
|-
 
| '''Summary'''
 
| '''Summary'''
−
|Returns <i>e</i> raised to the power of {{Code|$arg}}.<br/>If {{Code|$arg}} is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the value of <i>e</i> raised to the power of {{Code|$arg}}.
+
|Returns <i>e</i> raised to the power of {{Code|$arg}}.<br/>If {{Code|$arg}} is the empty sequence, the empty sequence is returned.<br/>Otherwise the result is the value of <i>e</i> raised to the power of {{Code|$arg}}.
 
|-
 
|-
 
| '''Examples'''
 
| '''Examples'''
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{| width='100%'
 
{| width='100%'
 
|-
 
|-
−
| width='120' | '''Signatures'''
+
| width='120' | '''Signature'''
−
|{{Func|math:log|$arg as xs:double?|xs:double?}}
+
|<pre>math:log(
 +
  $arg as xs:double?
 +
) as xs:double?</pre>
 
|-
 
|-
 
| '''Summary'''
 
| '''Summary'''
−
|Returns the natural logarithm of {{Code|$arg}}.<br/>If {{Code|$arg}} is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the natural logarithm (base <i>e</i>) of {{Code|$arg}}.
+
|Returns the natural logarithm of {{Code|$arg}}.<br/>If {{Code|$arg}} is the empty sequence, the empty sequence is returned.<br/>Otherwise the result is the natural logarithm (base <i>e</i>) of {{Code|$arg}}.
 
|-
 
|-
 
| '''Examples'''
 
| '''Examples'''
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{| width='100%'
 
{| width='100%'
 
|-
 
|-
−
| width='120' | '''Signatures'''
+
| width='120' | '''Signature'''
−
|{{Func|math:log10|$arg as xs:double?|xs:double?}}
+
|<pre>math:log10(
 +
  $arg as xs:double?
 +
) as xs:double?</pre>
 
|-
 
|-
 
| '''Summary'''
 
| '''Summary'''
−
|Returns the base 10 logarithm of {{Code|$arg}}.<br/>If {{Code|$arg}} is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the base 10 logarithm of {{Code|$arg}}.
+
|Returns the base 10 logarithm of {{Code|$arg}}.<br/>If {{Code|$arg}} is the empty sequence, the empty sequence is returned.<br/>Otherwise the result is the base 10 logarithm of {{Code|$arg}}.
 
|-
 
|-
 
| '''Examples'''
 
| '''Examples'''
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{| width='100%'
 
{| width='100%'
 
|-
 
|-
−
| width='120' | '''Signatures'''
+
| width='120' | '''Signature'''
−
|{{Func|math:e||xs:double}}
+
|<pre>math:e() as xs:double</pre>
 
|-
 
|-
 
| '''Summary'''
 
| '''Summary'''
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{| width='100%'
 
{| width='100%'
 
|-
 
|-
−
| width='120' | '''Signatures'''
+
| width='120' | '''Signature'''
−
|{{Func|math:sinh|$arg as xs:double?|xs:double?}}
+
|<pre>math:sinh(
 +
  $arg as xs:double?
 +
) as xs:double?</pre>
 
|-
 
|-
 
| '''Summary'''
 
| '''Summary'''
−
|Returns the hyperbolic sine of {{Code|$arg}}.<br/>If {{Code|$arg}} is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the hyperbolic sine of {{Code|$arg}}.
+
|Returns the hyperbolic sine of {{Code|$arg}}.<br/>If {{Code|$arg}} is the empty sequence, the empty sequence is returned.<br/>Otherwise the result is the hyperbolic sine of {{Code|$arg}}.
 
|-
 
|-
 
| '''Examples'''
 
| '''Examples'''
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{| width='100%'
 
{| width='100%'
 
|-
 
|-
−
| width='120' | '''Signatures'''
+
| width='120' | '''Signature'''
−
|{{Func|math:cosh|$arg as xs:double?|xs:double?}}
+
|<pre>math:cosh(
 +
  $arg as xs:double?
 +
) as xs:double?</pre>
 
|-
 
|-
 
| '''Summary'''
 
| '''Summary'''
−
|Returns the hyperbolic cosine of {{Code|$arg}}.<br/>If {{Code|$arg}} is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the hyperbolic cosine of {{Code|$arg}}.
+
|Returns the hyperbolic cosine of {{Code|$arg}}.<br/>If {{Code|$arg}} is the empty sequence, the empty sequence is returned.<br/>Otherwise the result is the hyperbolic cosine of {{Code|$arg}}.
 
|-
 
|-
 
| '''Examples'''
 
| '''Examples'''
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{| width='100%'
 
{| width='100%'
 
|-
 
|-
−
| width='120' | '''Signatures'''
+
| width='120' | '''Signature'''
−
|{{Func|math:tanh|$arg as xs:double?|xs:double?}}
+
|<pre>math:tanh(
 +
  $arg as xs:double?
 +
) as xs:double?</pre>
 
|-
 
|-
 
| '''Summary'''
 
| '''Summary'''
−
|Returns the hyperbolic tangent of {{Code|$arg}}.<br/>If {{Code|$arg}} is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the hyperbolic tangent of {{Code|$arg}}.
+
|Returns the hyperbolic tangent of {{Code|$arg}}.<br/>If {{Code|$arg}} is the empty sequence, the empty sequence is returned.<br/>Otherwise the result is the hyperbolic tangent of {{Code|$arg}}.
 
|-
 
|-
 
| '''Examples'''
 
| '''Examples'''
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==math:crc32==
 
==math:crc32==
−
 
−
{{Mark|Updated with Version 9.1:}} support for empty sequence.
 
  
 
{| width='100%'
 
{| width='100%'
 
|-
 
|-
−
| width='120' | '''Signatures'''
+
| width='120' | '''Signature'''
−
|{{Func|math:crc32|$string as xs:string?|xs:hexBinary}}<br />
+
|<pre>math:crc32(
 +
  $string as xs:string?
 +
) as xs:hexBinary?</pre>
 
|-
 
|-
 
| '''Summary'''
 
| '''Summary'''
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; Version 9.1
 
; Version 9.1
−
* Updated: [[#math:crc32|math:crc32]] can be called with empty sequence.
+
* Updated: {{Function||math:crc32}} can be called with empty sequence.
  
 
; Version 7.5
 
; Version 7.5
−
* Moved: [[Random Module#random:integer|math:random]] and [[Random Module#random:uuid|math:uuid]] have been moved to [[Random Module]].
+
* Moved: {{Code|math:random}} and {{Code|math:uuid}} have been moved to the [[Random Module]].
  
 
; Version 7.3
 
; Version 7.3
−
* Added: [[#math:crc32|math:crc32]] and [[Random Module#random:uuid|math:uuid]] have been adopted from the obsolete Utility Module.
+
* Added: {{Function||math:crc32}} and {{Function||math:uuid}} have been adopted from the obsolete Utility Module.

Latest revision as of 15:59, 9 March 2023

The math XQuery Module defines functions to perform mathematical operations, such as pi, asin and acos. Most functions are specified in the Functions and Operators Specification of the upcoming XQuery 3.0 Recommendation, and some additional ones have been added in this module.

Conventions[edit]

All functions in this module are assigned to the http://www.w3.org/2005/xpath-functions/math namespace, which is statically bound to the math prefix.

W3 Functions[edit]

math:pi[edit]

Signature 
math:pi() as xs:double
Summary Returns the xs:double value of the mathematical constant π whose lexical representation is 3.141592653589793.
Examples
  • 2*math:pi() returns 6.283185307179586e0.
  • 60 * (math:pi() div 180) converts an angle of 60 degrees to radians.

math:sqrt[edit]

Signature 
math:sqrt(
  $arg  as xs:double?
) as xs:double?
Summary Returns the square root of $arg.
If $arg is the empty sequence, the empty sequence is returned.
Otherwise the result is the xs:double value of the mathematical square root of $arg.

math:sin[edit]

Signature 
math:sin(
  $arg  as xs:double?
) as xs:double?
Summary Returns the sine of the $arg, expressed in radians.
If $arg is the empty sequence, the empty sequence is returned.
Otherwise the result is the sine of $arg, treated as an angle in radians.

math:cos[edit]

Signature 
math:cos(
  $arg  as xs:double?
) as xs:double?
Summary Returns the cosine of $arg, expressed in radians.
If $arg is the empty sequence, the empty sequence is returned.
Otherwise the result is the cosine of $arg, treated as an angle in radians.

math:tan[edit]

Signature 
math:tan(
  $arg  as xs:double?
) as xs:double?
Summary Returns the tangent of $arg, expressed in radians.
If $arg is the empty sequence, the empty sequence is returned.
Otherwise the result is the tangent of $arg, treated as an angle in radians.

math:asin[edit]

Signature 
math:asin(
  $arg  as xs:double?
) as xs:double?
Summary Returns the arc sine of $arg.
If $arg is the empty sequence, the empty sequence is returned.
Otherwise the result is the arc sine of $arg, returned as an angle in radians in the range -π/2 to +π/2.

math:acos[edit]

Signature 
math:acos(
  $arg  as xs:double?
) as xs:double?
Summary Returns the arc cosine of $arg.
If $arg is the empty sequence, the empty sequence is returned.
Otherwise the result is the arc cosine of $arg, returned as an angle in radians in the range 0 to +π.

math:atan[edit]

Signature 
math:atan(
  $arg  as xs:double?
) as xs:double?
Summary Returns the arc tangent of $arg.
If $arg is the empty sequence, the empty sequence is returned.
Otherwise the result is the arc tangent of $arg, returned as an angle in radians in the range -π/2 to +π/2.

math:atan2[edit]

Signature 
math:atan2(
  $arg1  as xs:double?,
  $arg2  as xs:double
) as xs:double?
Summary Returns the arc tangent of $arg1 divided by $arg2, the result being in the range -π/2 to +π/2 radians.
If $arg1 is the empty sequence, the empty sequence is returned.
Otherwise the result is the arc tangent of $arg1 divided by $arg2, returned as an angle in radians in the range -π to +π.

math:pow[edit]

Signature 
math:pow(
  $arg1  as xs:double?,
  $arg2  as xs:double
) as xs:double?
Summary Returns $arg1 raised to the power of $arg2.
If $arg1 is the empty sequence, the empty sequence is returned.
Otherwise the result is the $arg1 raised to the power of $arg2.
Examples
  • math:pow(2, 3) returns 8.

math:exp[edit]

Signature 
math:exp(
  $arg  as xs:double?
) as xs:double?
Summary Returns e raised to the power of $arg.
If $arg is the empty sequence, the empty sequence is returned.
Otherwise the result is the value of e raised to the power of $arg.
Examples
  • math:exp(1) returns e.

math:log[edit]

Signature 
math:log(
  $arg  as xs:double?
) as xs:double?
Summary Returns the natural logarithm of $arg.
If $arg is the empty sequence, the empty sequence is returned.
Otherwise the result is the natural logarithm (base e) of $arg.
Examples
  • math:log(math:e()) returns 1.

math:log10[edit]

Signature 
math:log10(
  $arg  as xs:double?
) as xs:double?
Summary Returns the base 10 logarithm of $arg.
If $arg is the empty sequence, the empty sequence is returned.
Otherwise the result is the base 10 logarithm of $arg.
Examples
  • math:log(100) returns 2.

Additional Functions[edit]

math:e[edit]

Signature 
math:e() as xs:double
Summary Returns the xs:double value of the mathematical constant e whose lexical representation is 2.718281828459045.
Examples
  • 5*math:e() returns 13.591409142295225.

math:sinh[edit]

Signature 
math:sinh(
  $arg  as xs:double?
) as xs:double?
Summary Returns the hyperbolic sine of $arg.
If $arg is the empty sequence, the empty sequence is returned.
Otherwise the result is the hyperbolic sine of $arg.
Examples
  • math:sinh(0) returns 0.

math:cosh[edit]

Signature 
math:cosh(
  $arg  as xs:double?
) as xs:double?
Summary Returns the hyperbolic cosine of $arg.
If $arg is the empty sequence, the empty sequence is returned.
Otherwise the result is the hyperbolic cosine of $arg.
Examples
  • math:cosh(0) returns 1.

math:tanh[edit]

Signature 
math:tanh(
  $arg  as xs:double?
) as xs:double?
Summary Returns the hyperbolic tangent of $arg.
If $arg is the empty sequence, the empty sequence is returned.
Otherwise the result is the hyperbolic tangent of $arg.
Examples
  • math:tanh(100) returns 1.

math:crc32[edit]

Signature 
math:crc32(
  $string  as xs:string?
) as xs:hexBinary?
Summary Calculates the CRC32 check sum of the given $string.
If an empty sequence is supplied, the empty sequence is returned.
Examples
  • math:crc32("") returns '00000000'.
  • math:crc32("BaseX") returns '4C06FC7F'.

Changelog[edit]

Version 9.1
  • Updated: math:crc32 can be called with empty sequence.
Version 7.5
  • Moved: math:random and math:uuid have been moved to the Random Module.
Version 7.3
Retrieved from "http://docs.basex.org/index.php?title=Math_Module&oldid=16453"