Difference between revisions of "Math Module"
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==math:pi== | ==math:pi== | ||
{| | {| | ||
| − | | | + | | width="90" | <b>Signatures</b> |
| − | | <code> | + | | <code> <b>math:pi'''() as xs:double</code> |
|- | |- | ||
| − | | | + | | <b>Summary</b> |
|Returns the value of the mathematical constant π. | |Returns the value of the mathematical constant π. | ||
|- | |- | ||
| − | | | + | | <b>Rules</b> |
|This function returns the <code>xs:double</code> value whose lexical representation is 3.141592653589793. | |This function returns the <code>xs:double</code> value whose lexical representation is 3.141592653589793. | ||
|- | |- | ||
| − | | | + | | <b>Examples</b> |
|The expression <code>2*math:pi()</code> returns <code>6.283185307179586e0</code>.The expression <code>60 * (math:pi() div 180)</code> converts an angle of 60 degrees to radians. | |The expression <code>2*math:pi()</code> returns <code>6.283185307179586e0</code>.The expression <code>60 * (math:pi() div 180)</code> converts an angle of 60 degrees to radians. | ||
|} | |} | ||
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==math:e== | ==math:e== | ||
{| | {| | ||
| − | | | + | | width="90" | <b>Signatures</b> |
| − | | <code> | + | | <code> <b>math:e'''() as xs:double</code> |
|- | |- | ||
| − | | | + | | <b>Summary</b> |
|Returns the value of the mathematical constant <i>e</i>. | |Returns the value of the mathematical constant <i>e</i>. | ||
|- | |- | ||
| − | | | + | | <b>Rules</b> |
|This function returns the <code>xs:double</code> value whose lexical representation is 2.718281828459045. | |This function returns the <code>xs:double</code> value whose lexical representation is 2.718281828459045. | ||
|- | |- | ||
| − | | | + | | <b>Examples</b> |
|The expression <code>5*math:e()</code> returns <code>13.591409142295225</code>. | |The expression <code>5*math:e()</code> returns <code>13.591409142295225</code>. | ||
|} | |} | ||
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{| | {| | ||
|- | |- | ||
| − | | | + | |width="90" | <b>Signatures</b> |
| − | | <code> | + | | <code> <b>math:sqrt'''($arg as xs:double?) as xs:double?</code> |
|- | |- | ||
| − | | | + | |<b>Summary</b> |
|Returns the square root of the argument. | |Returns the square root of the argument. | ||
|- | |- | ||
| − | | | + | |<b>Rules</b> |
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the <code>xs:double</code> value of the mathematical square root of <code>$arg</code>. | |If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the <code>xs:double</code> value of the mathematical square root of <code>$arg</code>. | ||
|} | |} | ||
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{| | {| | ||
|- | |- | ||
| − | | | + | |width="90" | <b>Signatures</b> |
| − | | <code> | + | | <code> <b>math:sin'''($arg as xs:double?) as xs:double?</code> |
|- | |- | ||
| − | | | + | |<b>Summary</b> |
|Returns the sine of the argument, expressed in radians. | |Returns the sine of the argument, expressed in radians. | ||
|- | |- | ||
| − | | | + | |<b>Rules</b> |
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the sine of <code>$arg</code>, treated as an angle in radians. | |If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the sine of <code>$arg</code>, treated as an angle in radians. | ||
|} | |} | ||
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{| | {| | ||
|- | |- | ||
| − | | | + | |width="90" | <b>Signatures</b> |
| − | | <code> | + | | <code> <b>math:cos'''($arg as xs:double?) as xs:double?</code> |
|- | |- | ||
| − | | | + | |<b>Summary</b> |
|Returns the cosine of the argument, expressed in radians. | |Returns the cosine of the argument, expressed in radians. | ||
|- | |- | ||
| − | | | + | |<b>Rules</b> |
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the cosine of <code>$arg</code>, treated as an angle in radians. | |If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the cosine of <code>$arg</code>, treated as an angle in radians. | ||
|} | |} | ||
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{| | {| | ||
|- | |- | ||
| − | | | + | |width="90" | <b>Signatures</b> |
| − | | <code> | + | | <code> <b>math:tan'''($ as xs:double?) as xs:double?</code> |
|- | |- | ||
| − | | | + | |<b>Summary</b> |
|Returns the tangent of the argument, expressed in radians. | |Returns the tangent of the argument, expressed in radians. | ||
|- | |- | ||
| − | | | + | |<b>Rules</b> |
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the tangent of <code>$arg</code>, treated as an angle in radians. | |If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the tangent of <code>$arg</code>, treated as an angle in radians. | ||
|} | |} | ||
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{| | {| | ||
|- | |- | ||
| − | | | + | |width="90" | <b>Signatures</b> |
| − | | <code> | + | | <code> <b>math:asin'''($arg as xs:double?) as xs:double?</code> |
|- | |- | ||
| − | | | + | |<b>Summary</b> |
|Returns the arc sine of the argument. | |Returns the arc sine of the argument. | ||
|- | |- | ||
| − | | | + | |<b>Rules</b> |
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the arc sine of <code>$arg</code>, returned as an angle in radians in the range -π/2 to +π/2. | |If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the arc sine of <code>$arg</code>, returned as an angle in radians in the range -π/2 to +π/2. | ||
|} | |} | ||
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{| | {| | ||
|- | |- | ||
| − | | | + | |width="90" | <b>Signatures</b> |
| − | | <code> | + | | <code> <b>math:acos'''($arg as xs:double?) as xs:double?</code> |
|- | |- | ||
| − | | | + | |<b>Summary</b> |
|Returns the arc cosine of the argument. | |Returns the arc cosine of the argument. | ||
|- | |- | ||
| − | | | + | |<b>Rules</b> |
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the arc cosine of <code>$arg</code>, returned as an angle in radians in the range 0 to +π. | |If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the arc cosine of <code>$arg</code>, returned as an angle in radians in the range 0 to +π. | ||
|} | |} | ||
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{| | {| | ||
|- | |- | ||
| − | | | + | |width="90" | <b>Signatures</b> |
| − | | <code> | + | | <code> <b>math:atan'''($arg as xs:double?) as xs:double?</code> |
|- | |- | ||
| − | | | + | |<b>Summary</b> |
|Returns the arc tangent of the argument. | |Returns the arc tangent of the argument. | ||
|- | |- | ||
| − | | | + | |<b>Rules</b> |
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the arc tangent of <code>$arg</code>, returned as an angle in radians in the range -π/2 to +π/2. | |If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the arc tangent of <code>$arg</code>, returned as an angle in radians in the range -π/2 to +π/2. | ||
|} | |} | ||
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{| | {| | ||
|- | |- | ||
| − | | | + | |width="90" | <b>Signatures</b> |
| − | | <code> | + | | <code> <b>math:atan2'''($arg1 as xs:double?, $arg2 as xs:double?) as xs:double?</code> |
|- | |- | ||
| − | | | + | |<b>Summary</b> |
|Returns the arc tangent of the first argument divided by the second argument, the result being in the range -π/2 to +π/2 radians. | |Returns the arc tangent of the first argument divided by the second argument, the result being in the range -π/2 to +π/2 radians. | ||
|- | |- | ||
| − | | | + | |<b>Rules</b> |
|If <code>$arg1</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the arc tangent of <code>$arg1</code> divided by <code>$arg2</code>, returned as an angle in radians in the range -π to +π. | |If <code>$arg1</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the arc tangent of <code>$arg1</code> divided by <code>$arg2</code>, returned as an angle in radians in the range -π to +π. | ||
|} | |} | ||
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{| | {| | ||
|- | |- | ||
| − | | | + | |width="90" | <b>Signatures</b> |
| − | | <code> | + | | <code> <b>math:pow'''($arg1 as xs:double?, $arg2 as xs:double?) as xs:double?</code> |
|- | |- | ||
| − | | | + | |<b>Summary</b> |
|Returns the first argument raised to the power of the second argument. | |Returns the first argument raised to the power of the second argument. | ||
|- | |- | ||
| − | | | + | |<b>Rules</b> |
|If <code>$arg1</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the <code>$arg1</code> raised to the power of <code>$arg2</code>. | |If <code>$arg1</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the <code>$arg1</code> raised to the power of <code>$arg2</code>. | ||
|- | |- | ||
| − | | | + | |<b>Examples</b> |
|The expression <code>math:pow(2, 3)</code> returns <code>8</code>. | |The expression <code>math:pow(2, 3)</code> returns <code>8</code>. | ||
|} | |} | ||
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{| | {| | ||
|- | |- | ||
| − | | | + | |width="90" | <b>Signatures</b> |
| − | | <code> | + | | <code> <b>math:exp'''($arg as xs:double?) as xs:double?</code> |
|- | |- | ||
| − | | | + | |<b>Summary</b> |
|Returns <i>e</i> raised to the power of the argument. | |Returns <i>e</i> raised to the power of the argument. | ||
|- | |- | ||
| − | | | + | |<b>Rules</b> |
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the value of <i>e</i> raised to the power of <code>$arg</code>. | |If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the value of <i>e</i> raised to the power of <code>$arg</code>. | ||
|- | |- | ||
| − | | | + | |<b>Examples</b> |
|The expression <code>math:exp(1)</code> returns <i>e</i>. | |The expression <code>math:exp(1)</code> returns <i>e</i>. | ||
|} | |} | ||
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{| | {| | ||
|- | |- | ||
| − | | | + | |width="90" | <b>Signatures</b> |
| − | | <code> | + | | <code> <b>math:log'''($arg as xs:double?) as xs:double?</code> |
|- | |- | ||
| − | | | + | |<b>Summary</b> |
|Returns the natural logarithm of the argument. | |Returns the natural logarithm of the argument. | ||
|- | |- | ||
| − | | | + | |<b>Rules</b> |
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the natural logarithm (base <i>e</i>) of <code>$arg</code>. | |If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the natural logarithm (base <i>e</i>) of <code>$arg</code>. | ||
|- | |- | ||
| − | | | + | |<b>Examples</b> |
|The expression <code>math:log(math:e())</code> returns <code>1</code>. | |The expression <code>math:log(math:e())</code> returns <code>1</code>. | ||
|} | |} | ||
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{| | {| | ||
|- | |- | ||
| − | | | + | |width="90" | <b>Signatures</b> |
| − | | <code> | + | | <code> <b>math:log10'''($arg as xs:double?) as xs:double?</code> |
|- | |- | ||
| − | | | + | |<b>Summary</b> |
|Returns the base 10 logarithm of the argument. | |Returns the base 10 logarithm of the argument. | ||
|- | |- | ||
| − | | | + | |<b>Rules</b> |
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the base 10 logarithm of <code>$arg</code>. | |If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the base 10 logarithm of <code>$arg</code>. | ||
|- | |- | ||
| − | | | + | |<b>Examples</b> |
|The expression <code>math:log(100)</code> returns <code>2</code>. | |The expression <code>math:log(100)</code> returns <code>2</code>. | ||
|} | |} | ||
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{| | {| | ||
|- | |- | ||
| − | | | + | |width="90" | <b>Signatures</b> |
| − | | <code> | + | | <code> <b>math:random'''() as xs:double?</code> |
|- | |- | ||
| − | | | + | |<b>Summary</b> |
|Returns a random value. | |Returns a random value. | ||
|- | |- | ||
| − | | | + | |<b>Rules</b> |
|This function returns a random <code>xs:double</code> value between <code>0.0</code> and <code>1.0</code>. | |This function returns a random <code>xs:double</code> value between <code>0.0</code> and <code>1.0</code>. | ||
|} | |} | ||
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{| | {| | ||
|- | |- | ||
| − | | | + | |width="90" | <b>Signatures</b> |
| − | | <code> | + | | <code> <b>math:sinh'''($arg as xs:double?) as xs:double?</code> |
|- | |- | ||
| − | | | + | |<b>Summary</b> |
|Returns the hyperbolic sine of the argument. | |Returns the hyperbolic sine of the argument. | ||
|- | |- | ||
| − | | | + | |<b>Rules</b> |
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the hyperbolic sine of <code>$arg</code>. | |If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the hyperbolic sine of <code>$arg</code>. | ||
|- | |- | ||
| − | | | + | |<b>Examples</b> |
|The expression <code>math:sinh(0)</code> returns <code>0</code>. | |The expression <code>math:sinh(0)</code> returns <code>0</code>. | ||
|} | |} | ||
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{| | {| | ||
|- | |- | ||
| − | | | + | |width="90" | <b>Signatures</b> |
| − | | <code> | + | | <code> <b>math:cosh'''($arg as xs:double?) as xs:double?</code> |
|- | |- | ||
| − | | | + | |<b>Summary</b> |
|Returns the hyperbolic cosine of the argument. | |Returns the hyperbolic cosine of the argument. | ||
|- | |- | ||
| − | | | + | |<b>Rules</b> |
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the hyperbolic cosine of <code>$arg</code>. | |If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the hyperbolic cosine of <code>$arg</code>. | ||
|- | |- | ||
| − | | | + | |<b>Examples</b> |
|The expression <code>math:cosh(0)</code> returns <code>1</code>. | |The expression <code>math:cosh(0)</code> returns <code>1</code>. | ||
|} | |} | ||
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{| | {| | ||
|- | |- | ||
| − | | | + | |width="90" | <b>Signatures</b> |
| − | | <code> | + | | <code> <b>math:tanh'''($arg as xs:double?) as xs:double?</code> |
|- | |- | ||
| − | | | + | |<b>Summary</b> |
|Returns the hyperbolic tangent of the argument. | |Returns the hyperbolic tangent of the argument. | ||
|- | |- | ||
| − | | | + | |<b>Rules</b> |
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the hyperbolic tangent of <code>$arg</code>. | |If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the hyperbolic tangent of <code>$arg</code>. | ||
|- | |- | ||
| − | | | + | |<b>Examples</b> |
|The expression <code>math:tanh(100)</code> returns <code>1</code>. | |The expression <code>math:tanh(100)</code> returns <code>1</code>. | ||
|} | |} | ||
| − | |||
| − | |||
[[Category:XQuery]] | [[Category:XQuery]] | ||
Revision as of 17:25, 12 December 2010
Contents
Math Module
The math module defines extension functions to perform mathematical operations, such as pi, asin and acos. All functions are preceded by the math: prefix. Some of the functions have also been specified in the
Functions and Operators Specification of the upcoming XQuery 1.1 Recommendation.
math:pi
| Signatures | math:pi() as xs:double
|
| Summary | Returns the value of the mathematical constant π. |
| Rules | This function returns the xs:double value whose lexical representation is 3.141592653589793.
|
| Examples | The expression 2*math:pi() returns 6.283185307179586e0.The expression 60 * (math:pi() div 180) converts an angle of 60 degrees to radians.
|
math:e
| Signatures | math:e() as xs:double
|
| Summary | Returns the value of the mathematical constant e. |
| Rules | This function returns the xs:double value whose lexical representation is 2.718281828459045.
|
| Examples | The expression 5*math:e() returns 13.591409142295225.
|
math:sqrt
| Signatures | math:sqrt($arg as xs:double?) as xs:double?
|
| Summary | Returns the square root of the argument. |
| Rules | If $arg is the empty sequence, the function returns the empty sequence.Otherwise the result is the xs:double value of the mathematical square root of $arg.
|
math:sin
| Signatures | math:sin($arg as xs:double?) as xs:double?
|
| Summary | Returns the sine of the argument, expressed in radians. |
| Rules | If $arg is the empty sequence, the function returns the empty sequence.Otherwise the result is the sine of $arg, treated as an angle in radians.
|
math:cos
| Signatures | math:cos($arg as xs:double?) as xs:double?
|
| Summary | Returns the cosine of the argument, expressed in radians. |
| Rules | If $arg is the empty sequence, the function returns the empty sequence.Otherwise the result is the cosine of $arg, treated as an angle in radians.
|
math:tan
| Signatures | math:tan($ as xs:double?) as xs:double?
|
| Summary | Returns the tangent of the argument, expressed in radians. |
| Rules | If $arg is the empty sequence, the function returns the empty sequence.Otherwise the result is the tangent of $arg, treated as an angle in radians.
|
math:asin
| Signatures | math:asin($arg as xs:double?) as xs:double?
|
| Summary | Returns the arc sine of the argument. |
| Rules | If $arg is the empty sequence, the function returns the empty sequence.Otherwise the result is the arc sine of $arg, returned as an angle in radians in the range -π/2 to +π/2.
|
math:acos
| Signatures | math:acos($arg as xs:double?) as xs:double?
|
| Summary | Returns the arc cosine of the argument. |
| Rules | If $arg is the empty sequence, the function returns the empty sequence.Otherwise the result is the arc cosine of $arg, returned as an angle in radians in the range 0 to +π.
|
math:atan
| Signatures | math:atan($arg as xs:double?) as xs:double?
|
| Summary | Returns the arc tangent of the argument. |
| Rules | If $arg is the empty sequence, the function returns the empty sequence.Otherwise the result is the arc tangent of $arg, returned as an angle in radians in the range -π/2 to +π/2.
|
math:atan2
| Signatures | math:atan2($arg1 as xs:double?, $arg2 as xs:double?) as xs:double?
|
| Summary | Returns the arc tangent of the first argument divided by the second argument, the result being in the range -π/2 to +π/2 radians. |
| Rules | If $arg1 is the empty sequence, the function returns the empty sequence.Otherwise the result is the arc tangent of $arg1 divided by $arg2, returned as an angle in radians in the range -π to +π.
|
math:pow
| Signatures | math:pow($arg1 as xs:double?, $arg2 as xs:double?) as xs:double?
|
| Summary | Returns the first argument raised to the power of the second argument. |
| Rules | If $arg1 is the empty sequence, the function returns the empty sequence.Otherwise the result is the $arg1 raised to the power of $arg2.
|
| Examples | The expression math:pow(2, 3) returns 8.
|
math:exp
| Signatures | math:exp($arg as xs:double?) as xs:double?
|
| Summary | Returns e raised to the power of the argument. |
| Rules | If $arg is the empty sequence, the function returns the empty sequence.Otherwise the result is the value of e raised to the power of $arg.
|
| Examples | The expression math:exp(1) returns e.
|
math:log
| Signatures | math:log($arg as xs:double?) as xs:double?
|
| Summary | Returns the natural logarithm of the argument. |
| Rules | If $arg is the empty sequence, the function returns the empty sequence.Otherwise the result is the natural logarithm (base e) of $arg.
|
| Examples | The expression math:log(math:e()) returns 1.
|
math:log10
| Signatures | math:log10($arg as xs:double?) as xs:double?
|
| Summary | Returns the base 10 logarithm of the argument. |
| Rules | If $arg is the empty sequence, the function returns the empty sequence.Otherwise the result is the base 10 logarithm of $arg.
|
| Examples | The expression math:log(100) returns 2.
|
math:random
| Signatures | math:random() as xs:double?
|
| Summary | Returns a random value. |
| Rules | This function returns a random xs:double value between 0.0 and 1.0.
|
math:sinh
| Signatures | math:sinh($arg as xs:double?) as xs:double?
|
| Summary | Returns the hyperbolic sine of the argument. |
| Rules | If $arg is the empty sequence, the function returns the empty sequence.Otherwise the result is the hyperbolic sine of $arg.
|
| Examples | The expression math:sinh(0) returns 0.
|
math:cosh
| Signatures | math:cosh($arg as xs:double?) as xs:double?
|
| Summary | Returns the hyperbolic cosine of the argument. |
| Rules | If $arg is the empty sequence, the function returns the empty sequence.Otherwise the result is the hyperbolic cosine of $arg.
|
| Examples | The expression math:cosh(0) returns 1.
|
math:tanh
| Signatures | math:tanh($arg as xs:double?) as xs:double?
|
| Summary | Returns the hyperbolic tangent of the argument. |
| Rules | If $arg is the empty sequence, the function returns the empty sequence.Otherwise the result is the hyperbolic tangent of $arg.
|
| Examples | The expression math:tanh(100) returns 1.
|
