1. Zorba 3.0 Documentation
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  3. W3C
  4. XPath Math Functions

http://www.w3.org/2005/xpath-functions/math

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This module contains all the functions part of the W3C XPath and XQuery Functions and Operators 3.0 section "4.7 Trigonometric and exponential functions".

Function Summary

acos ($arg as xs:double?) as xs:double? external

Returns the arc cosine of the argument, the result being in the range zero to + π radians.
asin ($arg as xs:double?) as xs:double? external

Returns the arc sine of the argument, the result being in the range - π /2 to + π /2 radians.
atan ($arg as xs:double?) as xs:double? external

Returns the arc tangent of the argument, the result being in the range - π /2 to + π /2 radians.
atan2 ($y as xs:double, $x as xs:double) as xs:double external

Returns the angle in radians subtended at the origin by the point on a plane with coordinates (x, y) and the positive x-axis, the result being in the range - π to + π .
cos ($theta as xs:double?) as xs:double? external

Returns the cosine of the argument, expressed in radians.
exp ($arg as xs:double?) as xs:double? external

Returns the value of e x .
exp10 ($arg as xs:double?) as xs:double? external

Returns the value of 10 x .
log ($arg as xs:double?) as xs:double? external

Returns the natural logarithm of the argument.
log10 ($arg as xs:double?) as xs:double? external

Returns the base-ten logarithm of the argument.
pi () as xs:double external

Returns an approximation to the mathematical constant π .
pow ($x as xs:double?, $y as numeric) as xs:double? external

Returns the result of raising the first argument to the power of the second.
sin ($theta as xs:double?) as xs:double? external

Returns the sine of the argument, expressed in radians.
sqrt ($arg as xs:double?) as xs:double? external

Returns the non-negative square root of the argument.
tan ($theta as xs:double?) as xs:double? external

Returns the tangent of the argument, expressed in radians.

Functions

acos#1

declare  function math:acos($arg as xs:double?) as xs:double? external

Returns the arc cosine of the argument, the result being in the range zero to +π radians.

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

If $arg is the empty sequence, the function returns the empty sequence.

Otherwise the result is the arc cosine of $θ, treated as an angle in radians, as defined in the specification of the acos function applied to 64-bit binary floating point values.

The treatment of the invalidOperation exception is defined in .

If $arg is NaN, or if its absolute value is greater than one, then the result is NaN.

In other cases the result is an xs:double value representing an angle θ in radians in the range 0 <= $θ <= +π.

Parameters

arg as xs:double

Returns

xs:double?

asin#1

declare  function math:asin($arg as xs:double?) as xs:double? external

Returns the arc sine of the argument, the result being in the range -π/2 to +π/2 radians.

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

If $arg is the empty sequence, the function returns the empty sequence.

Otherwise the result is the arc sine of $θ, treated as an angle in radians, as defined in the specification of the asin function applied to 64-bit binary floating point values.

The treatment of the invalidOperation and underflow exceptions is defined in .

If $arg is positive or negative zero, the result is $arg.

If $arg is NaN, or if its absolute value is greater than one, then the result is NaN.

In other cases the result is an xs:double value representing an angle θ in radians in the range -π/2 <= $θ <= +π/2.

Parameters

arg as xs:double

Returns

xs:double?

atan#1

declare  function math:atan($arg as xs:double?) as xs:double? external

Returns the arc tangent of the argument, the result being in the range -π/2 to +π/2 radians.

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

If $arg is the empty sequence, the function returns the empty sequence.

Otherwise the result is the arc tangent of $θ, treated as an angle in radians, as defined in the specification of the atan function applied to 64-bit binary floating point values.

The treatment of the underflow exception is defined in .

If $arg is positive or negative zero, the result is $arg.

If $arg is NaN then the result is NaN.

In other cases the result is an xs:double value representing an angle θ in radians in the range -π/2 <= $θ <= +π/2.

Parameters

arg as xs:double

Returns

xs:double?

atan2#2

declare  function math:atan2($y as xs:double, $x as xs:double) as xs:double external

Returns the angle in radians subtended at the origin by the point on a plane with coordinates (x, y) and the positive x-axis, the result being in the range -π to +π.

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

The result is the value of atan2(y, x) as defined in the specification of the atan2 function applied to 64-bit binary floating point values.

The treatment of the underflow exception is defined in .

If either argument is NaN then the result is NaN.

If $y is positive and $x is positive and finite, then (subject to rules for overflow, underflow and approximation) the value of atan2($y, $x) is atan($y div $x).

If $y is positive and $x is negative and finite, then (subject to the same caveats) the value of atan2($y, $x) is π - atan($y div $x).

Some results for special values of the arguments are shown in the examples below.

Parameters

y as xs:double
x as xs:double

Returns

xs:double

cos#1

declare  function math:cos($theta as xs:double?) as xs:double? external

Returns the cosine of the argument, expressed in radians.

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

If $θ is the empty sequence, the function returns the empty sequence.

If $θ is positive or negative infinity, or NaN, then the result is NaN.

Otherwise the result is the cosine of $θ, treated as an angle in radians, as defined in the specification of the cos function applied to 64-bit binary floating point values.

The treatment of the invalidOperation exception is defined in .

If $θ is positive or negative zero, the result is $θ.

If $θ is positive or negative infinity, or NaN, then the result is NaN.

Otherwise the result is always in the range -1.0e0 to +1.0e0

Parameters

theta as xs:double

Returns

xs:double?

exp#1

declare  function math:exp($arg as xs:double?) as xs:double? external

Returns the value of ex.

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

If $arg is the empty sequence, the function returns the empty sequence.

Otherwise the result is the mathematical constant e raised to the power of $arg, as defined in the specification of the exp function applied to 64-bit binary floating point values.

The treatment of overflow and underflow is defined in .

Parameters

arg as xs:double

Returns

xs:double?

exp10#1

declare  function math:exp10($arg as xs:double?) as xs:double? external

Returns the value of 10x.

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

If $arg is the empty sequence, the function returns the empty sequence.

Otherwise the result is ten raised to the power of $arg, as defined in the specification of the exp10 function applied to 64-bit binary floating point values.

The treatment of overflow and underflow is defined in .

Parameters

arg as xs:double

Returns

xs:double?

log#1

declare  function math:log($arg as xs:double?) as xs:double? external

Returns the natural logarithm of the argument.

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

If $arg is the empty sequence, the function returns the empty sequence.

Otherwise the result is the natural logarithm of $arg, as defined in the specification of the log function applied to 64-bit binary floating point values.

The treatment of divideByZero and invalidOperation exceptions is defined in . The effect is that if the argument is less than or equal to zero, the result is NaN.

Parameters

arg as xs:double

Returns

xs:double?

log10#1

declare  function math:log10($arg as xs:double?) as xs:double? external

Returns the base-ten logarithm of the argument.

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

If $arg is the empty sequence, the function returns the empty sequence.

Otherwise the result is the base-10 logarithm of $arg, as defined in the specification of the log10 function applied to 64-bit binary floating point values.

The treatment of divideByZero and invalidOperation exceptions is defined in . The effect is that if the argument is less than or equal to zero, the result is NaN.

Parameters

arg as xs:double

Returns

xs:double?

pi#0

declare  function math:pi() as xs:double external

Returns an approximation to the mathematical constant π.

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

This function returns the xs:double value whose lexical representation is 3.141592653589793e0

The expression 2*math:pi() returns 6.283185307179586e0.

The expression 60 * (math:pi() div 180) converts an angle of 60 degrees to radians.

Parameters

Returns

xs:double

pow#2

declare  function math:pow($x as xs:double?, $y as numeric) as xs:double? external

Returns the result of raising the first argument to the power of the second.

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

If $x is the empty sequence, the function returns the empty sequence.

If $y is an instance of xs:integer, the result is $x raised to the power of $y as defined in the specification of the pown function applied to a 64-bit binary floating point value and an integer.

Otherwise $y is converted to an xs:double by numeric promotion, and the result is the value of $x raised to the power of $y as defined in the specification of the pow function applied to two 64-bit binary floating point values.

The treatment of the divideByZero and invalidOperation exceptions is defined in . Some of the consequences are illustrated in the examples below.

Parameters

x as xs:double
y as numeric

Returns

xs:double?

sin#1

declare  function math:sin($theta as xs:double?) as xs:double? external

Returns the sine of the argument, expressed in radians.

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

If $θ is the empty sequence, the function returns the empty sequence.

Otherwise the result is the sine of $θ, treated as an angle in radians, as defined in the specification of the sin function applied to 64-bit binary floating point values.

The treatment of the invalidOperation and underflow exceptions is defined in .

If $θ is positive or negative zero, the result is $θ.

If $θ is positive or negative infinity, or NaN, then the result is NaN.

Otherwise the result is always in the range -1.0e0 to +1.0e0

Parameters

theta as xs:double

Returns

xs:double?

sqrt#1

declare  function math:sqrt($arg as xs:double?) as xs:double? external

Returns the non-negative square root of the argument.

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

If $arg is the empty sequence, the function returns the empty sequence.

Otherwise the result is the mathematical non-negative square root of $arg as defined in the specification of the squareRoot function applied to 64-bit binary floating point values.

The treatment of the invalidOperation exception is defined in . The effect is that if the argument is less than zero, the result is NaN.

If $arg is positive or negative zero, positive infinity, or NaN, then the result is $arg. (Negative zero is the only case where the result can have negative sign)

Parameters

arg as xs:double

Returns

xs:double?

tan#1

declare  function math:tan($theta as xs:double?) as xs:double? external

Returns the tangent of the argument, expressed in radians.

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

If $θ is the empty sequence, the function returns the empty sequence.

Otherwise the result is the tangent of $θ, treated as an angle in radians, as defined in the specification of the tan function applied to 64-bit binary floating point values.

The treatment of the invalidOperation and underflow exceptions is defined in .

If $θ is positive or negative infinity, or NaN, then the result is NaN.

Parameters

theta as xs:double

Returns

xs:double?