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<h1 class="faldoc_title">Function set "Math functions."</h1>
<p class="faldoc_brief">Functions providing math support to Falcon. </p>
<p class="faldoc_brief"><a href="#more">more...</a></p>
<h2 class="faldoc_title">Summary</h2>
<table class="faldoc_list">
<tr><td><a href="#abs">abs()</a></td><td>Returns the absolute value of a number. </td></tr>
<tr><td><a href="#acos">acos()</a></td><td>Returns the arc cosine of the argument. </td></tr>
<tr><td><a href="#asin">asin()</a></td><td>Returns the arc sine of the argument. </td></tr>
<tr><td><a href="#atan">atan()</a></td><td>Returns the arc tangent of the argument. </td></tr>
<tr><td><a href="#atan2">atan2()</a></td><td>Returns the arc tangent of x / y. </td></tr>
<tr><td><a href="#ceil">ceil()</a></td><td>Returns the greatest integer near to the given value. </td></tr>
<tr><td><a href="#combinations">combinations()</a></td><td>Returns the combination of the arguments. </td></tr>
<tr><td><a href="#cos">cos()</a></td><td>Returns the cosine of the argument. </td></tr>
<tr><td><a href="#deg2rad">deg2rad()</a></td><td>Converts an angle expressed in degrees into radians. </td></tr>
<tr><td><a href="#exp">exp()</a></td><td>Returns exponential (e^x) of the argument. </td></tr>
<tr><td><a href="#factorial">factorial()</a></td><td>Returns the factorial of the argument. </td></tr>
<tr><td><a href="#fint">fint()</a></td><td>Returns the integer part of a floating point number as a floating point number. </td></tr>
<tr><td><a href="#floor">floor()</a></td><td>Returns the smallest integer near to the given value. </td></tr>
<tr><td><a href="#fract">fract()</a></td><td>Returns the fractional part of a number. </td></tr>
<tr><td><a href="#log">log()</a></td><td>Returns the natural logarithm of the argument. </td></tr>
<tr><td><a href="#permutations">permutations()</a></td><td>Returns the permutation of the arguments. </td></tr>
<tr><td><a href="#pow">pow()</a></td><td>Returns the first argument elevated to the second one (x^y) </td></tr>
<tr><td><a href="#rad2deg">rad2deg()</a></td><td>Converts an angle expressed in radians into degrees. </td></tr>
<tr><td><a href="#round">round()</a></td><td>Rounds a floating point to the nearest integer. </td></tr>
<tr><td><a href="#sin">sin()</a></td><td>Returns the sine of the argument. </td></tr>
<tr><td><a href="#tan">tan()</a></td><td>Returns the tangent of the argument. </td></tr>
</table>
<a name="more"><h2 class="faldoc_title">Detailed description</h2></a>
<table class="faldoc_function">
</table>
<br/>
<p class="item_brief">Functions providing math support to Falcon. </p>
<p class="faldoc_text">This group includes mathematical, trigonometrical and floating point conversion functions. </p>
<h2 class="faldoc_title">Members</h2>
<h3 class="faldoc_funcname"><a name="abs">abs()</a></h3>
<p class="item_brief">Returns the absolute value of a number. </p>
<p class="faldoc_funcdecl">abs( x )</p>
<table class="faldoc_function">
<tr><td class="faldoc_param">x</td><td class="faldoc_paramdesc">A number. </td></tr>
<tr><td class="faldoc_funcreturn">Returns:</td><td class="faldoc_funcreturndesc">The absolute value of the parameter. </td></tr>
</table>
<p class="faldoc_text"><p class="faldoc_text">If the argument is an integer, then an integer is returned, otherwise the return value will be a floating point number. </p>
</p>
<h3 class="faldoc_funcname"><a name="acos">acos()</a></h3>
<p class="item_brief">Returns the arc cosine of the argument. </p>
<p class="faldoc_funcdecl">acos( x )</p>
<table class="faldoc_function">
<tr><td class="faldoc_param">x</td><td class="faldoc_paramdesc">Argument. </td></tr>
<tr><td class="faldoc_funcreturn">Returns:</td><td class="faldoc_funcreturndesc">The arc cosine of the argument. </td></tr>
<tr><td class="faldoc_raise">Raises:</td><td class="faldoc_raisedesc">
<table class="faldoc_raise">
<tr><td class="faldoc_raiseitem"><a href="./class_MathError.html">MathError</a></td><td class="faldoc_raisedesc">If the argument is out of domain. </td></tr>
</table>
</td></tr>
</table>
<p class="faldoc_text"><p class="faldoc_text">This function computes the principal value of the arc cosine of its argument x. The value of x should be in the range [-1,1]. </p>
<p class="faldoc_text">The return value is expressed in radians. </p>
<p class="faldoc_text">The function may raise a Math error if the value cannot be computed because of domain or overflow errors. </p>
</p>
<h3 class="faldoc_funcname"><a name="asin">asin()</a></h3>
<p class="item_brief">Returns the arc sine of the argument. </p>
<p class="faldoc_funcdecl">asin( x )</p>
<table class="faldoc_function">
<tr><td class="faldoc_param">x</td><td class="faldoc_paramdesc">Argument. </td></tr>
<tr><td class="faldoc_funcreturn">Returns:</td><td class="faldoc_funcreturndesc">The arc sine of the argument. </td></tr>
<tr><td class="faldoc_raise">Raises:</td><td class="faldoc_raisedesc">
<table class="faldoc_raise">
<tr><td class="faldoc_raiseitem"><a href="./class_MathError.html">MathError</a></td><td class="faldoc_raisedesc">If the argument is out of domain. </td></tr>
</table>
</td></tr>
</table>
<p class="faldoc_text"><p class="faldoc_text">The return value is expressed in radians. </p>
<p class="faldoc_text">The function may raise an error if the value cannot be computed because of domain or overflow errors. </p>
</p>
<h3 class="faldoc_funcname"><a name="atan">atan()</a></h3>
<p class="item_brief">Returns the arc tangent of the argument. </p>
<p class="faldoc_funcdecl">atan( x )</p>
<table class="faldoc_function">
<tr><td class="faldoc_param">x</td><td class="faldoc_paramdesc">Argument. </td></tr>
<tr><td class="faldoc_funcreturn">Returns:</td><td class="faldoc_funcreturndesc">The arc tangent of the argument. </td></tr>
<tr><td class="faldoc_raise">Raises:</td><td class="faldoc_raisedesc">
<table class="faldoc_raise">
<tr><td class="faldoc_raiseitem"><a href="./class_MathError.html">MathError</a></td><td class="faldoc_raisedesc">If the argument is out of domain. </td></tr>
</table>
</td></tr>
</table>
<p class="faldoc_text"><p class="faldoc_text">This function computes the principal value of the arc tangent of its argument x. The value of x should be in the range [-1,1]. </p>
<p class="faldoc_text">The return value is expressed in radians. </p>
<p class="faldoc_text">The function may raise a Math error if the value cannot be computed because of domain or overflow errors. </p>
</p>
<h3 class="faldoc_funcname"><a name="atan2">atan2()</a></h3>
<p class="item_brief">Returns the arc tangent of x / y. </p>
<p class="faldoc_funcdecl">atan2( x, y )</p>
<table class="faldoc_function">
<tr><td class="faldoc_param">x</td><td class="faldoc_paramdesc">First argument. </td></tr><tr><td class="faldoc_param">y</td><td class="faldoc_paramdesc">Second argument. </td></tr>
<tr><td class="faldoc_funcreturn">Returns:</td><td class="faldoc_funcreturndesc">The arc tangent of the x / y. </td></tr>
<tr><td class="faldoc_raise">Raises:</td><td class="faldoc_raisedesc">
<table class="faldoc_raise">
<tr><td class="faldoc_raiseitem"><a href="./class_MathError.html">MathError</a></td><td class="faldoc_raisedesc">If the argument is out of domain. </td></tr>
</table>
</td></tr>
</table>
<p class="faldoc_text"><p class="faldoc_text">This function computes the principal value of the arc tangent of x/y, using the signs of both arguments to determine the quadrant of the return value. </p>
<p class="faldoc_text">The return value is expressed in radians. </p>
<p class="faldoc_text">The function may raise a Math error if the value cannot be computed because of domain or overflow errors. </p>
</p>
<h3 class="faldoc_funcname"><a name="ceil">ceil()</a></h3>
<p class="item_brief">Returns the greatest integer near to the given value. </p>
<p class="faldoc_funcdecl">ceil( x )</p>
<table class="faldoc_function">
<tr><td class="faldoc_param">x</td><td class="faldoc_paramdesc">Argument. </td></tr>
<tr><td class="faldoc_funcreturn">Returns:</td><td class="faldoc_funcreturndesc">The ceil value. </td></tr>
</table>
<p class="faldoc_text"><p class="faldoc_text">Ceil function returns the highest integer near to a given floating point number. For example, ceil of 1.1 is 2, and ceil of -1.1 is -1. If an integer number is given, then the function returns the same number. </p>
</p>
<h3 class="faldoc_funcname"><a name="combinations">combinations()</a></h3>
<p class="item_brief">Returns the combination of the arguments. </p>
<p class="faldoc_funcdecl">combinations( x, y )</p>
<table class="faldoc_function">
<tr><td class="faldoc_param">x</td><td class="faldoc_paramdesc">First argument. </td></tr><tr><td class="faldoc_param">y</td><td class="faldoc_paramdesc">Second arguments. </td></tr>
<tr><td class="faldoc_funcreturn">Returns:</td><td class="faldoc_funcreturndesc">The combination of the arguments. </td></tr>
</table>
<p class="faldoc_text"><p class="faldoc_text">The return value is expressed as a floating point value. </p>
<p class="faldoc_note"><span class="faldoc_notetype">Note:</span> For high values of <b>x</b>, the function may require exponential computational time and power. </p>
</p>
<h3 class="faldoc_funcname"><a name="cos">cos()</a></h3>
<p class="item_brief">Returns the cosine of the argument. </p>
<p class="faldoc_funcdecl">cos( x )</p>
<table class="faldoc_function">
<tr><td class="faldoc_param">x</td><td class="faldoc_paramdesc">Argument. </td></tr>
<tr><td class="faldoc_funcreturn">Returns:</td><td class="faldoc_funcreturndesc">The cosine of the argument. </td></tr>
<tr><td class="faldoc_raise">Raises:</td><td class="faldoc_raisedesc">
<table class="faldoc_raise">
<tr><td class="faldoc_raiseitem"><a href="./class_MathError.html">MathError</a></td><td class="faldoc_raisedesc">If the argument is out of domain. </td></tr>
</table>
</td></tr>
</table>
<p class="faldoc_text"><p class="faldoc_text">The return value is expressed in radians. </p>
<p class="faldoc_text">The function may raise an error if the value cannot be computed because of domain or overflow errors. </p>
</p>
<h3 class="faldoc_funcname"><a name="deg2rad">deg2rad()</a></h3>
<p class="item_brief">Converts an angle expressed in degrees into radians. </p>
<p class="faldoc_funcdecl">deg2rad( x )</p>
<table class="faldoc_function">
<tr><td class="faldoc_param">x</td><td class="faldoc_paramdesc">An angle expressed in degrees. </td></tr>
<tr><td class="faldoc_funcreturn">Returns:</td><td class="faldoc_funcreturndesc">The angle converted in radians. </td></tr>
</table>
<h3 class="faldoc_funcname"><a name="exp">exp()</a></h3>
<p class="item_brief">Returns exponential (e^x) of the argument. </p>
<p class="faldoc_funcdecl">exp( x )</p>
<table class="faldoc_function">
<tr><td class="faldoc_param">x</td><td class="faldoc_paramdesc">Argument. </td></tr>
<tr><td class="faldoc_funcreturn">Returns:</td><td class="faldoc_funcreturndesc">The exponential of the argument. </td></tr>
<tr><td class="faldoc_raise">Raises:</td><td class="faldoc_raisedesc">
<table class="faldoc_raise">
<tr><td class="faldoc_raiseitem"><a href="./class_MathError.html">MathError</a></td><td class="faldoc_raisedesc">If the argument is out of domain. </td></tr>
</table>
</td></tr>
</table>
<p class="faldoc_text"><p class="faldoc_text">The function may raise an error if the value cannot be computed because of domain or overflow errors. </p>
</p>
<h3 class="faldoc_funcname"><a name="factorial">factorial()</a></h3>
<p class="item_brief">Returns the factorial of the argument. </p>
<p class="faldoc_funcdecl">factorial( x )</p>
<table class="faldoc_function">
<tr><td class="faldoc_param">x</td><td class="faldoc_paramdesc">Argument. </td></tr>
<tr><td class="faldoc_funcreturn">Returns:</td><td class="faldoc_funcreturndesc">The factorial of the argument. </td></tr>
</table>
<p class="faldoc_text"><p class="faldoc_text">The return value is expressed as a floating point value. </p>
<p class="faldoc_note"><span class="faldoc_notetype">Note:</span> For high values of <b>x</b>, the function may require exponential computational time and power. </p>
</p>
<h3 class="faldoc_funcname"><a name="fint">fint()</a></h3>
<p class="item_brief">Returns the integer part of a floating point number as a floating point number. </p>
<p class="faldoc_funcdecl">fint( x )</p>
<table class="faldoc_function">
<tr><td class="faldoc_param">x</td><td class="faldoc_paramdesc">Argument. </td></tr>
<tr><td class="faldoc_funcreturn">Returns:</td><td class="faldoc_funcreturndesc">A floating point number with fractional part zeroed. </td></tr>
</table>
<p class="faldoc_text"><p class="faldoc_text"> Fint function works like the core <a href="./functions.html#int">int</a> function, but it returns a floating point number. For example, <b>fint</b> applied on 3.58e200 will return the same number, while <a href="./functions.html#int">int</a> would raise a math error, as the number cannot be represented in a integer number that can store numbers up to +-2^63. </p>
</p>
<h3 class="faldoc_funcname"><a name="floor">floor()</a></h3>
<p class="item_brief">Returns the smallest integer near to the given value. </p>
<p class="faldoc_funcdecl">floor( x )</p>
<table class="faldoc_function">
<tr><td class="faldoc_param">x</td><td class="faldoc_paramdesc">Argument. </td></tr>
<tr><td class="faldoc_funcreturn">Returns:</td><td class="faldoc_funcreturndesc">The smallest integer near to the given value. </td></tr>
</table>
<p class="faldoc_text"><p class="faldoc_text"> Floor function returns the smallest integer near to a given floating point number. For example, floor of 1.9 is 1, and floor of -1.9 is -2. If an integer number is given, then the function returns the same number. This is similar to fint(), but in case of negative numbers <a href="./functions.html#fint">fint</a> would return the integer part; in case of -1.9 it would return -1. </p>
</p>
<h3 class="faldoc_funcname"><a name="fract">fract()</a></h3>
<p class="item_brief">Returns the fractional part of a number. </p>
<p class="faldoc_funcdecl">fract( x )</p>
<table class="faldoc_function">
<tr><td class="faldoc_param">x</td><td class="faldoc_paramdesc">Argument. </td></tr>
<tr><td class="faldoc_funcreturn">Returns:</td><td class="faldoc_funcreturndesc">The fractional part of a number. </td></tr>
</table>
<p class="faldoc_text"><p class="faldoc_text">This function returns the non-integer part of a number. For example, </p>
<pre class="faldoc_code">
> fract( 1.234 )
</pre>
<p class="faldoc_text">would print 0.234. </p>
</p>
<h3 class="faldoc_funcname"><a name="log">log()</a></h3>
<p class="item_brief">Returns the natural logarithm of the argument. </p>
<p class="faldoc_funcdecl">log( x )</p>
<table class="faldoc_function">
<tr><td class="faldoc_param">x</td><td class="faldoc_paramdesc">Argument. </td></tr>
<tr><td class="faldoc_funcreturn">Returns:</td><td class="faldoc_funcreturndesc">The natural logarithm of the argument. </td></tr>
<tr><td class="faldoc_raise">Raises:</td><td class="faldoc_raisedesc">
<table class="faldoc_raise">
<tr><td class="faldoc_raiseitem"><a href="./class_MathError.html">MathError</a></td><td class="faldoc_raisedesc">If the argument is out of domain. </td></tr>
</table>
</td></tr>
</table>
<p class="faldoc_text"><p class="faldoc_text">The function may raise an error if the value cannot be computed because of domain or overflow errors. </p>
</p>
<h3 class="faldoc_funcname"><a name="permutations">permutations()</a></h3>
<p class="item_brief">Returns the permutation of the arguments. </p>
<p class="faldoc_funcdecl">permutations( x, y )</p>
<table class="faldoc_function">
<tr><td class="faldoc_param">x</td><td class="faldoc_paramdesc">First argument. </td></tr><tr><td class="faldoc_param">y</td><td class="faldoc_paramdesc">Second arguments. </td></tr>
<tr><td class="faldoc_funcreturn">Returns:</td><td class="faldoc_funcreturndesc">The permutation of the arguments. </td></tr>
</table>
<p class="faldoc_text"><p class="faldoc_text">The return value is expressed as a floating point value. </p>
<p class="faldoc_note"><span class="faldoc_notetype">Note:</span> For high values of <b>x</b>, the function may require exponential computational time and power. </p>
</p>
<h3 class="faldoc_funcname"><a name="pow">pow()</a></h3>
<p class="item_brief">Returns the first argument elevated to the second one (x^y) </p>
<p class="faldoc_funcdecl">pow( x, y )</p>
<table class="faldoc_function">
<tr><td class="faldoc_param">x</td><td class="faldoc_paramdesc">Base. </td></tr><tr><td class="faldoc_param">y</td><td class="faldoc_paramdesc">Exponent. </td></tr>
<tr><td class="faldoc_funcreturn">Returns:</td><td class="faldoc_funcreturndesc">x^y </td></tr>
<tr><td class="faldoc_raise">Raises:</td><td class="faldoc_raisedesc">
<table class="faldoc_raise">
<tr><td class="faldoc_raiseitem"><a href="./class_MathError.html">MathError</a></td><td class="faldoc_raisedesc">If the argument is out of domain. </td></tr>
</table>
</td></tr>
</table>
<p class="faldoc_text"><p class="faldoc_text">The function may raise an error if the value cannot be computed because of domain or overflow errors. </p>
</p>
<h3 class="faldoc_funcname"><a name="rad2deg">rad2deg()</a></h3>
<p class="item_brief">Converts an angle expressed in radians into degrees. </p>
<p class="faldoc_funcdecl">rad2deg( x )</p>
<table class="faldoc_function">
<tr><td class="faldoc_param">x</td><td class="faldoc_paramdesc">An angle expressed in radians. </td></tr>
<tr><td class="faldoc_funcreturn">Returns:</td><td class="faldoc_funcreturndesc">The angle converted in degrees. </td></tr>
</table>
<h3 class="faldoc_funcname"><a name="round">round()</a></h3>
<p class="item_brief">Rounds a floating point to the nearest integer. </p>
<p class="faldoc_funcdecl">round( x )</p>
<table class="faldoc_function">
<tr><td class="faldoc_param">x</td><td class="faldoc_paramdesc">Argument. </td></tr>
<tr><td class="faldoc_funcreturn">Returns:</td><td class="faldoc_funcreturndesc">Nearest integer to x. </td></tr>
</table>
<p class="faldoc_text"><p class="faldoc_text">Round returns the nearest integer value of a given floating point number. If the fractional part of the number is greater or equal to 0.5, the number is rounded up to the nearest biggest integer in absolute value, while if it's less than 0.5 the number is rounded down to the mere integer part. For example, 1.6 is rounded to 2, -1.6 is rounded to -2, 1.2 is rounded to 1 and -1.2 is rounded to -1. </p>
</p>
<h3 class="faldoc_funcname"><a name="sin">sin()</a></h3>
<p class="item_brief">Returns the sine of the argument. </p>
<p class="faldoc_funcdecl">sin( x )</p>
<table class="faldoc_function">
<tr><td class="faldoc_param">x</td><td class="faldoc_paramdesc">Argument. </td></tr>
<tr><td class="faldoc_funcreturn">Returns:</td><td class="faldoc_funcreturndesc">The sine of the argument. </td></tr>
<tr><td class="faldoc_raise">Raises:</td><td class="faldoc_raisedesc">
<table class="faldoc_raise">
<tr><td class="faldoc_raiseitem"><a href="./class_MathError.html">MathError</a></td><td class="faldoc_raisedesc">If the argument is out of domain. </td></tr>
</table>
</td></tr>
</table>
<p class="faldoc_text"><p class="faldoc_text">The return value is expressed in radians. </p>
<p class="faldoc_text">The function may raise an error if the value cannot be computed because of domain or overflow errors. </p>
</p>
<h3 class="faldoc_funcname"><a name="tan">tan()</a></h3>
<p class="item_brief">Returns the tangent of the argument. </p>
<p class="faldoc_funcdecl">tan( x )</p>
<table class="faldoc_function">
<tr><td class="faldoc_param">x</td><td class="faldoc_paramdesc">Argument. </td></tr>
<tr><td class="faldoc_funcreturn">Returns:</td><td class="faldoc_funcreturndesc">The tangent of the argument. </td></tr>
<tr><td class="faldoc_raise">Raises:</td><td class="faldoc_raisedesc">
<table class="faldoc_raise">
<tr><td class="faldoc_raiseitem"><a href="./class_MathError.html">MathError</a></td><td class="faldoc_raisedesc">If the argument is out of domain. </td></tr>
</table>
</td></tr>
</table>
<p class="faldoc_text"><p class="faldoc_text">The return value is expressed in radians. </p>
<p class="faldoc_text">The function may raise an error if the value cannot be computed because of domain or overflow errors. </p>
</p>
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