Vnano Math Plugin Group
(org.vcssl.nano.plugin.math package)
Abstract
Plugins in this package/subpackages provide elementary math & statistical functions available in scripts of the Vnano (VCSSL nano).
Features provided by these plugins is a subset (*) of the VCSSL Math Library and
the math.StatisticalFunction Library which are a standard libraries of the VCSSL,
so same features are also available in scripts of the VCSSL by default, with importing them at the head of the script as:
" import Math; import math.StatisticalFunction; "
* Features of some math functions (e.g.: sin) provided by plugins in this package are extended to make it possible to get/return arrays. It has not been supported yet on the VCSSL, so it is only available on the Vnano.
List of Provided Plugins and Features
 MathElementaryXnci1Plugin

Provides elementary math functions.
Variable: PI
Function: rad(degree) / deg(radian) / sin(x) / cos(x) / tan(x) /
asin(x) / acos(x) / atan(x) /
sqrt(x) / ln(x) / log10(x) / pow(x,exponent) / exp(x) /
abs(x)
 MathStatisticalXnci1Plugin

Provides elementary statistical functions.
Function: sum(...) / mean(...) / van(...) / van1(...) / sdn(...) / sdn1(...)
License
All of the above plugins are released under CC0.
MathElementaryXnci1Plugin
(org.vcssl.nano.math.xnci1.MathElementaryXnci1Plugin)
The plugin providing elementary math functions.
Variables
Variable 
PI 
Value 
Storing the value of the circle ratio . 
Data Type 
float (constant) 
Functions
Function 
rad( degree ) 
Feature 
The conversion function from degree to radian.
Converts the value in the unit of degree passed as an argument "degree" to the value in the unit of radian, and returns it.
When an array is passed, converts each elements of it, stores them in another array, and returns it.
Please note that, the conversion result will not be shifted automatically to taking value in the range of [0, 2),
so you will get the result value exceeding 2 if you will pass the argument exceeding 360.

Signature 
float[...] rad( const float °ree[...] ) 
Params 
(float type, any rank) degree: The value in the unit of degree to be converted to the value in the unit of radian. 
Return value 
(float type, having same ranl/length with the param) The converted value in the unit of radian. 
Example 
print( rad(180.0) ); // 3.14... 
Function 
deg( radian ) 
Feature 
The conversion function from radian to degree.
Converts the value in the unit of degree passed as an argument "degree" to the value in the unit of radian, and returns it.
When an array is passed, converts each elements of it, stores them in another array, and returns it.
Please note that, the conversion result will not be shifted automatically to taking value in the range of [0, 360),
so you will get the result value exceeding 360 if you will pass the argument exceeding 2.

Signature 
float[...] deg( const float &radian[...] ) 
Params 
(float type, any rank) radian: The value in the unit of radian to be converted to the value in the unit of degree. 
Return 
(float type, having same rank/length with the param) The converted value in the unit of degree. 
Example 
print( deg(PI) ); // 180.0 
Function 
sin( x ) 
Feature 
The sine function. The unit of the argument "x" is radian.
When an array is passed, computes the value of sin(x[i]) for each elements x[i], stores them in another array, and returns it.

Singature 
float[...] sin( const float &x[...] ) 
Params 
(float type, any rank) x: The argument of the sine function in the unit of radian. 
Return 
(float type, having same rank/length with the param) The value of the sine function. 
Example 
print( sin(PI/2.0) ); // 1.0 
Function 
cos( x ) 
Feature 
The cosine function. The unit of the argument "x" is radian.
When an array is passed, computes the value of cos(x[i]) for each elements x[i], stores them in another array, and returns it.

Singature 
float[...] cos( const float &x[...] ) 
Params 
(float type, any rank) x: The argument of the cosine function in the unit of radian. 
Return 
(float type, having same rank/length with the param) The value of the cosine function. 
Example 
print( cos(PI*2.0) ); // 1.0 
Function 
tan( x ) 
Feature 
The tangent function. The unit of the argument "x" is radian.
When an array is passed, computes the value of tan(x[i]) for each elements x[i], stores them in another array, and returns it.

Signature 
float[...] tan( const float &x[...] ) 
Params 
(float type, any rank) x: The argument of the tangent function in the unit of radian. 
Return 
(float type, having same rank/length with the param) The value of the tangent function. 
Example 
print( tan(PI/4.0) ); // 0.99999... (The true value is 1. The difference between the result and the true value is caused by tiny numerical error related with precisions of data/algorithm/etc., so it is not a bug.) 
Function 
asin( x ) 
Feature 
The inverse function of sine (arcsine). The unit of the result is radian.
When an array is passed, computes the value of asin(x[i]) for each elements x[i], stores them in another array, and returns it.

Signature 
float[...] asin( const float &x[...] ) 
Params 
(float type, any rank) x: The argument of the arcsine function. 
Return 
(float type, having same rank/length with the param) The value of the arcsine function in the unit of radian. 
Example 
print( asin(1.0) ); // 1.5707963... (/2) 
Function 
acos( x ) 
Feature 
The inverse function of cosine (arccosine). The unit of the result is radian.
When an array is passed, computes the value of acos(x[i]) for each elements x[i], stores them in another array, and returns it.

Signature 
float[...] acos( const float &x[...] ) 
Params 
(float type, any rank) x: The argument of the arccosine function. 
Return 
(float type, having same rank/length with the param) The value of the arccosine function in the unit of radian. 
Example 
print( acos(1.0) ); // 3.14... () 
Function 
atan( x ) 
Feature 
The inverse function of cosine (arctangent). The unit of the result is radian.
When an array is passed, computes the value of atan(x[i]) for each elements x[i], stores them in another array, and returns it.

Signature 
float[...] atan( const float &x[...] ) 
Params 
(float type, any rank) x: The argument of the arctangent function. 
Return 
(float type, having same rank/length with the param) The value of the arctangent function in the unit of radian. 
Example 
print( atan(1.0) ); // 0.78539... (/4) 
Function 
sqrt( x ) 
Feature 
The squareroot function.
When an array is passed, computes the value of sqrt(x[i]) for each elements x[i], stores them in another array, and returns it.

Signature 
float[...] sqrt( const float &x[...] ) 
Params 
(float type, any rank) x: The value of which square root should be computed. 
Return 
(float type, having same rank/length with the param) The square root value of the argument. 
Example 
print( sqrt(4.0) ); // 2.0 
Function 
ln( x ) 
Feature 
The logarithm function with the base "e" (napier number).
When an array is passed, computes the value of ln(x[i]) for each elements x[i], stores them in another array, and returns it.

Signature 
float[...] ln( const float &x[...] ) 
Params 
(float type, any rank) x: The argument of the logarithm function. 
Return 
(float type, having same rank/length with the param) The value of the logarithm function with the base "e" (napier number). 
Example 
print( ln(10.0) ); // 2.3025... 
Function 
log10( x ) 
Feature 
The logarithm function with the base 10.
When an array is passed, computes the value of ln(x[i]) for each elements x[i], stores them in another array, and returns it.

Signature 
float[...] log10( const float &x[...] ) 
Params 
(float type, any rank) x: The argument of the logarithm function. 
Return 
(float type, having same rank/length with the param) The value of the logarithm function with the base 10. 
Example 
print( log10(10.0) ); // 1.0 
Function 
pow( x, exponent ) 
Feature 
The function which returns the value of &qupt;x&qupt; to &qupt;exponent&qupt;power.
When an array is passed, computes the value of pow(x[i], exponent) for each elements x[i], stores them in another array, and returns it.

Signature 
float[...] pow( const float &x[...], const float &exponent ) 
Params 
(float type, any rank) x: see "Feature" section.
(float type) exponent: see "Feature" section.

Return 
(float type, having same rank/length with the param x) The value of &qupt;x&qupt; to &qupt;exponent&qupt;power. 
Example 
print( pow(2.0,3.0) ); // 8.0 
Function 
exp( exponent ) 
Fearure 
The function which returns the value of &qupt;e&qupt; (napier number) to &qupt;exponent&qupt;power.
When an array is passed, computes the value of exp(x[i]) for each elements x[i], stores them in another array, and returns it.

Signature 
float[...] exp( const float &exponent[...] ) 
Params 
(float type, any rank) exponent: see "Feature" section.

Return 
(float type, having same rank/length with the param) The value of &qupt;e&qupt; (napier number) to &qupt;exponent&qupt;power. 
Example 
print( exp(2.0) ); // 7.38905... ( squared value of "e") 
Function 
abs( x ) 
Feature 
The absolutevalue function.
When an array is passed, computes the value of abs(x[i]) for each elements x[i], stores them in another array, and returns it.

Signature 
float[...] abs( const float &x[...] ) 
Params 
(float type, any rank) x: The value of which absolute value should be computed.

Return 
(float type, having same rank/length with the param) The absolute value. 
Example 
print( abs(1.23) ); // 1.23 
MathStatisticalXnci1Plugin
(org.vcssl.nano.math.xnci1.MathStatisticalXnci1Plugin)
The plugin providing elementary statistical functions.
Functions
Function 
sum(...) 
Feature 
Computes the summation value.

Signature 
float sum( ... float ) 
Params 
(float type, can pass any number of values) Values of which summation value should be computed.

Return 
(float type) The summation value. 
Example 
print( sum(1.0, 2.5, 4.0) ); // 7.5 
Function 
mean(...) 
Feature 
Computes the arithmetic mean value.

Signature 
float mean( ... float ) 
Params 
(float type, can pass any number of values) Values of which arithmetic mean value should be computed.

Return 
(float type) The arithmetic mean value. 
Example 
print( mean(1.0, 2.5, 4.0) ); // 2.5 
Function 
van(...) 
Fearure 
Computes the value of the variance ( denominator : N ).

Signature 
float van( ... float ) 
Params 
(float type, can pass any number of values) Values of which value of the variable should be computed.

Return 
(float type) The value of the variance ( denominator : N ). 
Example 
print( van(1.0, 2.5, 4.0) ); // 1.5 
Function 
van1(...) 
Fearure 
Computes the value of the variance ( denominator : N1 ).

Signature 
float van( ... float ) 
Params 
(float type, can pass any number of values) Values of which value of the variable should be computed.

Return 
(float type) The value of the variance ( denominator : N1 ). 
Example 
print( van1(1.0, 2.5, 4.0) ); // 2.25 
Function 
sdn(...) 
Feature 
Computes the value of the standarddeviation ( denominator : N ).

Signature 
float sdn( ... float ) 
Params 
(float type, can pass any number of values) Values of which value of the standarddeviation should be computed.

Return 
(float type) The value of the standarddeviation ( denominator : N ). 
Example 
print( sdn(1.0, 2.5, 4.0) ); // 1.2247... (1.5) 
Function 
sdn1(...) 
Feature 
Computes the value of the standarddeviation ( denominator : N1 ).

Signature 
float sdn1( ... float ) 
Params 
(float type, can pass any number of values) Values of which value of the standarddeviation should be computed.

Return 
(float type) The value of the standarddeviation ( denominator : N1 ). 
Example 
print( sdn1(1.0, 2.5, 4.0) ); // 1.5 (=2.25) 