Ai Modules

====== Formula ======

^ section | Math |
^ short description | Outputs a value calculated from the input value(s), with an easy-to-use formula language. |
^ licence level | Anjuna |
^ ports | Input A [numeric/control]\\ Input B [numeric/control]\\ Input C [numeric/control]\\ Input D [numeric/control]\\ Out [numeric/control]\\ Compile Formula [pushbutton] |
^ skins | Small, **Medium** |

Type in the formula, wire inputs and output, hit ''Compile''. Now the output value is dynamically computed from the input value(s).

==== used in example ====

{{backlinks>.#ai:examples}}

===== Manual =====
> Applies a user defined formula to the inputs and outputs the value on the Out port.  The formula syntax follows the mu parser format as specifed here:  http://muparser.beltoforion.de/ with a few additional functions such as the Modulus function mod(a, b) and the addition of vector component access in the Vector Formula module.
> {{:ai:modules:math:formula_skins.png|}}

===== Skins =====

==== Medium ====

4 inputs, medium-sized formula textfield. Can be resized.

==== Small ====

2 inputs, slightly smaller formula textfield. Can be resized.

===== Formula language =====

Currently a list of the available commands is available here: http://beltoforion.de/article.php?a=muparser&hl=en&p=features&da=1. 

For ease of use it is replicated here, however, as always you are reeferred to the original source.

==== Built-in functions ====
The following table gives an overview of the functions supported by the default implementation. It lists the function names, the number of arguments and a brief description.

^ Name ^ Argc. ^ Explanation ^
| sin | 1 | sine function |
| cos | 1 | cosine function |
| tan | 1 | tangens function  |
| asin | 1 | arcus sine function  |
| acos | 1 | arcus cosine function |
| atan | 1 | arcus tangens function |
| sinh | 1 | hyperbolic sine function |
| cosh | 1 | hyperbolic cosine |
| tanh | 1 | hyperbolic tangens function |
| asinh | 1 | hyperbolic arcus sine function |
| acosh | 1 | hyperbolic arcus tangens function |
| atanh | 1 | hyperbolic arcus tangens function |
| log2  | 1 | logarithm to the base 2  |
| log10 | 1 | logarithm to the base 10 |
| log  | 1  | logarithm to base e (2.71828...)  |
| ln   | 1  | logarithm to base e (2.71828...)  |
| exp  | 1  | e raised to the power of x   |
| sqrt | 1  | square root of a value  |
| sign | 1  | sign function -1 if x<0; 1 if x>0  |
| rint | 1  | round to nearest integer |
| abs  | 1  | absolute value   |
| min  | var. | min of all arguments  |
| max  | var. | max of all arguments  |
| sum  | var. | sum of all arguments  |
| avg  | var. | mean value of all arguments |


==== Built-in binary operators ====

The following table lists the default binary operators supported by the parser. 

^ Operator ^ Description  ^ Priority ^
| =  | assignement | -1 |
| && | logical and | 1  |
| <nowiki>||</nowiki> | logical or  | 2  |
| <= | less or equal  | 4 |
| >= | greater or equal | 4 |
| != | not equal | 4 |
| == | equal  | 4  |
| > | greater than  | 4 |
| < | less than | 4  |
| + | addition  | 5  |
| - | subtraction | 5  |
| * | multiplication | 6 |
| / | division  | 6 |
| <nowiki>^</nowiki> | raise x to the power of y | 7  |
 
  * The assignment operator is special since it changes one of its arguments and can only by applied to variables. 

==== Ternary Operators ====

> muParser has built in support for the if then else operator. It uses lazy evaluation in order to make sure only the necessary branch of the expression is evaluated. 


^ Operator ^ Description  ^ Remarks ^
| ?: | if then else operator  | C++ style syntax  |