Package	system.evaluators
Class	public class MathEvaluator
Inheritance	MathEvaluator Object
Implements	Evaluable

Evaluates mathematical string expressions.

The MathEvaluator implementation, support all of the following :

Decimal, hexadecimal, octal notation :

     1 + 1
     0.5 + 0.7
     0xff + 0xbb
     010 + 5
     etc.
     

operators :

     % / ∗ + - << >> >>> & ^ | ~
     

functions :

     abs acos asin atan atan2 ceil cos exp
     floor log max min pow random round
     sin sqrt tan 
     

Those functions replicate exactly what you can find in the Math object.

operators priority : from higher to lower priority

example : multiplication is performed before addition

     (14) fcn(...) (...)
     

function call and expression grouping

example : sin(4) + 25

sin(4) will be evaluated first

example : 5 ∗ (4 + 0.5)

the expression within the parenthesis will occurs first

     (13) ~ + - 
     

Unary operators

ex: +5 - +5 translate to (+5) - (+5)

ex: -5 + -5 translate to (-5) + (-5)

ex: ~3 - 7 translate to (~3) - 7

any unary operators will be evaluated first

     (12) ∗ / %
     

multiplication, division, modulo division

ex: 5 ∗ 3 + 1 translate to (5 ∗ 3) + 1

ex: 2 % 8 - 4 translate to (2 % 8) - 4

     (11) + -
     

addition, subtraction

     (10) << >> <<<
     

bit shifting

     (7)  &
     

bitwise AND

     (6)  ^
     

bitwise XOR

     (5)  |
     

bitwise OR

context

When instanciating the MathEvaluator you can pass a context containing either variables or functions

Example :

     var me:MathEvaluator = new MathEvaluator( { x:100, test:function(a:Number):Number {return a*a;} );
     trace( me.eval( "test(100) + 1" ) ); // return 10001
     

but there are some limitations

• your function can only have one argument
• your function name can not override default math functions as cos, sin, etc.
• your variable or function name must me lowercase
• your variable or function name must contains only letter from a to z and can end with only one digit

Example :

     test()  // OK
     test2() // OK
     2test() // BAD
     te2st() // BAD
     

we do not support logical ( || && ! ) or assignement operators ( = == += etc. )

reasons:

logical operators deal with boolean, here we want to deal only with numbers and math expression we do not support variables nor variable assignation

Parenthesis are used to alter the order of evaluation determined by operator precedence.

Operators with the same priority are evaluated left to right.

How the parser work :

1) we first filter some multiple char operators to single chars

ex: >> translate to « and other filtering

2) then we parse char by char (top to bottom parsing) to generate tokens in postfix order(reverse polish notation)

the expression 5 + 4 become [5,4,+] but while doing that we also do a lot of other things

evaluate function call

remove space chars

re-order tokens by operators priority

evaluate hexadecimal notation to decimal

etc.

3) finally we iterate trough our tokens and evaluate them by operators

ex: [5,4,+]

we find the op +, then addition the 2 values, etc.

till the end of the tokens list

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