exp4j

# Extra Functions and Operators

There are a number of extra functions and operators included in this version of `exp4j`, non of this are enabled by default, they are in the [`net.objecthunter.exp4j.extras`](https://gitlab.com/riddler_arg/exp4j/tree/master/src/main/java/net/objecthunter/exp4j/extras) package.

## Comparison Operators

Aside from the arithmetic operators several comparison operators are included:

`<`, `<=`, `>`, `>=`, `!=` and `==`. Please note that since `exp4j` itself has

no concept of `boolean`, the results given by all of the comparison operators

will be `1.0` if `true` and `0.0` if `false`. Let it be noted that due to

rounding, equality operators use a radix in which they consider numbers to be

"equal", that is:

Let `a` and `b` be two real numbers, `a == b` will evaluate to `true` if and

only if the distance between `a` and `b` (`dist(a, b) := abs(a - b)`) is less or

equal than [`1e-12` (`0.000000000001`)](https://gitlab.com/riddler_arg/exp4j/blob/master/src/main/java/net/objecthunter/exp4j/extras/FunctionsMisc.java#L38) and `false` otherwise.

### Precedence

Operator precedence is altered when using the comparison operators, the new precedence is:

~~~

FIRST->  * / %  - +  > >= < <=  ¬  &  |  == !=   <-LAST

         -----  ---  ---------  -  -  -  -----    

         ^^^ The dashes indicate groups with the same precedence

~~~

## Boolean Functions

Even though we have boolean operators, there are also a number of boolean functions that can be used (some people prefer functions)

* `and(a, b)`: Logical and _equivalent to `a & b`_

* `or(a, b)`: Logical or _equivalent to `a | b`_

* `xor(a, b)`: Exclusive or

* `nand(a, b)`: _equivalent to `¬(a & b)`_

* `nor(a, b)`: _equivalent to `¬(a | b)`_

* `xnor(a, b)`: Negated exclusive or 

* `not(a)`: _equivalent to `¬a`_

## Boolean Constants

* `true()`: true value `1.0` (true is actually any value different than zero, but this is the value returned by comparison operators, boolean operators and boolean functions.

* `false()`: false value `0.0`

## Extra Functions

* `if(e, v_true, v_false)`: Branches the formula, it will be evaluated as `v_true` if `e == true()` and `v_false`  if `e == false()` 

* `equals(a, b)`: Equivalent to `a == b`, so the same conditions apply.

* `sinc(x)`: [Cardinal sine of `x`](https://en.wikipedia.org/wiki/Sinc_function) (not normalized), equivalent to `sin(x)/x`

## Code

The code for the functions is [here](https://gitlab.com/riddler_arg/exp4j/blob/master/src/main/java/net/objecthunter/exp4j/extras/OperatorsComparison.java), [here](https://gitlab.com/riddler_arg/exp4j/blob/master/src/main/java/net/objecthunter/exp4j/extras/FunctionsMisc.java) and [here](https://gitlab.com/riddler_arg/exp4j/blob/master/src/main/java/net/objecthunter/exp4j/extras/FunctionsBoolean.java).