exp4j

# Extra Functions and Operators

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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://redmine.riddler.com.ar/projects/exp4j/repository/revisions/master/show/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://redmine.riddler.com.ar/projects/exp4j/repository/exp4j/revisions/master/entry/src/main/java/net/objecthunter/exp4j/operator/Operator.java#L74) 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

~~~

### Warning!

See [[Warnings#Concatenating-comparison-operators|Warning -> Concatenating Comparison Operators]]

## 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.

* `isNan(a)`: Tells if a value is `Not A Number`

* `min(x, y)`: Returns the smallest (closest to negative infinity) of two numbers.

* `max(x, y)`: Returns the largest (closest to positive infinity) of two numbers.

* `lcm(x, y)`: Returns the Least Common Multiple of two numbers.

* `gcd(x, y)`: Returns the Greatest Common Divisor of two numbers.

* `round(x)`: Returns the closest integer of `x`.

* `deg2rad(x)`: Returns the value of `x` expressed in radians.

* `rad2deg(x)`: Returns the value of `x` expressed in degrees.

## Signal Functions

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

* `triangle(t)`: Triangle wave

* `sawtooth(t)`: Sawtooth wave

* `heavyside(t)`: Heavyside Step function

* `rectangle(t, X, Y)`: Rectangular function

## Extra constants

* `inf()`: Retrieves the value of `Double.POSITIVE_INFINITY`

## Expression based functions

* It's now possible to create expression based functions! See: [[Expression Based Functions]]

## Code

The code for the functions is [here](https://redmine.riddler.com.ar/projects/exp4j/repository/revisions/master/entry/src/main/java/net/objecthunter/exp4j/extras/OperatorsComparison.java), [here](https://redmine.riddler.com.ar/projects/exp4j/repository/revisions/master/entry/src/main/java/net/objecthunter/exp4j/extras/FunctionsMisc.java) and [here](https://redmine.riddler.com.ar/projects/exp4j/repository/revisions/master/entry/src/main/java/net/objecthunter/exp4j/extras/FunctionsBoolean.java).