MRFT

# Expressions

All the expressions that are used in `mrft` are backed by `exp4j`, so basically it will handle all the expressions `exp4j` does plus a couple of additions.

Expressions should be written in `infix notation`, arguments of functions must be surrounded by parentheses and separated by commas; so basically you should write them in the natural way.

## Operators

There are three basic sets of operators available:

### Arithmetic

All of the arithmetic operators are included and available: `+`, `-`, `*`, `/` and of course `%` (modulo).

### Comparison

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`) and `false` otherwise.

### Boolean

As with comparison operators, boolean operators will consider `false` every value equal to zero (`0 ± 0.000000000001`), and `true` every other value. But they are warrantied to return `1.0` for `true` and `0.0` for `false`. The available operators are: `&` (and), `|` (or), `¬` (not).

### Precedence

For those who don't know, precedence of operators refers to which of the operators will be evaluated first when left alone. I won't bother you with numbers, the order of evaluation is as follows:

```

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

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

         ^^^ The dashes indicate groups with the same precedence

```

When operators have the same precedence they will be evaluated from left to right.

***Note:*** as in primary school (and beyond) you can always alter the precedence of operators with the use of parentheses.

## Functions

There are quite a few functions available, basically all the ones in [Java Math](https://docs.oracle.com/javase/7/docs/api/java/lang/Math.html), and a couple of additions.

I'll just name them, I'm assuming everyone reading this over the Internet, has Google access to find the ones that don't actually know.

### Trigonometric

Please note that all of the trigonometric functions work in radian: `sin`, `cos`, `tan`, `asin`, `acos`, `atan`, `sinh`, `cosh`, `tanh` and `sinc`.

### Boolean

- No arguments: `false`, `true`

- One argument: `not`

- Two arguments:`and`, `or`, `xor`, `nand`, `nor`, `xnor`, `equals` (this one is not exactly boolean)

- Three arguments: `if` which is used like this `if(boolean_exp, val_if_true, val_if_false)` that means that `if(0 < 1, 5, 10) -> 5`

### Misc

`abs`, `log`, `log10`, `log2`, `log1p`, `ceil`, `floor`, `sqrt`, `cbrt`, `pow`, `exp`, `expm1`, `signum`.

### Random (noise)

There are 4 random (non deterministic) functions available:

- No arguments: 

  - `rand`: random uniformly distributed number between `0.0` (inclusive) and `1.0` (exclusive).

  - `gaussian`: random gaussianly distributed number with average `0.0` and variance `1.0`

- Two arguments:

  - `rand2(start, end)`: random uniformly distributed number between `start` (inclusive) and `end` (exclusive).

  - `gaussian2(avg, var)`: random gaussianly distributed number with average `avg` and  variance `var`

### Constants

There are two constants implemented as functions (for reasons I will not discuss here), which are `pi` and `e`.