# Arithmetic

Basic math operations. All arithmetic words pop their operands and push the result.

## Basic Operations

```
3 4 +      ( 7 )
10 3 -     ( 7 )
3 4 *      ( 12 )
10 3 /     ( 3.333... )
10 3 mod   ( 1 )
```

Division always produces a float. Use `floor` if you need an integer result.

## Negative Numbers

```
5 neg      ( -5 )
-3 abs     ( 3 )
```

## Rounding

```
3.7 floor  ( 3 )
3.2 ceil   ( 4 )
3.5 round  ( 4 )
```

## Min and Max

```
3 7 min    ( 3 )
3 7 max    ( 7 )
```

## Power and Root

```
2 3 pow    ( 8 )
9 sqrt     ( 3 )
```

## Examples

Calculate a frequency ratio:

```
440 2 12 / pow *   ( 440 * 2^(1/12) ≈ 466.16 )
```

Clamp a value between 0 and 1:

```
1.5 0 max 1 min    ( 1 )
-0.5 0 max 1 min   ( 0 )
```

Scale a 0-1 range to 200-800:

```
0.5 600 * 200 +    ( 500 )
```

## Words

| Word | Stack | Description |
|------|-------|-------------|
| `+` | (a b -- sum) | Add |
| `-` | (a b -- diff) | Subtract |
| `*` | (a b -- prod) | Multiply |
| `/` | (a b -- quot) | Divide |
| `mod` | (a b -- rem) | Modulo |
| `neg` | (a -- -a) | Negate |
| `abs` | (a -- \|a\|) | Absolute value |
| `floor` | (a -- n) | Round down |
| `ceil` | (a -- n) | Round up |
| `round` | (a -- n) | Round to nearest |
| `min` | (a b -- min) | Minimum |
| `max` | (a b -- max) | Maximum |
| `pow` | (a b -- a^b) | Power |
| `sqrt` | (a -- √a) | Square root |