# Data Encoding

## Custom data types

Sphinx uses several custom data types on top of the primitive types offered by Cairo. 

We do not rely on the native signed integer type as we rely on math operations that are not currently implemented by the Cairo core lib.

### `i32`

```rust
i32 {
    val: u32
    sign: bool
}
```

The `i32` type is used for storing unshifted limits. 

### `i128`

```rust
i128 {
    val: u128
    sign: bool
}
```

The `i128` type is used for storing liquidity deltas. 

### `i256`

```rust
i256 {
    val: u256
    sign: bool
}
```

The `i256` type is used for storing token amount deltas. 

## Limit shifting

For simplicity and efficiency, limits are stored in shifted form by mapping unshifted `i32` limits to shifted `u32` limits.

Specifically, an `offset` equal to the largest possible multiple of the market `width` is applied for shifting and unshifting.