# Math
### Functions
#### min
```solidity
function min(uint256 x, uint256 y) internal pure returns (uint256 z);
```
#### min128
```solidity
function min128(uint128 x, uint128 y) internal pure returns (uint128 z);
```
#### min
```solidity
function min(int256 x, int256 y) internal pure returns (int256 z);
```
#### max
```solidity
function max(uint256 x, uint256 y) internal pure returns (uint256 z);
```
#### max
```solidity
function max(int256 x, int256 y) internal pure returns (int256 z);
```
#### max128
```solidity
function max128(uint128 x, uint128 y) internal pure returns (uint128 z);
```
#### clip128
```solidity
function clip128(uint128 x, uint128 y) internal pure returns (uint128);
```
#### clip
```solidity
function clip(uint256 x, uint256 y) internal pure returns (uint256);
```
#### divFloor
```solidity
function divFloor(uint256 x, uint256 y) internal pure returns (uint256);
```
#### divCeil
```solidity
function divCeil(uint256 x, uint256 y) internal pure returns (uint256);
```
#### mulFloor
```solidity
function mulFloor(uint256 x, uint256 y) internal pure returns (uint256);
```
#### mulCeil
```solidity
function mulCeil(uint256 x, uint256 y) internal pure returns (uint256);
```
#### invFloor
```solidity
function invFloor(uint256 x) internal pure returns (uint256);
```
#### invCeil
```solidity
function invCeil(uint256 denominator) internal pure returns (uint256 z);
```
#### mulDivFloor
```solidity
function mulDivFloor(uint256 x, uint256 y, uint256 k) internal pure returns (uint256 result);
```
#### mulDivCeil
```solidity
function mulDivCeil(uint256 x, uint256 y, uint256 k) internal pure returns (uint256 result);
```
#### mulDivDown
```solidity
function mulDivDown(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 z);
```
#### mulDivUp
```solidity
function mulDivUp(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 z);
```
#### mulDown
```solidity
function mulDown(uint256 x, uint256 y) internal pure returns (uint256);
```
#### mulUp
```solidity
function mulUp(uint256 x, uint256 y) internal pure returns (uint256);
```
#### divDown
```solidity
function divDown(uint256 x, uint256 y) internal pure returns (uint256);
```
#### divUp
```solidity
function divUp(uint256 x, uint256 y) internal pure returns (uint256);
```
#### scale
```solidity
function scale(uint8 decimals) internal pure returns (uint256);
```
#### ammScaleToTokenScale
```solidity
function ammScaleToTokenScale(uint256 amount, uint256 scaleFactor, bool ceil) internal pure returns (uint256 z);
```
#### tokenScaleToAmmScale
```solidity
function tokenScaleToAmmScale(uint256 amount, uint256 scaleFactor) internal pure returns (uint256);
```
#### abs32
```solidity
function abs32(int32 x) internal pure returns (uint32);
```
#### abs
```solidity
function abs(int256 x) internal pure returns (uint256);
```
#### sqrt
```solidity
function sqrt(uint256 x) internal pure returns (uint256 z);
```
#### floorD8Unchecked
Floor of a D8 number without checking overflow in the cast to int32.
```solidity
function floorD8Unchecked(int256 val) internal pure returns (int32);
```