Numoen

An issue relating to custom error messages used in contracts can occur with the current solidity compiler settings. The solidity version is currently set to `pragma solidity ^0.8.0`, however the solidity version needs to be at least 0.8.4 or above to [support custom errors](https://blog.soliditylang.org/2021/04/21/custom-errors/).

It is expected that calls of the form `transfer(recipient, amount)` fail if the recipient address is the zero address.

The functions which are never called internally within the contract should have external visibility for gas optimization. #### ERC20.sol ```solidity=61 function approve(address spender, uint256 amount) public virtual returns (bool) { ``` --- ```solidity=69 function transfer(address to, uint256 amount) public virtual returns (bool) { ``` --- ```solidity=83 function transferFrom( ``` --- ```solidity=109 function permit( ```

The loss of precision on the calculation in L161~162 could cause the invariant check revert. ```solidity=161 uint256 amount0 = PRBMath.mulDiv(r0, liquidity, _totalSupply); uint256 amount1 = PRBMath.mulDiv(r1, liquidity, _totalSupply); if (!verifyInvariant(amount0, amount1, liquidity)) revert InvariantError(); ``` The `verifyInvariant()` requires the exact number of two tokens to be matched according to the formula. However, the loss of precision could cause the two token's amount to be unmatched, thus causing the revert on the invariant check.