Description
While reviewing the code from a project that uses the same Lib_MerkleTree library you're using, I noticed a sub-optimal loop iterator using uint8 instead of uint256.

Because of this, Solidity will generate more operations to make sure the iterator stays within the uint8 constraints, hence it will cost more gas to execute the loop.

I created a Solidity contract and ran a few tests which might help you decide if you want to include the change or not.

The following Solidity contract example was used to measure the difference between using uint8 and uint256 with a few example inputs.

contract FindBit {
    function find_highest_set_bit(
        uint value
    ) 
        public 
        pure 
        returns (
            uint
        ) 
    {
        uint _in = value;
        
        if (_in == 1) {
            return 0;
        }

        // Find the highest set bit (will be floor(log_2)).
        // Borrowed with <3 from https://github.com/ethereum/solidity-examples
        uint256 val = _in;
        uint256 highest = 0;
        for (uint8 i = 128; i >= 1; i >>= 1) {
            if (val & (uint(1) << i) - 1 << i != 0) {
                highest += i;
                val >>= i;
            }
        }

        // Increment by one if this is not a perfect logarithm.
        if ((uint(1) << highest) != _in) {
            highest += 1;
        }

        return highest;        
    }
}

Changing the line from uint8 to uint256

        for (uint8 i = 128; i >= 1; i >>= 1) {

        for (uint256 i = 128; i >= 1; i >>= 1) {

Gives the following different gas costs, while returning the same, identical results.

Solidity version 0.8.3+commit.8d00100c and 200 optimization runs were used in Remix IDE for tests.

Additional context

The Solidity example repository includes this method as an example for other developers to learn how to use the language. Because it does not strive to be the optimal implementation, its purpose is to show different features of the language itself.

https://github.com/ethereum/solidity-examples/blob/f44fe3b3b4cca94afe9c2a2d5b7840ff0fafb72e/src/bits/Bits.sol#L87-L99