naturalLog.sol

pragma solidity >=0.7.0 <0.9.0;

contract natural_log {
 
    function log2(uint x) public pure returns (uint){
        uint y;

    assembly {
            let arg := x
            x := sub(x,1)
            x := or(x, div(x, 0x02))
            x := or(x, div(x, 0x04))
            x := or(x, div(x, 0x10))
            x := or(x, div(x, 0x100))
            x := or(x, div(x, 0x10000))
            x := or(x, div(x, 0x100000000))
            x := or(x, div(x, 0x10000000000000000))
            x := or(x, div(x, 0x100000000000000000000000000000000))
            x := add(x, 1)
            let m := mload(0x40)
            mstore(m,           0xf8f9cbfae6cc78fbefe7cdc3a1793dfcf4f0e8bbd8cec470b6a28a7a5a3e1efd)
            mstore(add(m,0x20), 0xf5ecf1b3e9debc68e1d9cfabc5997135bfb7a7a3938b7b606b5b4b3f2f1f0ffe)
            mstore(add(m,0x40), 0xf6e4ed9ff2d6b458eadcdf97bd91692de2d4da8fd2d0ac50c6ae9a8272523616)
            mstore(add(m,0x60), 0xc8c0b887b0a8a4489c948c7f847c6125746c645c544c444038302820181008ff)
            mstore(add(m,0x80), 0xf7cae577eec2a03cf3bad76fb589591debb2dd67e0aa9834bea6925f6a4a2e0e)
            mstore(add(m,0xa0), 0xe39ed557db96902cd38ed14fad815115c786af479b7e83247363534337271707)
            mstore(add(m,0xc0), 0xc976c13bb96e881cb166a933a55e490d9d56952b8d4e801485467d2362422606)
            mstore(add(m,0xe0), 0x753a6d1b65325d0c552a4d1345224105391a310b29122104190a110309020100)
            mstore(0x40, add(m, 0x100))
            let magic := 0x818283848586878898a8b8c8d8e8f929395969799a9b9d9e9faaeb6bedeeff
            let shift := 0x100000000000000000000000000000000000000000000000000000000000000
            let a := div(mul(x, magic), shift)
            y := div(mload(add(m,sub(255,a))), shift)
            y := add(y, mul(256, gt(arg, 0x8000000000000000000000000000000000000000000000000000000000000000)))
        }  

        uint ln = y;
        return ln;

    }

}