Multiplication

// SPDX-License-Identifier: GPL-3.0
pragma solidity ^0.8.0;

contract Yul {
    function multiply(uint256 x, uint256 y) public pure returns (bytes32) {
        assembly {
            mstore(0x80, mul(x, y))
            return(0x80, 0x20)
        }
    }
}

The mul(a, b) Yul command takes in two numbers as arguments and returns their product, a * b.

🚨 Multiplications in Yul are unchecked, meaning that, Yul wraps around numbers if they exceed the highest possible number to be stored in a slot.

// SPDX-License-Identifier: GPL-3.0
pragma solidity ^0.8.0;

contract Yul {
    function multiply() public pure returns (bytes32) {
        assembly {
            let large := 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
            mstore(0x80, mul(large, 0x12345678))
            return(0x80, 0x20)
        }
    }
}

The above will return 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffedcba988 showing a wrap around.

To write a Yul multiplication code to check for overflows and prevent them, this will be the approach to use [6].

// SPDX-License-Identifier: GPL-3.0
pragma solidity ^0.8.0;

contract Yul {
    function multiply(uint256 x, uint256 y) public pure returns (bytes32) {
        assembly {
            if eq(x, 0) {
                return(0x80, 0x20)
            }

            if eq(y, 0) {
                return(0x80, 0x20)
            }

            let z := mul(x, y)
            if iszero(eq(div(z, x), y)) { revert(0x00, 0x00) }

            mstore(0x80, z)
            return(0x80, 0x20)
        }
    }
}

The eq(a, b) Yul function takes in two numbers as arguments and returns 1 meaning true if a == b and 0meaning false if a != b. The iszero(a) function takes in one number as arguments and returns 1 if a == 0 and 0 if a = 0. The eq(a, b) is used to check the truthiness of an expression, while, the iszero(a) is the method used to check the falsiness of an expression. The revert(0x<a>, 0x<b>) reverts the operation with some error message encoded according to the ABI Specification stored starting from positon 0x<a> and spanning 0x<b> bytes.