Can division underflow or overflow in Solidity?

Question

We know that:

1. Since Solidity v0.8, the compiler has checks for {over,under}flow by default for all arithmetic operations.
2. Division is an arithmetic operation that rounds down to the integer part of the quotient.

Excluding the case when the divisor is zero, is underflow or overflow possible?

Answer 1

Yes, there is at least one situation where overflow can occur. I don't know about underflows though.

When you divide the minimum of a signed type by -1, you get the mirror image of that number in the unsigned part, but the unsigned type only goes up to that number minus 1.

function div_overflow() public pure returns (int16 result) {
    int16 x = type(int16).min;
    int16 y = -1;
    // Overflows because doesn't fit in int16
    result = x / y;
}

In Solidity, signed numbers start at -1, while unsigned numbers start at 0. Read more about. Read more about two's complement in the Solidity docs.

Update: looks like this is specified in the docs:

The expression type(int).min / (-1) is the only case where division causes an overflow. In checked arithmetic mode, this will cause a failing assertion, while in wrapping mode, the value will be type(int).min.