Unary operator minus (-) cannot be applied to type uint256

Question

While trying to compile the mulDiv function part of the uniswap-v3-core code base, I got the following error:

Unary operator - cannot be applied to type uint256

This is the line that causes the compile error:

uint256 twos = -denominator & denominator;

I'm using using Solidity v0.8.3, while they used Solidity v0.7.6.

This doesn't seem to be listed in the v0.8.0 breaking changes. How can I make it work in v0.8 while ensuring that the logic stays the same?

Answer 1

The unary operator - negates the given number. It is easier to see what it does with signed integers. If we use the int8 type and we negate the positive number 10, we get -10 back.

Now, unsigned integers can't represent negative numbers, of course. What Solidity does when negating an uint8 x (in v0.7 and below) is to return type(uint8).max - x + 1. For example, negating 10 gives us 246.

The following function that I wrote returns true for all possible values of x:

function checkNegativeUnary(uint8 x) external pure returns (bool result) {
    uint8 a = -x;
    uint8 b = type(uint8).max - x + 1;
    result = a == b;
}

Since it seems like Solidity v0.8 forbids the negation of unsigned integers now, to make the mulDiv compile we should rewrite that denominator like this:

uint256 twos = (type(uint256).max - denominator + 1) & denominator;

This doesn't overflow because denominator can never be 0, due to another check made earlier in the function:

// Make sure the result is less than 2**256.
// Also prevents denominator == 0
require(denominator > prod1);

Update

I managed to find a shorter implementation, as per the answers in this Q&A I started in the CS SE: How to find the largest power of two divisor of a given integer?:

uint256 twos = denominator & (~denominator + 1);

Note that this is faster than the other solution only if you're using checked arithmetic.