Optimize Math.max and SignedMath.max

[gzliudan]

In Solidity, there is no single op-code for <= or >= expressions. Solidity compiler executes the LT/GT (less than/greater than) op-code and afterwards it executes an ISZERO op-code to check if the result of the previous comparison (LT/ GT) is zero and validate it or not. So the use of < and > are cheaper than <= and >=. Below is current version of max function:

    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        return a >= b ? a : b;
    }

The above code works as below steps:

    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        if (a > b) {
            return a;
        } else if (a == b) {
            return a;
        } else {
            return b;
        }
    }

If we use the new version:

    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        return a > b ? a : b;
    }

Then the function will works as below steps:

    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        if (a > b) {
            return a;
        } else {
            return b;
        }
    }

So the step of check a == b is omitted.

[Amxx]

Nice find @gzliudan

I was hopping the compiler would translate a >= b as !(a<b) and you "just" pay for the negation part (with can be done using isZero).

Still, that is a nice optimization!

Can you add a small changelog entry ?

[gzliudan]

Ok, I added a new entry to changelog.

[frangio]

It's not even necessary to do the negation. The compiler should be able to convert a >= b ? a : b into a < b ? b : a... Indeed, compiling with viaIR: true this optimization is done automatically.

Reluctantly approving this PR because these peephole optimizations are the job of the compiler.

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