Add SignedMath with math utilities for signed integers

[rotcivegaf]

• Tests
• Documentation
• Changelog entry

[Amxx]

Hello @rotcivegaf

I'm sorry we haven't reached out yet. This PR resurfaced as we are planning for the next release and we would love to merge it. Still some small issues must be addressed:

• In average, the function can overflow. If bot values are type(int256).max, then the function will revert despite the average fitting in an int256. I encourage you to have a look at Math.average to see how this can be addressed.

• In ceilDiv, you are using a int8 in a place where its not necessary. I would rather use int256 to avoid unnecessary implicit cast.

Can you have a go at this ?

[rotcivegaf]

Sorry for the delay, I was very busy

In the second point, when I remove the cast, I get this error from the compiler:
TypeError: Type uint8 is not implicitly convertible to expected type int256.

The other option I thought of is to replace that line with:

int256 r;
if(a % b != 0) r = 1;

I work in the first point, in this days

[Amxx]

Noted.

I think this point is less controversial, as it should not affect the produce bytecode
I think I would personally do

        int256 r = a % b == 0 ? int256(0) : int256(1);

[rotcivegaf]

In the ceilDiv signed average function, I think your idea its good, I commited

In the average signed average function, I try do with this way:

    function average(int256 a, int256 b) internal pure returns (int256) {
          return (a / 2) + (b / 2) + ((a % 2 + b % 2) / 2);
    }

But when calculate with an even signed number and an odd number, the return number is one(1) integer greater than the expect, this cause because this part of the equation (a % 2 + b % 2), I think the problem is because we have the number 0

I worked in this ugly solution, but I still thinking in another better

    function average(int256 a, int256 b) internal pure returns (int256) {
        if ((b < 0 && a > 0 && -b < a) || (a < 0 && b > 0 && -a < b))
            return (a / 2) + (b / 2) + (((a % 2 + b % 2) - 1) / 2);

        if ((b < 0 && a > 0 && -b > a) || (a < 0 && b > 0 && -a > b))
            return (a / 2) + (b / 2) + (((a % 2 + b % 2) + 1) / 2);

        return (a / 2) + (b / 2) + ((a % 2 + b % 2) / 2);
    }

[frangio]

This formula on StackOverflow looks really neat:

int avg = (a & b) + (a ^ b) / 2;

[Amxx]

This formula on StackOverflow looks really neat:

int avg = (a & b) + (a ^ b) / 2;

should we use that for Unsigned Math ? I guess it would be more gas efficient

[rotcivegaf]

Well with unsigned values its more complicated we have the number 0, and this a problem
This implementation int avg = (a & b) + (a ^ b) / 2; dont pass this tests:

• one even signed number and one odd signed number
• one even signed number and one odd number

But I use this idea in Math.sol to make another PR

EDIT: I update the code, the average function its ugly but works, I will research more to improve it. Any help are welcome

[frangio]

We want a nicer definition of div in order to merge this. We think it should be possible to find one by tweaking the proof for unsigned div formula:

[frangio]

I keep trying to adapt the formula in an elegant way but I can't find one.

The issue is that the formula seems to round towards negative infinity and we want it to round to zero.

[Amxx]

I've refactored the average code.

We still need a changelog entry and some documentation. I'll work on that tomorrow

[frangio]

@Amxx I've removed ceilDiv since it's not proper "ceiling". Let's add it back if someone requests something like it.

Please merge if it looks good.

[rotcivegaf]

I'm AFK, but I want to congratulate them
Great work!