Add Math.sqrt

[Dentrax]

🧐 Motivation
It would be nice to have. Currently, we have to write our "custom" function that we can find the logic on the internet. But I'm not so sure whether those are "safe" to use.

📝 Details
Something like:

https://github.com/Uniswap/v2-core/blob/4dd59067c76dea4a0e8e4bfdda41877a6b16dedc/contracts/libraries/Math.sol#L11

math.Sqrt(16)

function sqrt(uint x) constant returns (uint y) {
    uint z = (x + 1) / 2;
    y = x;
    while (z < y) {
        y = z;
        z = (x / z + z) / 2;
    }

In OpenZeppelin way:

   function sqrt(uint y) internal pure returns (uint z) {
        if (y > 3) {
            z = y;
            uint x = (y.div(2)).add(1);
            while (x < z) {
                z = x;
                x = ((y.div(x)).add(x)).div(2);
            }
        } else if (y != 0) {
            z = 1;
        }
    }

[frangio]

Thanks for the request @Dentrax!

The reason we don't have this function currently is that it's not constant time. But I think we should take a closer look to see if there is real risk of running out of gas in the worst case, and what is the "average" cost.

It would be interesting to see smart contracts in production that are using sqrt to see if they took any special precautions and what particular implementations they used.

[Amxx]

@frangio UniswapV2 pairs use sqrt.

[frangio]

O(1) implementation of pow in Balancer, can be used as sqrt with y = 0.5:

https://github.com/balancer-labs/balancer-v2-monorepo/blob/master/pkg/solidity-utils/contracts/math/LogExpMath.sol#L89