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optimize uq104 to avoid higher bit space math

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This commit is contained in:
Noah Zinsmeister
2019-11-22 15:48:23 -05:00
parent f9f8306af0
commit 897b61b78d
2 changed files with 17 additions and 13 deletions
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8
contracts/UniswapV2.sol
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@ -88,8 +88,8 @@ contract UniswapV2 is IUniswapV2, ERC20("Uniswap V2", "UNI-V2", 18, 0), SafeTran
uint128 blocksElapsed = (block.number - blockNumberLast).downcast128();
// get the prices according to the reserves as of the last official interaction with the contract
uint208 priceToken0 = UQ104x104.encode(reserves.token0).qdiv(UQ104x104.encode(reserves.token1));
uint208 priceToken1 = UQ104x104.encode(reserves.token1).qdiv(UQ104x104.encode(reserves.token0));
uint208 priceToken0 = UQ104x104.encode(reserves.token0).qdiv(reserves.token1);
uint208 priceToken1 = UQ104x104.encode(reserves.token1).qdiv(reserves.token0);
return (
priceToken0Accumulated + (uint240(priceToken0) * blocksElapsed),
@ -126,8 +126,8 @@ contract UniswapV2 is IUniswapV2, ERC20("Uniswap V2", "UNI-V2", 18, 0), SafeTran
uint32 blocksElapsed = blockNumber - blockNumberLast;
// get the prices according to the reserves as of the last official interaction with the contract
uint208 priceToken0 = UQ104x104.encode(reserves.token0).qdiv(UQ104x104.encode(reserves.token1));
uint208 priceToken1 = UQ104x104.encode(reserves.token1).qdiv(UQ104x104.encode(reserves.token0));
uint208 priceToken0 = UQ104x104.encode(reserves.token0).qdiv(reserves.token1);
uint208 priceToken1 = UQ104x104.encode(reserves.token1).qdiv(reserves.token0);
// multiply these prices by the number of elapsed blocks and add to the accumulators
priceToken0Accumulated = priceToken0Accumulated + (uint240(priceToken0) * blocksElapsed);

22
contracts/libraries/UQ104x104.sol
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@ -17,14 +17,18 @@ library UQ104x104 {
return uint232(y) * Q104;
}
// we want to divide two modified-UQ104.104s (the outputs of encode), and return a traditional Q104.
// for our purposes, we'll do that by flooring the output of the division with `uint208(-1)`.
// (this corresponds to capping the relative prices of x and y at `1 / 2**104` and `uint208(-1) / 2**104`.)
// unfortunately, before we can compute `min(uint208(-1), output), we need to compute `output = x * 2**104 / y`,
// for which we need at least 416 bits (possibly 438 or 464? TODO think this through).
// for now, we just mock the function
function qdiv(uint232 x, uint232 y) internal pure returns (uint208 z) {
// TODO replace mock with real logic
z = uint208(x * Q104 / y);
// we want to divide a modified UQ104.104 (the output of encode) by an unencoded uint128,
// and return a traditional Q104. since we're using a modified UQ104.104, though, we need to handle overflows.
// for the moment, we simply truncate these to 1 and uint208(-1), though it's likely we'll handle this slightly
// differently in the future
function qdiv(uint232 x, uint128 y) internal pure returns (uint208 z) {
uint232 temp = x / y;
if (temp == 0) {
z = 1;
} else if (temp > uint208(-1)) {
z = uint208(-1);
} else {
z = uint208(temp);
}
}
}