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use uint240 for q104.104

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This commit is contained in:
Hayden Adams
2019-11-25 16:34:40 -05:00
parent a480e3df21
commit 238b0a9658
2 changed files with 17 additions and 18 deletions
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18
contracts/UniswapV2.sol
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@ -12,7 +12,7 @@ import "./token/SafeTransfer.sol";
contract UniswapV2 is IUniswapV2, ERC20("Uniswap V2", "UNI-V2", 18, 0), SafeTransfer { contract UniswapV2 is IUniswapV2, ERC20("Uniswap V2", "UNI-V2", 18, 0), SafeTransfer {
using SafeMath128 for uint128; using SafeMath128 for uint128;
using SafeMath256 for uint256; using SafeMath256 for uint256;
using UQ104x104 for uint232; using UQ104x104 for uint240;
struct TokenData { struct TokenData {
uint128 token0; uint128 token0;
@ -88,12 +88,12 @@ contract UniswapV2 is IUniswapV2, ERC20("Uniswap V2", "UNI-V2", 18, 0), SafeTran
uint128 blocksElapsed = (block.number - blockNumberLast).downcast128(); uint128 blocksElapsed = (block.number - blockNumberLast).downcast128();
// get the prices according to the reserves as of the last official interaction with the contract // get the prices according to the reserves as of the last official interaction with the contract
uint208 priceToken0 = UQ104x104.encode(reserves.token0).qdiv(reserves.token1); uint240 priceToken0 = UQ104x104.encode(reserves.token0).qdiv(reserves.token1);
uint208 priceToken1 = UQ104x104.encode(reserves.token1).qdiv(reserves.token0); uint240 priceToken1 = UQ104x104.encode(reserves.token1).qdiv(reserves.token0);
return ( return (
priceToken0Accumulated + (uint240(priceToken0) * blocksElapsed), priceToken0Accumulated + priceToken0 * blocksElapsed,
priceToken1Accumulated + (uint240(priceToken1) * blocksElapsed) priceToken1Accumulated + priceToken1 * blocksElapsed
); );
} else { } else {
return ( return (
@ -126,12 +126,12 @@ contract UniswapV2 is IUniswapV2, ERC20("Uniswap V2", "UNI-V2", 18, 0), SafeTran
uint32 blocksElapsed = blockNumber - blockNumberLast; uint32 blocksElapsed = blockNumber - blockNumberLast;
// get the prices according to the reserves as of the last official interaction with the contract // get the prices according to the reserves as of the last official interaction with the contract
uint208 priceToken0 = UQ104x104.encode(reserves.token0).qdiv(reserves.token1); uint240 priceToken0 = UQ104x104.encode(reserves.token0).qdiv(reserves.token1);
uint208 priceToken1 = UQ104x104.encode(reserves.token1).qdiv(reserves.token0); uint240 priceToken1 = UQ104x104.encode(reserves.token1).qdiv(reserves.token0);
// multiply these prices by the number of elapsed blocks and add to the accumulators // multiply these prices by the number of elapsed blocks and add to the accumulators
priceToken0Accumulated = priceToken0Accumulated + (uint240(priceToken0) * blocksElapsed); priceToken0Accumulated = priceToken0Accumulated + priceToken0 * blocksElapsed;
priceToken1Accumulated = priceToken1Accumulated + (uint240(priceToken1) * blocksElapsed); priceToken1Accumulated = priceToken1Accumulated + priceToken1 * blocksElapsed;
} }
// update the last block number // update the last block number

17
contracts/libraries/UQ104x104.sol
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@ -6,29 +6,28 @@ pragma solidity 0.5.12;
// https://github.com/gnosis/solidity-arithmetic // https://github.com/gnosis/solidity-arithmetic
library UQ104x104 { library UQ104x104 {
uint232 constant Q104 = uint232(uint104(-1)) + 1; uint240 constant Q104 = 2**104;
// we want to encode a uint128 `y` s.t. `y := y_encoded / 2**104` (i.e. with a Q104 denominator). // we want to encode a uint128 `y` s.t. `y := y_encoded / 2**104` (i.e. with a Q104 denominator).
// in other words, to encode `y` we simply multiply by `2**104`, aka Q104. // in other words, to encode `y` we simply multiply by `2**104`, aka Q104.
// however, in the case of a traditional UQ104.104, we'd store this output in a 208-bit slot, // however, in the case of a traditional UQ104.104, we'd store this output in a 208-bit slot,
// which would overflow for values of `y` in (`uint104(-1)`, `uint128(-1)`], so instead we need to // which would overflow for values of `y` in (`uint104(-1)`, `uint128(-1)`], so instead we need to
// store the output in 232 bits (TODO check this logic). // store the output in 232 bits (TODO check this logic).
function encode(uint128 y) internal pure returns (uint232 z) { function encode(uint128 y) internal pure returns (uint240 z) {
return uint232(y) * Q104; return uint240(y) * Q104;
} }
// we want to divide a modified UQ104.104 (the output of encode) by an unencoded uint128, // 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. // 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 // 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 // differently in the future
function qdiv(uint232 x, uint128 y) internal pure returns (uint208 z) { function qdiv(uint240 x, uint128 y) internal pure returns (uint240 z) {
uint232 temp = x / y; z = x / y;
if (temp == 0) {
if (z == 0) {
z = 1; z = 1;
} else if (temp > uint208(-1)) { } else if (z > uint208(-1)) {
z = uint208(-1); z = uint208(-1);
} else {
z = uint208(temp);
} }
} }
} }