228 lines
10 KiB
Solidity
228 lines
10 KiB
Solidity
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// SPDX-License-Identifier: BUSL-1.1
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pragma solidity >=0.5.0;
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import './LowGasSafeMath.sol';
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import './SafeCast.sol';
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import './FullMath.sol';
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import './UnsafeMath.sol';
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import './FixedPoint96.sol';
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/// @title Functions based on Q64.96 sqrt price and liquidity
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/// @notice Contains the math that uses square root of price as a Q64.96 and liquidity to compute deltas
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library SqrtPriceMath {
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using LowGasSafeMath for uint256;
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using SafeCast for uint256;
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/// @notice Gets the next sqrt price given a delta of token0
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/// @dev Always rounds up, because in the exact output case (increasing price) we need to move the price at least
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/// far enough to get the desired output amount, and in the exact input case (decreasing price) we need to move the
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/// price less in order to not send too much output.
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/// The most precise formula for this is liquidity * sqrtPX96 / (liquidity +- amount * sqrtPX96),
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/// if this is impossible because of overflow, we calculate liquidity / (liquidity / sqrtPX96 +- amount).
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/// @param sqrtPX96 The starting price, i.e. before accounting for the token0 delta
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/// @param liquidity The amount of usable liquidity
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/// @param amount How much of token0 to add or remove from virtual reserves
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/// @param add Whether to add or remove the amount of token0
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/// @return The price after adding or removing amount, depending on add
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function getNextSqrtPriceFromAmount0RoundingUp(
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uint160 sqrtPX96,
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uint128 liquidity,
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uint256 amount,
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bool add
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) internal pure returns (uint160) {
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// we short circuit amount == 0 because the result is otherwise not guaranteed to equal the input price
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if (amount == 0) return sqrtPX96;
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uint256 numerator1 = uint256(liquidity) << FixedPoint96.RESOLUTION;
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if (add) {
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uint256 product;
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if ((product = amount * sqrtPX96) / amount == sqrtPX96) {
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uint256 denominator = numerator1 + product;
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if (denominator >= numerator1)
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// always fits in 160 bits
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return uint160(FullMath.mulDivRoundingUp(numerator1, sqrtPX96, denominator));
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}
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return uint160(UnsafeMath.divRoundingUp(numerator1, (numerator1 / sqrtPX96).add(amount)));
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} else {
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uint256 product;
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// if the product overflows, we know the denominator underflows
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// in addition, we must check that the denominator does not underflow
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require((product = amount * sqrtPX96) / amount == sqrtPX96 && numerator1 > product);
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uint256 denominator = numerator1 - product;
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return FullMath.mulDivRoundingUp(numerator1, sqrtPX96, denominator).toUint160();
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}
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}
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/// @notice Gets the next sqrt price given a delta of token1
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/// @dev Always rounds down, because in the exact output case (decreasing price) we need to move the price at least
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/// far enough to get the desired output amount, and in the exact input case (increasing price) we need to move the
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/// price less in order to not send too much output.
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/// The formula we compute is within <1 wei of the lossless version: sqrtPX96 +- amount / liquidity
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/// @param sqrtPX96 The starting price, i.e., before accounting for the token1 delta
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/// @param liquidity The amount of usable liquidity
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/// @param amount How much of token1 to add, or remove, from virtual reserves
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/// @param add Whether to add, or remove, the amount of token1
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/// @return The price after adding or removing `amount`
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function getNextSqrtPriceFromAmount1RoundingDown(
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uint160 sqrtPX96,
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uint128 liquidity,
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uint256 amount,
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bool add
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) internal pure returns (uint160) {
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// if we're adding (subtracting), rounding down requires rounding the quotient down (up)
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// in both cases, avoid a mulDiv for most inputs
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if (add) {
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uint256 quotient =
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(
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amount <= type(uint160).max
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? (amount << FixedPoint96.RESOLUTION) / liquidity
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: FullMath.mulDiv(amount, FixedPoint96.Q96, liquidity)
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);
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return uint256(sqrtPX96).add(quotient).toUint160();
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} else {
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uint256 quotient =
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(
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amount <= type(uint160).max
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? UnsafeMath.divRoundingUp(amount << FixedPoint96.RESOLUTION, liquidity)
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: FullMath.mulDivRoundingUp(amount, FixedPoint96.Q96, liquidity)
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);
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require(sqrtPX96 > quotient);
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// always fits 160 bits
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return uint160(sqrtPX96 - quotient);
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}
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}
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/// @notice Gets the next sqrt price given an input amount of token0 or token1
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/// @dev Throws if price or liquidity are 0, or if the next price is out of bounds
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/// @param sqrtPX96 The starting price, i.e., before accounting for the input amount
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/// @param liquidity The amount of usable liquidity
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/// @param amountIn How much of token0, or token1, is being swapped in
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/// @param zeroForOne Whether the amount in is token0 or token1
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/// @return sqrtQX96 The price after adding the input amount to token0 or token1
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function getNextSqrtPriceFromInput(
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uint160 sqrtPX96,
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uint128 liquidity,
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uint256 amountIn,
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bool zeroForOne
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) internal pure returns (uint160 sqrtQX96) {
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require(sqrtPX96 > 0);
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require(liquidity > 0);
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// round to make sure that we don't pass the target price
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return
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zeroForOne
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? getNextSqrtPriceFromAmount0RoundingUp(sqrtPX96, liquidity, amountIn, true)
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: getNextSqrtPriceFromAmount1RoundingDown(sqrtPX96, liquidity, amountIn, true);
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}
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/// @notice Gets the next sqrt price given an output amount of token0 or token1
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/// @dev Throws if price or liquidity are 0 or the next price is out of bounds
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/// @param sqrtPX96 The starting price before accounting for the output amount
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/// @param liquidity The amount of usable liquidity
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/// @param amountOut How much of token0, or token1, is being swapped out
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/// @param zeroForOne Whether the amount out is token0 or token1
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/// @return sqrtQX96 The price after removing the output amount of token0 or token1
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function getNextSqrtPriceFromOutput(
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uint160 sqrtPX96,
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uint128 liquidity,
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uint256 amountOut,
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bool zeroForOne
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) internal pure returns (uint160 sqrtQX96) {
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require(sqrtPX96 > 0);
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require(liquidity > 0);
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// round to make sure that we pass the target price
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return
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zeroForOne
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? getNextSqrtPriceFromAmount1RoundingDown(sqrtPX96, liquidity, amountOut, false)
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: getNextSqrtPriceFromAmount0RoundingUp(sqrtPX96, liquidity, amountOut, false);
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}
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/// @notice Gets the amount0 delta between two prices
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/// @dev Calculates liquidity / sqrt(lower) - liquidity / sqrt(upper),
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/// i.e. liquidity * (sqrt(upper) - sqrt(lower)) / (sqrt(upper) * sqrt(lower))
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/// @param sqrtRatioAX96 A sqrt price
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/// @param sqrtRatioBX96 Another sqrt price
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/// @param liquidity The amount of usable liquidity
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/// @param roundUp Whether to round the amount up or down
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/// @return amount0 Amount of token0 required to cover a position of size liquidity between the two passed prices
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function getAmount0Delta(
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uint160 sqrtRatioAX96,
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uint160 sqrtRatioBX96,
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uint128 liquidity,
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bool roundUp
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) internal pure returns (uint256 amount0) {
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if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);
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uint256 numerator1 = uint256(liquidity) << FixedPoint96.RESOLUTION;
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uint256 numerator2 = sqrtRatioBX96 - sqrtRatioAX96;
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require(sqrtRatioAX96 > 0);
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return
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roundUp
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? UnsafeMath.divRoundingUp(
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FullMath.mulDivRoundingUp(numerator1, numerator2, sqrtRatioBX96),
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sqrtRatioAX96
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)
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: FullMath.mulDiv(numerator1, numerator2, sqrtRatioBX96) / sqrtRatioAX96;
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}
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/// @notice Gets the amount1 delta between two prices
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/// @dev Calculates liquidity * (sqrt(upper) - sqrt(lower))
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/// @param sqrtRatioAX96 A sqrt price
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/// @param sqrtRatioBX96 Another sqrt price
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/// @param liquidity The amount of usable liquidity
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/// @param roundUp Whether to round the amount up, or down
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/// @return amount1 Amount of token1 required to cover a position of size liquidity between the two passed prices
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function getAmount1Delta(
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uint160 sqrtRatioAX96,
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uint160 sqrtRatioBX96,
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uint128 liquidity,
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bool roundUp
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) internal pure returns (uint256 amount1) {
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if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);
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return
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roundUp
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? FullMath.mulDivRoundingUp(liquidity, sqrtRatioBX96 - sqrtRatioAX96, FixedPoint96.Q96)
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: FullMath.mulDiv(liquidity, sqrtRatioBX96 - sqrtRatioAX96, FixedPoint96.Q96);
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}
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/// @notice Helper that gets signed token0 delta
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/// @param sqrtRatioAX96 A sqrt price
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/// @param sqrtRatioBX96 Another sqrt price
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/// @param liquidity The change in liquidity for which to compute the amount0 delta
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/// @return amount0 Amount of token0 corresponding to the passed liquidityDelta between the two prices
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function getAmount0Delta(
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uint160 sqrtRatioAX96,
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uint160 sqrtRatioBX96,
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int128 liquidity
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) internal pure returns (int256 amount0) {
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return
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liquidity < 0
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? -getAmount0Delta(sqrtRatioAX96, sqrtRatioBX96, uint128(-liquidity), false).toInt256()
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: getAmount0Delta(sqrtRatioAX96, sqrtRatioBX96, uint128(liquidity), true).toInt256();
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}
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/// @notice Helper that gets signed token1 delta
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/// @param sqrtRatioAX96 A sqrt price
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/// @param sqrtRatioBX96 Another sqrt price
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/// @param liquidity The change in liquidity for which to compute the amount1 delta
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/// @return amount1 Amount of token1 corresponding to the passed liquidityDelta between the two prices
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function getAmount1Delta(
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uint160 sqrtRatioAX96,
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uint160 sqrtRatioBX96,
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int128 liquidity
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) internal pure returns (int256 amount1) {
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return
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liquidity < 0
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? -getAmount1Delta(sqrtRatioAX96, sqrtRatioBX96, uint128(-liquidity), false).toInt256()
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: getAmount1Delta(sqrtRatioAX96, sqrtRatioBX96, uint128(liquidity), true).toInt256();
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}
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}
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