feat(libraries): add sqrt-price delta math

2026-08-23 22:40:00 +02:00
1 parent 72e670cd72
commit 7a1aff4521
@@ -0,0 +1,147 @@
+// SPDX-License-Identifier: MIT
+pragma solidity 0.8.36;
+
+import {FullMath} from "./FullMath.sol";
+import {UnsafeMath} from "./UnsafeMath.sol";
+import {FixedPoint96} from "./FixedPoint96.sol";
+import {SafeCast} from "./SafeCast.sol";
+
+/// @title Sqrt-price and token amount deltas along the constant-product curve.
+library SqrtPriceMath {
+    using SafeCast for uint256;
+
+    function getNextSqrtPriceFromAmount0RoundingUp(uint160 sqrtPX96, uint128 liquidity, uint256 amount, bool add)
+        internal
+        pure
+        returns (uint160)
+    {
+        if (amount == 0) return sqrtPX96;
+        uint256 numerator1 = uint256(liquidity) << FixedPoint96.resolution;
+
+        unchecked {
+            if (add) {
+                uint256 product = amount * sqrtPX96;
+                if (product / amount == sqrtPX96) {
+                    uint256 denominator = numerator1 + product;
+                    if (denominator >= numerator1) {
+                        return FullMath.mulDivRoundingUp(numerator1, sqrtPX96, denominator).toUint160();
+                    }
+                }
+                return uint160(UnsafeMath.divRoundingUp(numerator1, numerator1 / sqrtPX96 + amount));
+            } else {
+                uint256 product = amount * sqrtPX96;
+                require(product / amount == sqrtPX96 && numerator1 > product, "SqrtPriceMath: A0");
+                uint256 denominator = numerator1 - product;
+                return FullMath.mulDivRoundingUp(numerator1, sqrtPX96, denominator).toUint160();
+            }
+        }
+    }
+
+    function getNextSqrtPriceFromAmount1RoundingDown(uint160 sqrtPX96, uint128 liquidity, uint256 amount, bool add)
+        internal
+        pure
+        returns (uint160)
+    {
+        unchecked {
+            if (add) {
+                uint256 quotient =
+                    (amount <= type(uint160).max
+                        ? (amount << FixedPoint96.resolution) / liquidity
+                        : FullMath.mulDiv(amount, FixedPoint96.q96, liquidity));
+                return (uint256(sqrtPX96) + quotient).toUint160();
+            } else {
+                uint256 quotient =
+                    (amount <= type(uint160).max
+                        ? UnsafeMath.divRoundingUp(amount << FixedPoint96.resolution, liquidity)
+                        : FullMath.mulDivRoundingUp(amount, FixedPoint96.q96, liquidity));
+                require(sqrtPX96 > quotient, "SqrtPriceMath: A1");
+                return uint160(sqrtPX96 - quotient);
+            }
+        }
+    }
+
+    function getNextSqrtPriceFromInput(uint160 sqrtPX96, uint128 liquidity, uint256 amountIn, bool zeroForOne)
+        internal
+        pure
+        returns (uint160 sqrtQX96)
+    {
+        require(sqrtPX96 > 0, "SqrtPriceMath: PRICE");
+        require(liquidity > 0, "SqrtPriceMath: LIQ");
+
+        return zeroForOne
+            ? getNextSqrtPriceFromAmount0RoundingUp(sqrtPX96, liquidity, amountIn, true)
+            : getNextSqrtPriceFromAmount1RoundingDown(sqrtPX96, liquidity, amountIn, true);
+    }
+
+    function getNextSqrtPriceFromOutput(uint160 sqrtPX96, uint128 liquidity, uint256 amountOut, bool zeroForOne)
+        internal
+        pure
+        returns (uint160 sqrtQX96)
+    {
+        require(sqrtPX96 > 0, "SqrtPriceMath: PRICE");
+        require(liquidity > 0, "SqrtPriceMath: LIQ");
+
+        return zeroForOne
+            ? getNextSqrtPriceFromAmount1RoundingDown(sqrtPX96, liquidity, amountOut, false)
+            : getNextSqrtPriceFromAmount0RoundingUp(sqrtPX96, liquidity, amountOut, false);
+    }
+
+    function getAmount0Delta(uint160 sqrtRatioAX96, uint160 sqrtRatioBX96, uint128 liquidity, bool roundUp)
+        internal
+        pure
+        returns (uint256 amount0)
+    {
+        unchecked {
+            if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);
+
+            uint256 numerator1 = uint256(liquidity) << FixedPoint96.resolution;
+            uint256 numerator2 = sqrtRatioBX96 - sqrtRatioAX96;
+
+            require(sqrtRatioAX96 > 0, "SqrtPriceMath: A0Z");
+
+            return roundUp
+                ? UnsafeMath.divRoundingUp(
+                    FullMath.mulDivRoundingUp(numerator1, numerator2, sqrtRatioBX96), sqrtRatioAX96
+                )
+                : FullMath.mulDiv(numerator1, numerator2, sqrtRatioBX96) / sqrtRatioAX96;
+        }
+    }
+
+    function getAmount1Delta(uint160 sqrtRatioAX96, uint160 sqrtRatioBX96, uint128 liquidity, bool roundUp)
+        internal
+        pure
+        returns (uint256 amount1)
+    {
+        unchecked {
+            if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);
+
+            return roundUp
+                ? FullMath.mulDivRoundingUp(liquidity, sqrtRatioBX96 - sqrtRatioAX96, FixedPoint96.q96)
+                : FullMath.mulDiv(liquidity, sqrtRatioBX96 - sqrtRatioAX96, FixedPoint96.q96);
+        }
+    }
+
+    function getAmount0Delta(uint160 sqrtRatioAX96, uint160 sqrtRatioBX96, int128 liquidity)
+        internal
+        pure
+        returns (int256 amount0)
+    {
+        unchecked {
+            return liquidity < 0
+                ? -getAmount0Delta(sqrtRatioAX96, sqrtRatioBX96, uint128(-liquidity), false).toInt256()
+                : getAmount0Delta(sqrtRatioAX96, sqrtRatioBX96, uint128(liquidity), true).toInt256();
+        }
+    }
+
+    function getAmount1Delta(uint160 sqrtRatioAX96, uint160 sqrtRatioBX96, int128 liquidity)
+        internal
+        pure
+        returns (int256 amount1)
+    {
+        unchecked {
+            return liquidity < 0
+                ? -getAmount1Delta(sqrtRatioAX96, sqrtRatioBX96, uint128(-liquidity), false).toInt256()
+                : getAmount1Delta(sqrtRatioAX96, sqrtRatioBX96, uint128(liquidity), true).toInt256();
+        }
+    }
+}