feat(libraries): add single-step swap math

src/libraries/SwapMath.sol

@@ -0,0 +1,74 @@
+// SPDX-License-Identifier: MIT
+pragma solidity 0.8.36;
+
+import {FullMath} from "./FullMath.sol";
+import {SqrtPriceMath} from "./SqrtPriceMath.sol";
+
+/// @title One swap step within a single tick range, fee inclusive.
+library SwapMath {
+    function computeSwapStep(
+        uint160 sqrtRatioCurrentX96,
+        uint160 sqrtRatioTargetX96,
+        uint128 liquidity,
+        int256 amountRemaining,
+        uint24 feePips
+    ) internal pure returns (uint160 sqrtRatioNextX96, uint256 amountIn, uint256 amountOut, uint256 feeAmount) {
+        unchecked {
+            bool zeroForOne = sqrtRatioCurrentX96 >= sqrtRatioTargetX96;
+            bool exactIn = amountRemaining >= 0;
+
+            if (exactIn) {
+                uint256 amountRemainingLessFee = FullMath.mulDiv(uint256(amountRemaining), 1e6 - feePips, 1e6);
+                amountIn = zeroForOne
+                    ? SqrtPriceMath.getAmount0Delta(sqrtRatioTargetX96, sqrtRatioCurrentX96, liquidity, true)
+                    : SqrtPriceMath.getAmount1Delta(sqrtRatioCurrentX96, sqrtRatioTargetX96, liquidity, true);
+                if (amountRemainingLessFee >= amountIn) {
+                    sqrtRatioNextX96 = sqrtRatioTargetX96;
+                } else {
+                    sqrtRatioNextX96 = SqrtPriceMath.getNextSqrtPriceFromInput(
+                        sqrtRatioCurrentX96, liquidity, amountRemainingLessFee, zeroForOne
+                    );
+                }
+            } else {
+                amountOut = zeroForOne
+                    ? SqrtPriceMath.getAmount1Delta(sqrtRatioTargetX96, sqrtRatioCurrentX96, liquidity, false)
+                    : SqrtPriceMath.getAmount0Delta(sqrtRatioCurrentX96, sqrtRatioTargetX96, liquidity, false);
+                if (uint256(-amountRemaining) >= amountOut) {
+                    sqrtRatioNextX96 = sqrtRatioTargetX96;
+                } else {
+                    sqrtRatioNextX96 = SqrtPriceMath.getNextSqrtPriceFromOutput(
+                        sqrtRatioCurrentX96, liquidity, uint256(-amountRemaining), zeroForOne
+                    );
+                }
+            }
+
+            bool reachedTarget = sqrtRatioTargetX96 == sqrtRatioNextX96;
+
+            if (zeroForOne) {
+                amountIn = reachedTarget && exactIn
+                    ? amountIn
+                    : SqrtPriceMath.getAmount0Delta(sqrtRatioNextX96, sqrtRatioCurrentX96, liquidity, true);
+                amountOut = reachedTarget && !exactIn
+                    ? amountOut
+                    : SqrtPriceMath.getAmount1Delta(sqrtRatioNextX96, sqrtRatioCurrentX96, liquidity, false);
+            } else {
+                amountIn = reachedTarget && exactIn
+                    ? amountIn
+                    : SqrtPriceMath.getAmount1Delta(sqrtRatioCurrentX96, sqrtRatioNextX96, liquidity, true);
+                amountOut = reachedTarget && !exactIn
+                    ? amountOut
+                    : SqrtPriceMath.getAmount0Delta(sqrtRatioCurrentX96, sqrtRatioNextX96, liquidity, false);
+            }
+
+            if (!exactIn && amountOut > uint256(-amountRemaining)) {
+                amountOut = uint256(-amountRemaining);
+            }
+
+            if (exactIn && sqrtRatioNextX96 != sqrtRatioTargetX96) {
+                feeAmount = uint256(amountRemaining) - amountIn;
+            } else {
+                feeAmount = FullMath.mulDivRoundingUp(amountIn, feePips, 1e6 - feePips);
+            }
+        }
+    }
+}