diff --git a/src/libraries/Math.sol b/src/libraries/Math.sol
new file mode 100644
index 0000000..bccadbb
--- /dev/null
+++ b/src/libraries/Math.sol
@@ -0,0 +1,23 @@
+// SPDX-License-Identifier: MIT
+pragma solidity 0.8.36;
+
+/// @title Math helpers for the constant-product core.
+library Math {
+    function min(uint256 x, uint256 y) internal pure returns (uint256) {
+        return x < y ? x : y;
+    }
+
+    /// @notice Babylonian integer square root.
+    function sqrt(uint256 y) internal pure returns (uint256 z) {
+        if (y > 3) {
+            z = y;
+            uint256 x = y / 2 + 1;
+            while (x < z) {
+                z = x;
+                x = (y / x + x) / 2;
+            }
+        } else if (y != 0) {
+            z = 1;
+        }
+    }
+}
diff --git a/src/libraries/UQ112x112.sol b/src/libraries/UQ112x112.sol
new file mode 100644
index 0000000..ec1f9f5
--- /dev/null
+++ b/src/libraries/UQ112x112.sol
@@ -0,0 +1,17 @@
+// SPDX-License-Identifier: MIT
+pragma solidity 0.8.36;
+
+/// @title Fixed point unsigned Q112.112, used for price accumulators.
+library UQ112x112 {
+    uint224 constant q112 = 2 ** 112;
+
+    function encode(uint112 y) internal pure returns (uint224 z) {
+        unchecked {
+            z = uint224(y) * q112;
+        }
+    }
+
+    function uqdiv(uint224 x, uint112 y) internal pure returns (uint224 z) {
+        z = x / uint224(y);
+    }
+}