New staking mechanics: delay on entry opposed to exit

contracts/utils/contracts/src/LibSafeMath.sol

@@ -87,4 +87,62 @@ library LibSafeMath {
     {
         return a < b ? a : b;
     }
+
+    /// @dev Safely adds two fractions `n1/d1 + n2/d2`
+    /// @param n1 numerator of `1`
+    /// @param d1 denominator of `1`
+    /// @param n2 numerator of `2`
+    /// @param d2 denominator of `2`
+    /// @return numerator of sum
+    /// @return denominator of sum
+    function addFractions(
+        uint256 n1,
+        uint256 d1,
+        uint256 n2,
+        uint256 d2
+    )
+        internal
+        pure
+        returns (
+            uint256 numerator,
+            uint256 denominator
+        )
+    {
+        numerator = safeAdd(
+            safeMul(n1, d2),
+            safeMul(n2, d1)
+        );
+        denominator = safeMul(d1, d2);
+        return (numerator, denominator);
+    }
+
+    /// @dev Safely scales the difference two fractions.
+    /// @param n1 numerator of `1`
+    /// @param d1 denominator of `1`
+    /// @param n2 numerator of `2`
+    /// @param d2 denominator of `2`
+    /// @param s scalar to multiply by difference.
+    /// @return result = `s * (n1/d1 - n2/d2)`.
+    function scaleFractionalDifference(
+        uint256 n1,
+        uint256 d1,
+        uint256 n2,
+        uint256 d2,
+        uint256 s
+    )
+        internal
+        pure
+        returns (uint256)
+    {
+        uint256 numerator = safeSub(
+            safeMul(n1, d2),
+            safeMul(n2, d1)
+        );
+        uint256 tmp = safeDiv(numerator, d2);
+        uint256 result = safeDiv(
+            safeMul(s, tmp),
+            d1
+        );
+        return result;
+    }
 }