feat: mulDivSigned

contracts/PRBMathCommon.sol

@@ -301,6 +301,56 @@ library PRBMathCommon {
         }
     }
 
+    /// @notice Calculates floor(x*y÷denominator) with full precision.
+    ///
+    /// @dev An extension of "mulDiv" for signed numbers. Works by computing the signs and the absolute values separately.
+    ///
+    /// Requirements:
+    /// - None of the inputs can be type(int256).min.
+    /// - The result must fit within int256.
+    ///
+    /// @param x The multiplicand as an int256.
+    /// @param y The multiplier as an int256.
+    /// @param denominator The divisor as an int256.
+    /// @return result The result as an int256.
+    function mulDivSigned(
+        int256 x,
+        int256 y,
+        int256 denominator
+    ) internal pure returns (int256 result) {
+        require(x > type(int256).min);
+        require(y > type(int256).min);
+        require(denominator > type(int256).min);
+
+        // Get hold of the absolute values of x, y and the denominator.
+        uint256 ax;
+        uint256 ay;
+        uint256 ad;
+        unchecked {
+            ax = x < 0 ? uint256(-x) : uint256(x);
+            ay = y < 0 ? uint256(-y) : uint256(y);
+            ad = denominator < 0 ? uint256(-denominator) : uint256(denominator);
+        }
+
+        // Compute the absolute value of (x*y)÷denominator. The result must fit within int256.
+        uint256 resultUnsigned = mulDiv(ax, ay, ad);
+        require(resultUnsigned <= uint256(type(int256).max));
+
+        // Get the signs of x, y and the denominator.
+        uint256 sx;
+        uint256 sy;
+        uint256 sd;
+        assembly {
+            sx := sgt(x, sub(0, 1))
+            sy := sgt(y, sub(0, 1))
+            sd := sgt(denominator, sub(0, 1))
+        }
+
+        // XOR over sx, sy and sd. This is checking whether there are one or three negative signs in the inputs.
+        // If yes, the result should be negative.
+        result = sx ^ sy ^ sd == 0 ? -int256(resultUnsigned) : int256(resultUnsigned);
+    }
+
     /// @notice Calculates the square root of x, rounding down.
     /// @dev Uses the Babylonian method https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
     ///