Add 512bits add and mult operations (#5035)

test/utils/math/Math.t.sol

@@ -11,6 +11,48 @@ contract MathTest is Test {
         assertEq(Math.ternary(f, a, b), f ? a : b);
     }
 
+    // ADD512 & MUL512
+    function testAdd512(uint256 a, uint256 b) public pure {
+        (uint256 high, uint256 low) = Math.add512(a, b);
+
+        // test against tryAdd
+        (bool success, uint256 result) = Math.tryAdd(a, b);
+        if (success) {
+            assertEq(high, 0);
+            assertEq(low, result);
+        } else {
+            assertEq(high, 1);
+        }
+
+        // test against unchecked
+        unchecked {
+            assertEq(low, a + b); // unchecked allow overflow
+        }
+    }
+
+    function testMul512(uint256 a, uint256 b) public pure {
+        (uint256 high, uint256 low) = Math.mul512(a, b);
+
+        // test against tryMul
+        (bool success, uint256 result) = Math.tryMul(a, b);
+        if (success) {
+            assertEq(high, 0);
+            assertEq(low, result);
+        } else {
+            assertGt(high, 0);
+        }
+
+        // test against unchecked
+        unchecked {
+            assertEq(low, a * b); // unchecked allow overflow
+        }
+
+        // test against alternative method
+        (uint256 _high, uint256 _low) = _mulKaratsuba(a, b);
+        assertEq(high, _high);
+        assertEq(low, _low);
+    }
+
     // MIN & MAX
     function testSymbolicMinMax(uint256 a, uint256 b) public pure {
         assertEq(Math.min(a, b), a < b ? a : b);
@@ -184,7 +226,7 @@ contract MathTest is Test {
     // MULDIV
     function testMulDiv(uint256 x, uint256 y, uint256 d) public pure {
         // Full precision for x * y
-        (uint256 xyHi, uint256 xyLo) = _mulHighLow(x, y);
+        (uint256 xyHi, uint256 xyLo) = Math.mul512(x, y);
 
         // Assume result won't overflow (see {testMulDivDomain})
         // This also checks that `d` is positive
@@ -194,9 +236,9 @@ contract MathTest is Test {
         uint256 q = Math.mulDiv(x, y, d);
 
         // Full precision for q * d
-        (uint256 qdHi, uint256 qdLo) = _mulHighLow(q, d);
+        (uint256 qdHi, uint256 qdLo) = Math.mul512(q, d);
         // Add remainder of x * y / d (computed as rem = (x * y % d))
-        (uint256 qdRemLo, uint256 c) = _addCarry(qdLo, mulmod(x, y, d));
+        (uint256 c, uint256 qdRemLo) = Math.add512(qdLo, mulmod(x, y, d));
         uint256 qdRemHi = qdHi + c;
 
         // Full precision check that x * y = q * d + rem
@@ -206,7 +248,7 @@ contract MathTest is Test {
 
     /// forge-config: default.allow_internal_expect_revert = true
     function testMulDivDomain(uint256 x, uint256 y, uint256 d) public {
-        (uint256 xyHi, ) = _mulHighLow(x, y);
+        (uint256 xyHi, ) = Math.mul512(x, y);
 
         // Violate {testMulDiv} assumption (covers d is 0 and result overflow)
         vm.assume(xyHi >= d);
@@ -266,26 +308,13 @@ contract MathTest is Test {
         }
     }
 
-    function _nativeModExp(uint256 b, uint256 e, uint256 m) private pure returns (uint256) {
-        if (m == 1) return 0;
-        uint256 r = 1;
-        while (e > 0) {
-            if (e % 2 > 0) {
-                r = mulmod(r, b, m);
-            }
-            b = mulmod(b, b, m);
-            e >>= 1;
-        }
-        return r;
-    }
-
     // Helpers
     function _asRounding(uint8 r) private pure returns (Math.Rounding) {
         vm.assume(r < uint8(type(Math.Rounding).max));
         return Math.Rounding(r);
     }
 
-    function _mulHighLow(uint256 x, uint256 y) private pure returns (uint256 high, uint256 low) {
+    function _mulKaratsuba(uint256 x, uint256 y) private pure returns (uint256 high, uint256 low) {
         (uint256 x0, uint256 x1) = (x & type(uint128).max, x >> 128);
         (uint256 y0, uint256 y1) = (y & type(uint128).max, y >> 128);
 
@@ -305,10 +334,16 @@ contract MathTest is Test {
         }
     }
 
-    function _addCarry(uint256 x, uint256 y) private pure returns (uint256 res, uint256 carry) {
-        unchecked {
-            res = x + y;
+    function _nativeModExp(uint256 b, uint256 e, uint256 m) private pure returns (uint256) {
+        if (m == 1) return 0;
+        uint256 r = 1;
+        while (e > 0) {
+            if (e % 2 > 0) {
+                r = mulmod(r, b, m);
+            }
+            b = mulmod(b, b, m);
+            e >>= 1;
         }
-        carry = res < x ? 1 : 0;
+        return r;
     }
 }