Update comments on use of xor

Uniswap · May 21, 2024 · 192b294 · 192b294
1 parent 0f4d817
commit 192b294
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Showing 2 changed files with 9 additions and 5 deletions.
diff --git a/src/libraries/SqrtPriceMath.sol b/src/libraries/SqrtPriceMath.sol
@@ -169,11 +169,15 @@ library SqrtPriceMath {
         }
     }
 
-    /// @notice Equivalent to: `a > b ? a - b : b - a`
+    /// @notice Equivalent to: `a >= b ? a - b : b - a`
     function absDiff(uint160 a, uint160 b) internal pure returns (uint256 res) {
         assembly {
             let diff := sub(a, b)
+            // mask = 0 if a >= b else -1 (all 1s)
             let mask := sar(255, diff)
+            // if a >= b, res = a - b = 0 ^ (a - b)
+            // if a < b, res = b - a = ~~(b - a) = ~(-(b - a) - 1) = ~(a - b - 1) = (-1) ^ (a - b - 1)
+            // either way, res = mask ^ (a - b + mask)
             res := xor(mask, add(mask, diff))
         }
     }

diff --git a/src/libraries/TickMath.sol b/src/libraries/TickMath.sol
@@ -51,11 +51,11 @@ library TickMath {
         unchecked {
             uint256 absTick;
             assembly {
-                // mask = 0 if tick >= 0 else -1
+                // mask = 0 if tick >= 0 else -1 (all 1s)
                 let mask := sar(255, tick)
-                // If tick >= 0, |tick| = tick = 0 ^ tick
-                // If tick < 0, |tick| = ~~|tick| = ~(-|tick| - 1) = ~(tick - 1) = (-1) ^ (tick - 1)
-                // Either case, |tick| = mask ^ (tick + mask)
+                // if tick >= 0, |tick| = tick = 0 ^ tick
+                // if tick < 0, |tick| = ~~|tick| = ~(-|tick| - 1) = ~(tick - 1) = (-1) ^ (tick - 1)
+                // either way, |tick| = mask ^ (tick + mask)
                 absTick := xor(mask, add(mask, tick))
             }
             // Equivalent: if (absTick > MAX_TICK) revert InvalidTick();