From 8e3fc6d015118e0014089ec217fd15ef951976b3 Mon Sep 17 00:00:00 2001
From: Shuhui Luo <107524008+shuhuiluo@users.noreply.github.com>
Date: Sun, 19 May 2024 05:21:56 -0400
Subject: [PATCH 1/2] Optimize `SqrtPriceMath.getAmount1Delta`

Added a new function `absDiff` to `SqrtPriceMath` library which calculates the absolute difference between two numbers. Refactored the way price delta is computed between two prices in the `getAmount1Delta` function. The calculation is now more efficient.
---
 .../SwapMath_oneForZero_exactInCapped.snap    |  2 +-
 .../SwapMath_oneForZero_exactInPartial.snap   |  2 +-
 .../SwapMath_oneForZero_exactOutCapped.snap   |  2 +-
 .../SwapMath_oneForZero_exactOutPartial.snap  |  2 +-
 .../SwapMath_zeroForOne_exactInCapped.snap    |  2 +-
 .../SwapMath_zeroForOne_exactInPartial.snap   |  2 +-
 .../SwapMath_zeroForOne_exactOutCapped.snap   |  2 +-
 .../SwapMath_zeroForOne_exactOutPartial.snap  |  2 +-
 ...o already existing position with salt.snap |  2 +-
 .forge-snapshots/addLiquidity CA fee.snap     |  2 +-
 .../addLiquidity with empty hook.snap         |  2 +-
 .../addLiquidity with native token.snap       |  2 +-
 ...new liquidity to a position with salt.snap |  2 +-
 ..._gasCostForAmount1WhereRoundUpIsFalse.snap |  2 +-
 ...a_gasCostForAmount1WhereRoundUpIsTrue.snap |  2 +-
 .../poolManager bytecode size.snap            |  2 +-
 .forge-snapshots/removeLiquidity CA fee.snap  |  2 +-
 .../removeLiquidity with empty hook.snap      |  2 +-
 .../removeLiquidity with native token.snap    |  2 +-
 ...dLiquidity second addition same range.snap |  2 +-
 .forge-snapshots/simple addLiquidity.snap     |  2 +-
 ...emoveLiquidity some liquidity remains.snap |  2 +-
 .forge-snapshots/simple removeLiquidity.snap  |  2 +-
 .forge-snapshots/simple swap with native.snap |  2 +-
 .forge-snapshots/simple swap.snap             |  2 +-
 .../swap CA fee on unspecified.snap           |  2 +-
 ...p against liquidity with native token.snap |  2 +-
 .forge-snapshots/swap against liquidity.snap  |  2 +-
 .../swap burn 6909 for input.snap             |  2 +-
 .../swap burn native 6909 for input.snap      |  2 +-
 .../swap mint native output as 6909.snap      |  2 +-
 .../swap mint output as 6909.snap             |  2 +-
 ...wap skips hook call if hook is caller.snap |  2 +-
 .forge-snapshots/swap with dynamic fee.snap   |  2 +-
 .forge-snapshots/swap with hooks.snap         |  2 +-
 .../swap with lp fee and protocol fee.snap    |  2 +-
 .../swap with return dynamic fee.snap         |  2 +-
 .../update dynamic fee in before swap.snap    |  2 +-
 src/libraries/SqrtPriceMath.sol               | 32 ++++++++++++++++---
 39 files changed, 65 insertions(+), 43 deletions(-)

diff --git a/.forge-snapshots/SwapMath_oneForZero_exactInCapped.snap b/.forge-snapshots/SwapMath_oneForZero_exactInCapped.snap
index 19261c267..062bc1c2d 100644
--- a/.forge-snapshots/SwapMath_oneForZero_exactInCapped.snap
+++ b/.forge-snapshots/SwapMath_oneForZero_exactInCapped.snap
@@ -1 +1 @@
-2248
\ No newline at end of file
+1974
\ No newline at end of file
diff --git a/.forge-snapshots/SwapMath_oneForZero_exactInPartial.snap b/.forge-snapshots/SwapMath_oneForZero_exactInPartial.snap
index 43e6c3379..cebceba23 100644
--- a/.forge-snapshots/SwapMath_oneForZero_exactInPartial.snap
+++ b/.forge-snapshots/SwapMath_oneForZero_exactInPartial.snap
@@ -1 +1 @@
-3016
\ No newline at end of file
+2468
\ No newline at end of file
diff --git a/.forge-snapshots/SwapMath_oneForZero_exactOutCapped.snap b/.forge-snapshots/SwapMath_oneForZero_exactOutCapped.snap
index 01a646754..d7bda98e9 100644
--- a/.forge-snapshots/SwapMath_oneForZero_exactOutCapped.snap
+++ b/.forge-snapshots/SwapMath_oneForZero_exactOutCapped.snap
@@ -1 +1 @@
-1987
\ No newline at end of file
+1713
\ No newline at end of file
diff --git a/.forge-snapshots/SwapMath_oneForZero_exactOutPartial.snap b/.forge-snapshots/SwapMath_oneForZero_exactOutPartial.snap
index 72cd61fe0..ea9412b02 100644
--- a/.forge-snapshots/SwapMath_oneForZero_exactOutPartial.snap
+++ b/.forge-snapshots/SwapMath_oneForZero_exactOutPartial.snap
@@ -1 +1 @@
-3256
\ No newline at end of file
+2982
\ No newline at end of file
diff --git a/.forge-snapshots/SwapMath_zeroForOne_exactInCapped.snap b/.forge-snapshots/SwapMath_zeroForOne_exactInCapped.snap
index b038f6888..ab0cf33c5 100644
--- a/.forge-snapshots/SwapMath_zeroForOne_exactInCapped.snap
+++ b/.forge-snapshots/SwapMath_zeroForOne_exactInCapped.snap
@@ -1 +1 @@
-2238
\ No newline at end of file
+2091
\ No newline at end of file
diff --git a/.forge-snapshots/SwapMath_zeroForOne_exactInPartial.snap b/.forge-snapshots/SwapMath_zeroForOne_exactInPartial.snap
index 3832db4f7..849de8bc1 100644
--- a/.forge-snapshots/SwapMath_zeroForOne_exactInPartial.snap
+++ b/.forge-snapshots/SwapMath_zeroForOne_exactInPartial.snap
@@ -1 +1 @@
-3191
\ No newline at end of file
+3044
\ No newline at end of file
diff --git a/.forge-snapshots/SwapMath_zeroForOne_exactOutCapped.snap b/.forge-snapshots/SwapMath_zeroForOne_exactOutCapped.snap
index ca9836afa..ec2b293ea 100644
--- a/.forge-snapshots/SwapMath_zeroForOne_exactOutCapped.snap
+++ b/.forge-snapshots/SwapMath_zeroForOne_exactOutCapped.snap
@@ -1 +1 @@
-1977
\ No newline at end of file
+1830
\ No newline at end of file
diff --git a/.forge-snapshots/SwapMath_zeroForOne_exactOutPartial.snap b/.forge-snapshots/SwapMath_zeroForOne_exactOutPartial.snap
index d872354f5..bae32ca68 100644
--- a/.forge-snapshots/SwapMath_zeroForOne_exactOutPartial.snap
+++ b/.forge-snapshots/SwapMath_zeroForOne_exactOutPartial.snap
@@ -1 +1 @@
-2866
\ No newline at end of file
+2572
\ No newline at end of file
diff --git a/.forge-snapshots/add liquidity to already existing position with salt.snap b/.forge-snapshots/add liquidity to already existing position with salt.snap
index ff76e7f86..92c3e5a1d 100644
--- a/.forge-snapshots/add liquidity to already existing position with salt.snap	
+++ b/.forge-snapshots/add liquidity to already existing position with salt.snap	
@@ -1 +1 @@
-153643
\ No newline at end of file
+153373
\ No newline at end of file
diff --git a/.forge-snapshots/addLiquidity CA fee.snap b/.forge-snapshots/addLiquidity CA fee.snap
index b4678d19b..2be7e6f13 100644
--- a/.forge-snapshots/addLiquidity CA fee.snap	
+++ b/.forge-snapshots/addLiquidity CA fee.snap	
@@ -1 +1 @@
-331309
\ No newline at end of file
+331039
\ No newline at end of file
diff --git a/.forge-snapshots/addLiquidity with empty hook.snap b/.forge-snapshots/addLiquidity with empty hook.snap
index c59df0298..7085565a9 100644
--- a/.forge-snapshots/addLiquidity with empty hook.snap	
+++ b/.forge-snapshots/addLiquidity with empty hook.snap	
@@ -1 +1 @@
-286302
\ No newline at end of file
+286032
\ No newline at end of file
diff --git a/.forge-snapshots/addLiquidity with native token.snap b/.forge-snapshots/addLiquidity with native token.snap
index c5bed833e..dff5c01a7 100644
--- a/.forge-snapshots/addLiquidity with native token.snap	
+++ b/.forge-snapshots/addLiquidity with native token.snap	
@@ -1 +1 @@
-143853
\ No newline at end of file
+143583
\ No newline at end of file
diff --git a/.forge-snapshots/create new liquidity to a position with salt.snap b/.forge-snapshots/create new liquidity to a position with salt.snap
index cbb3de708..b8d09cd0e 100644
--- a/.forge-snapshots/create new liquidity to a position with salt.snap	
+++ b/.forge-snapshots/create new liquidity to a position with salt.snap	
@@ -1 +1 @@
-301821
\ No newline at end of file
+301551
\ No newline at end of file
diff --git a/.forge-snapshots/getAmount1Delta_gasCostForAmount1WhereRoundUpIsFalse.snap b/.forge-snapshots/getAmount1Delta_gasCostForAmount1WhereRoundUpIsFalse.snap
index 1fc188de7..8c19d14d4 100644
--- a/.forge-snapshots/getAmount1Delta_gasCostForAmount1WhereRoundUpIsFalse.snap
+++ b/.forge-snapshots/getAmount1Delta_gasCostForAmount1WhereRoundUpIsFalse.snap
@@ -1 +1 @@
-525
\ No newline at end of file
+369
\ No newline at end of file
diff --git a/.forge-snapshots/getAmount1Delta_gasCostForAmount1WhereRoundUpIsTrue.snap b/.forge-snapshots/getAmount1Delta_gasCostForAmount1WhereRoundUpIsTrue.snap
index 929530e88..6c8526a81 100644
--- a/.forge-snapshots/getAmount1Delta_gasCostForAmount1WhereRoundUpIsTrue.snap
+++ b/.forge-snapshots/getAmount1Delta_gasCostForAmount1WhereRoundUpIsTrue.snap
@@ -1 +1 @@
-653
\ No newline at end of file
+370
\ No newline at end of file
diff --git a/.forge-snapshots/poolManager bytecode size.snap b/.forge-snapshots/poolManager bytecode size.snap
index 81ca44cf1..68278427c 100644
--- a/.forge-snapshots/poolManager bytecode size.snap	
+++ b/.forge-snapshots/poolManager bytecode size.snap	
@@ -1 +1 @@
-21709
\ No newline at end of file
+21612
\ No newline at end of file
diff --git a/.forge-snapshots/removeLiquidity CA fee.snap b/.forge-snapshots/removeLiquidity CA fee.snap
index 082d59d10..fd74db276 100644
--- a/.forge-snapshots/removeLiquidity CA fee.snap	
+++ b/.forge-snapshots/removeLiquidity CA fee.snap	
@@ -1 +1 @@
-186775
\ No newline at end of file
+186632
\ No newline at end of file
diff --git a/.forge-snapshots/removeLiquidity with empty hook.snap b/.forge-snapshots/removeLiquidity with empty hook.snap
index e7fddfb22..48c05fb36 100644
--- a/.forge-snapshots/removeLiquidity with empty hook.snap	
+++ b/.forge-snapshots/removeLiquidity with empty hook.snap	
@@ -1 +1 @@
-123143
\ No newline at end of file
+123000
\ No newline at end of file
diff --git a/.forge-snapshots/removeLiquidity with native token.snap b/.forge-snapshots/removeLiquidity with native token.snap
index 8b983838d..59885c17c 100644
--- a/.forge-snapshots/removeLiquidity with native token.snap	
+++ b/.forge-snapshots/removeLiquidity with native token.snap	
@@ -1 +1 @@
-119930
\ No newline at end of file
+119787
\ No newline at end of file
diff --git a/.forge-snapshots/simple addLiquidity second addition same range.snap b/.forge-snapshots/simple addLiquidity second addition same range.snap
index ccf9f3450..9cd7a727d 100644
--- a/.forge-snapshots/simple addLiquidity second addition same range.snap	
+++ b/.forge-snapshots/simple addLiquidity second addition same range.snap	
@@ -1 +1 @@
-104932
\ No newline at end of file
+104662
\ No newline at end of file
diff --git a/.forge-snapshots/simple addLiquidity.snap b/.forge-snapshots/simple addLiquidity.snap
index 8f3accdaa..42dfbd0db 100644
--- a/.forge-snapshots/simple addLiquidity.snap	
+++ b/.forge-snapshots/simple addLiquidity.snap	
@@ -1 +1 @@
-167424
\ No newline at end of file
+167154
\ No newline at end of file
diff --git a/.forge-snapshots/simple removeLiquidity some liquidity remains.snap b/.forge-snapshots/simple removeLiquidity some liquidity remains.snap
index fc72404ca..12718e6db 100644
--- a/.forge-snapshots/simple removeLiquidity some liquidity remains.snap	
+++ b/.forge-snapshots/simple removeLiquidity some liquidity remains.snap	
@@ -1 +1 @@
-98529
\ No newline at end of file
+98386
\ No newline at end of file
diff --git a/.forge-snapshots/simple removeLiquidity.snap b/.forge-snapshots/simple removeLiquidity.snap
index 0eb1ac8de..73549beea 100644
--- a/.forge-snapshots/simple removeLiquidity.snap	
+++ b/.forge-snapshots/simple removeLiquidity.snap	
@@ -1 +1 @@
-90569
\ No newline at end of file
+90426
\ No newline at end of file
diff --git a/.forge-snapshots/simple swap with native.snap b/.forge-snapshots/simple swap with native.snap
index 4fc9f9feb..2dac06bf8 100644
--- a/.forge-snapshots/simple swap with native.snap	
+++ b/.forge-snapshots/simple swap with native.snap	
@@ -1 +1 @@
-116827
\ No newline at end of file
+116541
\ No newline at end of file
diff --git a/.forge-snapshots/simple swap.snap b/.forge-snapshots/simple swap.snap
index 7a20c6b3d..bbc66c518 100644
--- a/.forge-snapshots/simple swap.snap	
+++ b/.forge-snapshots/simple swap.snap	
@@ -1 +1 @@
-131988
\ No newline at end of file
+131702
\ No newline at end of file
diff --git a/.forge-snapshots/swap CA fee on unspecified.snap b/.forge-snapshots/swap CA fee on unspecified.snap
index 27c7f51ac..d493f7f2c 100644
--- a/.forge-snapshots/swap CA fee on unspecified.snap	
+++ b/.forge-snapshots/swap CA fee on unspecified.snap	
@@ -1 +1 @@
-183126
\ No newline at end of file
+182840
\ No newline at end of file
diff --git a/.forge-snapshots/swap against liquidity with native token.snap b/.forge-snapshots/swap against liquidity with native token.snap
index 8550686dc..223db8b25 100644
--- a/.forge-snapshots/swap against liquidity with native token.snap	
+++ b/.forge-snapshots/swap against liquidity with native token.snap	
@@ -1 +1 @@
-112548
\ No newline at end of file
+112405
\ No newline at end of file
diff --git a/.forge-snapshots/swap against liquidity.snap b/.forge-snapshots/swap against liquidity.snap
index 14ee97dfc..eefc75bf6 100644
--- a/.forge-snapshots/swap against liquidity.snap	
+++ b/.forge-snapshots/swap against liquidity.snap	
@@ -1 +1 @@
-123891
\ No newline at end of file
+123748
\ No newline at end of file
diff --git a/.forge-snapshots/swap burn 6909 for input.snap b/.forge-snapshots/swap burn 6909 for input.snap
index b19efd36d..6f9f02a9d 100644
--- a/.forge-snapshots/swap burn 6909 for input.snap	
+++ b/.forge-snapshots/swap burn 6909 for input.snap	
@@ -1 +1 @@
-135923
\ No newline at end of file
+135653
\ No newline at end of file
diff --git a/.forge-snapshots/swap burn native 6909 for input.snap b/.forge-snapshots/swap burn native 6909 for input.snap
index dc06b6c6a..1643c26df 100644
--- a/.forge-snapshots/swap burn native 6909 for input.snap	
+++ b/.forge-snapshots/swap burn native 6909 for input.snap	
@@ -1 +1 @@
-125140
\ No newline at end of file
+124854
\ No newline at end of file
diff --git a/.forge-snapshots/swap mint native output as 6909.snap b/.forge-snapshots/swap mint native output as 6909.snap
index fa5caa1ba..5f58a98f4 100644
--- a/.forge-snapshots/swap mint native output as 6909.snap	
+++ b/.forge-snapshots/swap mint native output as 6909.snap	
@@ -1 +1 @@
-147180
\ No newline at end of file
+146640
\ No newline at end of file
diff --git a/.forge-snapshots/swap mint output as 6909.snap b/.forge-snapshots/swap mint output as 6909.snap
index 1acf3c68f..c3e9bcf14 100644
--- a/.forge-snapshots/swap mint output as 6909.snap	
+++ b/.forge-snapshots/swap mint output as 6909.snap	
@@ -1 +1 @@
-163842
\ No newline at end of file
+163556
\ No newline at end of file
diff --git a/.forge-snapshots/swap skips hook call if hook is caller.snap b/.forge-snapshots/swap skips hook call if hook is caller.snap
index b2d6ca0cd..fd8c1ed24 100644
--- a/.forge-snapshots/swap skips hook call if hook is caller.snap	
+++ b/.forge-snapshots/swap skips hook call if hook is caller.snap	
@@ -1 +1 @@
-222199
\ No newline at end of file
+221770
\ No newline at end of file
diff --git a/.forge-snapshots/swap with dynamic fee.snap b/.forge-snapshots/swap with dynamic fee.snap
index 96c9f4d55..7c274c01f 100644
--- a/.forge-snapshots/swap with dynamic fee.snap	
+++ b/.forge-snapshots/swap with dynamic fee.snap	
@@ -1 +1 @@
-148043
\ No newline at end of file
+147757
\ No newline at end of file
diff --git a/.forge-snapshots/swap with hooks.snap b/.forge-snapshots/swap with hooks.snap
index 897a376b0..7b9207469 100644
--- a/.forge-snapshots/swap with hooks.snap	
+++ b/.forge-snapshots/swap with hooks.snap	
@@ -1 +1 @@
-123903
\ No newline at end of file
+123760
\ No newline at end of file
diff --git a/.forge-snapshots/swap with lp fee and protocol fee.snap b/.forge-snapshots/swap with lp fee and protocol fee.snap
index 9efd3b6c3..724f13fa4 100644
--- a/.forge-snapshots/swap with lp fee and protocol fee.snap	
+++ b/.forge-snapshots/swap with lp fee and protocol fee.snap	
@@ -1 +1 @@
-180223
\ No newline at end of file
+179794
\ No newline at end of file
diff --git a/.forge-snapshots/swap with return dynamic fee.snap b/.forge-snapshots/swap with return dynamic fee.snap
index cb2abe163..f6db374f2 100644
--- a/.forge-snapshots/swap with return dynamic fee.snap	
+++ b/.forge-snapshots/swap with return dynamic fee.snap	
@@ -1 +1 @@
-155902
\ No newline at end of file
+155616
\ No newline at end of file
diff --git a/.forge-snapshots/update dynamic fee in before swap.snap b/.forge-snapshots/update dynamic fee in before swap.snap
index 265212952..962367321 100644
--- a/.forge-snapshots/update dynamic fee in before swap.snap	
+++ b/.forge-snapshots/update dynamic fee in before swap.snap	
@@ -1 +1 @@
-158505
\ No newline at end of file
+158219
\ No newline at end of file
diff --git a/src/libraries/SqrtPriceMath.sol b/src/libraries/SqrtPriceMath.sol
index 71262ffa2..e8caf5adc 100644
--- a/src/libraries/SqrtPriceMath.sol
+++ b/src/libraries/SqrtPriceMath.sol
@@ -169,6 +169,15 @@ library SqrtPriceMath {
         }
     }
 
+    /// @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)
+            let mask := sar(255, diff)
+            res := xor(mask, add(mask, diff))
+        }
+    }
+
     /// @notice Gets the amount1 delta between two prices
     /// @dev Calculates liquidity * (sqrt(upper) - sqrt(lower))
     /// @param sqrtPriceAX96 A sqrt price
@@ -181,11 +190,24 @@ library SqrtPriceMath {
         pure
         returns (uint256 amount1)
     {
-        if (sqrtPriceAX96 > sqrtPriceBX96) (sqrtPriceAX96, sqrtPriceBX96) = (sqrtPriceBX96, sqrtPriceAX96);
-
-        return roundUp
-            ? FullMath.mulDivRoundingUp(liquidity, sqrtPriceBX96 - sqrtPriceAX96, FixedPoint96.Q96)
-            : FullMath.mulDiv(liquidity, sqrtPriceBX96 - sqrtPriceAX96, FixedPoint96.Q96);
+        uint256 numerator = absDiff(sqrtPriceAX96, sqrtPriceBX96);
+        uint256 denominator = FixedPoint96.Q96;
+        uint256 _liquidity;
+        assembly {
+            // avoid implicit upcasting
+            _liquidity := liquidity
+        }
+        /**
+         * Equivalent to:
+         *   amount1 = roundUp
+         *       ? FullMath.mulDivRoundingUp(liquidity, sqrtPriceBX96 - sqrtPriceAX96, FixedPoint96.Q96)
+         *       : FullMath.mulDiv(liquidity, sqrtPriceBX96 - sqrtPriceAX96, FixedPoint96.Q96);
+         * Cannot overflow because `type(uint128).max * type(uint160).max >> 96 < (1 << 192)`.
+         */
+        amount1 = FullMath.mulDiv(_liquidity, numerator, denominator);
+        assembly {
+            amount1 := add(amount1, and(gt(mulmod(_liquidity, numerator, denominator), 0), roundUp))
+        }
     }
 
     /// @notice Helper that gets signed currency0 delta

From 192b29497fadaa1455f0a94636aac08e1790795f Mon Sep 17 00:00:00 2001
From: Shuhui Luo <107524008+shuhuiluo@users.noreply.github.com>
Date: Tue, 21 May 2024 18:54:41 -0400
Subject: [PATCH 2/2] Update comments on use of `xor`

---
 src/libraries/SqrtPriceMath.sol | 6 +++++-
 src/libraries/TickMath.sol      | 8 ++++----
 2 files changed, 9 insertions(+), 5 deletions(-)

diff --git a/src/libraries/SqrtPriceMath.sol b/src/libraries/SqrtPriceMath.sol
index e8caf5adc..2b463be08 100644
--- 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
index a0c0f2180..3b0c73e74 100644
--- 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();