From fa5164a1e26b3b15366816a40e4e0ed6d740850b Mon Sep 17 00:00:00 2001
From: Shuhui Luo <107524008+shuhuiluo@users.noreply.github.com>
Date: Tue, 21 May 2024 15:21:34 -0500
Subject: [PATCH] Optimize `absTick` calculation in
 `TickMath.getSqrtPriceAtTick` (#663)

* Optimize `absTick` calculation in `TickMath.getSqrtPriceAtTick`

The getSqrtPriceAtTick function in the TickMath library has been refactored with a more efficient assembly implementation. This optimization significantly reduces the gas usage by using bitwise operations for computing absolute value of a tick.

* Add test case for `getSqrtPriceAtTick` with `type(int24).min`

The new test case asserts that the function `getSqrtPriceAtTick` throws an error when called with the minimum valid input. This ensures that the function behaves as expected for all possible input values, enhancing the overall test coverage.

* Add comments about rounding in `getSqrtPriceAtTick`
---
 .forge-snapshots/TickMathGetSqrtPriceAtTick.snap     |  2 +-
 .forge-snapshots/TickMathGetTickAtSqrtPrice.snap     |  2 +-
 ...idity to already existing position with salt.snap |  2 +-
 .forge-snapshots/addLiquidity CA fee.snap            |  2 +-
 .forge-snapshots/addLiquidity with empty hook.snap   |  2 +-
 .forge-snapshots/addLiquidity with native token.snap |  2 +-
 ...create new liquidity to a position with salt.snap |  2 +-
 .forge-snapshots/initialize.snap                     |  2 +-
 .forge-snapshots/poolManager bytecode size.snap      |  2 +-
 .forge-snapshots/removeLiquidity CA fee.snap         |  2 +-
 .../removeLiquidity with empty hook.snap             |  2 +-
 .../removeLiquidity with native token.snap           |  2 +-
 ...mple addLiquidity second addition same range.snap |  2 +-
 .forge-snapshots/simple addLiquidity.snap            |  2 +-
 ...imple removeLiquidity 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 +-
 .forge-snapshots/swap CA fee on unspecified.snap     |  2 +-
 .../swap against liquidity with native token.snap    |  2 +-
 .forge-snapshots/swap against liquidity.snap         |  2 +-
 .forge-snapshots/swap burn 6909 for input.snap       |  2 +-
 .../swap burn native 6909 for input.snap             |  2 +-
 .../swap mint native output as 6909.snap             |  2 +-
 .forge-snapshots/swap mint output as 6909.snap       |  2 +-
 .../swap 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 +-
 .forge-snapshots/swap with return dynamic fee.snap   |  2 +-
 .../update dynamic fee in before swap.snap           |  2 +-
 src/libraries/TickMath.sol                           | 12 +++++++++++-
 test/libraries/TickMath.t.sol                        |  5 +++++
 33 files changed, 47 insertions(+), 32 deletions(-)

diff --git a/.forge-snapshots/TickMathGetSqrtPriceAtTick.snap b/.forge-snapshots/TickMathGetSqrtPriceAtTick.snap
index 3f9b14365..a389bef6a 100644
--- a/.forge-snapshots/TickMathGetSqrtPriceAtTick.snap
+++ b/.forge-snapshots/TickMathGetSqrtPriceAtTick.snap
@@ -1 +1 @@
-80082
\ No newline at end of file
+76732
\ No newline at end of file
diff --git a/.forge-snapshots/TickMathGetTickAtSqrtPrice.snap b/.forge-snapshots/TickMathGetTickAtSqrtPrice.snap
index 6e3ae1235..611c1ba05 100644
--- a/.forge-snapshots/TickMathGetTickAtSqrtPrice.snap
+++ b/.forge-snapshots/TickMathGetTickAtSqrtPrice.snap
@@ -1 +1 @@
-227576
\ No newline at end of file
+224621
\ 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 243f23c8a..70cb20284 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 @@
-153494
\ No newline at end of file
+153427
\ No newline at end of file
diff --git a/.forge-snapshots/addLiquidity CA fee.snap b/.forge-snapshots/addLiquidity CA fee.snap
index 885c6a535..927bf0ecc 100644
--- a/.forge-snapshots/addLiquidity CA fee.snap	
+++ b/.forge-snapshots/addLiquidity CA fee.snap	
@@ -1 +1 @@
-331160
\ No newline at end of file
+331093
\ 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 0d0b571fd..75c65f10a 100644
--- a/.forge-snapshots/addLiquidity with empty hook.snap	
+++ b/.forge-snapshots/addLiquidity with empty hook.snap	
@@ -1 +1 @@
-286153
\ No newline at end of file
+286086
\ 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 c5edfa171..25ba858d4 100644
--- a/.forge-snapshots/addLiquidity with native token.snap	
+++ b/.forge-snapshots/addLiquidity with native token.snap	
@@ -1 +1 @@
-143704
\ No newline at end of file
+143637
\ 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 d633601b5..2f53eb249 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 @@
-301672
\ No newline at end of file
+301605
\ No newline at end of file
diff --git a/.forge-snapshots/initialize.snap b/.forge-snapshots/initialize.snap
index f6e21d211..32826ad3b 100644
--- a/.forge-snapshots/initialize.snap
+++ b/.forge-snapshots/initialize.snap
@@ -1 +1 @@
-61811
\ No newline at end of file
+61775
\ No newline at end of file
diff --git a/.forge-snapshots/poolManager bytecode size.snap b/.forge-snapshots/poolManager bytecode size.snap
index c6b439c0f..c94d9db46 100644
--- a/.forge-snapshots/poolManager bytecode size.snap	
+++ b/.forge-snapshots/poolManager bytecode size.snap	
@@ -1 +1 @@
-21667
\ No newline at end of file
+21647
\ No newline at end of file
diff --git a/.forge-snapshots/removeLiquidity CA fee.snap b/.forge-snapshots/removeLiquidity CA fee.snap
index bd25f2f9d..29e8612d9 100644
--- a/.forge-snapshots/removeLiquidity CA fee.snap	
+++ b/.forge-snapshots/removeLiquidity CA fee.snap	
@@ -1 +1 @@
-186626
\ No newline at end of file
+186559
\ 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 9aebeeca5..ee41dab80 100644
--- a/.forge-snapshots/removeLiquidity with empty hook.snap	
+++ b/.forge-snapshots/removeLiquidity with empty hook.snap	
@@ -1 +1 @@
-122994
\ No newline at end of file
+122927
\ 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 57ce483d8..4e26e8532 100644
--- a/.forge-snapshots/removeLiquidity with native token.snap	
+++ b/.forge-snapshots/removeLiquidity with native token.snap	
@@ -1 +1 @@
-119781
\ No newline at end of file
+119714
\ 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 56be2edd4..c63746e60 100644
--- a/.forge-snapshots/simple addLiquidity second addition same range.snap	
+++ b/.forge-snapshots/simple addLiquidity second addition same range.snap	
@@ -1 +1 @@
-104808
\ No newline at end of file
+104746
\ No newline at end of file
diff --git a/.forge-snapshots/simple addLiquidity.snap b/.forge-snapshots/simple addLiquidity.snap
index cb67d6f19..230487a70 100644
--- a/.forge-snapshots/simple addLiquidity.snap	
+++ b/.forge-snapshots/simple addLiquidity.snap	
@@ -1 +1 @@
-167300
\ No newline at end of file
+167238
\ 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 a0071306b..d525fb645 100644
--- a/.forge-snapshots/simple removeLiquidity some liquidity remains.snap	
+++ b/.forge-snapshots/simple removeLiquidity some liquidity remains.snap	
@@ -1 +1 @@
-98405
\ No newline at end of file
+98343
\ No newline at end of file
diff --git a/.forge-snapshots/simple removeLiquidity.snap b/.forge-snapshots/simple removeLiquidity.snap
index f1d44602e..aabdfdaea 100644
--- a/.forge-snapshots/simple removeLiquidity.snap	
+++ b/.forge-snapshots/simple removeLiquidity.snap	
@@ -1 +1 @@
-90445
\ No newline at end of file
+90383
\ 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 261cf66ae..4dde4a638 100644
--- a/.forge-snapshots/simple swap with native.snap	
+++ b/.forge-snapshots/simple swap with native.snap	
@@ -1 +1 @@
-116663
\ No newline at end of file
+116560
\ No newline at end of file
diff --git a/.forge-snapshots/simple swap.snap b/.forge-snapshots/simple swap.snap
index 5ee86dce6..235ed690c 100644
--- a/.forge-snapshots/simple swap.snap	
+++ b/.forge-snapshots/simple swap.snap	
@@ -1 +1 @@
-131824
\ No newline at end of file
+131721
\ 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 a75595573..bee51022c 100644
--- a/.forge-snapshots/swap CA fee on unspecified.snap	
+++ b/.forge-snapshots/swap CA fee on unspecified.snap	
@@ -1 +1 @@
-182962
\ No newline at end of file
+182859
\ 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 e5f8861df..9bda3178e 100644
--- a/.forge-snapshots/swap against liquidity with native token.snap	
+++ b/.forge-snapshots/swap against liquidity with native token.snap	
@@ -1 +1 @@
-112435
\ No newline at end of file
+112368
\ No newline at end of file
diff --git a/.forge-snapshots/swap against liquidity.snap b/.forge-snapshots/swap against liquidity.snap
index d0890ccf3..6bbd2798a 100644
--- a/.forge-snapshots/swap against liquidity.snap	
+++ b/.forge-snapshots/swap against liquidity.snap	
@@ -1 +1 @@
-123778
\ No newline at end of file
+123711
\ 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 d997832ef..38f8c1eea 100644
--- a/.forge-snapshots/swap burn 6909 for input.snap	
+++ b/.forge-snapshots/swap burn 6909 for input.snap	
@@ -1 +1 @@
-135785
\ No newline at end of file
+135713
\ 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 324ba79d2..8551647d0 100644
--- a/.forge-snapshots/swap burn native 6909 for input.snap	
+++ b/.forge-snapshots/swap burn native 6909 for input.snap	
@@ -1 +1 @@
-125038
\ No newline at end of file
+124966
\ 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 c290ce5bd..26292e4a0 100644
--- a/.forge-snapshots/swap mint native output as 6909.snap	
+++ b/.forge-snapshots/swap mint native output as 6909.snap	
@@ -1 +1 @@
-147042
\ No newline at end of file
+146970
\ 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 873d723a3..197a9f85e 100644
--- a/.forge-snapshots/swap mint output as 6909.snap	
+++ b/.forge-snapshots/swap mint output as 6909.snap	
@@ -1 +1 @@
-163678
\ No newline at end of file
+163575
\ 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 1f83ba701..82ca5681c 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 @@
-221922
\ No newline at end of file
+221752
\ 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 b6f7b05d8..981054d4f 100644
--- a/.forge-snapshots/swap with dynamic fee.snap	
+++ b/.forge-snapshots/swap with dynamic fee.snap	
@@ -1 +1 @@
-147879
\ No newline at end of file
+147776
\ No newline at end of file
diff --git a/.forge-snapshots/swap with hooks.snap b/.forge-snapshots/swap with hooks.snap
index 939a6cc8a..43d06fb97 100644
--- a/.forge-snapshots/swap with hooks.snap	
+++ b/.forge-snapshots/swap with hooks.snap	
@@ -1 +1 @@
-123790
\ No newline at end of file
+123723
\ 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 52d7b3932..aa2a23a21 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 @@
-180059
\ No newline at end of file
+179956
\ 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 cb4e4e791..586e9f078 100644
--- a/.forge-snapshots/swap with return dynamic fee.snap	
+++ b/.forge-snapshots/swap with return dynamic fee.snap	
@@ -1 +1 @@
-155738
\ No newline at end of file
+155635
\ 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 b9ffd5fe9..f55f8c4c4 100644
--- a/.forge-snapshots/update dynamic fee in before swap.snap	
+++ b/.forge-snapshots/update dynamic fee in before swap.snap	
@@ -1 +1 @@
-158341
\ No newline at end of file
+158238
\ No newline at end of file
diff --git a/src/libraries/TickMath.sol b/src/libraries/TickMath.sol
index 9f8b108ac..7498f9952 100644
--- a/src/libraries/TickMath.sol
+++ b/src/libraries/TickMath.sol
@@ -46,7 +46,15 @@ library TickMath {
     /// at the given tick
     function getSqrtPriceAtTick(int24 tick) internal pure returns (uint160 sqrtPriceX96) {
         unchecked {
-            uint256 absTick = tick < 0 ? uint256(-int256(tick)) : uint256(int256(tick));
+            uint256 absTick;
+            assembly {
+                // mask = 0 if tick >= 0 else -1
+                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)
+                absTick := xor(mask, add(mask, tick))
+            }
             if (absTick > uint256(int256(MAX_TICK))) revert InvalidTick();
 
             uint256 price =
@@ -78,6 +86,8 @@ library TickMath {
                 // this divides by 1<<32 rounding up to go from a Q128.128 to a Q128.96.
                 // we then downcast because we know the result always fits within 160 bits due to our tick input constraint
                 // we round up in the division so getTickAtSqrtPrice of the output price is always consistent
+                // `sub(shl(32, 1), 1)` is `type(uint32).max`
+                // `price + type(uint32).max` will not overflow because `price` fits in 192 bits
                 sqrtPriceX96 := shr(32, add(price, sub(shl(32, 1), 1)))
             }
         }
diff --git a/test/libraries/TickMath.t.sol b/test/libraries/TickMath.t.sol
index 93714f97a..fa04fc015 100644
--- a/test/libraries/TickMath.t.sol
+++ b/test/libraries/TickMath.t.sol
@@ -45,6 +45,11 @@ contract TickMathTestTest is Test, JavascriptFfi, GasSnapshot {
         assertEq(maxTick, MAX_TICK);
     }
 
+    function test_getSqrtPriceAtTick_throwsForInt24Min() public {
+        vm.expectRevert(TickMath.InvalidTick.selector);
+        tickMath.getSqrtPriceAtTick(type(int24).min);
+    }
+
     function test_getSqrtPriceAtTick_throwsForTooLow() public {
         vm.expectRevert(TickMath.InvalidTick.selector);
         tickMath.getSqrtPriceAtTick(MIN_TICK - 1);