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Optimize position and factor out logic to compute compressed tick in TickBitmap #654

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merged 5 commits into from
May 17, 2024
Merged

Optimize position and factor out logic to compute compressed tick in TickBitmap #654

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534b8d5
Optimize `TickBitmap.position` using assembly
shuhuiluo May 15, 2024
9ffb642
Factor out logic to compute `compressed` to a `compress` function
shuhuiluo May 15, 2024
692cc23
Add fuzz test for `compress` and `position`
shuhuiluo May 15, 2024
68d3322
Replace `compressed + 1` by `++compressed` in `nextInitializedTickWit…
shuhuiluo May 15, 2024
dd77e47
Merge and update snapshots
shuhuiluo May 17, 2024
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2 changes: 1 addition & 1 deletion .forge-snapshots/addLiquidity CA fee.snap
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30 changes: 22 additions & 8 deletions src/libraries/TickBitmap.sol
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Expand Up @@ -12,14 +12,29 @@ library TickBitmap {
/// @param tickSpacing The tick spacing of the pool
error TickMisaligned(int24 tick, int24 tickSpacing);

/// @dev round towards negative infinity
function compress(int24 tick, int24 tickSpacing) internal pure returns (int24 compressed) {
// compressed = tick / tickSpacing;
// if (tick < 0 && tick % tickSpacing != 0) compressed--;
assembly {
compressed :=
sub(
sdiv(tick, tickSpacing),
// if (tick < 0 && tick % tickSpacing != 0) then tick % tickSpacing < 0, vice versa
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nice

slt(smod(tick, tickSpacing), 0)
)
}
}

/// @notice Computes the position in the mapping where the initialized bit for a tick lives
/// @param tick The tick for which to compute the position
/// @return wordPos The key in the mapping containing the word in which the bit is stored
/// @return bitPos The bit position in the word where the flag is stored
function position(int24 tick) internal pure returns (int16 wordPos, uint8 bitPos) {
unchecked {
wordPos = int16(tick >> 8);
bitPos = uint8(int8(tick & (256 - 1)));
assembly {
// signed arithmetic shift right
wordPos := sar(8, tick)
bitPos := and(tick, 0xff)
}
}

Expand Down Expand Up @@ -51,8 +66,7 @@ library TickBitmap {
bool lte
) internal view returns (int24 next, bool initialized) {
unchecked {
int24 compressed = tick / tickSpacing;
if (tick < 0 && tick % tickSpacing != 0) compressed--; // round towards negative infinity
int24 compressed = compress(tick, tickSpacing);

if (lte) {
(int16 wordPos, uint8 bitPos) = position(compressed);
Expand All @@ -68,7 +82,7 @@ library TickBitmap {
: (compressed - int24(uint24(bitPos))) * tickSpacing;
} else {
// start from the word of the next tick, since the current tick state doesn't matter
(int16 wordPos, uint8 bitPos) = position(compressed + 1);
(int16 wordPos, uint8 bitPos) = position(++compressed);
// all the 1s at or to the left of the bitPos
uint256 mask = ~((1 << bitPos) - 1);
uint256 masked = self[wordPos] & mask;
Expand All @@ -77,8 +91,8 @@ library TickBitmap {
initialized = masked != 0;
// overflow/underflow is possible, but prevented externally by limiting both tickSpacing and tick
next = initialized
? (compressed + 1 + int24(uint24(BitMath.leastSignificantBit(masked) - bitPos))) * tickSpacing
: (compressed + 1 + int24(uint24(type(uint8).max - bitPos))) * tickSpacing;
? (compressed + int24(uint24(BitMath.leastSignificantBit(masked) - bitPos))) * tickSpacing
: (compressed + int24(uint24(type(uint8).max - bitPos))) * tickSpacing;
}
}
}
Expand Down
13 changes: 13 additions & 0 deletions test/libraries/TickBitmap.t.sol
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Expand Up @@ -23,6 +23,19 @@ contract TickBitmapTest is Test, GasSnapshot {
}
}

function test_fuzz_compress(int24 tick, int24 tickSpacing) public pure {
tickSpacing = int24(bound(tickSpacing, 1, type(int24).max));
int24 compressed = tick / tickSpacing;
if (tick < 0 && tick % tickSpacing != 0) compressed--;
assertEq(TickBitmap.compress(tick, tickSpacing), compressed);
}

function test_fuzz_position(int24 tick) public pure {
(int16 wordPos, uint8 bitPos) = TickBitmap.position(tick);
assertEq(wordPos, tick >> 8);
assertEq(bitPos, uint8(int8(tick % 256)));
}

function test_isInitialized_isFalseAtFirst() public view {
assertEq(isInitialized(1), false);
}
Expand Down
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