From f5d0bfbfb88fb70410a3f6396b74df117eedde80 Mon Sep 17 00:00:00 2001 From: "Dr. Shuhui Luo" <107524008+shuhuiluo@users.noreply.github.com> Date: Tue, 27 Jun 2023 22:49:09 -0700 Subject: [PATCH] Incorporate new optimizations (#16) * Optimize `getNextSqrtPriceFromAmount0RoundingUp` * Refactor * Refactor and optimize `TickMath` * Update README and version * Refactor and optimize `SwapMath` * Consistent license * Update version and dependencies * Update .gas-snapshot * Polish `TickBitmap` * Add comments and reference * Update src/TickBitmap.sol Co-authored-by: while1 * Resolve review comments * Remove duplicate --------- Co-authored-by: while1 --- .gas-snapshot | 57 +- README.md | 16 +- package.json | 6 +- src/BitMath.sol | 12 +- src/NPMCaller.sol | 2 +- src/PoolCaller.sol | 2 +- src/SqrtPriceMath.sol | 138 +- src/SwapMath.sol | 269 ++- src/TernaryLib.sol | 38 +- src/TickBitmap.sol | 44 +- src/TickMath.sol | 219 +- src/UnsafeMath.sol | 2 +- test/SwapMath.t.sol | 4 +- test/TickBitmap.t.sol | 12 + yarn.lock | 5298 ++++++++++++++++++++--------------------- 15 files changed, 3117 insertions(+), 3002 deletions(-) diff --git a/.gas-snapshot b/.gas-snapshot index dc2c055..8d8266f 100644 --- a/.gas-snapshot +++ b/.gas-snapshot @@ -1,6 +1,6 @@ -BitMathTest:testFuzz_LSB(uint256) (runs: 65536, μ: 14926, ~: 14924) +BitMathTest:testFuzz_LSB(uint256) (runs: 65536, μ: 14923, ~: 14921) BitMathTest:testFuzz_MSB(uint256) (runs: 65536, μ: 14798, ~: 14822) -BitMathTest:testGas_LSB() (gas: 211488) +BitMathTest:testGas_LSB() (gas: 210723) BitMathTest:testGas_LSB_Og() (gas: 303324) BitMathTest:testGas_MSB() (gas: 229272) BitMathTest:testGas_MSB_Og() (gas: 286673) @@ -63,45 +63,46 @@ PoolCallerTest:test_Slot0() (gas: 13245) PoolCallerTest:test_SqrtPriceX96AndTick() (gas: 9731) PoolCallerTest:test_Swap() (gas: 322383) PoolCallerTest:test_TickSpacing() (gas: 8242) -SqrtPriceMathTest:testFuzz_GetAmount0Delta(uint160,uint160,int128) (runs: 65536, μ: 12876, ~: 12589) -SqrtPriceMathTest:testFuzz_GetAmount0Delta(uint160,uint160,uint128,bool) (runs: 65536, μ: 12550, ~: 12262) +SqrtPriceMathTest:testFuzz_GetAmount0Delta(uint160,uint160,int128) (runs: 65536, μ: 12877, ~: 12598) +SqrtPriceMathTest:testFuzz_GetAmount0Delta(uint160,uint160,uint128,bool) (runs: 65536, μ: 12552, ~: 12262) SqrtPriceMathTest:testFuzz_GetAmount1Delta(uint160,uint160,int128) (runs: 65536, μ: 12483, ~: 12405) SqrtPriceMathTest:testFuzz_GetAmount1Delta(uint160,uint160,uint128,bool) (runs: 65536, μ: 12498, ~: 12432) -SqrtPriceMathTest:testFuzz_GetNextSqrtPriceFromAmount0RoundingUp(uint160,uint128,uint256,bool) (runs: 65536, μ: 16972, ~: 17536) -SqrtPriceMathTest:testFuzz_GetNextSqrtPriceFromAmount1RoundingDown(uint160,uint128,uint256,bool) (runs: 65536, μ: 19491, ~: 20148) -SqrtPriceMathTest:testFuzz_GetNextSqrtPriceFromInput(uint160,uint128,uint256,bool) (runs: 65536, μ: 13293, ~: 12479) -SqrtPriceMathTest:testFuzz_GetNextSqrtPriceFromOutput(uint160,uint128,uint256,bool) (runs: 65536, μ: 13854, ~: 14333) +SqrtPriceMathTest:testFuzz_GetNextSqrtPriceFromAmount0RoundingUp(uint160,uint128,uint256,bool) (runs: 65536, μ: 16963, ~: 17522) +SqrtPriceMathTest:testFuzz_GetNextSqrtPriceFromAmount1RoundingDown(uint160,uint128,uint256,bool) (runs: 65536, μ: 19498, ~: 20148) +SqrtPriceMathTest:testFuzz_GetNextSqrtPriceFromInput(uint160,uint128,uint256,bool) (runs: 65536, μ: 13295, ~: 12479) +SqrtPriceMathTest:testFuzz_GetNextSqrtPriceFromOutput(uint160,uint128,uint256,bool) (runs: 65536, μ: 13847, ~: 14333) SqrtPriceMathTest:testGas_GetAmount0Delta() (gas: 266947) SqrtPriceMathTest:testGas_GetAmount0Delta_Og() (gas: 285432) SqrtPriceMathTest:testGas_GetAmount1Delta() (gas: 219187) SqrtPriceMathTest:testGas_GetAmount1Delta_Og() (gas: 273563) SqrtPriceMathTest:testGas_GetNextSqrtPriceFromInput() (gas: 238690) SqrtPriceMathTest:testGas_GetNextSqrtPriceFromInput_Og() (gas: 248813) -SqrtPriceMathTest:testGas_GetNextSqrtPriceFromOutput() (gas: 222831) +SqrtPriceMathTest:testGas_GetNextSqrtPriceFromOutput() (gas: 221981) SqrtPriceMathTest:testGas_GetNextSqrtPriceFromOutput_Og() (gas: 229995) -SwapMathTest:testFuzz_ComputeSwapStep(uint160,uint160,uint128,int256,uint24) (runs: 65536, μ: 22502, ~: 22582) -SwapMathTest:testFuzz_ComputeSwapStepExactIn(uint160,uint160,uint128,uint256,uint24) (runs: 65536, μ: 23662, ~: 23680) -SwapMathTest:testFuzz_ComputeSwapStepExactOut(uint160,uint160,uint128,uint256,uint24) (runs: 65536, μ: 22998, ~: 22891) -SwapMathTest:testGas_ComputeSwapStep() (gas: 430173) -SwapMathTest:testGas_ComputeSwapStepExactIn() (gas: 404912) +SwapMathTest:testFuzz_ComputeSwapStep(uint160,uint160,uint128,int256,uint24) (runs: 65536, μ: 22165, ~: 22284) +SwapMathTest:testFuzz_ComputeSwapStepExactIn(uint160,uint160,uint128,uint256,uint24) (runs: 65536, μ: 23660, ~: 23677) +SwapMathTest:testFuzz_ComputeSwapStepExactOut(uint160,uint160,uint128,uint256,uint24) (runs: 65536, μ: 22994, ~: 22888) +SwapMathTest:testGas_ComputeSwapStep() (gas: 395439) +SwapMathTest:testGas_ComputeSwapStepExactIn() (gas: 404612) SwapMathTest:testGas_ComputeSwapStepExactIn_Og() (gas: 520633) SwapMathTest:testGas_ComputeSwapStepExactOut() (gas: 380584) SwapMathTest:testGas_ComputeSwapStepExactOut_Og() (gas: 515145) SwapMathTest:testGas_ComputeSwapStep_Og() (gas: 531437) -TickBitmapTest:testFuzz_Compress(int24,int24) (runs: 65536, μ: 8388, ~: 8448) -TickBitmapTest:testFuzz_FlipTick(int24) (runs: 65536, μ: 61598, ~: 61603) -TickBitmapTest:testFuzz_NextInitializedTickWithinOneWord(int24,uint8,bool) (runs: 65536, μ: 68031, ~: 68105) -TickBitmapTest:testGas_NextInitializedTickWithinOneWord() (gas: 6798501) -TickBitmapTest:testGas_NextInitializedTickWithinOneWord_Og() (gas: 7061998) -TickBitmapTest:test_NextInitializedTickWithinOneWord_GT() (gas: 204667) -TickBitmapTest:test_NextInitializedTickWithinOneWord_LTE() (gas: 216873) -TickBitmapTest:test_NextInitializedTick_GT() (gas: 359197) +TickBitmapTest:testFuzz_Compress(int24,int24) (runs: 65536, μ: 8410, ~: 8470) +TickBitmapTest:testFuzz_FlipTick(int24) (runs: 65536, μ: 61621, ~: 61625) +TickBitmapTest:testFuzz_NextInitializedTickWithinOneWord(int24,uint8,bool) (runs: 65536, μ: 68049, ~: 68124) +TickBitmapTest:testFuzz_Position(int24) (runs: 65536, μ: 492, ~: 492) +TickBitmapTest:testGas_NextInitializedTickWithinOneWord() (gas: 6795963) +TickBitmapTest:testGas_NextInitializedTickWithinOneWord_Og() (gas: 7062020) +TickBitmapTest:test_NextInitializedTickWithinOneWord_GT() (gas: 203665) +TickBitmapTest:test_NextInitializedTickWithinOneWord_LTE() (gas: 216895) +TickBitmapTest:test_NextInitializedTick_GT() (gas: 357171) TickBitmapTest:test_NextInitializedTick_LTE() (gas: 409484) -TickMathTest:testFuzz_GetSqrtRatioAtTick(int24) (runs: 65536, μ: 16630, ~: 16910) -TickMathTest:testFuzz_GetTickAtSqrtRatio(uint160) (runs: 65536, μ: 13244, ~: 13256) -TickMathTest:testGas_GetSqrtRatioAtTick() (gas: 147560) +TickMathTest:testFuzz_GetSqrtRatioAtTick(int24) (runs: 65536, μ: 16567, ~: 16847) +TickMathTest:testFuzz_GetTickAtSqrtRatio(uint160) (runs: 65536, μ: 13177, ~: 13193) +TickMathTest:testGas_GetSqrtRatioAtTick() (gas: 148160) TickMathTest:testGas_GetSqrtRatioAtTick_Og() (gas: 168533) -TickMathTest:testGas_GetTickAtSqrtRatio() (gas: 260917) +TickMathTest:testGas_GetTickAtSqrtRatio() (gas: 255519) TickMathTest:testGas_GetTickAtSqrtRatio_Og() (gas: 307781) -TickMathTest:testRevert_GetSqrtRatioAtTick() (gas: 10455) -TickMathTest:testRevert_GetTickAtSqrtRatio() (gas: 10555) \ No newline at end of file +TickMathTest:testRevert_GetSqrtRatioAtTick() (gas: 10467) +TickMathTest:testRevert_GetTickAtSqrtRatio() (gas: 10531) \ No newline at end of file diff --git a/README.md b/README.md index 1e5c4ad..8e03f81 100644 --- a/README.md +++ b/README.md @@ -4,10 +4,10 @@ [![Test](https://github.com/Aperture-Finance/uni-v3-lib/actions/workflows/test.yml/badge.svg)](https://github.com/Aperture-Finance/uni-v3-lib/actions/workflows/test.yml) [![npm version](https://img.shields.io/npm/v/@aperture_finance/uni-v3-lib/latest.svg)](https://www.npmjs.com/package/@aperture_finance/uni-v3-lib/v/latest) -The `uni-v3-lib` by Aperture Finance is a suite of Solidity libraries that have been imported and rewritten from -Uniswap's [v3-core](https://github.com/Uniswap/v3-core) and [v3-periphery](https://github.com/Uniswap/v3-periphery) -repositories. The goal of this project is to provide external integrators with a set of libraries that are crucial for -interaction with the Uniswap V3 protocol. +The `uni-v3-lib` by Aperture Finance consists of a suite of Solidity libraries that have been imported and rewritten +from Uniswap's [v3-core](https://github.com/Uniswap/v3-core) and [v3-periphery](https://github.com/Uniswap/v3-periphery) +repositories. This project aims to equip external integrators with a set of libraries crucial for interaction with the +Uniswap V3 protocol. ## Overview @@ -29,12 +29,12 @@ heuristics and techniques are documented by extensive annotations in the source | SqrtPriceMath | testGas_GetAmount0Delta | 285432 | 266947 | 6.47% | | SqrtPriceMath | testGas_GetAmount1Delta | 273563 | 219187 | 19.88% | | SwapMath | testGas_ComputeSwapStep | 531437 | 430173 | 19.03% | -| TickMath | testGas_GetSqrtRatioAtTick | 168533 | 147560 | 12.45% | -| TickMath | testGas_GetTickAtSqrtRatio | 307781 | 260917 | 15.24% | +| TickMath | testGas_GetSqrtRatioAtTick | 168533 | 148160 | 12.09% | +| TickMath | testGas_GetTickAtSqrtRatio | 307781 | 255519 | 16.98% | -The gas measured is the total gas used by the test transaction, including the gas used to call the test wrapper +*The gas measured is the total gas used by the test transaction, including the gas used to call the test wrapper contract. The actual percentage difference in gas for the internal library functions is higher than the numbers shown -above. +above.* ## Libraries diff --git a/package.json b/package.json index 4441499..f14809c 100644 --- a/package.json +++ b/package.json @@ -1,7 +1,7 @@ { "name": "@aperture_finance/uni-v3-lib", "description": "A suite of Solidity libraries that have been imported and rewritten from Uniswap's v3-core and v3-periphery", - "version": "1.0.3", + "version": "1.1.0", "author": "Aperture Finance", "homepage": "https://aperture.finance/", "license": "GPL-2.0-or-later", @@ -32,14 +32,14 @@ "prettier:fix": "prettier -w {src,test}/**/*.sol" }, "dependencies": { - "@openzeppelin/contracts": "^4.9.0", + "@openzeppelin/contracts": "^4.9.2", "@uniswap/v3-core": "^1.0.1", "@uniswap/v3-periphery": "^1.4.3", "solady": "^0.0.101" }, "devDependencies": { "@nomicfoundation/hardhat-foundry": "^1.0.1", - "hardhat": "^2.14.1", + "hardhat": "^2.15.0", "prettier": "^2.8.8", "prettier-plugin-solidity": "^1.1.3", "ts-node": "^10.9.1", diff --git a/src/BitMath.sol b/src/BitMath.sol index 1321bea..25fef87 100644 --- a/src/BitMath.sol +++ b/src/BitMath.sol @@ -15,11 +15,15 @@ library BitMath { /// @return r the index of the most significant bit function mostSignificantBit(uint256 x) internal pure returns (uint8 r) { assembly { + // r = x >= 2**128 ? 128 : 0 r := shl(7, lt(0xffffffffffffffffffffffffffffffff, x)) + // r += (x >> r) >= 2**64 ? 64 : 0 r := or(r, shl(6, lt(0xffffffffffffffff, shr(r, x)))) + // r += (x >> r) >= 2**32 ? 32 : 0 r := or(r, shl(5, lt(0xffffffff, shr(r, x)))) // For the remaining 32 bits, use a De Bruijn lookup. + // https://graphics.stanford.edu/~seander/bithacks.html#IntegerLogDeBruijn x := shr(r, x) x := or(x, shr(1, x)) x := or(x, shr(2, x)) @@ -46,14 +50,18 @@ library BitMath { /// @return r the index of the least significant bit function leastSignificantBit(uint256 x) internal pure returns (uint8 r) { assembly { - // Isolate the least significant bit. - x := and(x, add(not(x), 1)) + // Isolate the least significant bit, x = x & -x = x & (~x + 1) + x := and(x, sub(0, x)) + // r = x >= 2**128 ? 128 : 0 r := shl(7, lt(0xffffffffffffffffffffffffffffffff, x)) + // r += (x >> r) >= 2**64 ? 64 : 0 r := or(r, shl(6, lt(0xffffffffffffffff, shr(r, x)))) + // r += (x >> r) >= 2**32 ? 32 : 0 r := or(r, shl(5, lt(0xffffffff, shr(r, x)))) // For the remaining 32 bits, use a De Bruijn lookup. + // https://graphics.stanford.edu/~seander/bithacks.html#ZerosOnRightMultLookup r := or( r, byte( diff --git a/src/NPMCaller.sol b/src/NPMCaller.sol index 8350c81..1cc3f9e 100644 --- a/src/NPMCaller.sol +++ b/src/NPMCaller.sol @@ -1,4 +1,4 @@ -// SPDX-License-Identifier: GPL-3.0-or-later +// SPDX-License-Identifier: GPL-2.0-or-later pragma solidity >=0.8.0; import "@openzeppelin/contracts/token/ERC721/IERC721.sol"; diff --git a/src/PoolCaller.sol b/src/PoolCaller.sol index 4d423ef..e6417dc 100644 --- a/src/PoolCaller.sol +++ b/src/PoolCaller.sol @@ -1,4 +1,4 @@ -// SPDX-License-Identifier: GPL-3.0-or-later +// SPDX-License-Identifier: GPL-2.0-or-later // User defined value types are introduced in Solidity v0.8.8. // https://blog.soliditylang.org/2021/09/27/user-defined-value-types/ pragma solidity >=0.8.8; diff --git a/src/SqrtPriceMath.sol b/src/SqrtPriceMath.sol index c76b6ff..85ed182 100644 --- a/src/SqrtPriceMath.sol +++ b/src/SqrtPriceMath.sol @@ -1,4 +1,4 @@ -// SPDX-License-Identifier: BUSL-1.1 +// SPDX-License-Identifier: GPL-2.0-or-later pragma solidity >=0.8.4; import "@uniswap/v3-core/contracts/libraries/SafeCast.sol"; @@ -35,39 +35,53 @@ library SqrtPriceMath { ) internal pure returns (uint160) { // we short circuit amount == 0 because the result is otherwise not guaranteed to equal the input price if (amount == 0) return sqrtPX96; - uint256 numerator = uint256(liquidity) << FixedPoint96.RESOLUTION; + uint256 numerator1 = uint256(liquidity) << FixedPoint96.RESOLUTION; if (add) { - uint256 product; - // Check no overflow - // product = amount * sqrtPX96 - if ((product = amount.mul(sqrtPX96)).div(amount) == sqrtPX96) { - // denominator = liquidity + amount * sqrtPX96 - uint256 denominator = numerator.add(product); - // Check no overflow - if (denominator >= numerator) - // always fits in 160 bits - return - uint160( - FullMath.mulDivRoundingUp( - numerator, - sqrtPX96, - denominator - ) - ); + unchecked { + uint256 product = amount * sqrtPX96; + // checks for overflow + if (product.div(amount) == sqrtPX96) { + // denominator = liquidity + amount * sqrtPX96 + uint256 denominator = numerator1 + product; + // checks for overflow + if (denominator >= numerator1) + // always fits in 160 bits + return + uint160( + FullMath.mulDivRoundingUp( + numerator1, + sqrtPX96, + denominator + ) + ); + } } // liquidity / (liquidity / sqrtPX96 + amount) return uint160( - numerator.divRoundingUp(numerator.div(sqrtPX96) + amount) + numerator1.divRoundingUp(numerator1.div(sqrtPX96) + amount) ); } else { - // No overflows or underflows allowed - uint256 denominator = numerator - amount * sqrtPX96; + uint256 denominator; + assembly ("memory-safe") { + // if the product overflows, we know the denominator underflows + // in addition, we must check that the denominator does not underflow + let product := mul(amount, sqrtPX96) + if iszero( + and( + eq(div(product, amount), sqrtPX96), + gt(numerator1, product) + ) + ) { + revert(0, 0) + } + denominator := sub(numerator1, product) + } return FullMath - .mulDivRoundingUp(numerator, sqrtPX96, denominator) + .mulDivRoundingUp(numerator1, sqrtPX96, denominator) .toUint160(); } } @@ -193,60 +207,53 @@ library SqrtPriceMath { /// @notice Gets the amount0 delta between two prices /// @dev Calculates liquidity / sqrt(lower) - liquidity / sqrt(upper), /// i.e. liquidity * (sqrt(upper) - sqrt(lower)) / (sqrt(upper) * sqrt(lower)) - /// @param sqrtRatioX96Lower A sqrt price assumed to be lower otherwise swapped - /// @param sqrtRatioX96Upper Another sqrt price + /// @param sqrtRatioAX96 A sqrt price assumed to be lower otherwise swapped + /// @param sqrtRatioBX96 Another sqrt price /// @param liquidity The amount of usable liquidity /// @param roundUp Whether to round the amount up or down /// @return amount0 Amount of token0 required to cover a position of size liquidity between the two passed prices function getAmount0Delta( - uint160 sqrtRatioX96Lower, - uint160 sqrtRatioX96Upper, + uint160 sqrtRatioAX96, + uint160 sqrtRatioBX96, uint128 liquidity, bool roundUp ) internal pure returns (uint256 amount0) { - (sqrtRatioX96Lower, sqrtRatioX96Upper) = TernaryLib.sort2( - sqrtRatioX96Lower, - sqrtRatioX96Upper + (sqrtRatioAX96, sqrtRatioBX96) = TernaryLib.sort2( + sqrtRatioAX96, + sqrtRatioBX96 ); assembly ("memory-safe") { - if iszero(sqrtRatioX96Lower) { + if iszero(sqrtRatioAX96) { revert(0, 0) } } uint256 numerator1 = uint256(liquidity) << FixedPoint96.RESOLUTION; - uint256 numerator2 = sqrtRatioX96Upper.sub(sqrtRatioX96Lower); + uint256 numerator2 = sqrtRatioBX96.sub(sqrtRatioAX96); /** * Equivalent to: * roundUp - * ? UnsafeMath.divRoundingUp( - * FullMath.mulDivRoundingUp(numerator1, numerator2, sqrtRatioBX96), - * sqrtRatioAX96 - * ) + * ? FullMath.mulDivRoundingUp(numerator1, numerator2, sqrtRatioBX96).divRoundingUp(sqrtRatioAX96) * : FullMath.mulDiv(numerator1, numerator2, sqrtRatioBX96) / sqrtRatioAX96; - * If `md = mulDiv(n1, n2, sru) = mulDivRoundingUp(n1, n2, sru)`, add `roundUp && md % srl > 0`. - * If `md = mulDiv(n1, n2, sru)` and `mulDivRoundingUp(n1, n2, sru)` differs by 1 and `srl > 0`, - * then `(md + 1).divRoundingUp(srl)` = `md.div(srl) + 1` whether `srl` fully divides `md` or not. + * If `md = mulDiv(n1, n2, srb) == mulDivRoundingUp(n1, n2, srb)`, then `mulmod(n1, n2, srb) == 0`. + * Add `roundUp && md % sra > 0` to `div(md, sra)`. + * If `md = mulDiv(n1, n2, srb)` and `mulDivRoundingUp(n1, n2, srb)` differs by 1 and `sra > 0`, + * then `(md + 1).divRoundingUp(sra) == md.div(sra) + 1` whether `sra` fully divides `md` or not. */ uint256 mulDivResult = FullMath.mulDiv( numerator1, numerator2, - sqrtRatioX96Upper + sqrtRatioBX96 ); assembly { amount0 := add( - div(mulDivResult, sqrtRatioX96Lower), + div(mulDivResult, sqrtRatioAX96), and( - iszero( - iszero( - or( - mod(mulDivResult, sqrtRatioX96Lower), - mulmod( - numerator1, - numerator2, - sqrtRatioX96Upper - ) - ) - ) + gt( + or( + mod(mulDivResult, sqrtRatioAX96), + mulmod(numerator1, numerator2, sqrtRatioBX96) + ), + 0 ), roundUp ) @@ -256,38 +263,35 @@ library SqrtPriceMath { /// @notice Gets the amount1 delta between two prices /// @dev Calculates liquidity * (sqrt(upper) - sqrt(lower)) - /// @param sqrtRatioX96Lower A sqrt price assumed to be lower otherwise swapped - /// @param sqrtRatioX96Upper Another sqrt price + /// @param sqrtRatioAX96 A sqrt price assumed to be lower otherwise swapped + /// @param sqrtRatioBX96 Another sqrt price /// @param liquidity The amount of usable liquidity /// @param roundUp Whether to round the amount up, or down /// @return amount1 Amount of token1 required to cover a position of size liquidity between the two passed prices function getAmount1Delta( - uint160 sqrtRatioX96Lower, - uint160 sqrtRatioX96Upper, + uint160 sqrtRatioAX96, + uint160 sqrtRatioBX96, uint128 liquidity, bool roundUp ) internal pure returns (uint256 amount1) { - (sqrtRatioX96Lower, sqrtRatioX96Upper) = TernaryLib.sort2( - sqrtRatioX96Lower, - sqrtRatioX96Upper + (sqrtRatioAX96, sqrtRatioBX96) = TernaryLib.sort2( + sqrtRatioAX96, + sqrtRatioBX96 ); - uint256 numerator = sqrtRatioX96Upper.sub(sqrtRatioX96Lower); + uint256 numerator = sqrtRatioBX96.sub(sqrtRatioAX96); uint256 denominator = FixedPoint96.Q96; /** * Equivalent to: * amount1 = roundUp * ? FullMath.mulDivRoundingUp(liquidity, sqrtRatioBX96 - sqrtRatioAX96, FixedPoint96.Q96) * : FullMath.mulDiv(liquidity, sqrtRatioBX96 - sqrtRatioAX96, FixedPoint96.Q96); - * Cannot overflow because uint128 * uint160 >> 96 < 1 << 192. + * Cannot overflow because `type(uint128).max * type(uint160).max >> 96 < (1 << 192)`. */ amount1 = FullMath.mulDiv96(liquidity, numerator); assembly { amount1 := add( amount1, - and( - iszero(iszero(mulmod(liquidity, numerator, denominator))), - roundUp - ) + and(gt(mulmod(liquidity, numerator, denominator), 0), roundUp) ) } } @@ -320,7 +324,7 @@ library SqrtPriceMath { mask := sub(sign, 1) liquidityAbs := xor(mask, add(mask, liquidity)) } - // amount0Abs = liquidity / sqrt(lower) - liquidity / sqrt(upper) < 2**224 + // amount0Abs = liquidity / sqrt(lower) - liquidity / sqrt(upper) < type(uint224).max // always fits in 224 bits, no need for toInt256() uint256 amount0Abs = getAmount0Delta( sqrtRatioAX96, @@ -363,7 +367,7 @@ library SqrtPriceMath { mask := sub(sign, 1) liquidityAbs := xor(mask, add(mask, liquidity)) } - // amount1Abs = liquidity * (sqrt(upper) - sqrt(lower)) < 2**192 + // amount1Abs = liquidity * (sqrt(upper) - sqrt(lower)) < type(uint192).max // always fits in 192 bits, no need for toInt256() uint256 amount1Abs = getAmount1Delta( sqrtRatioAX96, diff --git a/src/SwapMath.sol b/src/SwapMath.sol index c171650..a4125b6 100644 --- a/src/SwapMath.sol +++ b/src/SwapMath.sol @@ -1,4 +1,4 @@ -// SPDX-License-Identifier: BUSL-1.1 +// SPDX-License-Identifier: GPL-2.0-or-later pragma solidity >=0.8.4; import "./SqrtPriceMath.sol"; @@ -10,6 +10,35 @@ import "./SqrtPriceMath.sol"; library SwapMath { uint256 internal constant MAX_FEE_PIPS = 1e6; + /// @notice Computes the sqrt price target for the next swap step + /// @param zeroForOne The direction of the swap, true for token0 to token1, false for token1 to token0 + /// @param sqrtPriceNextX96 The Q64.96 sqrt price for the next initialized tick + /// @param sqrtPriceLimitX96 The Q64.96 sqrt price limit. If zero for one, the price cannot be less than this + /// value after the swap. If one for zero, the price cannot be greater than this value after the swap + /// @return sqrtRatioTargetX96 The price target for the next swap step + function getSqrtRatioTarget( + bool zeroForOne, + uint160 sqrtPriceNextX96, + uint160 sqrtPriceLimitX96 + ) internal pure returns (uint160 sqrtRatioTargetX96) { + assembly { + // a flag to toggle between sqrtPriceNextX96 and sqrtPriceLimitX96 + // when zeroForOne == true, nextOrLimit reduces to sqrtPriceNextX96 > sqrtPriceLimitX96 + // sqrtRatioTargetX96 = max(sqrtPriceNextX96, sqrtPriceLimitX96) + // when zeroForOne == false, nextOrLimit reduces to sqrtPriceNextX96 <= sqrtPriceLimitX96 + // sqrtRatioTargetX96 = min(sqrtPriceNextX96, sqrtPriceLimitX96) + let nextOrLimit := xor( + gt(sqrtPriceNextX96, sqrtPriceLimitX96), + iszero(zeroForOne) + ) + let symDiff := xor(sqrtPriceNextX96, sqrtPriceLimitX96) + sqrtRatioTargetX96 := xor( + sqrtPriceLimitX96, + mul(symDiff, nextOrLimit) + ) + } + } + /// @notice Computes the result of swapping some amount in, or amount out, given the parameters of the swap /// @dev The fee, plus the amount in, will never exceed the amount remaining if the swap's `amountSpecified` is positive /// @param sqrtRatioCurrentX96 The current sqrt price of the pool @@ -37,133 +66,117 @@ library SwapMath { uint256 feeAmount ) { - bool zeroForOne = sqrtRatioCurrentX96 >= sqrtRatioTargetX96; - bool exactIn; - uint256 amountRemainingAbs; - assembly { - // exactIn = 1 if amountRemaining >= 0 else 0 - exactIn := iszero(slt(amountRemaining, 0)) - // mask = 0 if amountRemaining >= 0 else -1 - let mask := sub(exactIn, 1) - amountRemainingAbs := xor(mask, add(mask, amountRemaining)) - } - - if (exactIn) { - uint256 amountRemainingLessFee = FullMath.mulDiv( - amountRemainingAbs, - UnsafeMath.sub(MAX_FEE_PIPS, feePips), - MAX_FEE_PIPS - ); - amountIn = zeroForOne - ? SqrtPriceMath.getAmount0Delta( - sqrtRatioTargetX96, - sqrtRatioCurrentX96, - liquidity, - true - ) - : SqrtPriceMath.getAmount1Delta( - sqrtRatioCurrentX96, - sqrtRatioTargetX96, - liquidity, - true - ); - if (amountRemainingLessFee >= amountIn) { - // `amountIn` is capped by the target price - sqrtRatioNextX96 = sqrtRatioTargetX96; - } else { - // Exhaust the remaining amount - sqrtRatioNextX96 = SqrtPriceMath.getNextSqrtPriceFromInput( - sqrtRatioCurrentX96, - liquidity, - amountRemainingLessFee, - zeroForOne - ); - } - } else { - amountOut = zeroForOne - ? SqrtPriceMath.getAmount1Delta( - sqrtRatioTargetX96, - sqrtRatioCurrentX96, - liquidity, - false - ) - : SqrtPriceMath.getAmount0Delta( - sqrtRatioCurrentX96, - sqrtRatioTargetX96, - liquidity, - false - ); - if (amountRemainingAbs >= amountOut) { - // `amountOut` is capped by the target price - sqrtRatioNextX96 = sqrtRatioTargetX96; - } else { - // Exhaust the remaining amount - sqrtRatioNextX96 = SqrtPriceMath.getNextSqrtPriceFromOutput( - sqrtRatioCurrentX96, - liquidity, - amountRemainingAbs, - zeroForOne - ); + unchecked { + bool zeroForOne = sqrtRatioCurrentX96 >= sqrtRatioTargetX96; + uint256 feeComplement = MAX_FEE_PIPS - feePips; + bool exactIn; + uint256 amountRemainingAbs; + assembly { + // exactIn = 1 if amountRemaining >= 0 else 0 + exactIn := iszero(slt(amountRemaining, 0)) + // mask = 0 if amountRemaining >= 0 else -1 + let mask := sub(exactIn, 1) + amountRemainingAbs := xor(mask, add(mask, amountRemaining)) } - } - // Whether the target price is reached - bool max = sqrtRatioTargetX96 == sqrtRatioNextX96; - - // get the input/output amounts - if (zeroForOne) { - // No need to recompute `amountIn` if `amountIn` is capped by the target price when `exactIn` - amountIn = max && exactIn - ? amountIn - : SqrtPriceMath.getAmount0Delta( - sqrtRatioNextX96, - sqrtRatioCurrentX96, - liquidity, - true - ); - amountOut = max && !exactIn - ? amountOut - : SqrtPriceMath.getAmount1Delta( - sqrtRatioNextX96, - sqrtRatioCurrentX96, - liquidity, - false - ); - } else { - amountIn = max && exactIn - ? amountIn - : SqrtPriceMath.getAmount1Delta( - sqrtRatioCurrentX96, - sqrtRatioNextX96, - liquidity, - true + if (exactIn) { + uint256 amountRemainingLessFee = FullMath.mulDiv( + amountRemainingAbs, + feeComplement, + MAX_FEE_PIPS ); - amountOut = max && !exactIn - ? amountOut - : SqrtPriceMath.getAmount0Delta( - sqrtRatioCurrentX96, - sqrtRatioNextX96, - liquidity, - false + amountIn = zeroForOne + ? SqrtPriceMath.getAmount0Delta( + sqrtRatioTargetX96, + sqrtRatioCurrentX96, + liquidity, + true + ) + : SqrtPriceMath.getAmount1Delta( + sqrtRatioCurrentX96, + sqrtRatioTargetX96, + liquidity, + true + ); + if (amountRemainingLessFee >= amountIn) { + // `amountIn` is capped by the target price + sqrtRatioNextX96 = sqrtRatioTargetX96; + feeAmount = FullMath.mulDivRoundingUp( + amountIn, + feePips, + feeComplement + ); + } else { + // exhaust the remaining amount + amountIn = amountRemainingLessFee; + sqrtRatioNextX96 = SqrtPriceMath.getNextSqrtPriceFromInput( + sqrtRatioCurrentX96, + liquidity, + amountIn, + zeroForOne + ); + // we didn't reach the target, so take the remainder of the maximum input as fee + feeAmount = amountRemainingAbs - amountIn; + } + amountOut = zeroForOne + ? SqrtPriceMath.getAmount1Delta( + sqrtRatioNextX96, + sqrtRatioCurrentX96, + liquidity, + false + ) + : SqrtPriceMath.getAmount0Delta( + sqrtRatioCurrentX96, + sqrtRatioNextX96, + liquidity, + false + ); + } else { + amountOut = zeroForOne + ? SqrtPriceMath.getAmount1Delta( + sqrtRatioTargetX96, + sqrtRatioCurrentX96, + liquidity, + false + ) + : SqrtPriceMath.getAmount0Delta( + sqrtRatioCurrentX96, + sqrtRatioTargetX96, + liquidity, + false + ); + if (amountRemainingAbs >= amountOut) { + // `amountOut` is capped by the target price + sqrtRatioNextX96 = sqrtRatioTargetX96; + } else { + // cap the output amount to not exceed the remaining output amount + amountOut = amountRemainingAbs; + sqrtRatioNextX96 = SqrtPriceMath.getNextSqrtPriceFromOutput( + sqrtRatioCurrentX96, + liquidity, + amountOut, + zeroForOne + ); + } + amountIn = zeroForOne + ? SqrtPriceMath.getAmount0Delta( + sqrtRatioNextX96, + sqrtRatioCurrentX96, + liquidity, + true + ) + : SqrtPriceMath.getAmount1Delta( + sqrtRatioCurrentX96, + sqrtRatioNextX96, + liquidity, + true + ); + feeAmount = FullMath.mulDivRoundingUp( + amountIn, + feePips, + feeComplement ); - } - - // cap the output amount to not exceed the remaining output amount - if (!exactIn && amountOut > amountRemainingAbs) { - amountOut = amountRemainingAbs; - } - - if (exactIn && sqrtRatioNextX96 != sqrtRatioTargetX96) { - // we didn't reach the target, so take the remainder of the maximum input as fee - assembly { - feeAmount := sub(amountRemainingAbs, amountIn) } - } else { - feeAmount = FullMath.mulDivRoundingUp( - amountIn, - feePips, - UnsafeMath.sub(MAX_FEE_PIPS, feePips) - ); } } @@ -211,21 +224,21 @@ library SwapMath { if (amountRemainingLessFee >= amountIn) { // `amountIn` is capped by the target price sqrtRatioNextX96 = sqrtRatioTargetX96; - // Just add the fee amount + // add the fee amount amountIn = FullMath.mulDivRoundingUp( amountIn, MAX_FEE_PIPS, feeComplement ); } else { - // Exhaust the remaining amount + // exhaust the remaining amount + amountIn = amountRemaining; sqrtRatioNextX96 = SqrtPriceMath.getNextSqrtPriceFromInput( sqrtRatioCurrentX96, liquidity, amountRemainingLessFee, zeroForOne ); - amountIn = amountRemaining; } amountOut = zeroForOne ? SqrtPriceMath.getAmount1Delta( @@ -280,14 +293,14 @@ library SwapMath { // `amountOut` is capped by the target price sqrtRatioNextX96 = sqrtRatioTargetX96; } else { - // Exhaust the remaining amount + // cap the output amount to not exceed the remaining output amount + amountOut = amountRemaining; sqrtRatioNextX96 = SqrtPriceMath.getNextSqrtPriceFromOutput( sqrtRatioCurrentX96, liquidity, amountRemaining, zeroForOne ); - amountOut = amountRemaining; } amountIn = FullMath.mulDivRoundingUp( zeroForOne diff --git a/src/TernaryLib.sol b/src/TernaryLib.sol index 3aa893f..8155bed 100644 --- a/src/TernaryLib.sol +++ b/src/TernaryLib.sol @@ -26,14 +26,44 @@ library TernaryLib { } } + /// @notice Equivalent to: `uint256(x < 0 ? -x : x)` + function abs(int256 x) internal pure returns (uint256 y) { + assembly { + // mask = 0 if x >= 0 else -1 + let mask := sub(0, slt(x, 0)) + // If x >= 0, |x| = x = 0 ^ x + // If x < 0, |x| = ~~|x| = ~(-|x| - 1) = ~(x - 1) = -1 ^ (x - 1) + // Either case, |x| = mask ^ (x + mask) + y := xor(mask, add(mask, x)) + } + } + /// @notice Equivalent to: `a < b ? a : b` - function min(uint256 a, uint256 b) internal pure returns (uint256) { - return ternary(a < b, a, b); + function min(uint256 a, uint256 b) internal pure returns (uint256 res) { + assembly { + res := xor(b, mul(xor(a, b), lt(a, b))) + } } /// @notice Equivalent to: `a > b ? a : b` - function max(uint256 a, uint256 b) internal pure returns (uint256) { - return ternary(a > b, a, b); + function max(uint256 a, uint256 b) internal pure returns (uint256 res) { + assembly { + res := xor(b, mul(xor(a, b), gt(a, b))) + } + } + + /// @notice Equivalent to: `condition ? (b, a) : (a, b)` + function switchIf( + bool condition, + uint256 a, + uint256 b + ) internal pure returns (uint256, uint256) { + assembly { + let diff := mul(xor(a, b), condition) + a := xor(a, diff) + b := xor(b, diff) + } + return (a, b); } /// @notice Equivalent to: `condition ? (b, a) : (a, b)` diff --git a/src/TickBitmap.sol b/src/TickBitmap.sol index fff503c..bcd5d01 100644 --- a/src/TickBitmap.sol +++ b/src/TickBitmap.sol @@ -1,4 +1,4 @@ -// SPDX-License-Identifier: BUSL-1.1 +// SPDX-License-Identifier: GPL-2.0-or-later pragma solidity >=0.8.8; import "./BitMath.sol"; @@ -10,20 +10,6 @@ import "./PoolCaller.sol"; /// @notice Stores a packed mapping of tick index to its initialized state /// @dev The mapping uses int16 for keys since ticks are represented as int24 and there are 256 (2^8) values per word. library TickBitmap { - /// @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 - ) private pure returns (int16 wordPos, uint8 bitPos) { - assembly { - // signed arithmetic shift right - wordPos := sar(8, tick) - bitPos := and(tick, 255) - } - } - /// @dev round towards negative infinity function compress( int24 tick, @@ -34,12 +20,26 @@ library TickBitmap { assembly { compressed := sub( sdiv(tick, tickSpacing), - // If (tick < 0 && tick % tickSpacing != 0) then tick % tickSpacing < 0, vice versa + // if (tick < 0 && tick % tickSpacing != 0) then tick % tickSpacing < 0, vice versa slt(smod(tick, tickSpacing), 0) ) } } + /// @notice Computes the word position and the bit position given a tick. + /// @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 + ) private pure returns (int16 wordPos, uint8 bitPos) { + assembly { + // signed arithmetic shift right + wordPos := sar(8, tick) + bitPos := and(tick, 255) + } + } + /// @notice Flips the initialized state for a given tick from false to true, or vice versa /// @param self The mapping in which to flip the tick /// @param tick The tick to flip @@ -50,14 +50,18 @@ library TickBitmap { int24 tickSpacing ) internal { assembly ("memory-safe") { + // ensure that the tick is spaced if smod(tick, tickSpacing) { revert(0, 0) } tick := sdiv(tick, tickSpacing) // calculate the storage slot corresponding to the tick + // wordPos = tick >> 8 mstore(0, sar(8, tick)) mstore(0x20, self.slot) + // the slot of self[wordPos] is keccak256(abi.encode(wordPos, self.slot)) let slot := keccak256(0, 0x40) + // mask = 1 << bitPos = 1 << (tick % 256) // self[wordPos] ^= mask sstore(slot, xor(sload(slot), shl(and(tick, 255), 1))) } @@ -91,7 +95,7 @@ library TickBitmap { mstore(0x20, self.slot) let mask := sub(shl(add(bitPos, 1), 1), 1) masked := and(sload(keccak256(0, 0x40)), mask) - initialized := iszero(iszero(masked)) + initialized := gt(masked, 0) } // if there are no initialized ticks to the right of or at the current tick, return rightmost in the word @@ -120,7 +124,7 @@ library TickBitmap { mstore(0x20, self.slot) let mask := not(sub(shl(bitPos, 1), 1)) masked := and(sload(keccak256(0, 0x40)), mask) - initialized := iszero(iszero(masked)) + initialized := gt(masked, 0) } // if there are no initialized ticks to the left of the current tick, return leftmost in the word @@ -178,7 +182,7 @@ library TickBitmap { assembly { let mask := sub(shl(add(bitPos, 1), 1), 1) masked := and(tickWord, mask) - initialized := iszero(iszero(masked)) + initialized := gt(masked, 0) } // if there are no initialized ticks to the right of or at the current tick, return rightmost in the word @@ -207,7 +211,7 @@ library TickBitmap { assembly { let mask := not(sub(shl(bitPos, 1), 1)) masked := and(tickWord, mask) - initialized := iszero(iszero(masked)) + initialized := gt(masked, 0) } // if there are no initialized ticks to the left of the current tick, return leftmost in the word diff --git a/src/TickMath.sol b/src/TickMath.sol index eec264d..e4eca46 100644 --- a/src/TickMath.sol +++ b/src/TickMath.sol @@ -1,7 +1,7 @@ // SPDX-License-Identifier: GPL-2.0-or-later pragma solidity >=0.5.0; -import "./BitMath.sol"; +import "./TernaryLib.sol"; /// @title Math library for computing sqrt prices from ticks and vice versa /// @author Aperture Finance @@ -19,6 +19,9 @@ library TickMath { /// @dev The maximum value that can be returned from #getSqrtRatioAtTick. Equivalent to getSqrtRatioAtTick(MAX_TICK) uint160 internal constant MAX_SQRT_RATIO = 1461446703485210103287273052203988822378723970342; + /// @dev A threshold used for optimized bounds check, equals `MAX_SQRT_RATIO - MIN_SQRT_RATIO - 1` + uint160 internal constant MAX_SQRT_RATIO_MINUS_MIN_SQRT_RATIO_MINUS_ONE = + 1461446703485210103287273052203988822378723970342 - 4295128739 - 1; /// @notice Calculates sqrt(1.0001^tick) * 2^96 /// @dev Throws if |tick| > max tick @@ -29,16 +32,14 @@ library TickMath { int24 tick ) internal pure returns (uint160 sqrtPriceX96) { unchecked { - uint256 absTick; + int256 tick256; + assembly { + // sign extend to make tick an int256 in twos complement + tick256 := signextend(2, tick) + } + uint256 absTick = TernaryLib.abs(tick256); /// @solidity memory-safe-assembly assembly { - // Credit to Solady (https://github.com/Vectorized/solady/blob/1873046d2ed3428e236d83682f302afde369b2c2/src/utils/FixedPointMathLib.sol#L620) - // mask = 0 if tick >= 0 else -1 - // If tick >= 0, |tick| = tick = 0 ^ tick - // If tick < 0, |tick| = ~(-|tick| - 1) = ~(tick - 1) = -1 ^ (tick - 1) - tick := signextend(2, tick) - let mask := sub(0, slt(tick, 0)) - absTick := xor(mask, add(mask, tick)) // Equivalent: if (absTick > MAX_TICK) revert("T"); if gt(absTick, MAX_TICK) { // selector "Error(string)", [0x1c, 0x20) @@ -59,20 +60,22 @@ library TickMath { shr( // 128 if absTick & 0x1 else 0 shl(7, and(absTick, 0x1)), - // 2**256 / sqrt(1.0001) where the 128th bit is 1 + // upper 128 bits of 2**256 / sqrt(1.0001) where the 128th bit is 1 0xfffcb933bd6fad37aa2d162d1a59400100000000000000000000000000000000 ), - 0x1ffffffffffffffffffffffffffffffff // Keep lower 129 bits + 0x1ffffffffffffffffffffffffffffffff // mask lower 129 bits ) } + // Iterate through 1th to 19th bit of absTick because MAX_TICK < 2**20 + // Equivalent to: + // for i in range(1, 20): + // if absTick & 2 ** i: + // ratio = ratio * (2 ** 128 / 1.0001 ** (2 ** (i - 1))) / 2 ** 128 if (absTick & 0x2 != 0) - // ratio /= 1.0001 ratio = (ratio * 0xfff97272373d413259a46990580e213a) >> 128; if (absTick & 0x4 != 0) - // ratio /= 1.0001**2 ratio = (ratio * 0xfff2e50f5f656932ef12357cf3c7fdcc) >> 128; if (absTick & 0x8 != 0) - // ratio /= 1.0001**4 ratio = (ratio * 0xffe5caca7e10e4e61c3624eaa0941cd0) >> 128; if (absTick & 0x10 != 0) ratio = (ratio * 0xffcb9843d60f6159c9db58835c926644) >> 128; @@ -104,14 +107,12 @@ library TickMath { ratio = (ratio * 0x5d6af8dedb81196699c329225ee604) >> 128; if (absTick & 0x40000 != 0) ratio = (ratio * 0x2216e584f5fa1ea926041bedfe98) >> 128; - // absTick & 2**19 == 1 if (absTick & 0x80000 != 0) - // ratio /= 1.0001**(2**18) ratio = (ratio * 0x48a170391f7dc42444e8fa2) >> 128; // if (tick > 0) ratio = type(uint256).max / ratio; assembly { - if sgt(tick, 0) { + if sgt(tick256, 0) { ratio := div(not(0), ratio) } } @@ -134,12 +135,14 @@ library TickMath { uint160 sqrtPriceX96 ) internal pure returns (int24 tick) { // Equivalent: if (sqrtPriceX96 < MIN_SQRT_RATIO || sqrtPriceX96 >= MAX_SQRT_RATIO) revert("R"); + // second inequality must be >= because the price can never reach the price at the max tick /// @solidity memory-safe-assembly assembly { - // second inequality must be >= because the price can never reach the price at the max tick - if or( - lt(sqrtPriceX96, MIN_SQRT_RATIO), - iszero(lt(sqrtPriceX96, MAX_SQRT_RATIO)) + // if sqrtPriceX96 < MIN_SQRT_RATIO, the `sub` underflows and `gt` is true + // if sqrtPriceX96 >= MAX_SQRT_RATIO, sqrtPriceX96 - MIN_SQRT_RATIO > MAX_SQRT_RATIO - MAX_SQRT_RATIO - 1 + if gt( + sub(sqrtPriceX96, MIN_SQRT_RATIO), + MAX_SQRT_RATIO_MINUS_MIN_SQRT_RATIO_MINUS_ONE ) { // selector "Error(string)", [0x1c, 0x20) mstore(0, 0x08c379a0) @@ -153,92 +156,128 @@ library TickMath { } // Find the most significant bit of `sqrtPriceX96`, 160 > msb >= 32. - uint8 msb = BitMath.mostSignificantBit(sqrtPriceX96); - - // Fit `sqrtPriceX96` in 128 bits - // ratio = sqrtPriceX96 / 2**(msb - 127) - // 2**128 > ratio >= 2**127 - // sqrtPrice = 2**(msb - 96) * ratio / 2**127 - uint256 ratio; + uint8 msb; assembly { - // Shift left first because 160 > msb >= 32. If we shift right first, we'll lose precision. - ratio := shr(sub(msb, 31), shl(96, sqrtPriceX96)) + let x := sqrtPriceX96 + msb := shl(7, lt(0xffffffffffffffffffffffffffffffff, x)) + msb := or(msb, shl(6, lt(0xffffffffffffffff, shr(msb, x)))) + msb := or(msb, shl(5, lt(0xffffffff, shr(msb, x)))) + + // For the remaining 32 bits, use a De Bruijn lookup. + x := shr(msb, x) + x := or(x, shr(1, x)) + x := or(x, shr(2, x)) + x := or(x, shr(4, x)) + x := or(x, shr(8, x)) + x := or(x, shr(16, x)) + + msb := or( + msb, + byte( + shr(251, mul(x, shl(224, 0x07c4acdd))), + 0x0009010a0d15021d0b0e10121619031e080c141c0f111807131b17061a05041f + ) + ) } // 2**(msb - 95) > sqrtPrice >= 2**(msb - 96) - // log_2 = int(log_2(sqrtPrice)) = msb - 96 - // log_2X64 = (msb - 96) * 2**64 - int256 log_2X64; // 8.64 number + // the integer part of log_2(sqrtPrice) * 2**64 = (msb - 96) << 64, 8.64 number + int256 log_2X64; assembly { log_2X64 := shl(64, sub(msb, 96)) - } - // Approximate `log_2X64` to 14 binary digits after decimal - // log_2X64 = (msb - 96) * 2**64 + f_0 * 2**63 + f_1 * 2**62 + ...... - // sqrtPrice**2 = 2**(2 * (msb - 96)) * (r / 2**127)**2 = 2**(2 * log_2X64 / 2**64) = 2**(2 * (msb - 96) + f_0) - // 2**f_0 = (r / 2**127)**2 = r**2 / 2**255 * 2 - // f_0 = 1 if (r**2 >= 2**255) else 0 - // sqrtPrice**2 = 2**(2 * (msb - 96) + f_0) * r**2 / 2**(254 + f_0) = 2**(2 * (msb - 96) + f_0) * r' / 2**127 - // r' = r**2 / 2**(127 + f_0) - // sqrtPrice**4 = 2**(4 * (msb - 96) + 2 * f_0) * (r' / 2**127)**2 - // = 2**(4 * log_2X64 / 2**64) = 2**(4 * (msb - 96) + 2 * f_0 + f_1) - // 2**(f_1) = (r' / 2**127)**2 - // f_1 = 1 if (r'**2 >= 2**255) else 0 - assembly { + // Get the first 128 significant figures of `sqrtPriceX96`. + // r = sqrtPriceX96 / 2**(msb - 127), where 2**128 > r >= 2**127 + // sqrtPrice = 2**(msb - 96) * r / 2**127, in floating point math + // Shift left first because 160 > msb >= 32. If we shift right first, we'll lose precision. + let r := shr(sub(msb, 31), shl(96, sqrtPriceX96)) + + // Approximate `log_2X64` to 14 binary digits after decimal + // log_2X64 = (msb - 96) * 2**64 + f_0 * 2**63 + f_1 * 2**62 + ...... + // sqrtPrice**2 = 2**(2 * (msb - 96)) * (r / 2**127)**2 = 2**(2 * log_2X64 / 2**64) = 2**(2 * (msb - 96) + f_0) + // 2**f_0 = (r / 2**127)**2 = r**2 / 2**255 * 2 + // f_0 = 1 if (r**2 >= 2**255) else 0 + // sqrtPrice**2 = 2**(2 * (msb - 96) + f_0) * r**2 / 2**(254 + f_0) = 2**(2 * (msb - 96) + f_0) * r' / 2**127 + // r' = r**2 / 2**(127 + f_0) + // sqrtPrice**4 = 2**(4 * (msb - 96) + 2 * f_0) * (r' / 2**127)**2 + // = 2**(4 * log_2X64 / 2**64) = 2**(4 * (msb - 96) + 2 * f_0 + f_1) + // 2**(f_1) = (r' / 2**127)**2 + // f_1 = 1 if (r'**2 >= 2**255) else 0 + // Check whether r >= sqrt(2) * 2**127 - function ge_sqrt2(r) -> _r, f { - // 2**256 > r**2 >= 2**254 - let r2 := mul(r, r) - // f = (r**2 >= 2**255) - f := slt(r2, 0) - // _r = r**2 >> 128 if r**2 >= 2**255 else r**2 >> 127 - _r := shr(add(127, f), r2) - } - let r, f := ge_sqrt2(ratio) - log_2X64 := or(log_2X64, shl(63, f)) + // 2**256 > r**2 >= 2**254 + let square := mul(r, r) + // f = (r**2 >= 2**255) + let f := slt(square, 0) + // r = r**2 >> 128 if r**2 >= 2**255 else r**2 >> 127 + r := shr(add(127, f), square) + log_2X64 := or(shl(63, f), log_2X64) - r, f := ge_sqrt2(r) - log_2X64 := or(log_2X64, shl(62, f)) + square := mul(r, r) + f := slt(square, 0) + r := shr(add(127, f), square) + log_2X64 := or(shl(62, f), log_2X64) - r, f := ge_sqrt2(r) - log_2X64 := or(log_2X64, shl(61, f)) + square := mul(r, r) + f := slt(square, 0) + r := shr(add(127, f), square) + log_2X64 := or(shl(61, f), log_2X64) - r, f := ge_sqrt2(r) - log_2X64 := or(log_2X64, shl(60, f)) + square := mul(r, r) + f := slt(square, 0) + r := shr(add(127, f), square) + log_2X64 := or(shl(60, f), log_2X64) - r, f := ge_sqrt2(r) - log_2X64 := or(log_2X64, shl(59, f)) + square := mul(r, r) + f := slt(square, 0) + r := shr(add(127, f), square) + log_2X64 := or(shl(59, f), log_2X64) - r, f := ge_sqrt2(r) - log_2X64 := or(log_2X64, shl(58, f)) + square := mul(r, r) + f := slt(square, 0) + r := shr(add(127, f), square) + log_2X64 := or(shl(58, f), log_2X64) - r, f := ge_sqrt2(r) - log_2X64 := or(log_2X64, shl(57, f)) + square := mul(r, r) + f := slt(square, 0) + r := shr(add(127, f), square) + log_2X64 := or(shl(57, f), log_2X64) - r, f := ge_sqrt2(r) - log_2X64 := or(log_2X64, shl(56, f)) + square := mul(r, r) + f := slt(square, 0) + r := shr(add(127, f), square) + log_2X64 := or(shl(56, f), log_2X64) - r, f := ge_sqrt2(r) - log_2X64 := or(log_2X64, shl(55, f)) + square := mul(r, r) + f := slt(square, 0) + r := shr(add(127, f), square) + log_2X64 := or(shl(55, f), log_2X64) - r, f := ge_sqrt2(r) - log_2X64 := or(log_2X64, shl(54, f)) + square := mul(r, r) + f := slt(square, 0) + r := shr(add(127, f), square) + log_2X64 := or(shl(54, f), log_2X64) - r, f := ge_sqrt2(r) - log_2X64 := or(log_2X64, shl(53, f)) + square := mul(r, r) + f := slt(square, 0) + r := shr(add(127, f), square) + log_2X64 := or(shl(53, f), log_2X64) - r, f := ge_sqrt2(r) - log_2X64 := or(log_2X64, shl(52, f)) + square := mul(r, r) + f := slt(square, 0) + r := shr(add(127, f), square) + log_2X64 := or(shl(52, f), log_2X64) - r, f := ge_sqrt2(r) - log_2X64 := or(log_2X64, shl(51, f)) + square := mul(r, r) + f := slt(square, 0) + r := shr(add(127, f), square) + log_2X64 := or(shl(51, f), log_2X64) - log_2X64 := or(log_2X64, shl(50, slt(mul(r, r), 0))) + log_2X64 := or(shl(50, slt(mul(r, r), 0)), log_2X64) } // sqrtPrice = sqrt(1.0001^tick) - // log_2(sqrtPrice) = tick * log_2(sqrt(1.0001)) - // tick = log_sqrt10001(sqrtPrice) = log_2(sqrtPrice) / log_2(sqrt(1.0001)) + // tick = log_{sqrt(1.0001)}(sqrtPrice) = log_2(sqrtPrice) / log_2(sqrt(1.0001)) // 2**64 / log_2(sqrt(1.0001)) = 255738958999603826347141 int24 tickLow; int24 tickHi; @@ -254,10 +293,14 @@ library TickMath { ) } - tick = tickLow == tickHi - ? tickLow - : getSqrtRatioAtTick(tickHi) <= sqrtPriceX96 - ? tickHi - : tickLow; + // Equivalent: tick = tickLow == tickHi ? tickLow : getSqrtRatioAtTick(tickHi) <= sqrtPriceX96 ? tickHi : tickLow; + if (tickLow == tickHi) { + tick = tickHi; + } else { + uint160 sqrtRatioAtTickHi = getSqrtRatioAtTick(tickHi); + assembly { + tick := sub(tickHi, gt(sqrtRatioAtTickHi, sqrtPriceX96)) + } + } } } diff --git a/src/UnsafeMath.sol b/src/UnsafeMath.sol index 1b5391f..bb6dce3 100644 --- a/src/UnsafeMath.sol +++ b/src/UnsafeMath.sol @@ -40,7 +40,7 @@ library UnsafeMath { uint256 y ) internal pure returns (uint256 z) { assembly { - z := add(iszero(iszero(mod(x, y))), div(x, y)) + z := add(div(x, y), gt(mod(x, y), 0)) } } } diff --git a/test/SwapMath.t.sol b/test/SwapMath.t.sol index ce7f7de..f7a91ea 100644 --- a/test/SwapMath.t.sol +++ b/test/SwapMath.t.sol @@ -107,9 +107,9 @@ contract SwapMathTest is BaseTest { feePips ); assertEq(sqrtRatioNextX96, ogSqrtRatioNextX96); - assertEq(amountIn, ogAmountIn); + // The fee amount invariant is forgone but the total amount in and out should be the same. + assertEq(amountIn + feeAmount, ogAmountIn + ogFeeAmount); assertEq(amountOut, ogAmountOut); - assertEq(feeAmount, ogFeeAmount); } catch (bytes memory) { vm.expectRevert(); wrapper.computeSwapStep( diff --git a/test/TickBitmap.t.sol b/test/TickBitmap.t.sol index 81f2794..6cc4f40 100644 --- a/test/TickBitmap.t.sol +++ b/test/TickBitmap.t.sol @@ -40,6 +40,18 @@ contract TickBitmapTest is BaseTest { makeOriginalLibrary(address(ogWrapper), "TickBitmapTest"); } + function testFuzz_Position(int24 tick) public { + int16 wordPos; + uint8 bitPos; + assembly { + // signed arithmetic shift right + wordPos := sar(8, tick) + bitPos := and(tick, 255) + } + assertEq(int256(wordPos), tick >> 8); + assertEq(bitPos, uint8(int8(tick % 256))); + } + function testFuzz_Compress(int24 tick, int24 _tickSpacing) public { _tickSpacing = int24(bound(_tickSpacing, 1, 200)); int24 compressed = tick / _tickSpacing; diff --git a/yarn.lock b/yarn.lock index 114269d..eadd533 100644 --- a/yarn.lock +++ b/yarn.lock @@ -1,2649 +1,2649 @@ -# THIS IS AN AUTOGENERATED FILE. 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