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Merge pull request #157 from usmfum/feat/uniswap-v3-solidity-0.8-hack
Feat/uniswap v3 solidity 0.8 hack
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| Original file line number | Diff line number | Diff line change |
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| // SPDX-License-Identifier: MIT | ||
| pragma solidity >=0.4.0; | ||
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| /// @title Contains 512-bit math functions | ||
| /// @notice Facilitates multiplication and division that can have overflow of an intermediate value without any loss of precision | ||
| /// @dev Handles "phantom overflow" i.e., allows multiplication and division where an intermediate value overflows 256 bits | ||
| library FullMath { | ||
| /// @notice Calculates floor(a×b÷denominator) with full precision. Throws if result overflows a uint256 or denominator == 0 | ||
| /// @param a The multiplicand | ||
| /// @param b The multiplier | ||
| /// @param denominator The divisor | ||
| /// @return result The 256-bit result | ||
| /// @dev Credit to Remco Bloemen under MIT license https://xn--2-umb.com/21/muldiv | ||
| function mulDiv( | ||
| uint256 a, | ||
| uint256 b, | ||
| uint256 denominator | ||
| ) internal pure returns (uint256 result) { | ||
| unchecked { | ||
| // 512-bit multiply [prod1 prod0] = a * b | ||
| // Compute the product mod 2**256 and mod 2**256 - 1 | ||
| // then use the Chinese Remainder Theorem to reconstruct | ||
| // the 512 bit result. The result is stored in two 256 | ||
| // variables such that product = prod1 * 2**256 + prod0 | ||
| uint256 prod0; // Least significant 256 bits of the product | ||
| uint256 prod1; // Most significant 256 bits of the product | ||
| assembly { | ||
| let mm := mulmod(a, b, not(0)) | ||
| prod0 := mul(a, b) | ||
| prod1 := sub(sub(mm, prod0), lt(mm, prod0)) | ||
| } | ||
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| // Handle non-overflow cases, 256 by 256 division | ||
| if (prod1 == 0) { | ||
| require(denominator > 0); | ||
| assembly { | ||
| result := div(prod0, denominator) | ||
| } | ||
| return result; | ||
| } | ||
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| // Make sure the result is less than 2**256. | ||
| // Also prevents denominator == 0 | ||
| require(denominator > prod1); | ||
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| /////////////////////////////////////////////// | ||
| // 512 by 256 division. | ||
| /////////////////////////////////////////////// | ||
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| // Make division exact by subtracting the remainder from [prod1 prod0] | ||
| // Compute remainder using mulmod | ||
| uint256 remainder; | ||
| assembly { | ||
| remainder := mulmod(a, b, denominator) | ||
| } | ||
| // Subtract 256 bit number from 512 bit number | ||
| assembly { | ||
| prod1 := sub(prod1, gt(remainder, prod0)) | ||
| prod0 := sub(prod0, remainder) | ||
| } | ||
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| // Factor powers of two out of denominator | ||
| // Compute largest power of two divisor of denominator. | ||
| // Always >= 1. | ||
| uint256 twos = (~denominator + 1) & denominator; | ||
| // Divide denominator by power of two | ||
| assembly { | ||
| denominator := div(denominator, twos) | ||
| } | ||
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| // Divide [prod1 prod0] by the factors of two | ||
| assembly { | ||
| prod0 := div(prod0, twos) | ||
| } | ||
| // Shift in bits from prod1 into prod0. For this we need | ||
| // to flip `twos` such that it is 2**256 / twos. | ||
| // If twos is zero, then it becomes one | ||
| assembly { | ||
| twos := add(div(sub(0, twos), twos), 1) | ||
| } | ||
| prod0 |= prod1 * twos; | ||
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| // Invert denominator mod 2**256 | ||
| // Now that denominator is an odd number, it has an inverse | ||
| // modulo 2**256 such that denominator * inv = 1 mod 2**256. | ||
| // Compute the inverse by starting with a seed that is correct | ||
| // correct for four bits. That is, denominator * inv = 1 mod 2**4 | ||
| uint256 inv = (3 * denominator) ^ 2; | ||
| // Now use Newton-Raphson iteration to improve the precision. | ||
| // Thanks to Hensel's lifting lemma, this also works in modular | ||
| // arithmetic, doubling the correct bits in each step. | ||
| inv *= 2 - denominator * inv; // inverse mod 2**8 | ||
| inv *= 2 - denominator * inv; // inverse mod 2**16 | ||
| inv *= 2 - denominator * inv; // inverse mod 2**32 | ||
| inv *= 2 - denominator * inv; // inverse mod 2**64 | ||
| inv *= 2 - denominator * inv; // inverse mod 2**128 | ||
| inv *= 2 - denominator * inv; // inverse mod 2**256 | ||
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| // Because the division is now exact we can divide by multiplying | ||
| // with the modular inverse of denominator. This will give us the | ||
| // correct result modulo 2**256. Since the precoditions guarantee | ||
| // that the outcome is less than 2**256, this is the final result. | ||
| // We don't need to compute the high bits of the result and prod1 | ||
| // is no longer required. | ||
| result = prod0 * inv; | ||
| return result; | ||
| } | ||
| } | ||
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| /// @notice Calculates ceil(a×b÷denominator) with full precision. Throws if result overflows a uint256 or denominator == 0 | ||
| /// @param a The multiplicand | ||
| /// @param b The multiplier | ||
| /// @param denominator The divisor | ||
| /// @return result The 256-bit result | ||
| function mulDivRoundingUp( | ||
| uint256 a, | ||
| uint256 b, | ||
| uint256 denominator | ||
| ) internal pure returns (uint256 result) { | ||
| result = mulDiv(a, b, denominator); | ||
| if (mulmod(a, b, denominator) > 0) { | ||
| require(result < type(uint256).max); | ||
| result++; | ||
| } | ||
| } | ||
| } |
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