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* issue #1 * issue 2 * 0 tvl case * update mainnet_chains
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// SPDX-License-Identifier: MIT | ||
pragma solidity ^0.8.20; | ||
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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) { | ||
// diff: original lib works under 0.7.6 with overflows enabled | ||
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. | ||
// diff: original uint256 twos = -denominator & denominator; | ||
uint256 twos = uint256(-int256(denominator)) & 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) { | ||
// diff: original lib works under 0.7.6 with overflows enabled | ||
unchecked { | ||
result = mulDiv(a, b, denominator); | ||
if (mulmod(a, b, denominator) > 0) { | ||
require(result < type(uint256).max); | ||
result++; | ||
} | ||
} | ||
} | ||
} |
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