{
    "Function": "mulDiv",
    "File": "contracts/libraries/UniswapV3OracleLibrary/FullMath.sol",
    "Parent Contracts": [],
    "High-Level Calls": [],
    "Internal Calls": [
        "mulmod(uint256,uint256,uint256)",
        "require(bool)",
        "require(bool)",
        "mulmod(uint256,uint256,uint256)"
    ],
    "Library Calls": [],
    "Low-Level Calls": [],
    "Code": "function mulDiv(\n        uint256 a,\n        uint256 b,\n        uint256 denominator\n    ) internal pure returns (uint256 result) {\n        // 512-bit multiply [prod1 prod0] = a * b\n        // Compute the product mod 2**256 and mod 2**256 - 1\n        // then use the Chinese Remainder Theorem to reconstruct\n        // the 512 bit result. The result is stored in two 256\n        // variables such that product = prod1 * 2**256 + prod0\n        uint256 prod0; // Least significant 256 bits of the product\n        uint256 prod1; // Most significant 256 bits of the product\n        assembly {\n            let mm := mulmod(a, b, not(0))\n            prod0 := mul(a, b)\n            prod1 := sub(sub(mm, prod0), lt(mm, prod0))\n        }\n\n        // Handle non-overflow cases, 256 by 256 division\n        if (prod1 == 0) {\n            require(denominator > 0);\n            assembly {\n                result := div(prod0, denominator)\n            }\n            return result;\n        }\n\n        // Make sure the result is less than 2**256.\n        // Also prevents denominator == 0\n        require(denominator > prod1);\n\n        ///////////////////////////////////////////////\n        // 512 by 256 division.\n        ///////////////////////////////////////////////\n\n        // Make division exact by subtracting the remainder from [prod1 prod0]\n        // Compute remainder using mulmod\n        uint256 remainder;\n        assembly {\n            remainder := mulmod(a, b, denominator)\n        }\n        // Subtract 256 bit number from 512 bit number\n        assembly {\n            prod1 := sub(prod1, gt(remainder, prod0))\n            prod0 := sub(prod0, remainder)\n        }\n\n        // Factor powers of two out of denominator\n        // Compute largest power of two divisor of denominator.\n        // Always >= 1.\n        uint256 twos = uint256(-int256(denominator) & int256(denominator));\n        // Divide denominator by power of two\n        assembly {\n            denominator := div(denominator, twos)\n        }\n\n        // Divide [prod1 prod0] by the factors of two\n        assembly {\n            prod0 := div(prod0, twos)\n        }\n        // Shift in bits from prod1 into prod0. For this we need\n        // to flip `twos` such that it is 2**256 / twos.\n        // If twos is zero, then it becomes one\n        assembly {\n            twos := add(div(sub(0, twos), twos), 1)\n        }\n        prod0 |= prod1 * twos;\n\n        // Invert denominator mod 2**256\n        // Now that denominator is an odd number, it has an inverse\n        // modulo 2**256 such that denominator * inv = 1 mod 2**256.\n        // Compute the inverse by starting with a seed that is correct\n        // correct for four bits. That is, denominator * inv = 1 mod 2**4\n        uint256 inv = (3 * denominator) ^ 2;\n        // Now use Newton-Raphson iteration to improve the precision.\n        // Thanks to Hensel's lifting lemma, this also works in modular\n        // arithmetic, doubling the correct bits in each step.\n        inv *= 2 - denominator * inv; // inverse mod 2**8\n        inv *= 2 - denominator * inv; // inverse mod 2**16\n        inv *= 2 - denominator * inv; // inverse mod 2**32\n        inv *= 2 - denominator * inv; // inverse mod 2**64\n        inv *= 2 - denominator * inv; // inverse mod 2**128\n        inv *= 2 - denominator * inv; // inverse mod 2**256\n\n        // Because the division is now exact we can divide by multiplying\n        // with the modular inverse of denominator. This will give us the\n        // correct result modulo 2**256. Since the precoditions guarantee\n        // that the outcome is less than 2**256, this is the final result.\n        // We don't need to compute the high bits of the result and prod1\n        // is no longer required.\n        result = prod0 * inv;\n        return result;\n    }"
}