{
    "Function": "mulDiv",
    "File": "contracts/libraries/Math.sol",
    "Parent Contracts": [],
    "High-Level Calls": [],
    "Internal Calls": [
        "require(bool)",
        "mulmod(uint256,uint256,uint256)",
        "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        unchecked {\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 (\"memory-safe\") {\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 (\"memory-safe\") {\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 (\"memory-safe\") {\n                remainder := mulmod(a, b, denominator)\n            }\n            // Subtract 256 bit number from 512 bit number\n            assembly (\"memory-safe\") {\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 = (0 - denominator) & denominator;\n            // Divide denominator by power of two\n            assembly (\"memory-safe\") {\n                denominator := div(denominator, twos)\n            }\n\n            // Divide [prod1 prod0] by the factors of two\n            assembly (\"memory-safe\") {\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 (\"memory-safe\") {\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        }\n    }"
}