moonwalkerswap-v1-core

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Throws if result overflows a uint256 or denominator == 0\n /// @param a The multiplicand\n /// @param b The multiplier\n /// @param denominator The divisor\n /// @return result The 256-bit result\n /// @dev Credit to Remco Bloemen under MIT license https://xn--2-umb.com/21/muldiv\n 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 = -denominator & 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. 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