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Credit-Card-System-smartcon.../build/contracts/Math.json
snsd0805 9bd872d7d4
feat: On Chain ERC721
2023-06-04 19:59:46 +08:00

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{
"contractName": "Math",
"abi": [],
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"source": "// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts (last updated v4.9.0) (utils/math/Math.sol)\n\npragma solidity ^0.8.0;\n\n/**\n * @dev Standard math utilities missing in the Solidity language.\n */\nlibrary Math {\n enum Rounding {\n Down, // Toward negative infinity\n Up, // Toward infinity\n Zero // Toward zero\n }\n\n /**\n * @dev Returns the largest of two numbers.\n */\n function max(uint256 a, uint256 b) internal pure returns (uint256) {\n return a > b ? a : b;\n }\n\n /**\n * @dev Returns the smallest of two numbers.\n */\n function min(uint256 a, uint256 b) internal pure returns (uint256) {\n return a < b ? a : b;\n }\n\n /**\n * @dev Returns the average of two numbers. The result is rounded towards\n * zero.\n */\n function average(uint256 a, uint256 b) internal pure returns (uint256) {\n // (a + b) / 2 can overflow.\n return (a & b) + (a ^ b) / 2;\n }\n\n /**\n * @dev Returns the ceiling of the division of two numbers.\n *\n * This differs from standard division with `/` in that it rounds up instead\n * of rounding down.\n */\n function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {\n // (a + b - 1) / b can overflow on addition, so we distribute.\n return a == 0 ? 0 : (a - 1) / b + 1;\n }\n\n /**\n * @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or denominator == 0\n * @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv)\n * with further edits by Uniswap Labs also under MIT license.\n */\n function mulDiv(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 result) {\n unchecked {\n // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use\n // use the Chinese Remainder Theorem to reconstruct 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(x, y, not(0))\n prod0 := mul(x, y)\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 // Solidity will revert if denominator == 0, unlike the div opcode on its own.\n // The surrounding unchecked block does not change this fact.\n // See https://docs.soliditylang.org/en/latest/control-structures.html#checked-or-unchecked-arithmetic.\n return prod0 / denominator;\n }\n\n // Make sure the result is less than 2^256. Also prevents denominator == 0.\n require(denominator > prod1, \"Math: mulDiv overflow\");\n\n ///////////////////////////////////////////////\n // 512 by 256 division.\n ///////////////////////////////////////////////\n\n // Make division exact by subtracting the remainder from [prod1 prod0].\n uint256 remainder;\n assembly {\n // Compute remainder using mulmod.\n remainder := mulmod(x, y, denominator)\n\n // Subtract 256 bit number from 512 bit number.\n prod1 := sub(prod1, gt(remainder, prod0))\n prod0 := sub(prod0, remainder)\n }\n\n // Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.\n // See https://cs.stackexchange.com/q/138556/92363.\n\n // Does not overflow because the denominator cannot be zero at this stage in the function.\n uint256 twos = denominator & (~denominator + 1);\n assembly {\n // Divide denominator by twos.\n denominator := div(denominator, twos)\n\n // Divide [prod1 prod0] by twos.\n prod0 := div(prod0, twos)\n\n // Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.\n twos := add(div(sub(0, twos), twos), 1)\n }\n\n // Shift in bits from prod1 into prod0.\n prod0 |= prod1 * twos;\n\n // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such\n // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for\n // four bits. That is, denominator * inv = 1 mod 2^4.\n uint256 inverse = (3 * denominator) ^ 2;\n\n // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works\n // in modular arithmetic, doubling the correct bits in each step.\n inverse *= 2 - denominator * inverse; // inverse mod 2^8\n inverse *= 2 - denominator * inverse; // inverse mod 2^16\n inverse *= 2 - denominator * inverse; // inverse mod 2^32\n inverse *= 2 - denominator * inverse; // inverse mod 2^64\n inverse *= 2 - denominator * inverse; // inverse mod 2^128\n inverse *= 2 - denominator * inverse; // inverse mod 2^256\n\n // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.\n // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is\n // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1\n // is no longer required.\n result = prod0 * inverse;\n return result;\n }\n }\n\n /**\n * @notice Calculates x * y / denominator with full precision, following the selected rounding direction.\n */\n function mulDiv(uint256 x, uint256 y, uint256 denominator, Rounding rounding) internal pure returns (uint256) {\n uint256 result = mulDiv(x, y, denominator);\n if (rounding == Rounding.Up && mulmod(x, y, denominator) > 0) {\n result += 1;\n }\n return result;\n }\n\n /**\n * @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded down.\n *\n * Inspired by Henry S. 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Newton's method converges quadratically (precision doubles at\n // every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision\n // into the expected uint128 result.\n unchecked {\n result = (result + a / result) >> 1;\n result = (result + a / result) >> 1;\n result = (result + a / result) >> 1;\n result = (result + a / result) >> 1;\n result = (result + a / result) >> 1;\n result = (result + a / result) >> 1;\n result = (result + a / result) >> 1;\n return min(result, a / result);\n }\n }\n\n /**\n * @notice Calculates sqrt(a), following the selected rounding direction.\n */\n function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {\n unchecked {\n uint256 result = sqrt(a);\n return result + (rounding == Rounding.Up && result * result < a ? 1 : 0);\n }\n }\n\n /**\n * @dev Return the log in base 2, rounded down, of a positive value.\n * Returns 0 if given 0.\n */\n function log2(uint256 value) internal pure returns (uint256) {\n uint256 result = 0;\n unchecked {\n if (value >> 128 > 0) {\n value >>= 128;\n result += 128;\n }\n if (value >> 64 > 0) {\n value >>= 64;\n result += 64;\n }\n if (value >> 32 > 0) {\n value >>= 32;\n result += 32;\n }\n if (value >> 16 > 0) {\n value >>= 16;\n result += 16;\n }\n if (value >> 8 > 0) {\n value >>= 8;\n result += 8;\n }\n if (value >> 4 > 0) {\n value >>= 4;\n result += 4;\n }\n if (value >> 2 > 0) {\n value >>= 2;\n result += 2;\n }\n if (value >> 1 > 0) {\n result += 1;\n }\n }\n return result;\n }\n\n /**\n * @dev Return the log in base 2, following the selected rounding direction, of a positive value.\n * Returns 0 if given 0.\n */\n function log2(uint256 value, Rounding rounding) internal pure returns (uint256) {\n unchecked {\n uint256 result = log2(value);\n return result + (rounding == Rounding.Up && 1 << result < value ? 1 : 0);\n }\n }\n\n /**\n * @dev Return the log in base 10, rounded down, of a positive value.\n * Returns 0 if given 0.\n */\n function log10(uint256 value) internal pure returns (uint256) {\n uint256 result = 0;\n unchecked {\n if (value >= 10 ** 64) {\n value /= 10 ** 64;\n result += 64;\n }\n if (value >= 10 ** 32) {\n value /= 10 ** 32;\n result += 32;\n }\n if (value >= 10 ** 16) {\n value /= 10 ** 16;\n result += 16;\n }\n if (value >= 10 ** 8) {\n value /= 10 ** 8;\n result += 8;\n }\n if (value >= 10 ** 4) {\n value /= 10 ** 4;\n result += 4;\n }\n if (value >= 10 ** 2) {\n value /= 10 ** 2;\n result += 2;\n }\n if (value >= 10 ** 1) {\n result += 1;\n }\n }\n return result;\n }\n\n /**\n * @dev Return the log in base 10, following the selected rounding direction, of a positive value.\n * Returns 0 if given 0.\n */\n function log10(uint256 value, Rounding rounding) internal pure returns (uint256) {\n unchecked {\n uint256 result = log10(value);\n return result + (rounding == Rounding.Up && 10 ** result < value ? 1 : 0);\n }\n }\n\n /**\n * @dev Return the log in base 256, rounded down, of a positive value.\n * Returns 0 if given 0.\n *\n * Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.\n */\n function log256(uint256 value) internal pure returns (uint256) {\n uint256 result = 0;\n unchecked {\n if (value >> 128 > 0) {\n value >>= 128;\n result += 16;\n }\n if (value >> 64 > 0) {\n value >>= 64;\n result += 8;\n }\n if (value >> 32 > 0) {\n value >>= 32;\n result += 4;\n }\n if (value >> 16 > 0) {\n value >>= 16;\n result += 2;\n }\n if (value >> 8 > 0) {\n result += 1;\n }\n }\n return result;\n }\n\n /**\n * @dev Return the log in base 256, following the selected rounding direction, of a positive value.\n * Returns 0 if given 0.\n */\n function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {\n unchecked {\n uint256 result = log256(value);\n return result + (rounding == Rounding.Up && 1 << (result << 3) < value ? 1 : 0);\n }\n }\n}\n",
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"userdoc": {
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}
}
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