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This can easily result\n * in bugs, because programmers usually assume that an overflow raises an\n * error, which is the standard behavior in high level programming languages.\n * `SafeMath` restores this intuition by reverting the transaction when an\n * operation overflows.\n *\n * Using this library instead of the unchecked operations eliminates an entire\n * class of bugs, so it's recommended to use it always.\n */\nlibrary SafeMath {\n /**\n * @dev Returns the addition of two unsigned integers, reverting on\n * overflow.\n *\n * Counterpart to Solidity's `+` operator.\n *\n * Requirements:\n *\n * - Addition cannot overflow.\n */\n function add(uint256 a, uint256 b) internal pure returns (uint256) {\n uint256 c = a + b;\n require(c >= a, \"SafeMath: addition overflow\");\n\n return c;\n }\n\n /**\n * @dev Returns the subtraction of two unsigned integers, reverting on\n * overflow (when the result is negative).\n *\n * Counterpart to Solidity's `-` operator.\n *\n * Requirements:\n *\n * - Subtraction cannot overflow.\n */\n function sub(uint256 a, uint256 b) internal pure returns (uint256) {\n return sub(a, b, \"SafeMath: subtraction overflow\");\n }\n\n /**\n * @dev Returns the subtraction of two unsigned integers, reverting with custom message on\n * overflow (when the result is negative).\n *\n * Counterpart to Solidity's `-` operator.\n *\n * Requirements:\n *\n * - Subtraction cannot overflow.\n */\n function sub(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {\n require(b <= a, errorMessage);\n uint256 c = a - b;\n\n return c;\n }\n\n /**\n * @dev Returns the multiplication of two unsigned integers, reverting on\n * overflow.\n *\n * Counterpart to Solidity's `*` operator.\n *\n * Requirements:\n *\n * - Multiplication cannot overflow.\n */\n function mul(uint256 a, uint256 b) internal pure returns (uint256) {\n // Gas optimization: this is cheaper than requiring 'a' not being zero, but the\n // benefit is lost if 'b' is also tested.\n // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522\n if (a == 0) {\n return 0;\n }\n\n uint256 c = a * b;\n require(c / a == b, \"SafeMath: multiplication overflow\");\n\n return c;\n }\n\n /**\n * @dev Returns the integer division of two unsigned integers. 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"nodeType": "Return", "src": "2632:8:12" } ] }, "documentation": { "id": 2631, "nodeType": "StructuredDocumentation", "src": "1947:236:12", "text": " @dev Returns the multiplication of two unsigned integers, reverting on\n overflow.\n Counterpart to Solidity's `*` operator.\n Requirements:\n - Multiplication cannot overflow." }, "id": 2665, "implemented": true, "kind": "function", "modifiers": [], "name": "mul", "nodeType": "FunctionDefinition", "overrides": null, "parameters": { "id": 2636, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 2633, "mutability": "mutable", "name": "a", "nodeType": "VariableDeclaration", "overrides": null, "scope": 2665, "src": "2201:9:12", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 2632, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "2201:7:12", "typeDescriptions": { "typeIdentifier": "t_uint256", 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Reverts on\n division by zero. The result is rounded towards zero.\n Counterpart to Solidity's `/` operator. Note: this function uses a\n `revert` opcode (which leaves remaining gas untouched) while Solidity\n uses an invalid opcode to revert (consuming all remaining gas).\n Requirements:\n - The divisor cannot be zero." }, "id": 2682, "implemented": true, "kind": "function", "modifiers": [], "name": "div", "nodeType": "FunctionDefinition", "overrides": null, "parameters": { "id": 2671, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 2668, "mutability": "mutable", "name": "a", "nodeType": "VariableDeclaration", "overrides": null, "scope": 2682, "src": "3122:9:12", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 2667, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "3122:7:12", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": null, "visibility": "internal" }, { "constant": false, "id": 2670, "mutability": 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This function uses a `revert`\n opcode (which leaves remaining gas untouched) while Solidity uses an\n invalid opcode to revert (consuming all remaining gas).\n Requirements:\n - The divisor cannot be zero." }, "id": 2727, "implemented": true, "kind": "function", "modifiers": [], "name": "mod", "nodeType": "FunctionDefinition", "overrides": null, "parameters": { "id": 2716, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 2713, "mutability": "mutable", "name": "a", "nodeType": "VariableDeclaration", "overrides": null, "scope": 2727, "src": "4457:9:12", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 2712, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "4457:7:12", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": null, "visibility": "internal" }, { "constant": false, "id": 2715, "mutability": "mutable", 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(unsigned integer modulo),\n Reverts with custom message when dividing by zero.\n Counterpart to Solidity's `%` operator. This function uses a `revert`\n opcode (which leaves remaining gas untouched) while Solidity uses an\n invalid opcode to revert (consuming all remaining gas).\n Requirements:\n - The divisor cannot be zero." }, "id": 2751, "implemented": true, "kind": "function", "modifiers": [], "name": "mod", "nodeType": "FunctionDefinition", "overrides": null, "parameters": { "id": 2735, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 2730, "mutability": "mutable", "name": "a", "nodeType": "VariableDeclaration", "overrides": null, "scope": 2751, "src": "5056:9:12", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 2729, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "5056:7:12", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": null, "visibility": "internal" }, { "constant": false, "id": 2732, "mutability": "mutable", "name": "b", "nodeType": "VariableDeclaration", "overrides": null, "scope": 2751, "src": "5067:9:12", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 2731, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "5067:7:12", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": null, "visibility": "internal" }, { "constant": false, "id": 2734, "mutability": "mutable", "name": "errorMessage", "nodeType": "VariableDeclaration", "overrides": null, "scope": 2751, "src": "5078:26:12", "stateVariable": false, "storageLocation": "memory", "typeDescriptions": { "typeIdentifier": "t_string_memory_ptr", "typeString": "string" }, "typeName": { "id": 2733, "name": "string", "nodeType": "ElementaryTypeName", "src": "5078:6:12", "typeDescriptions": { "typeIdentifier": "t_string_storage_ptr", "typeString": "string" } }, "value": null, "visibility": "internal" } ], "src": "5055:50:12" }, "returnParameters": { "id": 2738, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 2737, "mutability": "mutable", "name": "", "nodeType": "VariableDeclaration", "overrides": null, "scope": 2751, "src": "5129:7:12", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 2736, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "5129:7:12", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": null, "visibility": "internal" } ], "src": "5128:9:12" }, "scope": 2752, "src": "5043:163:12", "stateMutability": "pure", "virtual": false, "visibility": "internal" } ], "scope": 2753, "src": "630:4578:12" } ], "src": "33:5176:12" }, "compiler": { "name": "solc", "version": "0.6.12+commit.27d51765.Emscripten.clang" }, "networks": {}, "schemaVersion": "3.3.2", "updatedAt": "2021-03-04T12:24:19.871Z", "devdoc": { "details": "Wrappers over Solidity's arithmetic operations with added overflow checks. Arithmetic operations in Solidity wrap on overflow. This can easily result in bugs, because programmers usually assume that an overflow raises an error, which is the standard behavior in high level programming languages. `SafeMath` restores this intuition by reverting the transaction when an operation overflows. Using this library instead of the unchecked operations eliminates an entire class of bugs, so it's recommended to use it always.", "kind": "dev", "methods": {}, "version": 1 }, "userdoc": { "kind": "user", "methods": {}, "version": 1 } }