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"Identifier", "overloadedDeclarations": [], "referencedDeclaration": 15944, "src": "5094:7:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "5080:21:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "5076:25:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "5065:36:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 15999, "nodeType": "ExpressionStatement", "src": "5065:36:5" }, { "expression": { "id": 16004, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 16000, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 15898, "src": "5535:6:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 16003, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 16001, "name": "prod0", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 15901, "src": "5544:5:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "*", "rightExpression": { "id": 16002, "name": "inverse", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 15944, "src": "5552:7:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "5544:15:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "5535:24:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 16005, "nodeType": "ExpressionStatement", "src": "5535:24:5" }, { "expression": { "id": 16006, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 15898, "src": "5580:6:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 15899, "id": 16007, "nodeType": "Return", "src": "5573:13:5" } ] } ] }, "documentation": { "id": 15889, "nodeType": "StructuredDocumentation", "src": "1368:305:5", "text": " @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." }, "id": 16010, "implemented": true, "kind": "function", "modifiers": [], "name": "mulDiv", "nameLocation": "1687:6:5", "nodeType": "FunctionDefinition", "parameters": { "id": 15896, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 15891, "mutability": "mutable", "name": "x", "nameLocation": "1711:1:5", "nodeType": "VariableDeclaration", "scope": 16010, "src": "1703:9:5", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 15890, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "1703:7:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 15893, "mutability": "mutable", "name": "y", "nameLocation": "1730:1:5", "nodeType": "VariableDeclaration", "scope": 16010, "src": "1722:9:5", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 15892, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "1722:7:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 15895, "mutability": "mutable", "name": "denominator", "nameLocation": "1749:11:5", "nodeType": "VariableDeclaration", "scope": 16010, "src": "1741:19:5", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 15894, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "1741:7:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "1693:73:5" }, "returnParameters": { "id": 15899, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 15898, "mutability": "mutable", "name": "result", "nameLocation": "1798:6:5", "nodeType": "VariableDeclaration", "scope": 16010, "src": "1790:14:5", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 15897, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "1790:7:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "1789:16:5" }, "scope": 16662, "src": "1678:3925:5", "stateMutability": "pure", "virtual": false, "visibility": "internal" }, { "body": { "id": 16053, "nodeType": "Block", "src": "5883:189:5", "statements": [ { "assignments": [ 16026 ], "declarations": [ { "constant": false, "id": 16026, "mutability": "mutable", "name": "result", "nameLocation": "5901:6:5", "nodeType": "VariableDeclaration", "scope": 16053, "src": "5893:14:5", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 16025, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "5893:7:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "id": 16032, "initialValue": { "arguments": [ { "id": 16028, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16013, "src": "5917:1:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 16029, "name": "y", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16015, "src": "5920:1:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 16030, "name": "denominator", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16017, "src": "5923:11:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 16027, "name": "mulDiv", "nodeType": "Identifier", "overloadedDeclarations": [ 16010, 16054 ], "referencedDeclaration": 16010, "src": "5910:6:5", "typeDescriptions": { "typeIdentifier": "t_function_internal_pure$_t_uint256_$_t_uint256_$_t_uint256_$returns$_t_uint256_$", "typeString": "function (uint256,uint256,uint256) pure returns (uint256)" } }, "id": 16031, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "nameLocations": [], "names": [], "nodeType": "FunctionCall", "src": "5910:25:5", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "VariableDeclarationStatement", "src": "5893:42:5" }, { "condition": { "commonType": { "typeIdentifier": "t_bool", "typeString": "bool" }, "id": 16044, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_enum$_Rounding_$15804", "typeString": "enum MathUpgradeable.Rounding" }, "id": 16036, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 16033, "name": "rounding", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16020, "src": "5949:8:5", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$15804", "typeString": "enum MathUpgradeable.Rounding" } }, "nodeType": "BinaryOperation", "operator": "==", "rightExpression": { "expression": { "id": 16034, "name": "Rounding", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 15804, "src": "5961:8:5", "typeDescriptions": { "typeIdentifier": "t_type$_t_enum$_Rounding_$15804_$", "typeString": "type(enum MathUpgradeable.Rounding)" } }, "id": 16035, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "memberLocation": "5970:2:5", "memberName": "Up", "nodeType": "MemberAccess", "referencedDeclaration": 15802, "src": "5961:11:5", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$15804", "typeString": "enum MathUpgradeable.Rounding" } }, "src": "5949:23:5", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "nodeType": "BinaryOperation", "operator": "&&", "rightExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 16043, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "arguments": [ { "id": 16038, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16013, "src": "5983:1:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 16039, "name": "y", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16015, "src": "5986:1:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 16040, "name": "denominator", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16017, "src": "5989:11:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 16037, "name": "mulmod", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": -16, "src": "5976:6:5", "typeDescriptions": { "typeIdentifier": "t_function_mulmod_pure$_t_uint256_$_t_uint256_$_t_uint256_$returns$_t_uint256_$", "typeString": "function (uint256,uint256,uint256) pure returns (uint256)" } }, "id": 16041, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "nameLocations": [], "names": [], "nodeType": "FunctionCall", "src": "5976:25:5", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 16042, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "6004:1:5", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "5976:29:5", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "src": "5949:56:5", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" 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"src": "6021:11:5" } ] } }, { "expression": { "id": 16051, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16026, "src": "6059:6:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 16024, "id": 16052, "nodeType": "Return", "src": "6052:13:5" } ] }, "documentation": { "id": 16011, "nodeType": "StructuredDocumentation", "src": "5609:121:5", "text": " @notice Calculates x * y / denominator with full precision, following the selected rounding direction." }, "id": 16054, "implemented": true, "kind": "function", "modifiers": [], "name": "mulDiv", "nameLocation": "5744:6:5", "nodeType": "FunctionDefinition", "parameters": { "id": 16021, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 16013, "mutability": "mutable", "name": "x", "nameLocation": "5768:1:5", "nodeType": "VariableDeclaration", "scope": 16054, "src": "5760:9:5", "stateVariable": false, 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"typeString": "uint256" } }, "nodeType": "VariableDeclarationStatement", "src": "9644:28:5" }, { "expression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 16366, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 16351, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16346, "src": "9693:6:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "+", "rightExpression": { "components": [ { "condition": { "commonType": { "typeIdentifier": "t_bool", "typeString": "bool" }, "id": 16361, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_enum$_Rounding_$15804", "typeString": "enum MathUpgradeable.Rounding" }, "id": 16355, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 16352, "name": "rounding", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16340, "src": "9703:8:5", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$15804", "typeString": "enum MathUpgradeable.Rounding" } }, "nodeType": "BinaryOperation", "operator": "==", "rightExpression": { "expression": { "id": 16353, "name": "Rounding", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 15804, "src": "9715:8:5", "typeDescriptions": { "typeIdentifier": "t_type$_t_enum$_Rounding_$15804_$", "typeString": "type(enum MathUpgradeable.Rounding)" } }, "id": 16354, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "memberLocation": "9724:2:5", "memberName": "Up", "nodeType": "MemberAccess", "referencedDeclaration": 15802, "src": "9715:11:5", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$15804", "typeString": "enum MathUpgradeable.Rounding" } }, "src": "9703:23:5", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "nodeType": "BinaryOperation", "operator": "&&", "rightExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 16360, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 16358, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "hexValue": "31", "id": 16356, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "9730:1:5", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "nodeType": "BinaryOperation", "operator": "<<", "rightExpression": { "id": 16357, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16346, "src": "9735:6:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "9730:11:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "<", "rightExpression": { "id": 16359, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16337, "src": "9744:5:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "9730:19:5", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "src": "9703:46:5", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "falseExpression": { "hexValue": "30", "id": 16363, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "9756:1:5", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "id": 16364, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "Conditional", "src": "9703:54:5", "trueExpression": { "hexValue": "31", "id": 16362, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "9752:1:5", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "typeDescriptions": { "typeIdentifier": "t_uint8", "typeString": "uint8" } } ], "id": 16365, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "9702:56:5", "typeDescriptions": { "typeIdentifier": "t_uint8", "typeString": "uint8" } }, "src": "9693:65:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 16344, "id": 16367, "nodeType": "Return", "src": "9686:72:5" } ] } ] }, "documentation": { "id": 16335, "nodeType": "StructuredDocumentation", "src": "9383:142:5", "text": " @dev Return the log in base 2, following the selected rounding direction, of a positive value.\n Returns 0 if given 0." }, "id": 16370, "implemented": true, "kind": "function", "modifiers": [], "name": "log2", "nameLocation": "9539:4:5", "nodeType": "FunctionDefinition", "parameters": { "id": 16341, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 16337, "mutability": "mutable", "name": "value", "nameLocation": "9552:5:5", "nodeType": "VariableDeclaration", "scope": 16370, "src": "9544:13:5", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 16336, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "9544:7:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 16340, "mutability": "mutable", "name": "rounding", "nameLocation": "9568:8:5", "nodeType": "VariableDeclaration", "scope": 16370, "src": "9559:17:5", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$15804", "typeString": "enum MathUpgradeable.Rounding" }, "typeName": { "id": 16339, "nodeType": "UserDefinedTypeName", "pathNode": { "id": 16338, "name": "Rounding", "nameLocations": [ "9559:8:5" ], "nodeType": "IdentifierPath", "referencedDeclaration": 15804, "src": "9559:8:5" }, "referencedDeclaration": 15804, "src": "9559:8:5", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$15804", "typeString": "enum MathUpgradeable.Rounding" } }, "visibility": "internal" } ], "src": "9543:34:5" }, "returnParameters": { "id": 16344, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 16343, "mutability": "mutable", "name": "", "nameLocation": "-1:-1:-1", "nodeType": 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"name": "uint256", "nodeType": "ElementaryTypeName", "src": "9972:7:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "id": 16381, "initialValue": { "hexValue": "30", "id": 16380, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "9989:1:5", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "nodeType": "VariableDeclarationStatement", "src": "9972:18:5" }, { "id": 16495, "nodeType": "UncheckedBlock", "src": "10000:761:5", "statements": [ { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 16386, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 16382, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16373, "src": "10028:5:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "commonType": { "typeIdentifier": "t_rational_10000000000000000000000000000000000000000000000000000000000000000_by_1", "typeString": "int_const 1000...(57 digits omitted)...0000" }, "id": 16385, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 16383, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10037:2:5", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "3634", "id": 16384, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10041:2:5", 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"typeIdentifier": "t_rational_10000000000000000000000000000000000000000000000000000000000000000_by_1", "typeString": "int_const 1000...(57 digits omitted)...0000" }, "id": 16390, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 16388, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10072:2:5", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "3634", "id": 16389, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10076:2:5", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "10072:6:5", "typeDescriptions": { "typeIdentifier": "t_rational_10000000000000000000000000000000000000000000000000000000000000000_by_1", "typeString": "int_const 1000...(57 digits omitted)...0000" } }, "src": "10063:15:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 16392, "nodeType": "ExpressionStatement", "src": "10063:15:5" }, { "expression": { "id": 16395, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 16393, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16379, "src": "10096:6:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "3634", "id": 16394, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10106:2:5", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "10096:12:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 16396, "nodeType": "ExpressionStatement", "src": "10096:12:5" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 16403, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 16399, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16373, "src": "10140:5:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "commonType": { "typeIdentifier": "t_rational_100000000000000000000000000000000_by_1", "typeString": "int_const 1000...(25 digits omitted)...0000" }, "id": 16402, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 16400, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10149:2:5", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "3332", "id": 16401, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10153:2:5", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "10149:6:5", "typeDescriptions": { "typeIdentifier": "t_rational_100000000000000000000000000000000_by_1", "typeString": "int_const 1000...(25 digits omitted)...0000" } }, "src": "10140:15:5", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 16415, "nodeType": "IfStatement", "src": "10136:99:5", "trueBody": { "id": 16414, "nodeType": "Block", "src": "10157:78:5", "statements": [ { "expression": { "id": 16408, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 16404, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16373, "src": "10175:5:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "/=", "rightHandSide": { "commonType": { "typeIdentifier": "t_rational_100000000000000000000000000000000_by_1", "typeString": "int_const 1000...(25 digits omitted)...0000" }, "id": 16407, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 16405, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10184:2:5", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "3332", "id": 16406, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10188:2:5", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "10184:6:5", "typeDescriptions": { "typeIdentifier": "t_rational_100000000000000000000000000000000_by_1", "typeString": "int_const 1000...(25 digits omitted)...0000" } }, "src": "10175:15:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 16409, "nodeType": "ExpressionStatement", "src": "10175:15:5" }, { "expression": { "id": 16412, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 16410, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16379, "src": "10208:6:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "3332", "id": 16411, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10218:2:5", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "10208:12:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 16413, "nodeType": "ExpressionStatement", "src": "10208:12:5" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 16420, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 16416, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16373, "src": "10252:5:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "commonType": { "typeIdentifier": "t_rational_10000000000000000_by_1", "typeString": "int_const 10000000000000000" }, "id": 16419, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 16417, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10261:2:5", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "3136", "id": 16418, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10265:2:5", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "10261:6:5", "typeDescriptions": { "typeIdentifier": "t_rational_10000000000000000_by_1", "typeString": "int_const 10000000000000000" } }, "src": "10252:15:5", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 16432, "nodeType": "IfStatement", "src": "10248:99:5", "trueBody": { "id": 16431, "nodeType": "Block", "src": "10269:78:5", "statements": [ { "expression": { "id": 16425, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 16421, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16373, "src": "10287:5:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "/=", "rightHandSide": { "commonType": { "typeIdentifier": "t_rational_10000000000000000_by_1", "typeString": "int_const 10000000000000000" }, "id": 16424, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 16422, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10296:2:5", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "3136", "id": 16423, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10300:2:5", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "10296:6:5", "typeDescriptions": { "typeIdentifier": "t_rational_10000000000000000_by_1", "typeString": "int_const 10000000000000000" } }, "src": "10287:15:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 16426, "nodeType": "ExpressionStatement", "src": "10287:15:5" }, { "expression": { "id": 16429, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 16427, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16379, "src": "10320:6:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "3136", "id": 16428, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10330:2:5", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "10320:12:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 16430, "nodeType": "ExpressionStatement", "src": "10320:12:5" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 16437, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 16433, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16373, "src": "10364:5:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "commonType": { "typeIdentifier": "t_rational_100000000_by_1", "typeString": "int_const 100000000" }, "id": 16436, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 16434, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10373:2:5", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "38", "id": 16435, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10377:1:5", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "10373:5:5", "typeDescriptions": { "typeIdentifier": "t_rational_100000000_by_1", "typeString": "int_const 100000000" } }, "src": "10364:14:5", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 16449, "nodeType": "IfStatement", "src": "10360:96:5", "trueBody": { "id": 16448, "nodeType": "Block", "src": "10380:76:5", "statements": [ { "expression": { "id": 16442, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 16438, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16373, "src": "10398:5:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "/=", "rightHandSide": { "commonType": { "typeIdentifier": "t_rational_100000000_by_1", "typeString": "int_const 100000000" }, "id": 16441, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 16439, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10407:2:5", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "38", "id": 16440, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10411:1:5", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "10407:5:5", "typeDescriptions": { "typeIdentifier": "t_rational_100000000_by_1", "typeString": "int_const 100000000" } }, "src": "10398:14:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 16443, "nodeType": "ExpressionStatement", "src": "10398:14:5" }, { "expression": { "id": 16446, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 16444, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16379, "src": "10430:6:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "38", "id": 16445, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10440:1:5", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "10430:11:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 16447, "nodeType": "ExpressionStatement", "src": "10430:11:5" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 16454, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 16450, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16373, "src": "10473:5:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "commonType": { "typeIdentifier": "t_rational_10000_by_1", "typeString": "int_const 10000" }, "id": 16453, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 16451, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10482:2:5", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "34", "id": 16452, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10486:1:5", "typeDescriptions": { "typeIdentifier": "t_rational_4_by_1", "typeString": "int_const 4" }, "value": "4" }, "src": "10482:5:5", "typeDescriptions": { "typeIdentifier": "t_rational_10000_by_1", "typeString": "int_const 10000" } }, "src": "10473:14:5", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 16466, "nodeType": "IfStatement", "src": "10469:96:5", "trueBody": { "id": 16465, "nodeType": "Block", "src": "10489:76:5", "statements": [ { "expression": { "id": 16459, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 16455, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16373, "src": "10507:5:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "/=", "rightHandSide": { "commonType": { "typeIdentifier": "t_rational_10000_by_1", "typeString": "int_const 10000" }, "id": 16458, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 16456, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10516:2:5", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "34", "id": 16457, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10520:1:5", "typeDescriptions": { "typeIdentifier": "t_rational_4_by_1", "typeString": "int_const 4" }, "value": "4" }, "src": "10516:5:5", "typeDescriptions": { "typeIdentifier": "t_rational_10000_by_1", "typeString": "int_const 10000" } }, "src": "10507:14:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 16460, "nodeType": "ExpressionStatement", "src": "10507:14:5" }, { "expression": { "id": 16463, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 16461, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16379, "src": "10539:6:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "34", "id": 16462, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10549:1:5", "typeDescriptions": { "typeIdentifier": "t_rational_4_by_1", "typeString": "int_const 4" }, "value": "4" }, "src": "10539:11:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 16464, "nodeType": "ExpressionStatement", "src": "10539:11:5" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 16471, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 16467, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16373, "src": "10582:5:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "commonType": { "typeIdentifier": "t_rational_100_by_1", "typeString": "int_const 100" }, "id": 16470, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 16468, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10591:2:5", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "32", "id": 16469, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10595:1:5", "typeDescriptions": { "typeIdentifier": "t_rational_2_by_1", "typeString": "int_const 2" }, "value": "2" }, "src": "10591:5:5", "typeDescriptions": { "typeIdentifier": "t_rational_100_by_1", "typeString": "int_const 100" } }, "src": "10582:14:5", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 16483, "nodeType": "IfStatement", "src": "10578:96:5", "trueBody": { "id": 16482, "nodeType": "Block", "src": "10598:76:5", "statements": [ { "expression": { "id": 16476, 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"isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11726:2:5", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "11716:12:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 16570, "nodeType": "ExpressionStatement", "src": "11716:12:5" }, { "expression": { "id": 16573, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 16571, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16544, "src": "11746:6:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "38", "id": 16572, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11756:1:5", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "11746:11:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 16574, "nodeType": "ExpressionStatement", "src": "11746:11:5" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 16581, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 16579, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 16577, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16538, "src": "11789:5:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "3332", "id": 16578, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11798:2:5", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "11789:11:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 16580, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11803:1:5", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "11789:15:5", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 16591, "nodeType": "IfStatement", "src": "11785:95:5", "trueBody": { "id": 16590, "nodeType": "Block", "src": "11806:74:5", "statements": [ { "expression": { "id": 16584, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 16582, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16538, "src": "11824:5:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "3332", "id": 16583, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11834:2:5", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "11824:12:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 16585, "nodeType": "ExpressionStatement", "src": "11824:12:5" }, { "expression": { "id": 16588, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 16586, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16544, "src": "11854:6:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "34", "id": 16587, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11864:1:5", "typeDescriptions": { "typeIdentifier": "t_rational_4_by_1", "typeString": "int_const 4" }, "value": "4" }, "src": "11854:11:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 16589, "nodeType": "ExpressionStatement", "src": "11854:11:5" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 16596, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 16594, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 16592, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16538, "src": "11897:5:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "3136", "id": 16593, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11906:2:5", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "11897:11:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 16595, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11911:1:5", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "11897:15:5", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 16606, "nodeType": "IfStatement", "src": "11893:95:5", "trueBody": { "id": 16605, "nodeType": "Block", "src": "11914:74:5", "statements": [ { "expression": { "id": 16599, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 16597, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16538, "src": "11932:5:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "3136", "id": 16598, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11942:2:5", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "11932:12:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 16600, "nodeType": "ExpressionStatement", "src": "11932:12:5" }, { "expression": { "id": 16603, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 16601, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16544, "src": "11962:6:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "32", "id": 16602, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11972:1:5", "typeDescriptions": { "typeIdentifier": "t_rational_2_by_1", "typeString": "int_const 2" }, "value": "2" }, "src": "11962:11:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 16604, "nodeType": "ExpressionStatement", "src": "11962:11:5" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 16611, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 16609, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 16607, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16538, "src": "12005:5:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "38", "id": 16608, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12014:1:5", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "12005:10:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 16610, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12018:1:5", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "12005:14:5", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 16617, "nodeType": "IfStatement", "src": "12001:64:5", "trueBody": { "id": 16616, "nodeType": "Block", "src": "12021:44:5", "statements": [ { "expression": { "id": 16614, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 16612, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16544, "src": "12039:6:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "31", "id": 16613, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12049:1:5", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "src": "12039:11:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 16615, "nodeType": "ExpressionStatement", "src": "12039:11:5" } ] } } ] }, { "expression": { "id": 16619, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16544, "src": "12091:6:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 16542, "id": 16620, "nodeType": "Return", "src": "12084:13:5" } ] }, "documentation": { "id": 16536, "nodeType": "StructuredDocumentation", "src": "11196:240:5", "text": " @dev Return the log in base 256, rounded down, of a positive value.\n Returns 0 if given 0.\n Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string." }, "id": 16622, "implemented": true, "kind": "function", "modifiers": [], "name": "log256", "nameLocation": "11450:6:5", "nodeType": "FunctionDefinition", "parameters": { "id": 16539, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 16538, "mutability": "mutable", "name": "value", "nameLocation": "11465:5:5", "nodeType": "VariableDeclaration", "scope": 16622, "src": "11457:13:5", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 16537, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "11457:7:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "11456:15:5" }, "returnParameters": { "id": 16542, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 16541, "mutability": "mutable", "name": "", "nameLocation": "-1:-1:-1", "nodeType": "VariableDeclaration", "scope": 16622, "src": "11495:7:5", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 16540, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "11495:7:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "11494:9:5" }, "scope": 16662, "src": "11441:663:5", "stateMutability": "pure", "virtual": false, "visibility": "internal" }, { "body": { "id": 16660, "nodeType": "Block", "src": "12340:173:5", "statements": [ { "id": 16659, "nodeType": "UncheckedBlock", "src": "12350:157:5", "statements": [ { "assignments": [ 16634 ], "declarations": [ { "constant": false, "id": 16634, "mutability": "mutable", "name": "result", "nameLocation": "12382:6:5", "nodeType": "VariableDeclaration", "scope": 16659, "src": "12374:14:5", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 16633, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "12374:7:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "id": 16638, "initialValue": { "arguments": [ { "id": 16636, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16625, "src": "12398:5:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 16635, "name": "log256", "nodeType": "Identifier", "overloadedDeclarations": [ 16622, 16661 ], "referencedDeclaration": 16622, "src": "12391:6:5", "typeDescriptions": { "typeIdentifier": "t_function_internal_pure$_t_uint256_$returns$_t_uint256_$", "typeString": "function (uint256) pure returns (uint256)" } }, "id": 16637, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "nameLocations": [], "names": [], "nodeType": "FunctionCall", "src": "12391:13:5", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "VariableDeclarationStatement", "src": "12374:30:5" }, { "expression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 16657, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 16639, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16634, "src": "12425:6:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "+", "rightExpression": { "components": [ { "condition": { "commonType": { "typeIdentifier": "t_bool", "typeString": "bool" }, "id": 16652, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_enum$_Rounding_$15804", "typeString": "enum MathUpgradeable.Rounding" }, "id": 16643, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 16640, "name": "rounding", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16628, "src": "12435:8:5", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$15804", "typeString": "enum MathUpgradeable.Rounding" } }, "nodeType": "BinaryOperation", "operator": "==", "rightExpression": { "expression": { "id": 16641, "name": "Rounding", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 15804, "src": "12447:8:5", "typeDescriptions": { "typeIdentifier": "t_type$_t_enum$_Rounding_$15804_$", "typeString": "type(enum MathUpgradeable.Rounding)" } }, "id": 16642, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "memberLocation": "12456:2:5", "memberName": "Up", "nodeType": "MemberAccess", "referencedDeclaration": 15802, "src": "12447:11:5", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$15804", "typeString": "enum MathUpgradeable.Rounding" } }, "src": "12435:23:5", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "nodeType": "BinaryOperation", "operator": "&&", "rightExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 16651, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 16649, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "hexValue": "31", "id": 16644, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12462:1:5", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "nodeType": "BinaryOperation", "operator": "<<", "rightExpression": { "components": [ { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 16647, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 16645, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16634, "src": "12468:6:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "*", "rightExpression": { "hexValue": "38", "id": 16646, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12477:1:5", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "12468:10:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "id": 16648, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "12467:12:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "12462:17:5", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "<", "rightExpression": { "id": 16650, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 16625, "src": "12482:5:5", "typeDescriptions": { "typeIdentifier": 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"offset": [ 202, 12515 ], "op": "PUSH1", "path": "5", "value": "0x0" }, "30": { "fn": null, "offset": [ 202, 12515 ], "op": "DUP1", "path": "5" }, "31": { "fn": null, "offset": [ 202, 12515 ], "op": "REVERT", "path": "5" } }, "sha1": "1cd8fc76e8a9ba278e25264990b8ce72307d0c7f", "source": "// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts (last updated v4.8.0) (utils/math/Math.sol)\n\npragma solidity ^0.8.0;\n\n/**\n * @dev Standard math utilities missing in the Solidity language.\n */\nlibrary MathUpgradeable {\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(\n uint256 x,\n uint256 y,\n uint256 denominator\n ) 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 return prod0 / denominator;\n }\n\n // Make sure the result is less than 2^256. 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 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(\n uint256 x,\n uint256 y,\n uint256 denominator,\n Rounding rounding\n ) 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. Warren, Jr.'s \"Hacker's Delight\" (Chapter 11).\n */\n function sqrt(uint256 a) internal pure returns (uint256) {\n if (a == 0) {\n return 0;\n }\n\n // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.\n //\n // We know that the \"msb\" (most significant bit) of our target number `a` is a power of 2 such that we have\n // `msb(a) <= a < 2*msb(a)`. This value can be written `msb(a)=2**k` with `k=log2(a)`.\n //\n // This can be rewritten `2**log2(a) <= a < 2**(log2(a) + 1)`\n // \u2192 `sqrt(2**k) <= sqrt(a) < sqrt(2**(k+1))`\n // \u2192 `2**(k/2) <= sqrt(a) < 2**((k+1)/2) <= 2**(k/2 + 1)`\n //\n // Consequently, `2**(log2(a) / 2)` is a good first approximation of `sqrt(a)` with at least 1 correct bit.\n uint256 result = 1 << (log2(a) >> 1);\n\n // At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,\n // since it is the square root of a uint256. 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 10, 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 * 8) < value ? 1 : 0);\n }\n }\n}\n", "sourceMap": "202:12313:5:-:0;;;;;;;;;;;;;;;-1:-1:-1;;;202:12313:5;;;;;;;;;;;;;;;;;", "sourcePath": "/home/vscode/.brownie/packages/OpenZeppelin/openzeppelin-contracts-upgradeable@4.8.2/contracts/utils/math/MathUpgradeable.sol", "type": "library" }