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"typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12939, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "hexValue": "32", "id": 12935, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "4784:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_2_by_1", "typeString": "int_const 2" }, "value": "2" }, "nodeType": "BinaryOperation", "operator": "-", "rightExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12938, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12936, "name": "denominator", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12869, "src": "4788:11:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "*", "rightExpression": { "id": 12937, "name": "inverse", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12918, "src": "4802:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "4788:21:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "4784:25:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "4773:36:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12941, "nodeType": "ExpressionStatement", "src": "4773:36:30" }, { "expression": { "id": 12948, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12942, "name": "inverse", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12918, "src": "4843:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": 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"uint256" } }, "nodeType": "BinaryOperation", "operator": "*", "rightExpression": { "id": 12945, "name": "inverse", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12918, "src": "4872:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "4858:21:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "4854:25:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "4843:36:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12949, "nodeType": "ExpressionStatement", "src": "4843:36:30" }, { "expression": { "id": 12956, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12950, "name": "inverse", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12918, "src": "4913:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "*=", "rightHandSide": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12955, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "hexValue": "32", "id": 12951, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "4924:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_2_by_1", "typeString": "int_const 2" }, "value": "2" }, "nodeType": "BinaryOperation", "operator": "-", "rightExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12954, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12952, "name": "denominator", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12869, "src": "4928:11:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "*", "rightExpression": { "id": 12953, "name": "inverse", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12918, "src": "4942:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "4928:21:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "4924:25:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "4913:36:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12957, "nodeType": "ExpressionStatement", "src": "4913:36:30" }, { "expression": { "id": 12964, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12958, "name": "inverse", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12918, "src": "4983:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "*=", "rightHandSide": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12963, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "hexValue": "32", "id": 12959, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "4994:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_2_by_1", "typeString": "int_const 2" }, "value": "2" }, "nodeType": "BinaryOperation", "operator": "-", "rightExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12962, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12960, "name": "denominator", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12869, "src": "4998:11:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "*", "rightExpression": { "id": 12961, "name": "inverse", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12918, "src": "5012:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "4998:21:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "4994:25:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "4983:36:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12965, "nodeType": "ExpressionStatement", "src": "4983:36:30" }, { "expression": { "id": 12972, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12966, "name": "inverse", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12918, "src": "5054:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "*=", "rightHandSide": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12971, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "hexValue": "32", "id": 12967, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "5065:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_2_by_1", "typeString": "int_const 2" }, "value": "2" }, "nodeType": "BinaryOperation", "operator": "-", "rightExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12970, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12968, "name": "denominator", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12869, "src": "5069:11:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "*", "rightExpression": { "id": 12969, "name": "inverse", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12918, "src": "5083:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "5069:21:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "5065:25:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "5054:36:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12973, "nodeType": "ExpressionStatement", "src": "5054:36:30" }, { "expression": { "id": 12978, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12974, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12872, "src": "5524:6:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12977, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12975, "name": "prod0", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12875, "src": "5533:5:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "*", "rightExpression": { "id": 12976, "name": "inverse", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12918, "src": "5541:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "5533:15:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "5524:24:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12979, "nodeType": "ExpressionStatement", "src": "5524:24:30" }, { "expression": { "id": 12980, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12872, "src": "5569:6:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 12873, "id": 12981, "nodeType": "Return", "src": "5562:13:30" } ] } ] }, "documentation": { "id": 12863, "nodeType": "StructuredDocumentation", "src": "1357:305:30", "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": 12984, "implemented": true, "kind": "function", "modifiers": [], "name": "mulDiv", "nameLocation": "1676:6:30", "nodeType": "FunctionDefinition", "parameters": { "id": 12870, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 12865, "mutability": "mutable", "name": "x", "nameLocation": "1700:1:30", "nodeType": "VariableDeclaration", "scope": 12984, "src": "1692:9:30", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12864, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "1692:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 12867, "mutability": "mutable", "name": "y", "nameLocation": "1719:1:30", "nodeType": "VariableDeclaration", "scope": 12984, "src": "1711:9:30", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12866, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "1711:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 12869, "mutability": "mutable", "name": "denominator", "nameLocation": "1738:11:30", "nodeType": "VariableDeclaration", "scope": 12984, "src": "1730:19:30", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12868, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "1730:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "1682:73:30" }, "returnParameters": { "id": 12873, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 12872, "mutability": "mutable", "name": "result", "nameLocation": "1787:6:30", "nodeType": "VariableDeclaration", "scope": 12984, "src": "1779:14:30", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12871, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "1779:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "1778:16:30" }, "scope": 13636, "src": "1667:3925:30", "stateMutability": "pure", "virtual": false, "visibility": "internal" }, { "body": { "id": 13027, "nodeType": "Block", "src": "5872:189:30", "statements": [ { "assignments": [ 13000 ], "declarations": [ { "constant": false, "id": 13000, "mutability": "mutable", "name": "result", "nameLocation": "5890:6:30", "nodeType": "VariableDeclaration", "scope": 13027, "src": "5882:14:30", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12999, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "5882:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "id": 13006, "initialValue": { "arguments": [ { "id": 13002, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12987, "src": "5906:1:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 13003, "name": "y", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12989, "src": "5909:1:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 13004, "name": "denominator", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12991, "src": "5912:11:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 13001, "name": "mulDiv", "nodeType": "Identifier", "overloadedDeclarations": [ 12984, 13028 ], "referencedDeclaration": 12984, "src": "5899:6:30", "typeDescriptions": { "typeIdentifier": "t_function_internal_pure$_t_uint256_$_t_uint256_$_t_uint256_$returns$_t_uint256_$", "typeString": "function (uint256,uint256,uint256) pure returns (uint256)" } }, "id": 13005, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "nameLocations": [], "names": [], "nodeType": "FunctionCall", "src": "5899:25:30", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "VariableDeclarationStatement", "src": "5882:42:30" }, { "condition": { "commonType": { "typeIdentifier": "t_bool", "typeString": "bool" }, "id": 13018, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_enum$_Rounding_$12778", "typeString": "enum Math.Rounding" }, "id": 13010, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 13007, "name": "rounding", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12994, "src": "5938:8:30", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$12778", "typeString": "enum Math.Rounding" } }, "nodeType": "BinaryOperation", "operator": "==", "rightExpression": { "expression": { "id": 13008, "name": "Rounding", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12778, "src": "5950:8:30", "typeDescriptions": { "typeIdentifier": "t_type$_t_enum$_Rounding_$12778_$", "typeString": "type(enum Math.Rounding)" } }, "id": 13009, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "memberLocation": "5959:2:30", "memberName": "Up", "nodeType": "MemberAccess", "referencedDeclaration": 12776, "src": "5950:11:30", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$12778", "typeString": "enum Math.Rounding" } }, "src": "5938:23:30", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "nodeType": "BinaryOperation", "operator": "&&", "rightExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 13017, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "arguments": [ { "id": 13012, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12987, "src": "5972:1:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 13013, "name": "y", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12989, "src": "5975:1:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 13014, "name": "denominator", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12991, "src": "5978:11:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 13011, "name": "mulmod", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": -16, "src": "5965:6:30", "typeDescriptions": { "typeIdentifier": "t_function_mulmod_pure$_t_uint256_$_t_uint256_$_t_uint256_$returns$_t_uint256_$", "typeString": "function (uint256,uint256,uint256) pure returns (uint256)" } }, "id": 13015, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "nameLocations": [], "names": [], "nodeType": "FunctionCall", "src": "5965:25:30", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 13016, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "5993:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "5965:29:30", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "src": "5938:56:30", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": 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"ExpressionStatement", "src": "6010:11:30" } ] } }, { "expression": { "id": 13025, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13000, "src": "6048:6:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 12998, "id": 13026, "nodeType": "Return", "src": "6041:13:30" } ] }, "documentation": { "id": 12985, "nodeType": "StructuredDocumentation", "src": "5598:121:30", "text": " @notice Calculates x * y / denominator with full precision, following the selected rounding direction." }, "id": 13028, "implemented": true, "kind": "function", "modifiers": [], "name": "mulDiv", "nameLocation": "5733:6:30", "nodeType": "FunctionDefinition", "parameters": { "id": 12995, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 12987, "mutability": "mutable", "name": "x", "nameLocation": "5757:1:30", "nodeType": "VariableDeclaration", "scope": 13028, "src": "5749:9:30", 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"VariableDeclaration", "scope": 13028, "src": "5787:19:30", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12990, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "5787:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 12994, "mutability": "mutable", "name": "rounding", "nameLocation": "5825:8:30", "nodeType": "VariableDeclaration", "scope": 13028, "src": "5816:17:30", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$12778", "typeString": "enum Math.Rounding" }, "typeName": { "id": 12993, "nodeType": "UserDefinedTypeName", "pathNode": { "id": 12992, "name": "Rounding", "nameLocations": [ "5816:8:30" ], "nodeType": "IdentifierPath", "referencedDeclaration": 12778, "src": "5816:8:30" }, "referencedDeclaration": 12778, "src": "5816:8:30", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$12778", "typeString": "enum Math.Rounding" } }, "visibility": "internal" } ], "src": "5739:100:30" }, "returnParameters": { "id": 12998, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 12997, "mutability": "mutable", "name": "", "nameLocation": "-1:-1:-1", "nodeType": "VariableDeclaration", "scope": 13028, "src": "5863:7:30", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12996, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "5863:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "5862:9:30" }, "scope": 13636, "src": "5724:337:30", "stateMutability": "pure", "virtual": false, "visibility": "internal" }, { "body": { "id": 13139, "nodeType": "Block", "src": "6337:1585:30", "statements": 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"lValueRequested": false, "nodeType": "Literal", "src": "8240:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "id": 13170, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "Conditional", "src": "8187:54:30", "trueExpression": { "hexValue": "31", "id": 13168, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "8236:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "typeDescriptions": { "typeIdentifier": "t_uint8", "typeString": "uint8" } } ], "id": 13171, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "8186:56:30", "typeDescriptions": { "typeIdentifier": "t_uint8", "typeString": "uint8" } }, "src": "8177:65:30", "typeDescriptions": { 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"rightExpression": { "hexValue": "30", "id": 13296, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "9280:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "9267:14:30", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 13303, "nodeType": "IfStatement", "src": "9263:64:30", "trueBody": { "id": 13302, "nodeType": "Block", "src": "9283:44:30", "statements": [ { "expression": { "id": 13300, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 13298, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13185, "src": "9301:6:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "31", "id": 13299, 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true, "kind": "function", "modifiers": [], "name": "log2", "nameLocation": "8392:4:30", "nodeType": "FunctionDefinition", "parameters": { "id": 13180, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 13179, "mutability": "mutable", "name": "value", "nameLocation": "8405:5:30", "nodeType": "VariableDeclaration", "scope": 13308, "src": "8397:13:30", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 13178, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "8397:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "8396:15:30" }, "returnParameters": { "id": 13183, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 13182, "mutability": "mutable", "name": "", "nameLocation": "-1:-1:-1", "nodeType": "VariableDeclaration", "scope": 13308, "src": "8435:7:30", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 13181, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "8435:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "8434:9:30" }, "scope": 13636, "src": "8383:983:30", "stateMutability": "pure", "virtual": false, "visibility": "internal" }, { "body": { "id": 13343, "nodeType": "Block", "src": "9599:165:30", "statements": [ { "id": 13342, "nodeType": "UncheckedBlock", "src": "9609:149:30", "statements": [ { "assignments": [ 13320 ], "declarations": [ { "constant": false, "id": 13320, "mutability": "mutable", "name": "result", "nameLocation": "9641:6:30", "nodeType": "VariableDeclaration", "scope": 13342, "src": "9633:14:30", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 13319, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "9633:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "id": 13324, "initialValue": { "arguments": [ { "id": 13322, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13311, "src": "9655:5:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 13321, "name": "log2", "nodeType": "Identifier", "overloadedDeclarations": [ 13308, 13344 ], "referencedDeclaration": 13308, "src": "9650:4:30", "typeDescriptions": { "typeIdentifier": "t_function_internal_pure$_t_uint256_$returns$_t_uint256_$", "typeString": "function (uint256) pure returns (uint256)" } }, "id": 13323, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "nameLocations": [], "names": [], "nodeType": "FunctionCall", "src": "9650:11:30", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "VariableDeclarationStatement", "src": "9633:28:30" }, { "expression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 13340, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 13325, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13320, "src": "9682:6:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "+", "rightExpression": { "components": [ { "condition": { "commonType": { "typeIdentifier": "t_bool", "typeString": "bool" }, "id": 13335, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_enum$_Rounding_$12778", "typeString": "enum Math.Rounding" }, "id": 13329, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 13326, "name": "rounding", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13314, "src": "9692:8:30", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$12778", "typeString": "enum Math.Rounding" } }, "nodeType": "BinaryOperation", "operator": "==", "rightExpression": { "expression": { "id": 13327, "name": "Rounding", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12778, "src": "9704:8:30", "typeDescriptions": { "typeIdentifier": "t_type$_t_enum$_Rounding_$12778_$", "typeString": "type(enum Math.Rounding)" } }, "id": 13328, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "memberLocation": "9713:2:30", "memberName": "Up", "nodeType": "MemberAccess", "referencedDeclaration": 12776, "src": "9704:11:30", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$12778", "typeString": "enum Math.Rounding" } }, "src": "9692:23:30", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "nodeType": "BinaryOperation", "operator": "&&", "rightExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 13334, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 13332, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "hexValue": "31", "id": 13330, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "9719:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "nodeType": "BinaryOperation", "operator": "<<", "rightExpression": { "id": 13331, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13320, "src": "9724:6:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "9719:11:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "<", "rightExpression": { "id": 13333, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13311, "src": "9733:5:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "9719:19:30", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "src": "9692:46:30", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "falseExpression": { "hexValue": "30", "id": 13337, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "9745:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "id": 13338, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "Conditional", "src": "9692:54:30", "trueExpression": { "hexValue": "31", "id": 13336, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "9741:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "typeDescriptions": { "typeIdentifier": "t_uint8", "typeString": "uint8" } } ], "id": 13339, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "9691:56:30", "typeDescriptions": { "typeIdentifier": "t_uint8", "typeString": "uint8" } }, "src": "9682:65:30", "typeDescriptions": { 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"ElementaryTypeName", "src": "9533:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 13314, "mutability": "mutable", "name": "rounding", "nameLocation": "9557:8:30", "nodeType": "VariableDeclaration", "scope": 13344, "src": "9548:17:30", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$12778", "typeString": "enum Math.Rounding" }, "typeName": { "id": 13313, "nodeType": "UserDefinedTypeName", "pathNode": { "id": 13312, "name": "Rounding", "nameLocations": [ "9548:8:30" ], "nodeType": "IdentifierPath", "referencedDeclaration": 12778, "src": "9548:8:30" }, "referencedDeclaration": 12778, "src": "9548:8:30", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$12778", "typeString": "enum Math.Rounding" } }, "visibility": "internal" } ], "src": "9532:34:30" }, "returnParameters": { "id": 13318, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 13317, "mutability": "mutable", "name": "", "nameLocation": "-1:-1:-1", "nodeType": "VariableDeclaration", "scope": 13344, "src": "9590:7:30", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 13316, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "9590:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "9589:9:30" }, "scope": 13636, "src": "9519:245:30", "stateMutability": "pure", "virtual": false, "visibility": "internal" }, { "body": { "id": 13472, "nodeType": "Block", "src": "9951:828:30", "statements": [ { "assignments": [ 13353 ], "declarations": [ { "constant": false, "id": 13353, "mutability": "mutable", "name": "result", "nameLocation": "9969:6:30", "nodeType": "VariableDeclaration", "scope": 13472, "src": "9961:14:30", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 13352, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "9961:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "id": 13355, "initialValue": { "hexValue": "30", "id": 13354, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "9978:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "nodeType": "VariableDeclarationStatement", "src": "9961:18:30" }, { "id": 13469, "nodeType": "UncheckedBlock", "src": "9989:761:30", "statements": [ { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 13360, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 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"isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10030:2:30", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "10026:6:30", "typeDescriptions": { "typeIdentifier": "t_rational_10000000000000000000000000000000000000000000000000000000000000000_by_1", "typeString": "int_const 1000...(57 digits omitted)...0000" } }, "src": "10017:15:30", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 13372, "nodeType": "IfStatement", "src": "10013:99:30", "trueBody": { "id": 13371, "nodeType": "Block", "src": "10034:78:30", "statements": [ { "expression": { "id": 13365, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 13361, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13347, "src": "10052:5:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "/=", "rightHandSide": { "commonType": { "typeIdentifier": "t_rational_10000000000000000000000000000000000000000000000000000000000000000_by_1", "typeString": "int_const 1000...(57 digits omitted)...0000" }, "id": 13364, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 13362, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10061:2:30", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "3634", "id": 13363, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10065:2:30", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "10061:6:30", "typeDescriptions": { "typeIdentifier": "t_rational_10000000000000000000000000000000000000000000000000000000000000000_by_1", "typeString": "int_const 1000...(57 digits omitted)...0000" } }, "src": "10052:15:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 13366, "nodeType": "ExpressionStatement", "src": "10052:15:30" }, { "expression": { "id": 13369, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 13367, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13353, "src": "10085:6:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "3634", "id": 13368, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10095:2:30", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "10085:12:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 13370, "nodeType": "ExpressionStatement", "src": "10085:12:30" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 13377, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 13373, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13347, "src": "10129:5:30", "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": 13376, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 13374, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10138:2:30", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "3332", "id": 13375, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10142:2:30", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "10138:6:30", "typeDescriptions": { "typeIdentifier": "t_rational_100000000000000000000000000000000_by_1", "typeString": "int_const 1000...(25 digits omitted)...0000" } }, "src": "10129:15:30", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 13389, "nodeType": "IfStatement", "src": "10125:99:30", "trueBody": { "id": 13388, "nodeType": "Block", "src": "10146:78:30", "statements": [ { "expression": { "id": 13382, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 13378, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13347, "src": "10164:5:30", "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": 13381, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 13379, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10173:2:30", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "3332", "id": 13380, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10177:2:30", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "10173:6:30", "typeDescriptions": { "typeIdentifier": "t_rational_100000000000000000000000000000000_by_1", "typeString": "int_const 1000...(25 digits omitted)...0000" } }, "src": "10164:15:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 13383, "nodeType": "ExpressionStatement", "src": "10164:15:30" }, { "expression": { "id": 13386, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 13384, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13353, "src": "10197:6:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "3332", "id": 13385, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10207:2:30", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "10197:12:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 13387, "nodeType": "ExpressionStatement", "src": "10197:12:30" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 13394, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 13390, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13347, "src": "10241:5:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "commonType": { "typeIdentifier": "t_rational_10000000000000000_by_1", "typeString": "int_const 10000000000000000" }, "id": 13393, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 13391, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10250:2:30", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "3136", "id": 13392, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10254:2:30", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "10250:6:30", "typeDescriptions": { "typeIdentifier": "t_rational_10000000000000000_by_1", "typeString": "int_const 10000000000000000" } }, "src": "10241:15:30", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 13406, "nodeType": "IfStatement", "src": "10237:99:30", "trueBody": { "id": 13405, "nodeType": "Block", "src": "10258:78:30", "statements": [ { "expression": { "id": 13399, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 13395, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13347, "src": "10276:5:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "/=", "rightHandSide": { "commonType": { "typeIdentifier": "t_rational_10000000000000000_by_1", "typeString": "int_const 10000000000000000" }, "id": 13398, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 13396, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10285:2:30", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "3136", "id": 13397, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10289:2:30", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "10285:6:30", "typeDescriptions": { "typeIdentifier": "t_rational_10000000000000000_by_1", "typeString": "int_const 10000000000000000" } }, "src": "10276:15:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 13400, "nodeType": "ExpressionStatement", "src": "10276:15:30" }, { "expression": { "id": 13403, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 13401, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13353, "src": "10309:6:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "3136", "id": 13402, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10319:2:30", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "10309:12:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 13404, "nodeType": "ExpressionStatement", "src": "10309:12:30" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 13411, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 13407, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13347, "src": "10353:5:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "commonType": { "typeIdentifier": "t_rational_100000000_by_1", "typeString": "int_const 100000000" }, "id": 13410, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 13408, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10362:2:30", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "38", "id": 13409, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10366:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "10362:5:30", "typeDescriptions": { "typeIdentifier": "t_rational_100000000_by_1", "typeString": "int_const 100000000" } }, "src": "10353:14:30", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 13423, "nodeType": "IfStatement", "src": "10349:96:30", "trueBody": { "id": 13422, "nodeType": "Block", "src": "10369:76:30", "statements": [ { "expression": { "id": 13416, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 13412, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13347, "src": "10387:5:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "/=", "rightHandSide": { "commonType": { "typeIdentifier": "t_rational_100000000_by_1", "typeString": "int_const 100000000" }, "id": 13415, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 13413, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10396:2:30", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "38", "id": 13414, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10400:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "10396:5:30", "typeDescriptions": { "typeIdentifier": "t_rational_100000000_by_1", "typeString": "int_const 100000000" } }, "src": "10387:14:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 13417, "nodeType": "ExpressionStatement", "src": "10387:14:30" }, { "expression": { "id": 13420, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 13418, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13353, "src": "10419:6:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "38", "id": 13419, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10429:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "10419:11:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 13421, "nodeType": "ExpressionStatement", "src": "10419:11:30" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 13428, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 13424, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13347, "src": "10462:5:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "commonType": { "typeIdentifier": "t_rational_10000_by_1", "typeString": "int_const 10000" }, "id": 13427, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 13425, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10471:2:30", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "34", "id": 13426, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10475:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_4_by_1", "typeString": "int_const 4" }, "value": "4" }, "src": "10471:5:30", "typeDescriptions": { "typeIdentifier": "t_rational_10000_by_1", "typeString": "int_const 10000" } }, "src": "10462:14:30", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 13440, "nodeType": "IfStatement", "src": "10458:96:30", "trueBody": { "id": 13439, "nodeType": "Block", "src": "10478:76:30", "statements": [ { "expression": { "id": 13433, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 13429, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13347, "src": "10496:5:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "/=", "rightHandSide": { "commonType": { "typeIdentifier": "t_rational_10000_by_1", "typeString": "int_const 10000" }, "id": 13432, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 13430, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10505:2:30", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "34", "id": 13431, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10509:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_4_by_1", "typeString": "int_const 4" }, "value": "4" }, "src": "10505:5:30", "typeDescriptions": { "typeIdentifier": "t_rational_10000_by_1", "typeString": "int_const 10000" } }, "src": "10496:14:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 13434, "nodeType": "ExpressionStatement", "src": "10496:14:30" }, { "expression": { "id": 13437, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 13435, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13353, "src": "10528:6:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "34", "id": 13436, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10538:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_4_by_1", "typeString": "int_const 4" }, "value": "4" }, "src": "10528:11:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 13438, "nodeType": "ExpressionStatement", "src": "10528:11:30" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 13445, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 13441, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13347, "src": "10571:5:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "commonType": { "typeIdentifier": "t_rational_100_by_1", "typeString": "int_const 100" }, "id": 13444, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "3130", "id": 13442, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10580:2:30", "typeDescriptions": { "typeIdentifier": "t_rational_10_by_1", "typeString": "int_const 10" }, "value": "10" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "32", "id": 13443, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10584:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_2_by_1", "typeString": "int_const 2" }, "value": "2" }, "src": "10580:5:30", "typeDescriptions": { "typeIdentifier": "t_rational_100_by_1", "typeString": "int_const 100" } }, "src": "10571:14:30", "typeDescriptions": { "typeIdentifier": 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"typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "38", "id": 13546, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11745:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "11735:11:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 13548, "nodeType": "ExpressionStatement", "src": "11735:11:30" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 13555, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 13553, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 13551, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13512, "src": "11778:5:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "3332", "id": 13552, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11787:2:30", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "11778:11:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 13554, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11792:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "11778:15:30", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 13565, "nodeType": "IfStatement", "src": "11774:95:30", "trueBody": { "id": 13564, "nodeType": "Block", "src": "11795:74:30", "statements": [ { "expression": { "id": 13558, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 13556, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13512, "src": "11813:5:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "3332", "id": 13557, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11823:2:30", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "11813:12:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 13559, "nodeType": "ExpressionStatement", "src": "11813:12:30" }, { "expression": { "id": 13562, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 13560, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13518, "src": "11843:6:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "34", "id": 13561, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11853:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_4_by_1", "typeString": "int_const 4" }, "value": "4" }, "src": "11843:11:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 13563, "nodeType": "ExpressionStatement", "src": "11843:11:30" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 13570, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 13568, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 13566, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13512, "src": "11886:5:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "3136", "id": 13567, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11895:2:30", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "11886:11:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 13569, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11900:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "11886:15:30", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 13580, "nodeType": "IfStatement", "src": "11882:95:30", "trueBody": { "id": 13579, "nodeType": "Block", "src": "11903:74:30", "statements": [ { "expression": { "id": 13573, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 13571, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13512, "src": "11921:5:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "3136", "id": 13572, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11931:2:30", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "11921:12:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 13574, "nodeType": "ExpressionStatement", "src": "11921:12:30" }, { "expression": { "id": 13577, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 13575, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13518, "src": "11951:6:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "32", "id": 13576, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11961:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_2_by_1", "typeString": "int_const 2" }, "value": "2" }, "src": "11951:11:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 13578, "nodeType": "ExpressionStatement", "src": "11951:11:30" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 13585, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 13583, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 13581, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13512, "src": "11994:5:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "38", "id": 13582, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12003:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "11994:10:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 13584, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12007:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "11994:14:30", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 13591, "nodeType": "IfStatement", "src": "11990:64:30", "trueBody": { "id": 13590, "nodeType": "Block", "src": "12010:44:30", "statements": [ { "expression": { "id": 13588, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 13586, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13518, "src": "12028:6:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "31", "id": 13587, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12038:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "src": "12028:11:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 13589, "nodeType": "ExpressionStatement", "src": "12028:11:30" } ] } } ] }, { "expression": { "id": 13593, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13518, "src": "12080:6:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 13516, "id": 13594, "nodeType": "Return", "src": "12073:13:30" } ] }, "documentation": { "id": 13510, "nodeType": "StructuredDocumentation", "src": "11185:240:30", "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": 13596, "implemented": true, "kind": "function", "modifiers": [], "name": "log256", "nameLocation": "11439:6:30", "nodeType": "FunctionDefinition", "parameters": { "id": 13513, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 13512, "mutability": "mutable", "name": "value", "nameLocation": "11454:5:30", "nodeType": "VariableDeclaration", "scope": 13596, "src": "11446:13:30", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 13511, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "11446:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "11445:15:30" }, "returnParameters": { "id": 13516, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 13515, "mutability": "mutable", "name": "", "nameLocation": "-1:-1:-1", "nodeType": "VariableDeclaration", "scope": 13596, "src": "11484:7:30", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 13514, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "11484:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "11483:9:30" }, "scope": 13636, "src": "11430:663:30", "stateMutability": "pure", "virtual": false, "visibility": "internal" }, { "body": { "id": 13634, "nodeType": "Block", "src": "12329:173:30", "statements": [ { "id": 13633, "nodeType": "UncheckedBlock", "src": "12339:157:30", "statements": [ { "assignments": [ 13608 ], "declarations": [ { "constant": false, "id": 13608, "mutability": "mutable", "name": "result", "nameLocation": "12371:6:30", "nodeType": "VariableDeclaration", "scope": 13633, "src": "12363:14:30", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 13607, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "12363:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "id": 13612, "initialValue": { "arguments": [ { "id": 13610, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13599, "src": "12387:5:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 13609, "name": "log256", "nodeType": "Identifier", "overloadedDeclarations": [ 13596, 13635 ], "referencedDeclaration": 13596, "src": "12380:6:30", "typeDescriptions": { "typeIdentifier": "t_function_internal_pure$_t_uint256_$returns$_t_uint256_$", "typeString": "function (uint256) pure returns (uint256)" } }, "id": 13611, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "nameLocations": [], "names": [], "nodeType": "FunctionCall", "src": "12380:13:30", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "VariableDeclarationStatement", "src": "12363:30:30" }, { "expression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 13631, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 13613, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13608, "src": "12414:6:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "+", "rightExpression": { "components": [ { "condition": { "commonType": { "typeIdentifier": "t_bool", "typeString": "bool" }, "id": 13626, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_enum$_Rounding_$12778", "typeString": "enum Math.Rounding" }, "id": 13617, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 13614, "name": "rounding", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13602, "src": "12424:8:30", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$12778", "typeString": "enum Math.Rounding" } }, "nodeType": "BinaryOperation", "operator": "==", "rightExpression": { "expression": { "id": 13615, "name": "Rounding", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12778, "src": "12436:8:30", "typeDescriptions": { "typeIdentifier": "t_type$_t_enum$_Rounding_$12778_$", "typeString": "type(enum Math.Rounding)" } }, "id": 13616, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "memberLocation": "12445:2:30", "memberName": "Up", "nodeType": "MemberAccess", "referencedDeclaration": 12776, "src": "12436:11:30", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$12778", "typeString": "enum Math.Rounding" } }, "src": "12424:23:30", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "nodeType": "BinaryOperation", "operator": "&&", "rightExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 13625, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 13623, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "hexValue": "31", "id": 13618, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12451:1:30", "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": 13621, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 13619, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13608, "src": "12457:6:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "*", "rightExpression": { "hexValue": "38", "id": 13620, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12466:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "12457:10:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "id": 13622, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "12456:12:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "12451:17:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "<", "rightExpression": { "id": 13624, "name": "value", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 13599, "src": "12471:5:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "12451:25:30", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "src": "12424:52:30", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "falseExpression": { "hexValue": "30", "id": 13628, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12483:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "id": 13629, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "Conditional", "src": "12424:60:30", "trueExpression": { "hexValue": "31", "id": 13627, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12479:1:30", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "typeDescriptions": { "typeIdentifier": "t_uint8", "typeString": "uint8" } } ], "id": 13630, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "12423:62:30", "typeDescriptions": { "typeIdentifier": "t_uint8", "typeString": "uint8" } }, "src": "12414:71:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 13606, "id": 13632, "nodeType": "Return", "src": "12407:78:30" } ] } ] }, "documentation": { "id": 13597, "nodeType": "StructuredDocumentation", "src": "12099:143:30", "text": " @dev Return the log in base 10, following the selected rounding direction, of a positive value.\n Returns 0 if given 0." }, "id": 13635, "implemented": true, "kind": "function", "modifiers": [], "name": "log256", "nameLocation": "12256:6:30", "nodeType": "FunctionDefinition", "parameters": { "id": 13603, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 13599, "mutability": "mutable", "name": "value", "nameLocation": "12271:5:30", "nodeType": "VariableDeclaration", "scope": 13635, "src": "12263:13:30", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 13598, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "12263:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 13602, "mutability": "mutable", "name": "rounding", "nameLocation": "12287:8:30", "nodeType": "VariableDeclaration", "scope": 13635, "src": "12278:17:30", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$12778", "typeString": "enum Math.Rounding" }, "typeName": { "id": 13601, "nodeType": "UserDefinedTypeName", "pathNode": { "id": 13600, "name": "Rounding", "nameLocations": [ "12278:8:30" ], "nodeType": "IdentifierPath", "referencedDeclaration": 12778, "src": "12278:8:30" }, "referencedDeclaration": 12778, "src": "12278:8:30", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$12778", "typeString": "enum Math.Rounding" } }, "visibility": "internal" } ], "src": "12262:34:30" }, "returnParameters": { "id": 13606, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 13605, "mutability": "mutable", "name": "", "nameLocation": "-1:-1:-1", "nodeType": "VariableDeclaration", "scope": 13635, "src": "12320:7:30", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", 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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": "202:12302:30:-:0;;;;;;;;;;;;;;;-1:-1:-1;;;202:12302:30;;;;;;;;;;;;;;;;;", "sourcePath": "/home/vscode/.brownie/packages/OpenZeppelin/openzeppelin-contracts@4.8.2/contracts/utils/math/Math.sol", "type": "library" }