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"text": "@notice Emitted when the result overflows uint256." }, "errorSelector": "d31b3402", "name": "PRBMath__MulDivFixedPointOverflow", "nameLocation": "125:33:15", "parameters": { "id": 24450, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 24449, "mutability": "mutable", "name": "prod1", "nameLocation": "167:5:15", "nodeType": "VariableDeclaration", "scope": 24451, "src": "159:13:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 24448, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "159:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "158:15:15" } }, { "id": 24458, "nodeType": "ErrorDefinition", "src": "231:66:15", "documentation": { "id": 24452, "nodeType": "StructuredDocumentation", "src": "176:55:15", "text": "@notice Emitted when the result overflows uint256." }, "errorSelector": "773cc18c", "name": "PRBMath__MulDivOverflow", "nameLocation": "237:23:15", "parameters": { "id": 24457, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 24454, "mutability": "mutable", "name": "prod1", "nameLocation": "269:5:15", "nodeType": "VariableDeclaration", "scope": 24458, "src": "261:13:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 24453, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "261:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 24456, "mutability": "mutable", "name": "denominator", "nameLocation": "284:11:15", "nodeType": "VariableDeclaration", "scope": 24458, "src": "276:19:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": 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}, { "id": 24477, "nodeType": "ErrorDefinition", "src": "797:41:15", "documentation": { "id": 24475, "nodeType": "StructuredDocumentation", "src": "738:59:15", "text": "@notice Emitted when one of the inputs is MIN_SD59x18." }, "errorSelector": "b3c754a3", "name": "PRBMathSD59x18__DivInputTooSmall", "nameLocation": "803:32:15", "parameters": { "id": 24476, "nodeType": "ParameterList", "parameters": [], "src": "835:2:15" } }, { "id": 24482, "nodeType": "ErrorDefinition", "src": "925:48:15", "documentation": { "id": 24478, "nodeType": "StructuredDocumentation", "src": "840:85:15", "text": "@notice Emitted when one of the intermediary unsigned results overflows SD59x18." }, "errorSelector": "7cb4bef5", "name": "PRBMathSD59x18__DivOverflow", "nameLocation": "931:27:15", "parameters": { "id": 24481, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 24480, "mutability": "mutable", "name": "rAbs", "nameLocation": "967:4:15", "nodeType": "VariableDeclaration", "scope": 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"typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" }, "typeName": { "id": 24489, "name": "int256", "nodeType": "ElementaryTypeName", "src": "1193:6:15", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "visibility": "internal" } ], "src": "1192:10:15" } }, { "id": 24497, "nodeType": "ErrorDefinition", "src": "1268:47:15", "documentation": { "id": 24493, "nodeType": "StructuredDocumentation", "src": "1205:63:15", "text": "@notice Emitted when flooring a number underflows SD59x18." }, "errorSelector": "7c00653f", "name": "PRBMathSD59x18__FloorUnderflow", "nameLocation": "1274:30:15", "parameters": { "id": 24496, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 24495, "mutability": "mutable", "name": "x", "nameLocation": "1312:1:15", "nodeType": "VariableDeclaration", "scope": 24497, "src": "1305:8:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" }, "typeName": { "id": 24494, "name": "int256", "nodeType": "ElementaryTypeName", "src": "1305:6:15", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "visibility": "internal" } ], "src": "1304:10:15" } }, { "id": 24502, "nodeType": "ErrorDefinition", "src": "1414:48:15", "documentation": { "id": 24498, "nodeType": "StructuredDocumentation", "src": "1317:97:15", "text": "@notice Emitted when converting a basic integer to the fixed-point format overflows SD59x18." }, "errorSelector": "71f72a31", "name": "PRBMathSD59x18__FromIntOverflow", "nameLocation": "1420:31:15", "parameters": { "id": 24501, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 24500, "mutability": "mutable", "name": "x", "nameLocation": "1459:1:15", "nodeType": "VariableDeclaration", "scope": 24502, "src": "1452:8:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" }, "typeName": { "id": 24499, "name": "int256", "nodeType": "ElementaryTypeName", "src": "1452:6:15", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "visibility": "internal" } ], "src": "1451:10:15" } }, { "id": 24507, "nodeType": "ErrorDefinition", "src": "1562:49:15", "documentation": { "id": 24503, "nodeType": "StructuredDocumentation", "src": "1464:98:15", "text": "@notice Emitted when converting a basic integer to the fixed-point format underflows SD59x18." }, "errorSelector": "e608e18b", "name": "PRBMathSD59x18__FromIntUnderflow", "nameLocation": "1568:32:15", "parameters": { "id": 24506, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 24505, "mutability": "mutable", "name": "x", "nameLocation": "1608:1:15", "nodeType": "VariableDeclaration", "scope": 24507, "src": "1601:8:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" }, "typeName": { "id": 24504, "name": "int256", "nodeType": "ElementaryTypeName", "src": "1601:6:15", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "visibility": "internal" } ], "src": "1600:10:15" } }, { "id": 24514, "nodeType": "ErrorDefinition", "src": "1677:60:15", "documentation": { "id": 24508, "nodeType": "StructuredDocumentation", "src": "1613:64:15", "text": "@notice Emitted when the product of the inputs is negative." }, "errorSelector": "fe31079a", "name": "PRBMathSD59x18__GmNegativeProduct", "nameLocation": "1683:33:15", "parameters": { "id": 24513, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 24510, "mutability": "mutable", "name": "x", "nameLocation": "1724:1:15", "nodeType": "VariableDeclaration", "scope": 24514, "src": "1717:8:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" }, "typeName": { "id": 24509, "name": "int256", "nodeType": "ElementaryTypeName", "src": "1717:6:15", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "visibility": "internal" }, { "constant": false, "id": 24512, "mutability": "mutable", "name": "y", "nameLocation": "1734:1:15", "nodeType": "VariableDeclaration", "scope": 24514, "src": "1727:8:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" }, "typeName": { "id": 24511, "name": "int256", "nodeType": "ElementaryTypeName", "src": "1727:6:15", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "visibility": "internal" } ], "src": "1716:20:15" } }, { "id": 24521, "nodeType": "ErrorDefinition", "src": "1806:53:15", "documentation": { "id": 24515, "nodeType": "StructuredDocumentation", "src": "1739:67:15", "text": "@notice Emitted when multiplying the inputs overflows SD59x18." }, "errorSelector": "0fb9098e", "name": "PRBMathSD59x18__GmOverflow", "nameLocation": "1812:26:15", "parameters": { "id": 24520, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 24517, "mutability": "mutable", "name": "x", "nameLocation": "1846:1:15", "nodeType": "VariableDeclaration", "scope": 24521, "src": "1839:8:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" }, "typeName": { "id": 24516, "name": "int256", "nodeType": "ElementaryTypeName", "src": "1839:6:15", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "visibility": "internal" }, { "constant": false, "id": 24519, "mutability": "mutable", "name": "y", "nameLocation": "1856:1:15", "nodeType": "VariableDeclaration", "scope": 24521, "src": "1849:8:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" }, "typeName": { "id": 24518, "name": "int256", "nodeType": "ElementaryTypeName", "src": "1849:6:15", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "visibility": "internal" } ], "src": "1838:20:15" } }, { "id": 24526, "nodeType": "ErrorDefinition", "src": "1927:49:15", "documentation": { "id": 24522, "nodeType": "StructuredDocumentation", "src": "1861:66:15", "text": "@notice Emitted when the input is less than or equal to zero." }, "errorSelector": "613f4fba", "name": "PRBMathSD59x18__LogInputTooSmall", "nameLocation": "1933:32:15", "parameters": { "id": 24525, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 24524, "mutability": "mutable", "name": "x", "nameLocation": "1973:1:15", "nodeType": "VariableDeclaration", "scope": 24526, "src": "1966:8:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" }, "typeName": { "id": 24523, "name": "int256", "nodeType": "ElementaryTypeName", "src": "1966:6:15", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "visibility": "internal" } ], "src": "1965:10:15" } }, { "id": 24529, "nodeType": "ErrorDefinition", "src": "2037:41:15", "documentation": { "id": 24527, "nodeType": "StructuredDocumentation", "src": "1978:59:15", "text": "@notice Emitted when one of the inputs is MIN_SD59x18." }, "errorSelector": "3406846c", "name": "PRBMathSD59x18__MulInputTooSmall", "nameLocation": "2043:32:15", "parameters": { "id": 24528, "nodeType": "ParameterList", "parameters": [], "src": "2075:2:15" } }, { "id": 24534, "nodeType": "ErrorDefinition", "src": "2157:48:15", "documentation": { "id": 24530, "nodeType": "StructuredDocumentation", "src": "2080:77:15", "text": "@notice Emitted when the intermediary absolute result overflows SD59x18." }, "errorSelector": "bf79e8d9", "name": "PRBMathSD59x18__MulOverflow", "nameLocation": "2163:27:15", "parameters": { "id": 24533, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 24532, "mutability": "mutable", "name": "rAbs", "nameLocation": "2199:4:15", "nodeType": "VariableDeclaration", "scope": 24534, "src": "2191:12:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 24531, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "2191:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "2190:14:15" } }, { "id": 24539, "nodeType": "ErrorDefinition", "src": "2284:49:15", "documentation": { "id": 24535, "nodeType": "StructuredDocumentation", "src": "2207:77:15", "text": "@notice Emitted when the intermediary absolute result overflows SD59x18." }, "errorSelector": "ffb15bcd", "name": "PRBMathSD59x18__PowuOverflow", "nameLocation": "2290:28:15", "parameters": { "id": 24538, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 24537, "mutability": "mutable", "name": "rAbs", "nameLocation": "2327:4:15", "nodeType": "VariableDeclaration", "scope": 24539, "src": "2319:12:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 24536, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "2319:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "2318:14:15" } }, { "id": 24544, "nodeType": "ErrorDefinition", "src": "2383:50:15", "documentation": { "id": 24540, "nodeType": "StructuredDocumentation", "src": "2335:48:15", "text": "@notice Emitted when the input is negative." }, "errorSelector": "c11907fe", "name": "PRBMathSD59x18__SqrtNegativeInput", "nameLocation": "2389:33:15", "parameters": { "id": 24543, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 24542, "mutability": "mutable", "name": "x", "nameLocation": "2430:1:15", "nodeType": "VariableDeclaration", "scope": 24544, "src": "2423:8:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" }, "typeName": { "id": 24541, "name": "int256", "nodeType": "ElementaryTypeName", "src": "2423:6:15", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "visibility": "internal" } ], "src": "2422:10:15" } }, { "id": 24549, "nodeType": "ErrorDefinition", "src": "2511:45:15", "documentation": { "id": 24545, "nodeType": "StructuredDocumentation", "src": "2435:76:15", "text": "@notice Emitted when the calculating the square root overflows SD59x18." }, "errorSelector": "2c482c39", "name": "PRBMathSD59x18__SqrtOverflow", "nameLocation": "2517:28:15", "parameters": { "id": 24548, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 24547, "mutability": "mutable", "name": "x", "nameLocation": "2553:1:15", "nodeType": "VariableDeclaration", "scope": 24549, "src": "2546:8:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" }, "typeName": { "id": 24546, "name": "int256", "nodeType": "ElementaryTypeName", "src": "2546:6:15", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "visibility": "internal" } ], "src": "2545:10:15" } }, { "id": 24556, "nodeType": "ErrorDefinition", "src": "2611:56:15", "documentation": { "id": 24550, "nodeType": "StructuredDocumentation", "src": "2558:53:15", "text": "@notice Emitted when addition overflows UD60x18." }, "errorSelector": "0aa6aef7", "name": "PRBMathUD60x18__AddOverflow", "nameLocation": "2617:27:15", "parameters": { "id": 24555, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 24552, "mutability": "mutable", "name": "x", "nameLocation": "2653:1:15", "nodeType": "VariableDeclaration", "scope": 24556, "src": "2645:9:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 24551, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "2645:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 24554, "mutability": "mutable", "name": "y", "nameLocation": "2664:1:15", "nodeType": "VariableDeclaration", "scope": 24556, "src": "2656:9:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 24553, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "2656:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "2644:22:15" } }, { "id": 24561, "nodeType": "ErrorDefinition", "src": "2730:46:15", "documentation": { "id": 24557, "nodeType": "StructuredDocumentation", "src": "2669:61:15", "text": "@notice Emitted when ceiling a number overflows UD60x18." }, "errorSelector": "7675d888", "name": "PRBMathUD60x18__CeilOverflow", "nameLocation": "2736:28:15", "parameters": { "id": 24560, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 24559, "mutability": "mutable", "name": "x", "nameLocation": "2773:1:15", "nodeType": "VariableDeclaration", "scope": 24561, "src": "2765:9:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 24558, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "2765:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "2764:11:15" } }, { "id": 24566, "nodeType": "ErrorDefinition", "src": "2853:48:15", "documentation": { "id": 24562, "nodeType": "StructuredDocumentation", "src": "2778:75:15", "text": "@notice Emitted when the input is greater than 133.084258667509499441." }, "errorSelector": "315da068", "name": "PRBMathUD60x18__ExpInputTooBig", "nameLocation": "2859:30:15", "parameters": { "id": 24565, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 24564, "mutability": "mutable", "name": "x", "nameLocation": "2898:1:15", "nodeType": "VariableDeclaration", "scope": 24566, "src": "2890:9:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 24563, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "2890:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "2889:11:15" } }, { "id": 24571, "nodeType": "ErrorDefinition", "src": "2959:49:15", "documentation": { "id": 24567, "nodeType": "StructuredDocumentation", "src": "2903:56:15", "text": "@notice Emitted when the input is greater than 192." }, "errorSelector": "4a4f26f1", "name": "PRBMathUD60x18__Exp2InputTooBig", "nameLocation": "2965:31:15", "parameters": { "id": 24570, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 24569, "mutability": "mutable", "name": "x", "nameLocation": "3005:1:15", "nodeType": "VariableDeclaration", "scope": 24571, "src": "2997:9:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 24568, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "2997:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "2996:11:15" } }, { "id": 24576, "nodeType": "ErrorDefinition", "src": "3114:50:15", "documentation": { "id": 24572, "nodeType": "StructuredDocumentation", "src": "3010:104:15", "text": "@notice Emitted when converting a basic integer to the fixed-point format format overflows UD60x18." }, "errorSelector": "3492ffd9", "name": "PRBMathUD60x18__FromUintOverflow", "nameLocation": "3120:32:15", "parameters": { "id": 24575, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 24574, "mutability": "mutable", "name": "x", "nameLocation": "3161:1:15", "nodeType": "VariableDeclaration", "scope": 24576, "src": "3153:9:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 24573, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "3153:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "3152:11:15" } }, { "id": 24583, "nodeType": "ErrorDefinition", "src": "3233:55:15", "documentation": { "id": 24577, "nodeType": "StructuredDocumentation", "src": "3166:67:15", "text": "@notice Emitted when multiplying the inputs overflows UD60x18." }, "errorSelector": "00c3efdf", "name": "PRBMathUD60x18__GmOverflow", "nameLocation": "3239:26:15", "parameters": { "id": 24582, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 24579, "mutability": "mutable", "name": "x", "nameLocation": "3274:1:15", "nodeType": "VariableDeclaration", "scope": 24583, "src": "3266:9:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 24578, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "3266:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 24581, "mutability": "mutable", "name": "y", "nameLocation": "3285:1:15", "nodeType": "VariableDeclaration", "scope": 24583, "src": "3277:9:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 24580, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "3277:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "3265:22:15" } }, { "id": 24588, "nodeType": "ErrorDefinition", "src": "3341:50:15", "documentation": { "id": 24584, "nodeType": "StructuredDocumentation", "src": "3290:51:15", "text": "@notice Emitted when the input is less than 1." }, "errorSelector": "d88504dc", "name": "PRBMathUD60x18__LogInputTooSmall", "nameLocation": "3347:32:15", "parameters": { "id": 24587, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 24586, "mutability": "mutable", "name": "x", "nameLocation": "3388:1:15", "nodeType": "VariableDeclaration", "scope": 24588, "src": "3380:9:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 24585, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "3380:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "3379:11:15" } }, { "id": 24593, "nodeType": "ErrorDefinition", "src": "3469:46:15", "documentation": { "id": 24589, "nodeType": "StructuredDocumentation", "src": "3393:76:15", "text": "@notice Emitted when the calculating the square root overflows UD60x18." }, "errorSelector": "6155b67d", "name": "PRBMathUD60x18__SqrtOverflow", "nameLocation": "3475:28:15", "parameters": { "id": 24592, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 24591, "mutability": "mutable", "name": "x", "nameLocation": "3512:1:15", "nodeType": "VariableDeclaration", "scope": 24593, "src": "3504:9:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 24590, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "3504:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "3503:11:15" } }, { "id": 24600, "nodeType": "ErrorDefinition", "src": "3574:57:15", "documentation": { "id": 24594, "nodeType": "StructuredDocumentation", "src": "3517:57:15", "text": "@notice Emitted when subtraction underflows UD60x18." }, "errorSelector": "41d96f39", "name": "PRBMathUD60x18__SubUnderflow", "nameLocation": "3580:28:15", "parameters": { "id": 24599, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 24596, "mutability": "mutable", "name": "x", "nameLocation": "3617:1:15", "nodeType": "VariableDeclaration", "scope": 24600, "src": "3609:9:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 24595, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "3609:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 24598, "mutability": "mutable", "name": "y", "nameLocation": "3628:1:15", "nodeType": "VariableDeclaration", "scope": 24600, "src": "3620:9:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 24597, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "3620:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "3608:22:15" } }, { "id": 26338, "nodeType": "ContractDefinition", "src": "3951:21323:15", "nodes": [ { "id": 24604, "nodeType": "StructDefinition", "src": "3994:44:15", "canonicalName": "PRBMath.SD59x18", "members": [ { "constant": false, "id": 24603, "mutability": "mutable", "name": "value", "nameLocation": "4026:5:15", "nodeType": "VariableDeclaration", "scope": 24604, "src": "4019:12:15", "stateVariable": false, "storageLocation": 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false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "11587:30:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "3634", "id": 25489, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "11621:2:15", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "11587:36:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "11578:45:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 25492, "nodeType": "ExpressionStatement", "src": "11578:45:15" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 25499, "isConstant": false, "isLValue": false, "isPure": false, 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"nodeType": "TupleExpression", "src": "12134:30:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "3634", "id": 25569, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12168:2:15", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "12134:36:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "12125:45:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 25572, "nodeType": "ExpressionStatement", "src": "12125:45:15" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 25579, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": 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"t_uint256", "typeString": "uint256" }, "id": 25595, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 25593, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 25591, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 24622, "src": "12311:1:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "&", "rightExpression": { "hexValue": "307838", "id": 25592, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12315:3:15", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "0x8" }, "src": "12311:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 25594, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12321:1:15", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "12311:11:15", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 25606, "nodeType": "IfStatement", "src": "12307:95:15", "trueBody": { "id": 25605, "nodeType": "Block", "src": "12324:78:15", "statements": [ { "expression": { "id": 25603, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 25596, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 24625, "src": "12342:6:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 25602, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "components": [ { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 25599, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 25597, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 24625, "src": "12352:6:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "*", "rightExpression": { "hexValue": "30783130303030303030303030303030303036", "id": 25598, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12361:19:15", "typeDescriptions": { "typeIdentifier": "t_rational_18446744073709551622_by_1", "typeString": "int_const 18446744073709551622" }, "value": "0x10000000000000006" }, "src": "12352:28:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "id": 25600, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "12351:30:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "3634", "id": 25601, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12385:2:15", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "12351:36:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "12342:45:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 25604, "nodeType": "ExpressionStatement", "src": "12342:45:15" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 25611, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 25609, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 25607, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 24622, "src": "12419:1:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "&", "rightExpression": { "hexValue": "307834", "id": 25608, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12423:3:15", "typeDescriptions": { "typeIdentifier": "t_rational_4_by_1", "typeString": "int_const 4" }, "value": "0x4" }, "src": "12419:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 25610, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12429:1:15", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "12419:11:15", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 25622, "nodeType": "IfStatement", "src": "12415:95:15", "trueBody": { "id": 25621, "nodeType": "Block", "src": "12432:78:15", "statements": [ { "expression": { "id": 25619, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 25612, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 24625, "src": "12450:6:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 25618, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "components": [ { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 25615, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 25613, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 24625, "src": "12460:6:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "*", "rightExpression": { "hexValue": "30783130303030303030303030303030303033", "id": 25614, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12469:19:15", "typeDescriptions": { "typeIdentifier": "t_rational_18446744073709551619_by_1", "typeString": "int_const 18446744073709551619" }, "value": "0x10000000000000003" }, "src": "12460:28:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "id": 25616, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "12459:30:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "3634", "id": 25617, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12493:2:15", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "12459:36:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "12450:45:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 25620, "nodeType": "ExpressionStatement", "src": "12450:45:15" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 25627, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 25625, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 25623, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 24622, "src": "12527:1:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "&", "rightExpression": { "hexValue": "307832", "id": 25624, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12531:3:15", "typeDescriptions": { "typeIdentifier": "t_rational_2_by_1", "typeString": "int_const 2" }, "value": "0x2" }, "src": "12527:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 25626, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12537:1:15", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "12527:11:15", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 25638, "nodeType": "IfStatement", "src": "12523:95:15", "trueBody": { "id": 25637, "nodeType": "Block", "src": "12540:78:15", "statements": [ { "expression": { "id": 25635, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 25628, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 24625, "src": "12558:6:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 25634, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "components": [ { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 25631, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 25629, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 24625, "src": "12568:6:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "*", "rightExpression": { "hexValue": "30783130303030303030303030303030303031", "id": 25630, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12577:19:15", "typeDescriptions": { "typeIdentifier": "t_rational_18446744073709551617_by_1", "typeString": "int_const 18446744073709551617" }, "value": "0x10000000000000001" }, "src": "12568:28:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "id": 25632, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "12567:30:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "3634", "id": 25633, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12601:2:15", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "12567:36:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "12558:45:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 25636, "nodeType": "ExpressionStatement", "src": "12558:45:15" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 25643, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 25641, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 25639, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 24622, "src": "12635:1:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "&", "rightExpression": { "hexValue": "307831", "id": 25640, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12639:3:15", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "0x1" }, "src": "12635:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 25642, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12645:1:15", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "12635:11:15", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 25654, "nodeType": "IfStatement", "src": "12631:95:15", "trueBody": { "id": 25653, "nodeType": "Block", "src": "12648:78:15", "statements": [ { "expression": { "id": 25651, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 25644, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 24625, "src": "12666:6:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 25650, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "components": [ { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 25647, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 25645, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 24625, "src": "12676:6:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "*", "rightExpression": { "hexValue": "30783130303030303030303030303030303031", "id": 25646, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12685:19:15", "typeDescriptions": { "typeIdentifier": "t_rational_18446744073709551617_by_1", "typeString": "int_const 18446744073709551617" }, "value": "0x10000000000000001" }, "src": "12676:28:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "id": 25648, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "12675:30:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "3634", "id": 25649, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12709:2:15", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "12675:36:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "12666:45:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 25652, "nodeType": "ExpressionStatement", "src": "12666:45:15" } ] } }, { "expression": { "id": 25657, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 25655, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 24625, "src": "13286:6:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "*=", "rightHandSide": { "id": 25656, "name": "SCALE", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 24611, "src": "13296:5:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "13286:15:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 25658, "nodeType": "ExpressionStatement", "src": "13286:15:15" }, { "expression": { "id": 25667, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 25659, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 24625, "src": "13315:6:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "components": [ { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 25665, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "hexValue": "313931", "id": 25660, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "13327:3:15", "typeDescriptions": { "typeIdentifier": "t_rational_191_by_1", "typeString": "int_const 191" }, "value": "191" }, "nodeType": "BinaryOperation", "operator": "-", "rightExpression": { "components": [ { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 25663, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 25661, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 24622, "src": "13334:1:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "3634", "id": 25662, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "13339:2:15", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "13334:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "id": 25664, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "13333:9:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "13327:15:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "id": 25666, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "13326:17:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "13315:28:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 25668, "nodeType": "ExpressionStatement", "src": "13315:28:15" } ] } ] }, "documentation": { "id": 24620, "nodeType": "StructuredDocumentation", "src": "4523:358:15", "text": "@notice Calculates the binary exponent of x using the binary fraction method.\n @dev Has to use 192.64-bit fixed-point numbers.\n See https://ethereum.stackexchange.com/a/96594/24693.\n @param x The exponent as an unsigned 192.64-bit fixed-point number.\n @return result The result as an unsigned 60.18-decimal fixed-point number." }, "implemented": true, "kind": "function", "modifiers": [], "name": "exp2", "nameLocation": "4895:4:15", "parameters": { "id": 24623, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 24622, "mutability": "mutable", "name": "x", "nameLocation": "4908:1:15", "nodeType": "VariableDeclaration", "scope": 25671, "src": "4900:9:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 24621, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "4900:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "4899:11:15" }, "returnParameters": { "id": 24626, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 24625, "mutability": "mutable", "name": "result", "nameLocation": "4942:6:15", "nodeType": "VariableDeclaration", "scope": 25671, "src": "4934:14:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 24624, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "4934:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "4933:16:15" }, "scope": 26338, "stateMutability": "pure", "virtual": false, "visibility": "internal" }, { "id": 25796, "nodeType": "FunctionDefinition", "src": "13747:744:15", "body": { "id": 25795, "nodeType": "Block", "src": "13822:669:15", "statements": [ { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 25683, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 25679, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 25674, "src": "13836:1:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "commonType": { "typeIdentifier": "t_rational_340282366920938463463374607431768211456_by_1", "typeString": "int_const 3402...(31 digits omitted)...1456" }, "id": 25682, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "32", "id": 25680, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "13841:1:15", "typeDescriptions": { "typeIdentifier": "t_rational_2_by_1", "typeString": "int_const 2" }, "value": "2" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "313238", "id": 25681, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "13844:3:15", "typeDescriptions": { "typeIdentifier": "t_rational_128_by_1", "typeString": "int_const 128" }, "value": "128" }, "src": "13841:6:15", "typeDescriptions": { "typeIdentifier": "t_rational_340282366920938463463374607431768211456_by_1", "typeString": "int_const 3402...(31 digits omitted)...1456" } }, "src": "13836:11:15", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 25693, "nodeType": "IfStatement", "src": "13832:75:15", "trueBody": { "id": 25692, "nodeType": "Block", "src": "13849:58:15", "statements": [ { "expression": { "id": 25686, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 25684, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 25674, "src": "13863:1:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "313238", "id": 25685, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "13869:3:15", "typeDescriptions": { "typeIdentifier": "t_rational_128_by_1", "typeString": "int_const 128" }, "value": "128" }, "src": "13863:9:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 25687, "nodeType": "ExpressionStatement", "src": "13863:9:15" }, { "expression": { "id": 25690, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 25688, "name": "msb", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 25677, "src": "13886:3:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "313238", "id": 25689, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "13893:3:15", "typeDescriptions": { "typeIdentifier": "t_rational_128_by_1", "typeString": "int_const 128" }, "value": "128" }, "src": "13886:10:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 25691, "nodeType": "ExpressionStatement", "src": "13886:10:15" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 25698, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 25694, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 25674, "src": "13920:1:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "commonType": { "typeIdentifier": "t_rational_18446744073709551616_by_1", "typeString": "int_const 18446744073709551616" }, "id": 25697, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "32", "id": 25695, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "13925:1:15", "typeDescriptions": { "typeIdentifier": "t_rational_2_by_1", "typeString": "int_const 2" }, "value": "2" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "3634", "id": 25696, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "13928:2:15", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "13925:5:15", "typeDescriptions": { "typeIdentifier": "t_rational_18446744073709551616_by_1", "typeString": "int_const 18446744073709551616" } }, "src": "13920:10:15", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 25708, "nodeType": "IfStatement", "src": "13916:72:15", "trueBody": { "id": 25707, "nodeType": "Block", "src": "13932:56:15", "statements": [ { "expression": { "id": 25701, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 25699, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 25674, "src": "13946:1:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "3634", "id": 25700, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "13952:2:15", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "13946:8:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 25702, "nodeType": "ExpressionStatement", "src": "13946:8:15" }, { "expression": { "id": 25705, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 25703, "name": "msb", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 25677, "src": "13968:3:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "3634", "id": 25704, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "13975:2:15", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "13968:9:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 25706, "nodeType": "ExpressionStatement", "src": "13968:9:15" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 25713, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 25709, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 25674, "src": "14001:1:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "commonType": { "typeIdentifier": "t_rational_4294967296_by_1", "typeString": "int_const 4294967296" }, "id": 25712, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "32", "id": 25710, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "14006:1:15", "typeDescriptions": { "typeIdentifier": "t_rational_2_by_1", "typeString": "int_const 2" }, "value": "2" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "3332", "id": 25711, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "14009:2:15", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "14006:5:15", "typeDescriptions": { "typeIdentifier": "t_rational_4294967296_by_1", "typeString": "int_const 4294967296" } }, "src": "14001:10:15", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 25723, "nodeType": "IfStatement", "src": "13997:72:15", "trueBody": { "id": 25722, "nodeType": "Block", "src": "14013:56:15", "statements": [ { "expression": { "id": 25716, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 25714, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 25674, "src": "14027:1:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "3332", "id": 25715, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "14033:2:15", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "14027:8:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 25717, "nodeType": "ExpressionStatement", "src": "14027:8:15" }, { "expression": { "id": 25720, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 25718, "name": "msb", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 25677, "src": "14049:3:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "3332", "id": 25719, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "14056:2:15", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "14049:9:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 25721, "nodeType": "ExpressionStatement", "src": "14049:9:15" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 25728, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 25724, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 25674, "src": "14082:1:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "commonType": { "typeIdentifier": "t_rational_65536_by_1", "typeString": "int_const 65536" }, "id": 25727, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "32", "id": 25725, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "14087:1:15", "typeDescriptions": { "typeIdentifier": "t_rational_2_by_1", "typeString": "int_const 2" }, "value": "2" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "3136", "id": 25726, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "14090:2:15", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "14087:5:15", "typeDescriptions": { "typeIdentifier": "t_rational_65536_by_1", "typeString": "int_const 65536" } }, "src": "14082:10:15", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 25738, "nodeType": "IfStatement", "src": "14078:72:15", "trueBody": { "id": 25737, "nodeType": "Block", "src": "14094:56:15", "statements": [ { "expression": { "id": 25731, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 25729, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 25674, "src": "14108:1:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "3136", "id": 25730, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "14114:2:15", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "14108:8:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 25732, "nodeType": "ExpressionStatement", "src": "14108:8:15" }, { "expression": { "id": 25735, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 25733, "name": "msb", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 25677, "src": "14130:3:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "3136", "id": 25734, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "14137:2:15", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "14130:9:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 25736, "nodeType": "ExpressionStatement", "src": "14130:9:15" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 25743, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 25739, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 25674, "src": "14163:1:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "commonType": { "typeIdentifier": "t_rational_256_by_1", "typeString": "int_const 256" }, "id": 25742, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "32", "id": 25740, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "14168:1:15", "typeDescriptions": { "typeIdentifier": "t_rational_2_by_1", "typeString": "int_const 2" }, "value": "2" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "38", "id": 25741, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "14171:1:15", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "14168:4:15", "typeDescriptions": { "typeIdentifier": "t_rational_256_by_1", "typeString": "int_const 256" } }, "src": "14163:9:15", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 25753, "nodeType": "IfStatement", "src": "14159:69:15", "trueBody": { "id": 25752, "nodeType": "Block", "src": "14174:54:15", "statements": [ { "expression": { "id": 25746, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 25744, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 25674, "src": "14188:1:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "38", "id": 25745, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "14194:1:15", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "14188:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 25747, "nodeType": "ExpressionStatement", "src": "14188:7:15" }, { "expression": { "id": 25750, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 25748, "name": "msb", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 25677, "src": "14209:3:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "38", "id": 25749, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "14216:1:15", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "14209:8:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 25751, "nodeType": "ExpressionStatement", "src": "14209:8:15" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 25758, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 25754, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 25674, "src": "14241:1:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "commonType": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "id": 25757, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "leftExpression": { "hexValue": "32", "id": 25755, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "14246:1:15", "typeDescriptions": { "typeIdentifier": "t_rational_2_by_1", "typeString": "int_const 2" }, "value": "2" }, "nodeType": "BinaryOperation", "operator": "**", "rightExpression": { "hexValue": "34", "id": 25756, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, 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"isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "14272:1:15", "typeDescriptions": { "typeIdentifier": "t_rational_4_by_1", "typeString": "int_const 4" }, "value": "4" }, "src": "14266:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 25762, "nodeType": "ExpressionStatement", "src": "14266:7:15" }, { "expression": { "id": 25765, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 25763, "name": "msb", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 25677, "src": "14287:3:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "34", "id": 25764, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "14294:1:15", "typeDescriptions": { 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Before returning the\n final result, we add 1 if (x * y) % SCALE >= HALF_SCALE. Without this, 6.6e-19 would be truncated to 0 instead of\n being rounded to 1e-18. See \"Listing 6\" and text above it at https://accu.org/index.php/journals/1717.\n Requirements:\n - The result must fit within uint256.\n Caveats:\n - The body is purposely left uncommented; see the NatSpec comments in \"PRBMath.mulDiv\" to understand how this works.\n - It is assumed that the result can never be type(uint256).max when x and y solve the following two equations:\n 1. x * y = type(uint256).max * SCALE\n 2. 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"rAbs", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 26078, "src": "23263:4:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 26125, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "nodeType": "ElementaryTypeNameExpression", "src": "23256:6:15", "typeDescriptions": { "typeIdentifier": "t_type$_t_int256_$", "typeString": "type(int256)" }, "typeName": { "id": 26124, "name": "int256", "nodeType": "ElementaryTypeName", "src": "23256:6:15", "typeDescriptions": {} } }, "id": 26127, "isConstant": false, "isLValue": false, "isPure": false, "kind": "typeConversion", "lValueRequested": false, "nameLocations": [], "names": [], "nodeType": "FunctionCall", "src": "23256:12:15", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "id": 26128, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "Conditional", "src": "23220:48:15", "trueExpression": { "id": 26123, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "UnaryOperation", "operator": "-", "prefix": true, "src": "23240:13:15", "subExpression": { "arguments": [ { "id": 26121, "name": "rAbs", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 26078, "src": "23248:4:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 26120, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "nodeType": "ElementaryTypeNameExpression", "src": "23241:6:15", "typeDescriptions": { "typeIdentifier": "t_type$_t_int256_$", "typeString": "type(int256)" }, "typeName": { "id": 26119, "name": "int256", "nodeType": "ElementaryTypeName", "src": "23241:6:15", "typeDescriptions": {} } }, "id": 26122, "isConstant": false, "isLValue": false, "isPure": false, "kind": "typeConversion", "lValueRequested": false, "nameLocations": [], "names": [], "nodeType": "FunctionCall", "src": "23241:12:15", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "src": "23211:57:15", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "id": 26130, "nodeType": "ExpressionStatement", "src": "23211:57:15" } ] }, "documentation": { "id": 25980, "nodeType": "StructuredDocumentation", "src": "21346:530:15", "text": "@notice Calculates floor(x*y÷denominator) with full precision.\n @dev An extension of \"mulDiv\" for signed numbers. Works by computing the signs and the absolute values separately.\n Requirements:\n - None of the inputs can be type(int256).min.\n - The result must fit within int256.\n @param x The multiplicand as an int256.\n @param y The multiplier as an int256.\n @param denominator The divisor as an int256.\n @return result The result as an int256." }, "implemented": true, "kind": "function", "modifiers": [], "name": "mulDivSigned", "nameLocation": "21890:12:15", "parameters": { "id": 25987, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 25982, "mutability": "mutable", "name": "x", "nameLocation": "21919:1:15", "nodeType": "VariableDeclaration", "scope": 26132, "src": "21912:8:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" }, "typeName": { "id": 25981, "name": "int256", "nodeType": "ElementaryTypeName", "src": "21912:6:15", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "visibility": "internal" }, { "constant": false, "id": 25984, "mutability": "mutable", "name": "y", "nameLocation": "21937:1:15", "nodeType": "VariableDeclaration", "scope": 26132, "src": "21930:8:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" }, "typeName": { "id": 25983, "name": "int256", "nodeType": "ElementaryTypeName", "src": "21930:6:15", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "visibility": "internal" }, { "constant": false, "id": 25986, "mutability": "mutable", "name": "denominator", "nameLocation": "21955:11:15", "nodeType": "VariableDeclaration", "scope": 26132, "src": "21948:18:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" }, "typeName": { "id": 25985, "name": "int256", "nodeType": "ElementaryTypeName", "src": "21948:6:15", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "visibility": "internal" } ], "src": "21902:70:15" }, "returnParameters": { "id": 25990, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 25989, "mutability": "mutable", "name": "result", "nameLocation": "22003:6:15", "nodeType": "VariableDeclaration", "scope": 26132, "src": "21996:13:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" }, "typeName": { "id": 25988, "name": "int256", "nodeType": "ElementaryTypeName", "src": "21996:6:15", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "visibility": "internal" } ], "src": "21995:15:15" }, "scope": 26338, "stateMutability": "pure", "virtual": false, "visibility": "internal" }, { "id": 26337, "nodeType": "FunctionDefinition", "src": "23690:1582:15", "body": { "id": 26336, "nodeType": "Block", "src": "23754:1518:15", "statements": [ { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 26142, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 26140, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 26135, "src": "23768:1:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "==", "rightExpression": { "hexValue": "30", "id": 26141, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "23773:1:15", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "23768:6:15", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 26146, "nodeType": "IfStatement", "src": "23764:45:15", "trueBody": { "id": 26145, "nodeType": "Block", "src": "23776:33:15", "statements": [ { "expression": { "hexValue": "30", "id": 26143, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "23797:1:15", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "functionReturnParameters": 26139, "id": 26144, "nodeType": "Return", "src": "23790:8:15" } ] } }, { "assignments": [ 26148 ], "declarations": [ { "constant": false, "id": 26148, "mutability": "mutable", "name": "xAux", "nameLocation": "23928:4:15", "nodeType": "VariableDeclaration", "scope": 26336, "src": "23920:12:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 26147, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "23920:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "id": 26153, "initialValue": { "arguments": [ { "id": 26151, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 26135, "src": "23943:1:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 26150, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "nodeType": "ElementaryTypeNameExpression", "src": "23935:7:15", "typeDescriptions": { "typeIdentifier": "t_type$_t_uint256_$", "typeString": "type(uint256)" }, "typeName": { "id": 26149, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "23935:7:15", "typeDescriptions": {} } }, "id": 26152, "isConstant": false, "isLValue": false, "isPure": false, "kind": "typeConversion", "lValueRequested": false, "nameLocations": [], "names": [], "nodeType": "FunctionCall", "src": "23935:10:15", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "VariableDeclarationStatement", "src": "23920:25:15" }, { "expression": { "id": 26156, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 26154, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 26138, "src": "23955:6:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "hexValue": "31", "id": 26155, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "23964:1:15", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "src": "23955:10:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 26157, "nodeType": "ExpressionStatement", "src": "23955:10:15" }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 26160, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 26158, "name": "xAux", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 26148, "src": "23979:4:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "hexValue": "3078313030303030303030303030303030303030303030303030303030303030303030", "id": 26159, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "23987:35:15", "typeDescriptions": { "typeIdentifier": "t_rational_340282366920938463463374607431768211456_by_1", "typeString": "int_const 3402...(31 digits omitted)...1456" }, "value": "0x100000000000000000000000000000000" }, "src": "23979:43:15", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 26170, "nodeType": "IfStatement", "src": "23975:113:15", "trueBody": { "id": 26169, "nodeType": "Block", "src": "24024:64:15", "statements": [ { "expression": { "id": 26163, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 26161, "name": "xAux", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 26148, "src": "24038:4:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "313238", "id": 26162, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "24047:3:15", "typeDescriptions": { "typeIdentifier": "t_rational_128_by_1", "typeString": "int_const 128" }, "value": "128" }, "src": "24038:12:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 26164, "nodeType": "ExpressionStatement", "src": "24038:12:15" }, { "expression": { "id": 26167, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 26165, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 26138, "src": "24064:6:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "<<=", "rightHandSide": { "hexValue": "3634", "id": 26166, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "24075:2:15", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "24064:13:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 26168, "nodeType": "ExpressionStatement", "src": "24064:13:15" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 26173, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 26171, "name": "xAux", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 26148, "src": "24101:4:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "hexValue": "30783130303030303030303030303030303030", "id": 26172, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "24109:19:15", "typeDescriptions": { "typeIdentifier": "t_rational_18446744073709551616_by_1", "typeString": "int_const 18446744073709551616" }, "value": "0x10000000000000000" }, "src": "24101:27:15", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 26183, "nodeType": "IfStatement", "src": "24097:96:15", "trueBody": { "id": 26182, "nodeType": "Block", "src": "24130:63:15", "statements": [ { "expression": { "id": 26176, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 26174, "name": "xAux", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 26148, "src": "24144:4:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "3634", "id": 26175, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "24153:2:15", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "24144:11:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 26177, "nodeType": "ExpressionStatement", "src": "24144:11:15" }, { "expression": { "id": 26180, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 26178, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 26138, "src": "24169:6:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "<<=", "rightHandSide": { "hexValue": "3332", "id": 26179, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "24180:2:15", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "24169:13:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 26181, "nodeType": "ExpressionStatement", "src": "24169:13:15" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 26186, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 26184, "name": "xAux", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 26148, "src": "24206:4:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "hexValue": "3078313030303030303030", "id": 26185, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "24214:11:15", "typeDescriptions": { "typeIdentifier": "t_rational_4294967296_by_1", "typeString": "int_const 4294967296" }, "value": "0x100000000" }, "src": "24206:19:15", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 26196, "nodeType": "IfStatement", "src": "24202:88:15", "trueBody": { "id": 26195, "nodeType": "Block", "src": "24227:63:15", "statements": [ { "expression": { "id": 26189, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 26187, "name": "xAux", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 26148, "src": "24241:4:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "3332", "id": 26188, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "24250:2:15", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "24241:11:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 26190, "nodeType": "ExpressionStatement", "src": "24241:11:15" }, { "expression": { "id": 26193, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 26191, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 26138, "src": "24266:6:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "<<=", "rightHandSide": { "hexValue": "3136", "id": 26192, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "24277:2:15", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "24266:13:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 26194, "nodeType": "ExpressionStatement", "src": "24266:13:15" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 26199, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 26197, "name": "xAux", "nodeType": 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"typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "31", "id": 26307, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "25039:1:15", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "src": "25014:26:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "25005:35:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 26310, "nodeType": "ExpressionStatement", "src": "25005:35:15" }, { "expression": { "id": 26320, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 26311, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 26138, "src": "25054:6:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 26319, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "components": [ { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 26316, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 26312, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 26138, "src": "25064:6:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "+", "rightExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 26315, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 26313, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 26135, "src": "25073:1:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "/", "rightExpression": { "id": 26314, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 26138, "src": "25077:6:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "25073:10:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "25064:19:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "id": 26317, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "25063:21:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "31", "id": 26318, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "25088:1:15", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "src": "25063:26:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "25054:35:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 26321, "nodeType": "ExpressionStatement", "src": "25054:35:15" }, { "assignments": [ 26323 ], "declarations": [ { "constant": false, "id": 26323, "mutability": "mutable", "name": "roundedDownResult", "nameLocation": "25148:17:15", "nodeType": "VariableDeclaration", "scope": 26335, "src": "25140:25:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 26322, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "25140:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "id": 26327, "initialValue": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 26326, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 26324, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 26135, "src": "25168:1:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "/", "rightExpression": { "id": 26325, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 26138, "src": "25172:6:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "25168:10:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "VariableDeclarationStatement", "src": "25140:38:15" }, { "expression": { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 26330, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 26328, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 26138, "src": "25199:6:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "id": 26329, "name": "roundedDownResult", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 26323, "src": "25209:17:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "25199:27:15", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "falseExpression": { "id": 26332, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 26138, "src": "25249:6:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 26333, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "Conditional", "src": "25199:56:15", "trueExpression": { "id": 26331, "name": "roundedDownResult", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 26323, "src": "25229:17:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 26139, "id": 26334, "nodeType": "Return", "src": "25192:63:15" } ] } ] }, "documentation": { "id": 26133, "nodeType": "StructuredDocumentation", "src": "23281:404:15", "text": "@notice Calculates the square root of x, rounding down.\n @dev Uses the Babylonian method https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.\n Caveats:\n - This function does not work with fixed-point numbers.\n @param x The uint256 number for which to calculate the square root.\n @return result The result as an uint256." }, "implemented": true, "kind": "function", "modifiers": [], "name": "sqrt", "nameLocation": "23699:4:15", "parameters": { "id": 26136, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 26135, "mutability": "mutable", "name": "x", "nameLocation": "23712:1:15", "nodeType": "VariableDeclaration", "scope": 26337, "src": "23704:9:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 26134, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "23704:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "23703:11:15" }, "returnParameters": { "id": 26139, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 26138, "mutability": "mutable", "name": "result", "nameLocation": "23746:6:15", "nodeType": "VariableDeclaration", "scope": 26337, "src": "23738:14:15", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 26137, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "23738:7:15", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "23737:16:15" }, "scope": 26338, "stateMutability": "pure", "virtual": false, "visibility": "internal" } ], "abstract": false, "baseContracts": [], "canonicalName": "PRBMath", "contractDependencies": [], "contractKind": "library", "documentation": { "id": 24601, "nodeType": "StructuredDocumentation", "src": "3633:318:15", "text": "@dev Common mathematical functions used in both PRBMathSD59x18 and PRBMathUD60x18. Note that this shared library\n does not always assume the signed 59.18-decimal fixed-point or the unsigned 60.18-decimal fixed-point\n representation. When it does not, it is explicitly mentioned in the NatSpec documentation." }, "fullyImplemented": true, "linearizedBaseContracts": [ 26338 ], "name": "PRBMath", "nameLocation": "3959:7:15", "scope": 26339, "usedErrors": [] } ], "license": "Unlicense" }, "id": 15 }