{ "contractName": "Math", "abi": [], "metadata": "{\"compiler\":{\"version\":\"0.8.7+commit.e28d00a7\"},\"language\":\"Solidity\",\"output\":{\"abi\":[],\"devdoc\":{\"details\":\"Standard math utilities missing in the Solidity language.\",\"kind\":\"dev\",\"methods\":{},\"version\":1},\"userdoc\":{\"kind\":\"user\",\"methods\":{},\"version\":1}},\"settings\":{\"compilationTarget\":{\"@openzeppelin/contracts/utils/math/Math.sol\":\"Math\"},\"evmVersion\":\"london\",\"libraries\":{},\"metadata\":{\"bytecodeHash\":\"ipfs\"},\"optimizer\":{\"enabled\":true,\"runs\":200},\"remappings\":[]},\"sources\":{\"@openzeppelin/contracts/utils/math/Math.sol\":{\"keccak256\":\"0xd15c3e400531f00203839159b2b8e7209c5158b35618f570c695b7e47f12e9f0\",\"license\":\"MIT\",\"urls\":[\"bzz-raw://b600b852e0597aa69989cc263111f02097e2827edc1bdc70306303e3af5e9929\",\"dweb:/ipfs/QmU4WfM28A1nDqghuuGeFmN3CnVrk6opWtiF65K4vhFPeC\"]}},\"version\":1}", "bytecode": "0x60566037600b82828239805160001a607314602a57634e487b7160e01b600052600060045260246000fd5b30600052607381538281f3fe73000000000000000000000000000000000000000030146080604052600080fdfea264697066735822122095d33d3dc9105e0420d4cf361291b7d3c8f0bcc1516ec5b66ab83aab4ccbd9fd64736f6c63430008070033", "deployedBytecode": "0x73000000000000000000000000000000000000000030146080604052600080fdfea264697066735822122095d33d3dc9105e0420d4cf361291b7d3c8f0bcc1516ec5b66ab83aab4ccbd9fd64736f6c63430008070033", "immutableReferences": {}, "sourceMap": "202:8624:61:-:0;;;;;;;;;;;;;;;-1:-1:-1;;;202:8624:61;;;;;;;;;;;;;;;;;", "deployedSourceMap": "202:8624:61:-:0;;;;;;;;", "source": "// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts (last updated v4.7.0) (utils/math/Math.sol)\n\npragma solidity ^0.8.0;\n\n/**\n * @dev Standard math utilities missing in the Solidity language.\n */\nlibrary Math {\n enum Rounding {\n Down, // Toward negative infinity\n Up, // Toward infinity\n Zero // Toward zero\n }\n\n /**\n * @dev Returns the largest of two numbers.\n */\n function max(uint256 a, uint256 b) internal pure returns (uint256) {\n return a >= b ? a : b;\n }\n\n /**\n * @dev Returns the smallest of two numbers.\n */\n function min(uint256 a, uint256 b) internal pure returns (uint256) {\n return a < b ? a : b;\n }\n\n /**\n * @dev Returns the average of two numbers. The result is rounded towards\n * zero.\n */\n function average(uint256 a, uint256 b) internal pure returns (uint256) {\n // (a + b) / 2 can overflow.\n return (a & b) + (a ^ b) / 2;\n }\n\n /**\n * @dev Returns the ceiling of the division of two numbers.\n *\n * This differs from standard division with `/` in that it rounds up instead\n * of rounding down.\n */\n function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {\n // (a + b - 1) / b can overflow on addition, so we distribute.\n return a == 0 ? 0 : (a - 1) / b + 1;\n }\n\n /**\n * @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or denominator == 0\n * @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv)\n * with further edits by Uniswap Labs also under MIT license.\n */\n function mulDiv(\n uint256 x,\n uint256 y,\n uint256 denominator\n ) internal pure returns (uint256 result) {\n unchecked {\n // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use\n // use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256\n // variables such that product = prod1 * 2^256 + prod0.\n uint256 prod0; // Least significant 256 bits of the product\n uint256 prod1; // Most significant 256 bits of the product\n assembly {\n let mm := mulmod(x, y, not(0))\n prod0 := mul(x, y)\n prod1 := sub(sub(mm, prod0), lt(mm, prod0))\n }\n\n // Handle non-overflow cases, 256 by 256 division.\n if (prod1 == 0) {\n return prod0 / denominator;\n }\n\n // Make sure the result is less than 2^256. Also prevents denominator == 0.\n require(denominator > prod1);\n\n ///////////////////////////////////////////////\n // 512 by 256 division.\n ///////////////////////////////////////////////\n\n // Make division exact by subtracting the remainder from [prod1 prod0].\n uint256 remainder;\n assembly {\n // Compute remainder using mulmod.\n remainder := mulmod(x, y, denominator)\n\n // Subtract 256 bit number from 512 bit number.\n prod1 := sub(prod1, gt(remainder, prod0))\n prod0 := sub(prod0, remainder)\n }\n\n // Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.\n // See https://cs.stackexchange.com/q/138556/92363.\n\n // Does not overflow because the denominator cannot be zero at this stage in the function.\n uint256 twos = denominator & (~denominator + 1);\n assembly {\n // Divide denominator by twos.\n denominator := div(denominator, twos)\n\n // Divide [prod1 prod0] by twos.\n prod0 := div(prod0, twos)\n\n // Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.\n twos := add(div(sub(0, twos), twos), 1)\n }\n\n // Shift in bits from prod1 into prod0.\n prod0 |= prod1 * twos;\n\n // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such\n // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for\n // four bits. That is, denominator * inv = 1 mod 2^4.\n uint256 inverse = (3 * denominator) ^ 2;\n\n // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works\n // in modular arithmetic, doubling the correct bits in each step.\n inverse *= 2 - denominator * inverse; // inverse mod 2^8\n inverse *= 2 - denominator * inverse; // inverse mod 2^16\n inverse *= 2 - denominator * inverse; // inverse mod 2^32\n inverse *= 2 - denominator * inverse; // inverse mod 2^64\n inverse *= 2 - denominator * inverse; // inverse mod 2^128\n inverse *= 2 - denominator * inverse; // inverse mod 2^256\n\n // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.\n // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is\n // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1\n // is no longer required.\n result = prod0 * inverse;\n return result;\n }\n }\n\n /**\n * @notice Calculates x * y / denominator with full precision, following the selected rounding direction.\n */\n function mulDiv(\n uint256 x,\n uint256 y,\n uint256 denominator,\n Rounding rounding\n ) internal pure returns (uint256) {\n uint256 result = mulDiv(x, y, denominator);\n if (rounding == Rounding.Up && mulmod(x, y, denominator) > 0) {\n result += 1;\n }\n return result;\n }\n\n /**\n * @dev Returns the square root of a number. It the number is not a perfect square, the value is rounded down.\n *\n * Inspired by Henry S. Warren, Jr.'s \"Hacker's Delight\" (Chapter 11).\n */\n function sqrt(uint256 a) internal pure returns (uint256) {\n if (a == 0) {\n return 0;\n }\n\n // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.\n // We know that the \"msb\" (most significant bit) of our target number `a` is a power of 2 such that we have\n // `msb(a) <= a < 2*msb(a)`.\n // We also know that `k`, the position of the most significant bit, is such that `msb(a) = 2**k`.\n // This gives `2**k < a <= 2**(k+1)` → `2**(k/2) <= sqrt(a) < 2 ** (k/2+1)`.\n // Using an algorithm similar to the msb conmputation, we are able to compute `result = 2**(k/2)` which is a\n // good first aproximation of `sqrt(a)` with at least 1 correct bit.\n uint256 result = 1;\n uint256 x = a;\n if (x >> 128 > 0) {\n x >>= 128;\n result <<= 64;\n }\n if (x >> 64 > 0) {\n x >>= 64;\n result <<= 32;\n }\n if (x >> 32 > 0) {\n x >>= 32;\n result <<= 16;\n }\n if (x >> 16 > 0) {\n x >>= 16;\n result <<= 8;\n }\n if (x >> 8 > 0) {\n x >>= 8;\n result <<= 4;\n }\n if (x >> 4 > 0) {\n x >>= 4;\n result <<= 2;\n }\n if (x >> 2 > 0) {\n result <<= 1;\n }\n\n // At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,\n // since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at\n // every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision\n // into the expected uint128 result.\n unchecked {\n result = (result + a / result) >> 1;\n result = (result + a / result) >> 1;\n result = (result + a / result) >> 1;\n result = (result + a / result) >> 1;\n result = (result + a / result) >> 1;\n result = (result + a / result) >> 1;\n result = (result + a / result) >> 1;\n return min(result, a / result);\n }\n }\n\n /**\n * @notice Calculates sqrt(a), following the selected rounding direction.\n */\n function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {\n uint256 result = sqrt(a);\n if (rounding == Rounding.Up && result * result < a) {\n result += 1;\n }\n return result;\n }\n}\n", "sourcePath": "@openzeppelin/contracts/utils/math/Math.sol", "ast": { "absolutePath": "@openzeppelin/contracts/utils/math/Math.sol", "exportedSymbols": { "Math": [ 12856 ] }, "id": 12857, "license": "MIT", "nodeType": "SourceUnit", "nodes": [ { 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"typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "5525:24:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12560, "nodeType": "ExpressionStatement", "src": "5525:24:61" }, { "expression": { "id": 12561, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12453, "src": "5570:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 12454, "id": 12562, "nodeType": "Return", "src": "5563:13:61" } ] } ] }, "documentation": { "id": 12444, "nodeType": "StructuredDocumentation", "src": "1358:305:61", "text": " @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or denominator == 0\n @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv)\n with further edits by Uniswap Labs also under MIT license." }, "id": 12565, "implemented": true, "kind": "function", "modifiers": [], "name": "mulDiv", "nameLocation": "1677:6:61", "nodeType": "FunctionDefinition", "parameters": { "id": 12451, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 12446, "mutability": "mutable", "name": "x", "nameLocation": "1701:1:61", "nodeType": "VariableDeclaration", "scope": 12565, "src": "1693:9:61", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12445, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "1693:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 12448, 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"internal" } ], "src": "1683:73:61" }, "returnParameters": { "id": 12454, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 12453, "mutability": "mutable", "name": "result", "nameLocation": "1788:6:61", "nodeType": "VariableDeclaration", "scope": 12565, "src": "1780:14:61", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12452, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "1780:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "1779:16:61" }, "scope": 12856, "src": "1668:3925:61", "stateMutability": "pure", "virtual": false, "visibility": "internal" }, { "body": { "id": 12608, "nodeType": "Block", "src": "5873:189:61", "statements": [ { "assignments": [ 12581 ], "declarations": [ { "constant": false, "id": 12581, "mutability": "mutable", "name": "result", "nameLocation": "5891:6:61", "nodeType": "VariableDeclaration", "scope": 12608, "src": "5883:14:61", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12580, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "5883:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "id": 12587, "initialValue": { "arguments": [ { "id": 12583, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12568, "src": "5907:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 12584, "name": "y", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12570, "src": "5910:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 12585, "name": "denominator", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12572, "src": "5913:11:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 12582, "name": "mulDiv", "nodeType": "Identifier", "overloadedDeclarations": [ 12565, 12609 ], "referencedDeclaration": 12565, "src": "5900:6:61", "typeDescriptions": { "typeIdentifier": "t_function_internal_pure$_t_uint256_$_t_uint256_$_t_uint256_$returns$_t_uint256_$", "typeString": "function (uint256,uint256,uint256) pure returns (uint256)" } }, "id": 12586, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "5900:25:61", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "VariableDeclarationStatement", "src": "5883:42:61" }, { "condition": { "commonType": { "typeIdentifier": "t_bool", "typeString": "bool" }, "id": 12599, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_enum$_Rounding_$12359", "typeString": "enum Math.Rounding" }, "id": 12591, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12588, "name": "rounding", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12575, "src": "5939:8:61", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$12359", "typeString": "enum Math.Rounding" } }, "nodeType": "BinaryOperation", "operator": "==", "rightExpression": { "expression": { "id": 12589, "name": "Rounding", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12359, "src": "5951:8:61", "typeDescriptions": { "typeIdentifier": "t_type$_t_enum$_Rounding_$12359_$", "typeString": "type(enum Math.Rounding)" } }, "id": 12590, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "memberName": "Up", "nodeType": "MemberAccess", "referencedDeclaration": 12357, "src": "5951:11:61", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$12359", "typeString": "enum Math.Rounding" } }, "src": "5939:23:61", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "nodeType": "BinaryOperation", "operator": "&&", "rightExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12598, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "arguments": [ { "id": 12593, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12568, "src": "5973:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 12594, "name": "y", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12570, "src": "5976:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 12595, "name": "denominator", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12572, "src": "5979:11:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 12592, "name": "mulmod", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4294967280, "src": "5966:6:61", "typeDescriptions": { "typeIdentifier": "t_function_mulmod_pure$_t_uint256_$_t_uint256_$_t_uint256_$returns$_t_uint256_$", "typeString": "function (uint256,uint256,uint256) pure returns (uint256)" } }, "id": 12596, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "5966:25:61", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 12597, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "5994:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "5966:29:61", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "src": "5939:56:61", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 12605, "nodeType": "IfStatement", "src": "5935:98:61", "trueBody": { "id": 12604, "nodeType": "Block", "src": "5997:36:61", "statements": [ { "expression": { "id": 12602, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12600, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12581, "src": "6011:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "31", "id": 12601, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "6021:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "src": "6011:11:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12603, "nodeType": "ExpressionStatement", "src": "6011:11:61" } ] } }, { "expression": { "id": 12606, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12581, "src": "6049:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 12579, "id": 12607, "nodeType": "Return", "src": "6042:13:61" } ] }, "documentation": { "id": 12566, "nodeType": "StructuredDocumentation", "src": "5599:121:61", "text": " @notice Calculates x * y / denominator with full precision, following the selected rounding direction." }, "id": 12609, "implemented": true, "kind": "function", "modifiers": [], "name": "mulDiv", "nameLocation": "5734:6:61", "nodeType": "FunctionDefinition", "parameters": { "id": 12576, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 12568, "mutability": "mutable", "name": "x", "nameLocation": "5758:1:61", "nodeType": "VariableDeclaration", "scope": 12609, "src": "5750:9:61", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12567, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "5750:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 12570, "mutability": "mutable", "name": "y", "nameLocation": "5777:1:61", "nodeType": "VariableDeclaration", "scope": 12609, "src": "5769:9:61", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12569, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "5769:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 12572, "mutability": "mutable", "name": "denominator", "nameLocation": "5796:11:61", "nodeType": "VariableDeclaration", "scope": 12609, "src": "5788:19:61", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12571, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "5788:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 12575, "mutability": "mutable", "name": "rounding", "nameLocation": "5826:8:61", "nodeType": "VariableDeclaration", "scope": 12609, "src": "5817:17:61", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$12359", "typeString": "enum Math.Rounding" }, "typeName": { "id": 12574, "nodeType": "UserDefinedTypeName", "pathNode": { "id": 12573, "name": "Rounding", "nodeType": "IdentifierPath", "referencedDeclaration": 12359, "src": "5817:8:61" }, "referencedDeclaration": 12359, "src": "5817:8:61", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$12359", "typeString": "enum Math.Rounding" } }, "visibility": "internal" } ], "src": "5740:100:61" }, "returnParameters": { "id": 12579, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 12578, "mutability": "mutable", "name": "", "nameLocation": "-1:-1:-1", "nodeType": "VariableDeclaration", "scope": 12609, "src": "5864:7:61", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12577, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "5864:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "5863:9:61" }, "scope": 12856, "src": "5725:337:61", "stateMutability": "pure", "virtual": false, "visibility": "internal" }, { "body": { "id": 12818, "nodeType": "Block", "src": "6338:2149:61", "statements": [ { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12619, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12617, "name": "a", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12612, "src": "6352:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "==", "rightExpression": { "hexValue": "30", "id": 12618, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "6357:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "6352:6:61", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 12623, "nodeType": "IfStatement", "src": "6348:45:61", "trueBody": { "id": 12622, "nodeType": "Block", "src": "6360:33:61", "statements": [ { "expression": { "hexValue": "30", "id": 12620, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "6381:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "functionReturnParameters": 12616, "id": 12621, "nodeType": "Return", "src": "6374:8:61" } ] } }, { "assignments": [ 12625 ], "declarations": [ { "constant": false, "id": 12625, "mutability": "mutable", "name": "result", "nameLocation": "7066:6:61", "nodeType": "VariableDeclaration", "scope": 12818, "src": "7058:14:61", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12624, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "7058:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "id": 12627, "initialValue": { "hexValue": "31", "id": 12626, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7075:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "nodeType": "VariableDeclarationStatement", "src": "7058:18:61" }, { "assignments": [ 12629 ], "declarations": [ { "constant": false, "id": 12629, "mutability": "mutable", "name": "x", "nameLocation": "7094:1:61", "nodeType": "VariableDeclaration", "scope": 12818, "src": "7086:9:61", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12628, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "7086:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "id": 12631, "initialValue": { "id": 12630, "name": "a", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12612, "src": "7098:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "VariableDeclarationStatement", "src": "7086:13:61" }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12636, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12634, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12632, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12629, "src": "7113:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "313238", "id": 12633, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7118:3:61", "typeDescriptions": { "typeIdentifier": "t_rational_128_by_1", "typeString": "int_const 128" }, "value": "128" }, "src": "7113:8:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 12635, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7124:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "7113:12:61", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 12646, "nodeType": "IfStatement", "src": "7109:79:61", "trueBody": { "id": 12645, "nodeType": "Block", "src": "7127:61:61", "statements": [ { "expression": { "id": 12639, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12637, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12629, "src": "7141:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "313238", "id": 12638, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7147:3:61", "typeDescriptions": { "typeIdentifier": "t_rational_128_by_1", "typeString": "int_const 128" }, "value": "128" }, "src": "7141:9:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12640, "nodeType": "ExpressionStatement", "src": "7141:9:61" }, { "expression": { "id": 12643, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12641, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "7164:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "<<=", "rightHandSide": { "hexValue": "3634", "id": 12642, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7175:2:61", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "7164:13:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12644, "nodeType": "ExpressionStatement", "src": "7164:13:61" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12651, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12649, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12647, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12629, "src": "7201:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "3634", "id": 12648, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7206:2:61", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "7201:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 12650, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7211:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "7201:11:61", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 12661, "nodeType": "IfStatement", "src": "7197:77:61", "trueBody": { "id": 12660, "nodeType": "Block", "src": "7214:60:61", "statements": [ { "expression": { "id": 12654, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12652, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12629, "src": "7228:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "3634", "id": 12653, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7234:2:61", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "7228:8:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12655, "nodeType": "ExpressionStatement", "src": "7228:8:61" }, { "expression": { "id": 12658, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12656, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "7250:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "<<=", "rightHandSide": { "hexValue": "3332", "id": 12657, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7261:2:61", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "7250:13:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12659, "nodeType": "ExpressionStatement", "src": "7250:13:61" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12666, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12664, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12662, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12629, "src": "7287:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "3332", "id": 12663, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7292:2:61", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "7287:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 12665, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7297:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "7287:11:61", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 12676, "nodeType": "IfStatement", "src": "7283:77:61", "trueBody": { "id": 12675, "nodeType": "Block", "src": "7300:60:61", "statements": [ { "expression": { "id": 12669, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12667, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12629, "src": "7314:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "3332", "id": 12668, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7320:2:61", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "7314:8:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12670, "nodeType": "ExpressionStatement", "src": "7314:8:61" }, { "expression": { "id": 12673, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12671, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "7336:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "<<=", "rightHandSide": { "hexValue": "3136", "id": 12672, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7347:2:61", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "7336:13:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12674, "nodeType": "ExpressionStatement", "src": "7336:13:61" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12681, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12679, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12677, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12629, "src": "7373:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "3136", "id": 12678, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7378:2:61", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "7373:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 12680, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7383:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "7373:11:61", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 12691, "nodeType": "IfStatement", "src": "7369:76:61", "trueBody": { "id": 12690, "nodeType": "Block", "src": "7386:59:61", "statements": [ { "expression": { "id": 12684, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12682, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12629, "src": "7400:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "3136", "id": 12683, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7406:2:61", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "7400:8:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12685, "nodeType": "ExpressionStatement", "src": "7400:8:61" }, { "expression": { "id": 12688, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12686, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "7422:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "<<=", "rightHandSide": { "hexValue": "38", "id": 12687, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7433:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "7422:12:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12689, "nodeType": "ExpressionStatement", "src": "7422:12:61" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12696, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12694, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12692, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12629, "src": "7458:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "38", "id": 12693, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7463:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "7458:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 12695, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7467:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "7458:10:61", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 12706, "nodeType": "IfStatement", "src": "7454:74:61", "trueBody": { "id": 12705, "nodeType": "Block", "src": "7470:58:61", "statements": [ { "expression": { "id": 12699, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12697, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12629, "src": "7484:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "38", "id": 12698, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7490:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "7484:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12700, "nodeType": "ExpressionStatement", "src": "7484:7:61" }, { "expression": { "id": 12703, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12701, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "7505:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "<<=", "rightHandSide": { "hexValue": "34", "id": 12702, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7516:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_4_by_1", "typeString": "int_const 4" }, "value": "4" }, "src": "7505:12:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12704, "nodeType": "ExpressionStatement", "src": "7505:12:61" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12711, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12709, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12707, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12629, "src": "7541:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "34", "id": 12708, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7546:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_4_by_1", "typeString": "int_const 4" }, "value": "4" }, "src": "7541:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 12710, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7550:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "7541:10:61", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 12721, "nodeType": "IfStatement", "src": "7537:74:61", "trueBody": { "id": 12720, "nodeType": "Block", "src": "7553:58:61", "statements": [ { "expression": { "id": 12714, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12712, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12629, "src": "7567:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "34", "id": 12713, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7573:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_4_by_1", "typeString": "int_const 4" }, "value": "4" }, "src": "7567:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12715, "nodeType": "ExpressionStatement", "src": "7567:7:61" }, { "expression": { "id": 12718, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12716, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "7588:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "<<=", "rightHandSide": { "hexValue": "32", "id": 12717, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7599:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_2_by_1", "typeString": "int_const 2" }, "value": "2" }, "src": "7588:12:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12719, "nodeType": "ExpressionStatement", "src": "7588:12:61" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12726, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12724, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12722, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12629, "src": "7624:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "32", "id": 12723, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7629:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_2_by_1", "typeString": "int_const 2" }, "value": "2" }, "src": "7624:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 12725, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7633:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "7624:10:61", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 12732, "nodeType": "IfStatement", "src": "7620:53:61", "trueBody": { "id": 12731, "nodeType": "Block", "src": "7636:37:61", "statements": [ { "expression": { "id": 12729, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12727, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "7650:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "<<=", "rightHandSide": { "hexValue": "31", "id": 12728, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7661:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "src": "7650:12:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12730, "nodeType": "ExpressionStatement", "src": "7650:12:61" } ] } }, { "id": 12817, "nodeType": "UncheckedBlock", "src": "8073:408:61", "statements": [ { "expression": { "id": 12742, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12733, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "8097:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12741, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "components": [ { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12738, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12734, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "8107:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "+", "rightExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12737, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12735, "name": "a", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12612, "src": "8116:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "/", "rightExpression": { "id": 12736, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "8120:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "8116:10:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "8107:19:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "id": 12739, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "8106:21:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "31", "id": 12740, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "8131:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "src": "8106:26:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "8097:35:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12743, "nodeType": "ExpressionStatement", "src": "8097:35:61" }, { "expression": { "id": 12753, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12744, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "8146:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12752, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "components": [ { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12749, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12745, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "8156:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "+", "rightExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12748, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12746, "name": "a", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12612, "src": "8165:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "/", "rightExpression": { "id": 12747, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "8169:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": 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"Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "8342:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12796, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "components": [ { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12793, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12789, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "8352:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "+", "rightExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" 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"8351:21:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "31", "id": 12795, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "8376:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "src": "8351:26:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "8342:35:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12798, "nodeType": "ExpressionStatement", "src": "8342:35:61" }, { "expression": { "id": 12808, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12799, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "8391:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12807, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "components": [ { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12804, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12800, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "8401:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "+", "rightExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12803, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12801, "name": "a", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12612, "src": "8410:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "/", "rightExpression": { "id": 12802, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "8414:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "8410:10:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "8401:19:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "id": 12805, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "8400:21:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "31", "id": 12806, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "8425:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "src": "8400:26:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "8391:35:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12809, "nodeType": "ExpressionStatement", "src": "8391:35:61" }, { "expression": { "arguments": [ { "id": 12811, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "8451:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12814, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12812, "name": "a", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12612, "src": "8459:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "/", "rightExpression": { "id": 12813, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "8463:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "8459:10:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 12810, "name": "min", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12395, "src": "8447:3:61", "typeDescriptions": { "typeIdentifier": "t_function_internal_pure$_t_uint256_$_t_uint256_$returns$_t_uint256_$", "typeString": "function (uint256,uint256) pure returns (uint256)" } }, "id": 12815, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "8447:23:61", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 12616, "id": 12816, "nodeType": "Return", "src": "8440:30:61" } ] } ] }, "documentation": { "id": 12610, "nodeType": "StructuredDocumentation", "src": "6068:208:61", "text": " @dev Returns the square root of a number. It the number is not a perfect square, the value is rounded down.\n Inspired by Henry S. Warren, Jr.'s \"Hacker's Delight\" (Chapter 11)." }, "id": 12819, "implemented": true, "kind": "function", "modifiers": [], "name": "sqrt", "nameLocation": "6290:4:61", "nodeType": "FunctionDefinition", "parameters": { "id": 12613, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 12612, "mutability": "mutable", "name": "a", "nameLocation": "6303:1:61", "nodeType": "VariableDeclaration", "scope": 12819, "src": "6295:9:61", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12611, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "6295:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "6294:11:61" }, "returnParameters": { "id": 12616, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 12615, "mutability": "mutable", "name": "", "nameLocation": "-1:-1:-1", "nodeType": "VariableDeclaration", "scope": 12819, "src": "6329:7:61", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12614, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "6329:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "6328:9:61" }, "scope": 12856, "src": "6281:2206:61", "stateMutability": "pure", "virtual": false, "visibility": "internal" }, { "body": { "id": 12854, "nodeType": "Block", "src": "8663:161:61", "statements": [ { "assignments": [ 12831 ], "declarations": [ { "constant": false, "id": 12831, "mutability": "mutable", "name": "result", "nameLocation": "8681:6:61", "nodeType": "VariableDeclaration", "scope": 12854, "src": "8673:14:61", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, 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"typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "5525:24:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12560, "nodeType": "ExpressionStatement", "src": "5525:24:61" }, { "expression": { "id": 12561, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12453, "src": "5570:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 12454, "id": 12562, "nodeType": "Return", "src": "5563:13:61" } ] } ] }, "documentation": { "id": 12444, "nodeType": "StructuredDocumentation", "src": "1358:305:61", "text": " @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or denominator == 0\n @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv)\n with further edits by Uniswap Labs also under MIT license." }, "id": 12565, "implemented": true, "kind": "function", "modifiers": [], "name": "mulDiv", "nameLocation": "1677:6:61", "nodeType": "FunctionDefinition", "parameters": { "id": 12451, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 12446, "mutability": "mutable", "name": "x", "nameLocation": "1701:1:61", "nodeType": "VariableDeclaration", "scope": 12565, "src": "1693:9:61", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12445, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "1693:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 12448, 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"internal" } ], "src": "1683:73:61" }, "returnParameters": { "id": 12454, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 12453, "mutability": "mutable", "name": "result", "nameLocation": "1788:6:61", "nodeType": "VariableDeclaration", "scope": 12565, "src": "1780:14:61", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12452, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "1780:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "1779:16:61" }, "scope": 12856, "src": "1668:3925:61", "stateMutability": "pure", "virtual": false, "visibility": "internal" }, { "body": { "id": 12608, "nodeType": "Block", "src": "5873:189:61", "statements": [ { "assignments": [ 12581 ], "declarations": [ { "constant": false, "id": 12581, "mutability": "mutable", "name": "result", "nameLocation": "5891:6:61", "nodeType": "VariableDeclaration", "scope": 12608, "src": "5883:14:61", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12580, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "5883:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "id": 12587, "initialValue": { "arguments": [ { "id": 12583, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12568, "src": "5907:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 12584, "name": "y", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12570, "src": "5910:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 12585, "name": "denominator", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12572, "src": "5913:11:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 12582, "name": "mulDiv", "nodeType": "Identifier", "overloadedDeclarations": [ 12565, 12609 ], "referencedDeclaration": 12565, "src": "5900:6:61", "typeDescriptions": { "typeIdentifier": "t_function_internal_pure$_t_uint256_$_t_uint256_$_t_uint256_$returns$_t_uint256_$", "typeString": "function (uint256,uint256,uint256) pure returns (uint256)" } }, "id": 12586, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "5900:25:61", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "VariableDeclarationStatement", "src": "5883:42:61" }, { "condition": { "commonType": { "typeIdentifier": "t_bool", "typeString": "bool" }, "id": 12599, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_enum$_Rounding_$12359", "typeString": "enum Math.Rounding" }, "id": 12591, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12588, "name": "rounding", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12575, "src": "5939:8:61", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$12359", "typeString": "enum Math.Rounding" } }, "nodeType": "BinaryOperation", "operator": "==", "rightExpression": { "expression": { "id": 12589, "name": "Rounding", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12359, "src": "5951:8:61", "typeDescriptions": { "typeIdentifier": "t_type$_t_enum$_Rounding_$12359_$", "typeString": "type(enum Math.Rounding)" } }, "id": 12590, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "memberName": "Up", "nodeType": "MemberAccess", "referencedDeclaration": 12357, "src": "5951:11:61", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$12359", "typeString": "enum Math.Rounding" } }, "src": "5939:23:61", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "nodeType": "BinaryOperation", "operator": "&&", "rightExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12598, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "arguments": [ { "id": 12593, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12568, "src": "5973:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 12594, "name": "y", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12570, "src": "5976:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 12595, "name": "denominator", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12572, "src": "5979:11:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 12592, "name": "mulmod", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4294967280, "src": "5966:6:61", "typeDescriptions": { "typeIdentifier": "t_function_mulmod_pure$_t_uint256_$_t_uint256_$_t_uint256_$returns$_t_uint256_$", "typeString": "function (uint256,uint256,uint256) pure returns (uint256)" } }, "id": 12596, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "5966:25:61", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 12597, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "5994:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "5966:29:61", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "src": "5939:56:61", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 12605, "nodeType": "IfStatement", "src": "5935:98:61", "trueBody": { "id": 12604, "nodeType": "Block", "src": "5997:36:61", "statements": [ { "expression": { "id": 12602, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12600, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12581, "src": "6011:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "31", "id": 12601, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "6021:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "src": "6011:11:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12603, "nodeType": "ExpressionStatement", "src": "6011:11:61" } ] } }, { "expression": { "id": 12606, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12581, "src": "6049:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 12579, "id": 12607, "nodeType": "Return", "src": "6042:13:61" } ] }, "documentation": { "id": 12566, "nodeType": "StructuredDocumentation", "src": "5599:121:61", "text": " @notice Calculates x * y / denominator with full precision, following the selected rounding direction." }, "id": 12609, "implemented": true, "kind": "function", "modifiers": [], "name": "mulDiv", "nameLocation": "5734:6:61", "nodeType": "FunctionDefinition", "parameters": { "id": 12576, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 12568, "mutability": "mutable", "name": "x", "nameLocation": "5758:1:61", "nodeType": "VariableDeclaration", "scope": 12609, "src": "5750:9:61", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12567, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "5750:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 12570, "mutability": "mutable", "name": "y", "nameLocation": "5777:1:61", "nodeType": "VariableDeclaration", "scope": 12609, "src": "5769:9:61", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12569, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "5769:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 12572, "mutability": "mutable", "name": "denominator", "nameLocation": "5796:11:61", "nodeType": "VariableDeclaration", "scope": 12609, "src": "5788:19:61", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12571, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "5788:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 12575, "mutability": "mutable", "name": "rounding", "nameLocation": "5826:8:61", "nodeType": "VariableDeclaration", "scope": 12609, "src": "5817:17:61", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$12359", "typeString": "enum Math.Rounding" }, "typeName": { "id": 12574, "nodeType": "UserDefinedTypeName", "pathNode": { "id": 12573, "name": "Rounding", "nodeType": "IdentifierPath", "referencedDeclaration": 12359, "src": "5817:8:61" }, "referencedDeclaration": 12359, "src": "5817:8:61", "typeDescriptions": { "typeIdentifier": "t_enum$_Rounding_$12359", "typeString": "enum Math.Rounding" } }, "visibility": "internal" } ], "src": "5740:100:61" }, "returnParameters": { "id": 12579, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 12578, "mutability": "mutable", "name": "", "nameLocation": "-1:-1:-1", "nodeType": "VariableDeclaration", "scope": 12609, "src": "5864:7:61", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12577, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "5864:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "5863:9:61" }, "scope": 12856, "src": "5725:337:61", "stateMutability": "pure", "virtual": false, "visibility": "internal" }, { "body": { "id": 12818, "nodeType": "Block", "src": "6338:2149:61", "statements": [ { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12619, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12617, "name": "a", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12612, "src": "6352:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "==", "rightExpression": { "hexValue": "30", "id": 12618, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "6357:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "6352:6:61", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 12623, "nodeType": "IfStatement", "src": "6348:45:61", "trueBody": { "id": 12622, "nodeType": "Block", "src": "6360:33:61", "statements": [ { "expression": { "hexValue": "30", "id": 12620, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "6381:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "functionReturnParameters": 12616, "id": 12621, "nodeType": "Return", "src": "6374:8:61" } ] } }, { "assignments": [ 12625 ], "declarations": [ { "constant": false, "id": 12625, "mutability": "mutable", "name": "result", "nameLocation": "7066:6:61", "nodeType": "VariableDeclaration", "scope": 12818, "src": "7058:14:61", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12624, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "7058:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "id": 12627, "initialValue": { "hexValue": "31", "id": 12626, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7075:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "nodeType": "VariableDeclarationStatement", "src": "7058:18:61" }, { "assignments": [ 12629 ], "declarations": [ { "constant": false, "id": 12629, "mutability": "mutable", "name": "x", "nameLocation": "7094:1:61", "nodeType": "VariableDeclaration", "scope": 12818, "src": "7086:9:61", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12628, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "7086:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "id": 12631, "initialValue": { "id": 12630, "name": "a", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12612, "src": "7098:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "VariableDeclarationStatement", "src": "7086:13:61" }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12636, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12634, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12632, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12629, "src": "7113:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "313238", "id": 12633, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7118:3:61", "typeDescriptions": { "typeIdentifier": "t_rational_128_by_1", "typeString": "int_const 128" }, "value": "128" }, "src": "7113:8:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 12635, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7124:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "7113:12:61", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 12646, "nodeType": "IfStatement", "src": "7109:79:61", "trueBody": { "id": 12645, "nodeType": "Block", "src": "7127:61:61", "statements": [ { "expression": { "id": 12639, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12637, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12629, "src": "7141:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "313238", "id": 12638, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7147:3:61", "typeDescriptions": { "typeIdentifier": "t_rational_128_by_1", "typeString": "int_const 128" }, "value": "128" }, "src": "7141:9:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12640, "nodeType": "ExpressionStatement", "src": "7141:9:61" }, { "expression": { "id": 12643, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12641, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "7164:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "<<=", "rightHandSide": { "hexValue": "3634", "id": 12642, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7175:2:61", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "7164:13:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12644, "nodeType": "ExpressionStatement", "src": "7164:13:61" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12651, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12649, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12647, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12629, "src": "7201:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "3634", "id": 12648, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7206:2:61", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "7201:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 12650, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7211:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "7201:11:61", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 12661, "nodeType": "IfStatement", "src": "7197:77:61", "trueBody": { "id": 12660, "nodeType": "Block", "src": "7214:60:61", "statements": [ { "expression": { "id": 12654, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12652, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12629, "src": "7228:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "3634", "id": 12653, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7234:2:61", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "7228:8:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12655, "nodeType": "ExpressionStatement", "src": "7228:8:61" }, { "expression": { "id": 12658, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12656, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "7250:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "<<=", "rightHandSide": { "hexValue": "3332", "id": 12657, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7261:2:61", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "7250:13:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12659, "nodeType": "ExpressionStatement", "src": "7250:13:61" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12666, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12664, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12662, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12629, "src": "7287:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "3332", "id": 12663, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7292:2:61", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "7287:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 12665, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7297:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "7287:11:61", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 12676, "nodeType": "IfStatement", "src": "7283:77:61", "trueBody": { "id": 12675, "nodeType": "Block", "src": "7300:60:61", "statements": [ { "expression": { "id": 12669, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12667, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12629, "src": "7314:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "3332", "id": 12668, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7320:2:61", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "7314:8:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12670, "nodeType": "ExpressionStatement", "src": "7314:8:61" }, { "expression": { "id": 12673, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12671, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "7336:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "<<=", "rightHandSide": { "hexValue": "3136", "id": 12672, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7347:2:61", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "7336:13:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12674, "nodeType": "ExpressionStatement", "src": "7336:13:61" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12681, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12679, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12677, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12629, "src": "7373:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "3136", "id": 12678, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7378:2:61", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "7373:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 12680, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7383:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "7373:11:61", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 12691, "nodeType": "IfStatement", "src": "7369:76:61", "trueBody": { "id": 12690, "nodeType": "Block", "src": "7386:59:61", "statements": [ { "expression": { "id": 12684, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12682, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12629, "src": "7400:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "3136", "id": 12683, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7406:2:61", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "7400:8:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12685, "nodeType": "ExpressionStatement", "src": "7400:8:61" }, { "expression": { "id": 12688, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12686, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "7422:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "<<=", "rightHandSide": { "hexValue": "38", "id": 12687, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7433:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "7422:12:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12689, "nodeType": "ExpressionStatement", "src": "7422:12:61" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12696, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12694, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12692, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12629, "src": "7458:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "38", "id": 12693, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7463:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "7458:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 12695, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7467:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "7458:10:61", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 12706, "nodeType": "IfStatement", "src": "7454:74:61", "trueBody": { "id": 12705, "nodeType": "Block", "src": "7470:58:61", "statements": [ { "expression": { "id": 12699, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12697, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12629, "src": "7484:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "38", "id": 12698, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7490:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "7484:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12700, "nodeType": "ExpressionStatement", "src": "7484:7:61" }, { "expression": { "id": 12703, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12701, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "7505:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "<<=", "rightHandSide": { "hexValue": "34", "id": 12702, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7516:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_4_by_1", "typeString": "int_const 4" }, "value": "4" }, "src": "7505:12:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12704, "nodeType": "ExpressionStatement", "src": "7505:12:61" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12711, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12709, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12707, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12629, "src": "7541:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "34", "id": 12708, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7546:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_4_by_1", "typeString": "int_const 4" }, "value": "4" }, "src": "7541:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 12710, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7550:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "7541:10:61", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 12721, "nodeType": "IfStatement", "src": "7537:74:61", "trueBody": { "id": 12720, "nodeType": "Block", "src": "7553:58:61", "statements": [ { "expression": { "id": 12714, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12712, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12629, "src": "7567:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "34", "id": 12713, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7573:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_4_by_1", "typeString": "int_const 4" }, "value": "4" }, "src": "7567:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12715, "nodeType": "ExpressionStatement", "src": "7567:7:61" }, { "expression": { "id": 12718, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12716, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "7588:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "<<=", "rightHandSide": { "hexValue": "32", "id": 12717, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7599:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_2_by_1", "typeString": "int_const 2" }, "value": "2" }, "src": "7588:12:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12719, "nodeType": "ExpressionStatement", "src": "7588:12:61" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12726, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12724, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12722, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12629, "src": "7624:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "32", "id": 12723, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7629:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_2_by_1", "typeString": "int_const 2" }, "value": "2" }, "src": "7624:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 12725, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7633:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "7624:10:61", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 12732, "nodeType": "IfStatement", "src": "7620:53:61", "trueBody": { "id": 12731, "nodeType": "Block", "src": "7636:37:61", "statements": [ { "expression": { "id": 12729, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12727, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "7650:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "<<=", "rightHandSide": { "hexValue": "31", "id": 12728, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7661:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "src": "7650:12:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12730, "nodeType": "ExpressionStatement", "src": "7650:12:61" } ] } }, { "id": 12817, "nodeType": "UncheckedBlock", "src": "8073:408:61", "statements": [ { "expression": { "id": 12742, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12733, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "8097:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12741, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "components": [ { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12738, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12734, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "8107:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "+", "rightExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12737, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12735, "name": "a", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12612, "src": "8116:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "/", "rightExpression": { "id": 12736, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "8120:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "8116:10:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "8107:19:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "id": 12739, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "8106:21:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "31", "id": 12740, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "8131:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "src": "8106:26:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "8097:35:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12743, "nodeType": "ExpressionStatement", "src": "8097:35:61" }, { "expression": { "id": 12753, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12744, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "8146:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12752, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "components": [ { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12749, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12745, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "8156:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "+", "rightExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12748, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12746, "name": "a", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12612, "src": "8165:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "/", "rightExpression": { "id": 12747, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "8169:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": 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"Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "8342:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12796, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "components": [ { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12793, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12789, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "8352:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "+", "rightExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" 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"8351:21:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "31", "id": 12795, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "8376:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "src": "8351:26:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "8342:35:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12798, "nodeType": "ExpressionStatement", "src": "8342:35:61" }, { "expression": { "id": 12808, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 12799, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "8391:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12807, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "components": [ { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12804, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12800, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "8401:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "+", "rightExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12803, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12801, "name": "a", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12612, "src": "8410:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "/", "rightExpression": { "id": 12802, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "8414:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "8410:10:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "8401:19:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "id": 12805, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "8400:21:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "31", "id": 12806, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "8425:1:61", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "src": "8400:26:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "8391:35:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 12809, "nodeType": "ExpressionStatement", "src": "8391:35:61" }, { "expression": { "arguments": [ { "id": 12811, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "8451:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 12814, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 12812, "name": "a", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12612, "src": "8459:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "/", "rightExpression": { "id": 12813, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12625, "src": "8463:6:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "8459:10:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 12810, "name": "min", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12395, "src": "8447:3:61", "typeDescriptions": { "typeIdentifier": "t_function_internal_pure$_t_uint256_$_t_uint256_$returns$_t_uint256_$", "typeString": "function (uint256,uint256) pure returns (uint256)" } }, "id": 12815, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "8447:23:61", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 12616, "id": 12816, "nodeType": "Return", "src": "8440:30:61" } ] } ] }, "documentation": { "id": 12610, "nodeType": "StructuredDocumentation", "src": "6068:208:61", "text": " @dev Returns the square root of a number. It the number is not a perfect square, the value is rounded down.\n Inspired by Henry S. Warren, Jr.'s \"Hacker's Delight\" (Chapter 11)." }, "id": 12819, "implemented": true, "kind": "function", "modifiers": [], "name": "sqrt", "nameLocation": "6290:4:61", "nodeType": "FunctionDefinition", "parameters": { "id": 12613, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 12612, "mutability": "mutable", "name": "a", "nameLocation": "6303:1:61", "nodeType": "VariableDeclaration", "scope": 12819, "src": "6295:9:61", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12611, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "6295:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "6294:11:61" }, "returnParameters": { "id": 12616, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 12615, "mutability": "mutable", "name": "", "nameLocation": "-1:-1:-1", "nodeType": "VariableDeclaration", "scope": 12819, "src": "6329:7:61", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12614, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "6329:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "6328:9:61" }, "scope": 12856, "src": "6281:2206:61", "stateMutability": "pure", "virtual": false, "visibility": "internal" }, { "body": { "id": 12854, "nodeType": "Block", "src": "8663:161:61", "statements": [ { "assignments": [ 12831 ], "declarations": [ { "constant": false, "id": 12831, "mutability": "mutable", "name": "result", "nameLocation": "8681:6:61", "nodeType": "VariableDeclaration", "scope": 12854, "src": "8673:14:61", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 12830, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "8673:7:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "id": 12835, "initialValue": { "arguments": [ { "id": 12833, "name": "a", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 12822, "src": "8695:1:61", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 12832, "name": "sqrt", "nodeType": "Identifier", "overloadedDeclarations": [ 12819, 12855 ], "referencedDeclaration": 12819, "src": "8690:4:61", "typeDescriptions": { "typeIdentifier": "t_function_internal_pure$_t_uint256_$returns$_t_uint256_$", "typeString": "function (uint256) pure returns (uint256)" } }, "id": 12834, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", 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