{ "contractName": "FixedPoint", "abi": [ { "inputs": [], "name": "Q112", "outputs": [ { "internalType": "uint256", "name": "", "type": "uint256" } ], "stateMutability": "view", "type": "function" }, { "inputs": [], "name": "RESOLUTION", "outputs": [ { "internalType": "uint8", "name": "", "type": "uint8" } ], "stateMutability": "view", "type": "function" } ], "metadata": 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"bytecode": "0x60b9610025600b82828239805160001a60731461001857fe5b30600052607381538281f3fe7300000000000000000000000000000000000000003014608060405260043610603d5760003560e01c80633bf7a83e146042578063552f888a14605a575b600080fd5b60486076565b60408051918252519081900360200190f35b6060607e565b6040805160ff9092168252519081900360200190f35b600160701b81565b60708156fea264697066735822122039464c00e097d24c8ff78d267b2c31104088a05143247629ee167558b89a3b9b64736f6c63430006060033", "deployedBytecode": "0x7300000000000000000000000000000000000000003014608060405260043610603d5760003560e01c80633bf7a83e146042578063552f888a14605a575b600080fd5b60486076565b60408051918252519081900360200190f35b6060607e565b6040805160ff9092168252519081900360200190f35b600160701b81565b60708156fea264697066735822122039464c00e097d24c8ff78d267b2c31104088a05143247629ee167558b89a3b9b64736f6c63430006060033", "immutableReferences": {}, "sourceMap": "251:5884:20:-:0;;132:2:-1;166:7;155:9;146:7;137:37;255:7;249:14;246:1;241:23;235:4;232:33;222:2;;269:9;222:2;293:9;290:1;283:20;323:4;314:7;306:22;347:7;338;331:24", "deployedSourceMap": "251:5884:20:-:0;;;;;;;;;;;;;;;;;;;;;;;;;;12:1:-1;9;2:12;540:62:20;;;:::i;:::-;;;;;;;;;;;;;;;;496:38;;;:::i;:::-;;;;;;;;;;;;;;;;;;;540:62;-1:-1:-1;;;540:62:20;:::o;496:38::-;531:3;496:38;:::o", "source": "// SPDX-License-Identifier: GPL-3.0-or-later\npragma solidity >=0.4.0;\n\nimport './FullMath.sol';\nimport './Babylonian.sol';\nimport './BitMath.sol';\n\n// a library for handling binary fixed point numbers (https://en.wikipedia.org/wiki/Q_(number_format))\nlibrary FixedPoint {\n // range: [0, 2**112 - 1]\n // resolution: 1 / 2**112\n struct uq112x112 {\n uint224 _x;\n }\n\n // range: [0, 2**144 - 1]\n // resolution: 1 / 2**112\n struct uq144x112 {\n uint256 _x;\n }\n\n uint8 public constant RESOLUTION = 112;\n uint256 public constant Q112 = 0x10000000000000000000000000000; // 2**112\n uint256 private constant Q224 = 0x100000000000000000000000000000000000000000000000000000000; // 2**224\n uint256 private constant LOWER_MASK = 0xffffffffffffffffffffffffffff; // decimal of UQ*x112 (lower 112 bits)\n\n // encode a uint112 as a UQ112x112\n function encode(uint112 x) internal pure returns (uq112x112 memory) {\n return uq112x112(uint224(x) << RESOLUTION);\n }\n\n // encodes a uint144 as a UQ144x112\n function encode144(uint144 x) internal pure returns (uq144x112 memory) {\n return uq144x112(uint256(x) << RESOLUTION);\n }\n\n // decode a UQ112x112 into a uint112 by truncating after the radix point\n function decode(uq112x112 memory self) internal pure returns (uint112) {\n return uint112(self._x >> RESOLUTION);\n }\n\n // decode a UQ144x112 into a uint144 by truncating after the radix point\n function decode144(uq144x112 memory self) internal pure returns (uint144) {\n return uint144(self._x >> RESOLUTION);\n }\n\n // multiply a UQ112x112 by a uint, returning a UQ144x112\n // reverts on overflow\n function mul(uq112x112 memory self, uint256 y) internal pure returns (uq144x112 memory) {\n uint256 z = 0;\n require(y == 0 || (z = self._x * y) / y == self._x, 'FixedPoint::mul: overflow');\n return uq144x112(z);\n }\n\n // multiply a UQ112x112 by an int and decode, returning an int\n // reverts on overflow\n function muli(uq112x112 memory self, int256 y) internal pure returns (int256) {\n uint256 z = FullMath.mulDiv(self._x, uint256(y < 0 ? -y : y), Q112);\n require(z < 2**255, 'FixedPoint::muli: overflow');\n return y < 0 ? -int256(z) : int256(z);\n }\n\n // multiply a UQ112x112 by a UQ112x112, returning a UQ112x112\n // lossy\n function muluq(uq112x112 memory self, uq112x112 memory other) internal pure returns (uq112x112 memory) {\n if (self._x == 0 || other._x == 0) {\n return uq112x112(0);\n }\n uint112 upper_self = uint112(self._x >> RESOLUTION); // * 2^0\n uint112 lower_self = uint112(self._x & LOWER_MASK); // * 2^-112\n uint112 upper_other = uint112(other._x >> RESOLUTION); // * 2^0\n uint112 lower_other = uint112(other._x & LOWER_MASK); // * 2^-112\n\n // partial products\n uint224 upper = uint224(upper_self) * upper_other; // * 2^0\n uint224 lower = uint224(lower_self) * lower_other; // * 2^-224\n uint224 uppers_lowero = uint224(upper_self) * lower_other; // * 2^-112\n uint224 uppero_lowers = uint224(upper_other) * lower_self; // * 2^-112\n\n // so the bit shift does not overflow\n require(upper <= uint112(-1), 'FixedPoint::muluq: upper overflow');\n\n // this cannot exceed 256 bits, all values are 224 bits\n uint256 sum = uint256(upper << RESOLUTION) + uppers_lowero + uppero_lowers + (lower >> RESOLUTION);\n\n // so the cast does not overflow\n require(sum <= uint224(-1), 'FixedPoint::muluq: sum overflow');\n\n return uq112x112(uint224(sum));\n }\n\n // divide a UQ112x112 by a UQ112x112, returning a UQ112x112\n function divuq(uq112x112 memory self, uq112x112 memory other) internal pure returns (uq112x112 memory) {\n require(other._x > 0, 'FixedPoint::divuq: division by zero');\n if (self._x == other._x) {\n return uq112x112(uint224(Q112));\n }\n if (self._x <= uint144(-1)) {\n uint256 value = (uint256(self._x) << RESOLUTION) / other._x;\n require(value <= uint224(-1), 'FixedPoint::divuq: overflow');\n return uq112x112(uint224(value));\n }\n\n uint256 result = FullMath.mulDiv(Q112, self._x, other._x);\n require(result <= uint224(-1), 'FixedPoint::divuq: overflow');\n return uq112x112(uint224(result));\n }\n\n // returns a UQ112x112 which represents the ratio of the numerator to the denominator\n // can be lossy\n function fraction(uint256 numerator, uint256 denominator) internal pure returns (uq112x112 memory) {\n require(denominator > 0, 'FixedPoint::fraction: division by zero');\n if (numerator == 0) return FixedPoint.uq112x112(0);\n\n if (numerator <= uint144(-1)) {\n uint256 result = (numerator << RESOLUTION) / denominator;\n require(result <= uint224(-1), 'FixedPoint::fraction: overflow');\n return uq112x112(uint224(result));\n } else {\n uint256 result = FullMath.mulDiv(numerator, Q112, denominator);\n require(result <= uint224(-1), 'FixedPoint::fraction: overflow');\n return uq112x112(uint224(result));\n }\n }\n\n // take the reciprocal of a UQ112x112\n // reverts on overflow\n // lossy\n function reciprocal(uq112x112 memory self) internal pure returns (uq112x112 memory) {\n require(self._x != 0, 'FixedPoint::reciprocal: reciprocal of zero');\n require(self._x != 1, 'FixedPoint::reciprocal: overflow');\n return uq112x112(uint224(Q224 / self._x));\n }\n\n // square root of a UQ112x112\n // lossy between 0/1 and 40 bits\n function sqrt(uq112x112 memory self) internal pure returns (uq112x112 memory) {\n if (self._x <= uint144(-1)) {\n return uq112x112(uint224(Babylonian.sqrt(uint256(self._x) << 112)));\n }\n\n uint8 safeShiftBits = 255 - BitMath.mostSignificantBit(self._x);\n safeShiftBits -= safeShiftBits % 2;\n return uq112x112(uint224(Babylonian.sqrt(uint256(self._x) << safeShiftBits) << ((112 - safeShiftBits) / 2)));\n }\n}\n", "sourcePath": "moonwalkerswap-libraries/contracts/libraries/FixedPoint.sol", "ast": { "absolutePath": "moonwalkerswap-libraries/contracts/libraries/FixedPoint.sol", "exportedSymbols": { "FixedPoint": [ 7858 ] }, "id": 7859, "nodeType": "SourceUnit", "nodes": [ { "id": 7231, "literals": [ "solidity", ">=", "0.4", ".0" ], "nodeType": "PragmaDirective", "src": "45:24:20" }, { "absolutePath": "moonwalkerswap-libraries/contracts/libraries/FullMath.sol", "file": "./FullMath.sol", "id": 7232, "nodeType": "ImportDirective", "scope": 7859, "sourceUnit": 8080, "src": "71:24:20", "symbolAliases": [], "unitAlias": "" }, { "absolutePath": "moonwalkerswap-libraries/contracts/libraries/Babylonian.sol", "file": "./Babylonian.sol", "id": 7233, "nodeType": "ImportDirective", "scope": 7859, "sourceUnit": 6952, "src": "96:26:20", "symbolAliases": [], "unitAlias": "" }, { "absolutePath": "moonwalkerswap-libraries/contracts/libraries/BitMath.sol", "file": "./BitMath.sol", "id": 7234, "nodeType": "ImportDirective", "scope": 7859, "sourceUnit": 7230, "src": "123:23:20", "symbolAliases": [], "unitAlias": "" }, { "abstract": false, "baseContracts": [], "contractDependencies": [], "contractKind": "library", "documentation": null, "fullyImplemented": true, "id": 7858, "linearizedBaseContracts": [ 7858 ], "name": "FixedPoint", "nodeType": "ContractDefinition", "nodes": [ { "canonicalName": "FixedPoint.uq112x112", "id": 7237, "members": [ { "constant": false, "id": 7236, "mutability": "mutable", "name": "_x", "nodeType": "VariableDeclaration", "overrides": null, "scope": 7237, "src": "363:10:20", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint224", "typeString": "uint224" }, "typeName": { "id": 7235, "name": "uint224", "nodeType": "ElementaryTypeName", "src": "363:7:20", "typeDescriptions": { "typeIdentifier": "t_uint224", "typeString": "uint224" } }, "value": null, "visibility": 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"scope": 7858, "src": "725:68:20", "stateVariable": true, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 7250, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "725:7:20", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": { "argumentTypes": null, "hexValue": "307866666666666666666666666666666666666666666666666666666666", "id": 7251, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "763:30:20", "subdenomination": null, "typeDescriptions": { "typeIdentifier": "t_rational_5192296858534827628530496329220095_by_1", "typeString": "int_const 5192...(26 digits omitted)...0095" }, "value": "0xffffffffffffffffffffffffffff" }, "visibility": "private" }, { "body": { "id": 7268, "nodeType": "Block", "src": "946:59:20", "statements": [ { "expression": { "argumentTypes": null, 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