{ "contractName": "FixedPoint", "abi": [], "bytecode": "0x604c602c600b82828239805160001a60731460008114601c57601e565bfe5b5030600052607381538281f3fe73000000000000000000000000000000000000000030146080604052600080fdfea165627a7a72305820d1d956bfd6c986231bde1a437dd4ecdcfb1b967fc85e78ed695d74daaa90cb830029", "deployedBytecode": "0x73000000000000000000000000000000000000000030146080604052600080fdfea165627a7a72305820d1d956bfd6c986231bde1a437dd4ecdcfb1b967fc85e78ed695d74daaa90cb830029", "sourceMap": "188:5028:11:-;;132:2:-1;166:7;155:9;146:7;137:37;252:7;246:14;243:1;238:23;232:4;229:33;270:1;265:20;;;;222:63;;265:20;274:9;222:63;;298:9;295:1;288:20;328:4;319:7;311:22;352:7;343;336:24", "deployedSourceMap": "188:5028:11:-;;;;;;;;", "source": "pragma solidity >=0.4.0;\r\n\r\nimport './FullMath.sol';\r\nimport './Babylonian.sol';\r\n\r\n// a library for handling binary fixed point numbers (https://en.wikipedia.org/wiki/Q_(number_format))\r\nlibrary FixedPoint {\r\n // range: [0, 2**112 - 1]\r\n // resolution: 1 / 2**112\r\n struct uq112x112 {\r\n uint224 _x;\r\n }\r\n\r\n // range: [0, 2**144 - 1]\r\n // resolution: 1 / 2**112\r\n struct uq144x112 {\r\n uint256 _x;\r\n }\r\n\r\n uint8 private constant RESOLUTION = 112;\r\n uint256 private constant Q112 = uint256(1) << RESOLUTION;\r\n uint256 private constant Q224 = Q112 << RESOLUTION;\r\n uint256 private constant LOWER_MASK = 0xffffffffffffffffffffffffffff; // decimal of UQ*x112 (lower 112 bits)\r\n\r\n // encode a uint112 as a UQ112x112\r\n function encode(uint112 x) internal pure returns (uq112x112 memory) {\r\n return uq112x112(uint224(x) << RESOLUTION);\r\n }\r\n\r\n // encodes a uint144 as a UQ144x112\r\n function encode144(uint144 x) internal pure returns (uq144x112 memory) {\r\n return uq144x112(uint256(x) << RESOLUTION);\r\n }\r\n\r\n // decode a UQ112x112 into a uint112 by truncating after the radix point\r\n function decode(uq112x112 memory self) internal pure returns (uint112) {\r\n return uint112(self._x >> RESOLUTION);\r\n }\r\n\r\n // decode a UQ144x112 into a uint144 by truncating after the radix point\r\n function decode144(uq144x112 memory self) internal pure returns (uint144) {\r\n return uint144(self._x >> RESOLUTION);\r\n }\r\n\r\n // multiply a UQ112x112 by a uint, returning a UQ144x112\r\n // reverts on overflow\r\n function mul(uq112x112 memory self, uint256 y) internal pure returns (uq144x112 memory) {\r\n uint256 z = 0;\r\n require(y == 0 || (z = self._x * y) / y == self._x, 'FixedPoint: MUL_OVERFLOW');\r\n return uq144x112(z);\r\n }\r\n\r\n // multiply a UQ112x112 by an int and decode, returning an int\r\n // reverts on overflow\r\n function muli(uq112x112 memory self, int256 y) internal pure returns (int256) {\r\n uint144 z = decode144(mul(self, uint256(y < 0 ? -y : y)));\r\n return y < 0 ? -int256(z) : z;\r\n }\r\n\r\n // multiply a UQ112x112 by a UQ112x112, returning a UQ112x112\r\n // lossy\r\n function muluq(uq112x112 memory self, uq112x112 memory other) internal pure returns (uq112x112 memory) {\r\n if (self._x == 0 || other._x == 0) {\r\n return uq112x112(0);\r\n }\r\n uint112 upper_self = uint112(self._x >> RESOLUTION); // * 2^0\r\n uint112 lower_self = uint112(self._x & LOWER_MASK); // * 2^-112\r\n uint112 upper_other = uint112(other._x >> RESOLUTION); // * 2^0\r\n uint112 lower_other = uint112(other._x & LOWER_MASK); // * 2^-112\r\n\r\n // partial products\r\n uint224 upper = uint224(upper_self) * upper_other; // * 2^0\r\n uint224 lower = uint224(lower_self) * lower_other; // * 2^-224\r\n uint224 uppers_lowero = uint224(upper_self) * lower_other; // * 2^-112\r\n uint224 uppero_lowers = uint224(upper_other) * lower_self; // * 2^-112\r\n\r\n // so the bit shift does not overflow\r\n require(upper <= uint112(-1), 'FixedPoint: MULUQ_OVERFLOW_UPPER');\r\n\r\n // this cannot exceed 256 bits, all values are 224 bits\r\n uint256 sum = uint256(upper << RESOLUTION) + uppers_lowero + uppero_lowers + (lower >> RESOLUTION);\r\n\r\n // so the cast does not overflow\r\n require(sum <= uint224(-1), 'FixedPoint: MULUQ_OVERFLOW_SUM');\r\n\r\n return uq112x112(uint224(sum));\r\n }\r\n\r\n // divide a UQ112x112 by a UQ112x112, returning a UQ112x112\r\n function divuq(uq112x112 memory self, uq112x112 memory other) internal pure returns (uq112x112 memory) {\r\n require(other._x > 0, 'FixedPoint: DIV_BY_ZERO_DIVUQ');\r\n if (self._x == other._x) {\r\n return uq112x112(uint224(Q112));\r\n }\r\n if (self._x <= uint144(-1)) {\r\n uint256 value = (uint256(self._x) << RESOLUTION) / other._x;\r\n require(value <= uint224(-1), 'FixedPoint: DIVUQ_OVERFLOW');\r\n return uq112x112(uint224(value));\r\n }\r\n\r\n uint256 result = FullMath.mulDiv(Q112, self._x, other._x);\r\n require(result <= uint224(-1), 'FixedPoint: DIVUQ_OVERFLOW');\r\n return uq112x112(uint224(result));\r\n }\r\n\r\n // returns a UQ112x112 which represents the ratio of the numerator to the denominator\r\n // lossy\r\n function fraction(uint112 numerator, uint112 denominator) internal pure returns (uq112x112 memory) {\r\n require(denominator > 0, 'FixedPoint: DIV_BY_ZERO_FRACTION');\r\n return uq112x112((uint224(numerator) << RESOLUTION) / denominator);\r\n }\r\n\r\n // take the reciprocal of a UQ112x112\r\n // reverts on overflow\r\n // lossy\r\n function reciprocal(uq112x112 memory self) internal pure returns (uq112x112 memory) {\r\n require(self._x > 1, 'FixedPoint: DIV_BY_ZERO_RECIPROCAL_OR_OVERFLOW');\r\n return uq112x112(uint224(Q224 / self._x));\r\n }\r\n\r\n // square root of a UQ112x112\r\n // lossy to 40 bits\r\n function sqrt(uq112x112 memory self) internal pure returns (uq112x112 memory) {\r\n return uq112x112(uint224(Babylonian.sqrt(uint256(self._x) << 32) << 40));\r\n }\r\n}\r\n", "sourcePath": "@sonicxchain/soxswap-lib/contracts/libraries/FixedPoint.sol", "ast": { "absolutePath": "@sonicxchain/soxswap-lib/contracts/libraries/FixedPoint.sol", "exportedSymbols": { "FixedPoint": [ 4186 ] }, "id": 4187, "nodeType": "SourceUnit", "nodes": [ { "id": 3713, 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