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"bytecode": "0x60566023600b82828239805160001a607314601657fe5b30600052607381538281f3fe73000000000000000000000000000000000000000030146080604052600080fdfea26469706673582212209a10e10cd2552f461b45a2d94fc7c624abd86af191070d1a5c4c2d9534c4619864736f6c634300060a0033", "deployedBytecode": "0x73000000000000000000000000000000000000000030146080604052600080fdfea26469706673582212209a10e10cd2552f461b45a2d94fc7c624abd86af191070d1a5c4c2d9534c4619864736f6c634300060a0033", "immutableReferences": {}, "sourceMap": "251:5329:4:-:0;;;;;;;;;;;;;;;;;;;;;;;;;", "deployedSourceMap": "251:5329:4:-:0;;;;;;;;", "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 private constant RESOLUTION = 112;\n uint256 private constant Q112 = 0x10000000000000000000000000000;\n uint256 private constant Q224 = 0x100000000000000000000000000000000000000000000000000000000;\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_OVERFLOW_UPPER');\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_OVERFLOW_SUM');\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: DIV_BY_ZERO_DIVUQ');\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 // lossy\n function fraction(uint112 numerator, uint112 denominator) internal pure returns (uq112x112 memory) {\n require(denominator > 0, 'FixedPoint: DIV_BY_ZERO_FRACTION');\n return uq112x112((uint224(numerator) << RESOLUTION) / denominator);\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 > 1, 'FixedPoint: DIV_BY_ZERO_RECIPROCAL_OR_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": "@uniswap/lib/contracts/libraries/FixedPoint.sol", "ast": { "absolutePath": "@uniswap/lib/contracts/libraries/FixedPoint.sol", "exportedSymbols": { "FixedPoint": [ 1166 ] }, "id": 1167, "license": 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