// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity 0.8.10;

import "./IntMath.sol";

// solhint-disable
/**
 * @notice We copied the functions we needed from https://github.com/Uniswap/solidity-lib/blob/master/contracts/libraries/FixedPoint.sol
 * @notice We also changed a line in uniswap full math to be compliant with solidity 0.8.10.
 */
// a library for handling binary fixed point numbers (https://en.wikipedia.org/wiki/Q_(number_format))
library FixedPoint {
    // range: [0, 2**112 - 1]
    // resolution: 1 / 2**112
    struct uq112x112 {
        uint224 _x;
    }

    // range: [0, 2**144 - 1]
    // resolution: 1 / 2**112
    struct uq144x112 {
        uint256 _x;
    }

    uint8 public constant RESOLUTION = 112;
    uint256 public constant Q112 = 0x10000000000000000000000000000; // 2**112

    // decode a UQ144x112 into a uint144 by truncating after the radix point
    function decode144(uq144x112 memory self) internal pure returns (uint144) {
        return uint144(self._x >> RESOLUTION);
    }

    // multiply a UQ112x112 by a uint, returning a UQ144x112
    // reverts on overflow
    function mul(uq112x112 memory self, uint256 y)
        internal
        pure
        returns (uq144x112 memory)
    {
        uint256 z = 0;
        require(
            y == 0 || (z = self._x * y) / y == self._x,
            "FixedPoint::mul: overflow"
        );
        return uq144x112(z);
    }

    // returns a UQ112x112 which represents the ratio of the numerator to the denominator
    // can be lossy
    function fraction(uint256 numerator, uint256 denominator)
        internal
        pure
        returns (uq112x112 memory)
    {
        require(denominator > 0, "FixedPoint::fraction: division by zero");
        if (numerator == 0) return FixedPoint.uq112x112(0);

        if (numerator <= type(uint144).max) {
            uint256 result = (numerator << RESOLUTION) / denominator;
            require(
                result <= type(uint224).max,
                "FixedPoint::fraction: overflow"
            );
            return uq112x112(uint224(result));
        } else {
            uint256 result = IntMath.mulDiv(numerator, Q112, denominator);
            require(
                result <= type(uint224).max,
                "FixedPoint::fraction: overflow"
            );
            return uq112x112(uint224(result));
        }
    }
}