// SPDX-License-Identifier: AGPL-3.0-or-later
pragma solidity 0.7.5;

library FullMath {
    function fullMul(uint256 x, uint256 y)
        private
        pure
        returns (uint256 l, uint256 h)
    {
        uint256 mm = mulmod(x, y, uint256(-1));
        l = x * y;
        h = mm - l;
        if (mm < l) h -= 1;
    }

    function fullDiv(
        uint256 l,
        uint256 h,
        uint256 d
    ) private pure returns (uint256) {
        uint256 pow2 = d & -d;
        d /= pow2;
        l /= pow2;
        l += h * ((-pow2) / pow2 + 1);
        uint256 r = 1;
        r *= 2 - d * r;
        r *= 2 - d * r;
        r *= 2 - d * r;
        r *= 2 - d * r;
        r *= 2 - d * r;
        r *= 2 - d * r;
        r *= 2 - d * r;
        r *= 2 - d * r;
        return l * r;
    }

    function mulDiv(
        uint256 x,
        uint256 y,
        uint256 d
    ) internal pure returns (uint256) {
        (uint256 l, uint256 h) = fullMul(x, y);
        uint256 mm = mulmod(x, y, d);
        if (mm > l) h -= 1;
        l -= mm;
        require(h < d, "FullMath::mulDiv: overflow");
        return fullDiv(l, h, d);
    }
}

library Babylonian {
    function sqrt(uint256 x) internal pure returns (uint256) {
        if (x == 0) return 0;

        uint256 xx = x;
        uint256 r = 1;
        if (xx >= 0x100000000000000000000000000000000) {
            xx >>= 128;
            r <<= 64;
        }
        if (xx >= 0x10000000000000000) {
            xx >>= 64;
            r <<= 32;
        }
        if (xx >= 0x100000000) {
            xx >>= 32;
            r <<= 16;
        }
        if (xx >= 0x10000) {
            xx >>= 16;
            r <<= 8;
        }
        if (xx >= 0x100) {
            xx >>= 8;
            r <<= 4;
        }
        if (xx >= 0x10) {
            xx >>= 4;
            r <<= 2;
        }
        if (xx >= 0x8) {
            r <<= 1;
        }
        r = (r + x / r) >> 1;
        r = (r + x / r) >> 1;
        r = (r + x / r) >> 1;
        r = (r + x / r) >> 1;
        r = (r + x / r) >> 1;
        r = (r + x / r) >> 1;
        r = (r + x / r) >> 1; // Seven iterations should be enough
        uint256 r1 = x / r;
        return (r < r1 ? r : r1);
    }
}

library BitMath {
    function mostSignificantBit(uint256 x) internal pure returns (uint8 r) {
        require(x > 0, "BitMath::mostSignificantBit: zero");

        if (x >= 0x100000000000000000000000000000000) {
            x >>= 128;
            r += 128;
        }
        if (x >= 0x10000000000000000) {
            x >>= 64;
            r += 64;
        }
        if (x >= 0x100000000) {
            x >>= 32;
            r += 32;
        }
        if (x >= 0x10000) {
            x >>= 16;
            r += 16;
        }
        if (x >= 0x100) {
            x >>= 8;
            r += 8;
        }
        if (x >= 0x10) {
            x >>= 4;
            r += 4;
        }
        if (x >= 0x4) {
            x >>= 2;
            r += 2;
        }
        if (x >= 0x2) r += 1;
    }
}

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 private constant RESOLUTION = 112;
    uint256 private constant Q112 = 0x10000000000000000000000000000;
    uint256 private constant Q224 =
        0x100000000000000000000000000000000000000000000000000000000;
    uint256 private constant LOWER_MASK = 0xffffffffffffffffffffffffffff; // decimal of UQ*x112 (lower 112 bits)

    // decode a UQ112x112 into a uint112 by truncating after the radix point
    function decode(uq112x112 memory self) internal pure returns (uint112) {
        return uint112(self._x >> RESOLUTION);
    }

    // decode a uq112x112 into a uint with 18 decimals of precision
    function decode112with18(uq112x112 memory self)
        internal
        pure
        returns (uint256)
    {
        return uint256(self._x) / 5192296858534827;
    }

    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 <= uint144(-1)) {
            uint256 result = (numerator << RESOLUTION) / denominator;
            require(result <= uint224(-1), "FixedPoint::fraction: overflow");
            return uq112x112(uint224(result));
        } else {
            uint256 result = FullMath.mulDiv(numerator, Q112, denominator);
            require(result <= uint224(-1), "FixedPoint::fraction: overflow");
            return uq112x112(uint224(result));
        }
    }

    // square root of a UQ112x112
    // lossy between 0/1 and 40 bits
    function sqrt(uq112x112 memory self)
        internal
        pure
        returns (uq112x112 memory)
    {
        if (self._x <= uint144(-1)) {
            return uq112x112(uint224(Babylonian.sqrt(uint256(self._x) << 112)));
        }

        uint8 safeShiftBits = 255 - BitMath.mostSignificantBit(self._x);
        safeShiftBits -= safeShiftBits % 2;
        return
            uq112x112(
                uint224(
                    Babylonian.sqrt(uint256(self._x) << safeShiftBits) <<
                        ((112 - safeShiftBits) / 2)
                )
            );
    }
}

library SafeMath {
    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        require(c >= a, "SafeMath: addition overflow");

        return c;
    }

    function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        return sub(a, b, "SafeMath: subtraction overflow");
    }

    function sub(
        uint256 a,
        uint256 b,
        string memory errorMessage
    ) internal pure returns (uint256) {
        require(b <= a, errorMessage);
        uint256 c = a - b;

        return c;
    }

    function mul(uint256 a, uint256 b) internal pure returns (uint256) {
        if (a == 0) {
            return 0;
        }

        uint256 c = a * b;
        require(c / a == b, "SafeMath: multiplication overflow");

        return c;
    }

    function div(uint256 a, uint256 b) internal pure returns (uint256) {
        return div(a, b, "SafeMath: division by zero");
    }

    function div(
        uint256 a,
        uint256 b,
        string memory errorMessage
    ) internal pure returns (uint256) {
        require(b > 0, errorMessage);
        uint256 c = a / b;
        // assert(a == b * c + a % b); // There is no case in which this doesn't hold

        return c;
    }

    function sqrrt(uint256 a) internal pure returns (uint256 c) {
        if (a > 3) {
            c = a;
            uint256 b = add(div(a, 2), 1);
            while (b < c) {
                c = b;
                b = div(add(div(a, b), b), 2);
            }
        } else if (a != 0) {
            c = 1;
        }
    }
}

interface IERC20 {
    function decimals() external view returns (uint8);
}

interface IUniswapV2ERC20 {
    function totalSupply() external view returns (uint256);
}

interface IUniswapV2Pair is IUniswapV2ERC20 {
    function getReserves()
        external
        view
        returns (
            uint112 reserve0,
            uint112 reserve1,
            uint32 blockTimestampLast
        );

    function token0() external view returns (address);

    function token1() external view returns (address);
}

interface IBondingCalculator {
    function valuation(address pair_, uint256 amount_)
        external
        view
        returns (uint256 _value);
}

contract ImmortalBondingCalculator is IBondingCalculator {
    using FixedPoint for *;
    using SafeMath for uint256;
    using SafeMath for uint112;

    address public immutable IMMO;

    constructor(address _IMMO) {
        require(_IMMO != address(0));
        IMMO = _IMMO;
    }

    function getKValue(address _pair) public view returns (uint256 k_) {
        uint256 token0 = IERC20(IUniswapV2Pair(_pair).token0()).decimals();
        uint256 token1 = IERC20(IUniswapV2Pair(_pair).token1()).decimals();
        uint256 decimals = token0.add(token1).sub(IERC20(_pair).decimals());

        (uint256 reserve0, uint256 reserve1, ) = IUniswapV2Pair(_pair)
            .getReserves();
        k_ = reserve0.mul(reserve1).div(10**decimals);
    }

    function getTotalValue(address _pair) public view returns (uint256 _value) {
        _value = getKValue(_pair).sqrrt().mul(2);
    }

    function valuation(address _pair, uint256 amount_)
        external
        view
        override
        returns (uint256 _value)
    {
        uint256 totalValue = getTotalValue(_pair);
        uint256 totalSupply = IUniswapV2Pair(_pair).totalSupply();

        _value = totalValue
            .mul(FixedPoint.fraction(amount_, totalSupply).decode112with18())
            .div(1e18);
    }

    function markdown(address _pair) external view returns (uint256) {
        (uint256 reserve0, uint256 reserve1, ) = IUniswapV2Pair(_pair)
            .getReserves();

        uint256 reserve;
        if (IUniswapV2Pair(_pair).token0() == IMMO) {
            reserve = reserve1;
        } else {
            reserve = reserve0;
        }
        return
            reserve.mul(2 * (10**IERC20(IMMO).decimals())).div(
                getTotalValue(_pair)
            );
    }
}