library PMMPricing {
    using SafeMath for uint256;

    enum RState {ONE, ABOVE_ONE, BELOW_ONE}

    struct PMMState {
        uint256 i;
        uint256 K;
        uint256 B;
        uint256 Q;
        uint256 B0;
        uint256 Q0;
        RState R;
    }

    // ============ buy & sell ============

    function sellBaseToken(PMMState memory state, uint256 payBaseAmount)
        internal
        pure
        returns (uint256 receiveQuoteAmount, RState newR)
    {
        if (state.R == RState.ONE) {
            // case 1: R=1
            // R falls below one
            receiveQuoteAmount = _ROneSellBaseToken(state, payBaseAmount);
            newR = RState.BELOW_ONE;
        } else if (state.R == RState.ABOVE_ONE) {
            uint256 backToOnePayBase = state.B0.sub(state.B);
            uint256 backToOneReceiveQuote = state.Q.sub(state.Q0);
            // case 2: R>1
            // complex case, R status depends on trading amount
            if (payBaseAmount < backToOnePayBase) {
                // case 2.1: R status do not change
                receiveQuoteAmount = _RAboveSellBaseToken(state, payBaseAmount);
                newR = RState.ABOVE_ONE;
                if (receiveQuoteAmount > backToOneReceiveQuote) {
                    // [Important corner case!] may enter this branch when some precision problem happens. And consequently contribute to negative spare quote amount
                    // to make sure spare quote>=0, mannually set receiveQuote=backToOneReceiveQuote
                    receiveQuoteAmount = backToOneReceiveQuote;
                }
            } else if (payBaseAmount == backToOnePayBase) {
                // case 2.2: R status changes to ONE
                receiveQuoteAmount = backToOneReceiveQuote;
                newR = RState.ONE;
            } else {
                // case 2.3: R status changes to BELOW_ONE
                receiveQuoteAmount = backToOneReceiveQuote.add(
                    _ROneSellBaseToken(state, payBaseAmount.sub(backToOnePayBase))
                );
                newR = RState.BELOW_ONE;
            }
        } else {
            // state.R == RState.BELOW_ONE
            // case 3: R<1
            receiveQuoteAmount = _RBelowSellBaseToken(state, payBaseAmount);
            newR = RState.BELOW_ONE;
        }
    }

    function sellQuoteToken(PMMState memory state, uint256 payQuoteAmount)
        internal
        pure
        returns (uint256 receiveBaseAmount, RState newR)
    {
        if (state.R == RState.ONE) {
            receiveBaseAmount = _ROneSellQuoteToken(state, payQuoteAmount);
            newR = RState.ABOVE_ONE;
        } else if (state.R == RState.ABOVE_ONE) {
            receiveBaseAmount = _RAboveSellQuoteToken(state, payQuoteAmount);
            newR = RState.ABOVE_ONE;
        } else {
            uint256 backToOnePayQuote = state.Q0.sub(state.Q);
            uint256 backToOneReceiveBase = state.B.sub(state.B0);
            if (payQuoteAmount < backToOnePayQuote) {
                receiveBaseAmount = _RBelowSellQuoteToken(state, payQuoteAmount);
                newR = RState.BELOW_ONE;
                if (receiveBaseAmount > backToOneReceiveBase) {
                    receiveBaseAmount = backToOneReceiveBase;
                }
            } else if (payQuoteAmount == backToOnePayQuote) {
                receiveBaseAmount = backToOneReceiveBase;
                newR = RState.ONE;
            } else {
                receiveBaseAmount = backToOneReceiveBase.add(
                    _ROneSellQuoteToken(state, payQuoteAmount.sub(backToOnePayQuote))
                );
                newR = RState.ABOVE_ONE;
            }
        }
    }

    // ============ R = 1 cases ============

    function _ROneSellBaseToken(PMMState memory state, uint256 payBaseAmount)
        internal
        pure
        returns (
            uint256 // receiveQuoteToken
        )
    {
        // in theory Q2 <= targetQuoteTokenAmount
        // however when amount is close to 0, precision problems may cause Q2 > targetQuoteTokenAmount
        return
            DODOMath._SolveQuadraticFunctionForTrade(
                state.Q0,
                state.Q0,
                payBaseAmount,
                state.i,
                state.K
            );
    }

    function _ROneSellQuoteToken(PMMState memory state, uint256 payQuoteAmount)
        internal
        pure
        returns (
            uint256 // receiveBaseToken
        )
    {
        return
            DODOMath._SolveQuadraticFunctionForTrade(
                state.B0,
                state.B0,
                payQuoteAmount,
                DecimalMath.reciprocalFloor(state.i),
                state.K
            );
    }

    // ============ R < 1 cases ============

    function _RBelowSellQuoteToken(PMMState memory state, uint256 payQuoteAmount)
        internal
        pure
        returns (
            uint256 // receiveBaseToken
        )
    {
        return
            DODOMath._GeneralIntegrate(
                state.Q0,
                state.Q.add(payQuoteAmount),
                state.Q,
                DecimalMath.reciprocalFloor(state.i),
                state.K
            );
    }

    function _RBelowSellBaseToken(PMMState memory state, uint256 payBaseAmount)
        internal
        pure
        returns (
            uint256 // receiveQuoteToken
        )
    {
        return
            DODOMath._SolveQuadraticFunctionForTrade(
                state.Q0,
                state.Q,
                payBaseAmount,
                state.i,
                state.K
            );
    }

    // ============ R > 1 cases ============

    function _RAboveSellBaseToken(PMMState memory state, uint256 payBaseAmount)
        internal
        pure
        returns (
            uint256 // receiveQuoteToken
        )
    {
        return
            DODOMath._GeneralIntegrate(
                state.B0,
                state.B.add(payBaseAmount),
                state.B,
                state.i,
                state.K
            );
    }

    function _RAboveSellQuoteToken(PMMState memory state, uint256 payQuoteAmount)
        internal
        pure
        returns (
            uint256 // receiveBaseToken
        )
    {
        return
            DODOMath._SolveQuadraticFunctionForTrade(
                state.B0,
                state.B,
                payQuoteAmount,
                DecimalMath.reciprocalFloor(state.i),
                state.K
            );
    }

    // ============ Helper functions ============

    function adjustedTarget(PMMState memory state) internal pure {
        if (state.R == RState.BELOW_ONE) {
            state.Q0 = DODOMath._SolveQuadraticFunctionForTarget(
                state.Q,
                state.B.sub(state.B0),
                state.i,
                state.K
            );
        } else if (state.R == RState.ABOVE_ONE) {
            state.B0 = DODOMath._SolveQuadraticFunctionForTarget(
                state.B,
                state.Q.sub(state.Q0),
                DecimalMath.reciprocalFloor(state.i),
                state.K
            );
        }
    }

    function getMidPrice(PMMState memory state) internal pure returns (uint256) {
        if (state.R == RState.BELOW_ONE) {
            uint256 R = DecimalMath.divFloor(state.Q0.mul(state.Q0).div(state.Q), state.Q);
            R = DecimalMath.ONE.sub(state.K).add(DecimalMath.mulFloor(state.K, R));
            return DecimalMath.divFloor(state.i, R);
        } else {
            uint256 R = DecimalMath.divFloor(state.B0.mul(state.B0).div(state.B), state.B);
            R = DecimalMath.ONE.sub(state.K).add(DecimalMath.mulFloor(state.K, R));
            return DecimalMath.mulFloor(state.i, R);
        }
    }
}
/**
 * @title Pricing
 * @author DODO Breeder
 *
 * @notice DODO Pricing model
 */
function adjustedTarget(PMMState memory state) internal pure {
    if (state.R == RState.BELOW_ONE) {
        state.Q0 = DODOMath._SolveQuadraticFunctionForTarget(
            state.Q,
            state.B.sub(state.B0),
            state.i,
            state.K
        );
    } else if (state.R == RState.ABOVE_ONE) {
        state.B0 = DODOMath._SolveQuadraticFunctionForTarget(
            state.B,
            state.Q.sub(state.Q0),
            DecimalMath.reciprocalFloor(state.i),
            state.K
        );
    }
}

// ============ Helper functions ============