library SwapMath {
    /// @notice Computes the result of swapping some amount in, or amount out, given the parameters of the swap
    /// @dev The fee, plus the amount in, will never exceed the amount remaining if the swap's `amountSpecified` is positive
    /// @param sqrtRatioCurrentX96 The current sqrt price of the pool
    /// @param sqrtRatioTargetX96 The price that cannot be exceeded, from which the direction of the swap is inferred
    /// @param liquidity The usable liquidity
    /// @param amountRemaining How much input or output amount is remaining to be swapped in/out
    /// @param feePips The fee taken from the input amount, expressed in hundredths of a bip
    /// @return sqrtRatioNextX96 The price after swapping the amount in/out, not to exceed the price target
    /// @return amountIn The amount to be swapped in, of either token0 or token1, based on the direction of the swap
    /// @return amountOut The amount to be received, of either token0 or token1, based on the direction of the swap
    /// @return feeAmount The amount of input that will be taken as a fee
    function computeSwapStep(
        uint160 sqrtRatioCurrentX96,
        uint160 sqrtRatioTargetX96,
        uint128 liquidity,
        int256 amountRemaining,
        uint24 feePips
    )
        internal
        pure
        returns (
            uint160 sqrtRatioNextX96,
            uint256 amountIn,
            uint256 amountOut,
            uint256 feeAmount
        )
    {
        bool zeroForOne = sqrtRatioCurrentX96 >= sqrtRatioTargetX96;
        bool exactIn = amountRemaining >= 0;

        if (exactIn) {
            uint256 amountRemainingLessFee = FullMath.mulDiv(uint256(amountRemaining), 1e6 - feePips, 1e6);
            amountIn = zeroForOne
                ? SqrtPriceMath.getAmount0Delta(sqrtRatioTargetX96, sqrtRatioCurrentX96, liquidity, true)
                : SqrtPriceMath.getAmount1Delta(sqrtRatioCurrentX96, sqrtRatioTargetX96, liquidity, true);
            if (amountRemainingLessFee >= amountIn) sqrtRatioNextX96 = sqrtRatioTargetX96;
            else
                sqrtRatioNextX96 = SqrtPriceMath.getNextSqrtPriceFromInput(
                    sqrtRatioCurrentX96,
                    liquidity,
                    amountRemainingLessFee,
                    zeroForOne
                );
        } else {
            amountOut = zeroForOne
                ? SqrtPriceMath.getAmount1Delta(sqrtRatioTargetX96, sqrtRatioCurrentX96, liquidity, false)
                : SqrtPriceMath.getAmount0Delta(sqrtRatioCurrentX96, sqrtRatioTargetX96, liquidity, false);
            if (uint256(-amountRemaining) >= amountOut) sqrtRatioNextX96 = sqrtRatioTargetX96;
            else
                sqrtRatioNextX96 = SqrtPriceMath.getNextSqrtPriceFromOutput(
                    sqrtRatioCurrentX96,
                    liquidity,
                    uint256(-amountRemaining),
                    zeroForOne
                );
        }

        bool max = sqrtRatioTargetX96 == sqrtRatioNextX96;

        // get the input/output amounts
        if (zeroForOne) {
            amountIn = max && exactIn
                ? amountIn
                : SqrtPriceMath.getAmount0Delta(sqrtRatioNextX96, sqrtRatioCurrentX96, liquidity, true);
            amountOut = max && !exactIn
                ? amountOut
                : SqrtPriceMath.getAmount1Delta(sqrtRatioNextX96, sqrtRatioCurrentX96, liquidity, false);
        } else {
            amountIn = max && exactIn
                ? amountIn
                : SqrtPriceMath.getAmount1Delta(sqrtRatioCurrentX96, sqrtRatioNextX96, liquidity, true);
            amountOut = max && !exactIn
                ? amountOut
                : SqrtPriceMath.getAmount0Delta(sqrtRatioCurrentX96, sqrtRatioNextX96, liquidity, false);
        }

        // cap the output amount to not exceed the remaining output amount
        if (!exactIn && amountOut > uint256(-amountRemaining)) {
            amountOut = uint256(-amountRemaining);
        }

        if (exactIn && sqrtRatioNextX96 != sqrtRatioTargetX96) {
            // we didn't reach the target, so take the remainder of the maximum input as fee
            feeAmount = uint256(amountRemaining) - amountIn;
        } else {
            feeAmount = FullMath.mulDivRoundingUp(amountIn, feePips, 1e6 - feePips);
        }
    }
}
/// @title Computes the result of a swap within ticks
/// @notice Contains methods for computing the result of a swap within a single tick price range, i.e., a single tick.
function computeSwapStep(
    uint160 sqrtRatioCurrentX96,
    uint160 sqrtRatioTargetX96,
    uint128 liquidity,
    int256 amountRemaining,
    uint24 feePips
)
    internal
    pure
    returns (
        uint160 sqrtRatioNextX96,
        uint256 amountIn,
        uint256 amountOut,
        uint256 feeAmount
    )
{
    bool zeroForOne = sqrtRatioCurrentX96 >= sqrtRatioTargetX96;
    bool exactIn = amountRemaining >= 0;

    if (exactIn) {
        uint256 amountRemainingLessFee = FullMath.mulDiv(uint256(amountRemaining), 1e6 - feePips, 1e6);
        amountIn = zeroForOne
            ? SqrtPriceMath.getAmount0Delta(sqrtRatioTargetX96, sqrtRatioCurrentX96, liquidity, true)
            : SqrtPriceMath.getAmount1Delta(sqrtRatioCurrentX96, sqrtRatioTargetX96, liquidity, true);
        if (amountRemainingLessFee >= amountIn) sqrtRatioNextX96 = sqrtRatioTargetX96;
        else
            sqrtRatioNextX96 = SqrtPriceMath.getNextSqrtPriceFromInput(
                sqrtRatioCurrentX96,
                liquidity,
                amountRemainingLessFee,
                zeroForOne
            );
    } else {
        amountOut = zeroForOne
            ? SqrtPriceMath.getAmount1Delta(sqrtRatioTargetX96, sqrtRatioCurrentX96, liquidity, false)
            : SqrtPriceMath.getAmount0Delta(sqrtRatioCurrentX96, sqrtRatioTargetX96, liquidity, false);
        if (uint256(-amountRemaining) >= amountOut) sqrtRatioNextX96 = sqrtRatioTargetX96;
        else
            sqrtRatioNextX96 = SqrtPriceMath.getNextSqrtPriceFromOutput(
                sqrtRatioCurrentX96,
                liquidity,
                uint256(-amountRemaining),
                zeroForOne
            );
    }

    bool max = sqrtRatioTargetX96 == sqrtRatioNextX96;

    // get the input/output amounts
    if (zeroForOne) {
        amountIn = max && exactIn
            ? amountIn
            : SqrtPriceMath.getAmount0Delta(sqrtRatioNextX96, sqrtRatioCurrentX96, liquidity, true);
        amountOut = max && !exactIn
            ? amountOut
            : SqrtPriceMath.getAmount1Delta(sqrtRatioNextX96, sqrtRatioCurrentX96, liquidity, false);
    } else {
        amountIn = max && exactIn
            ? amountIn
            : SqrtPriceMath.getAmount1Delta(sqrtRatioCurrentX96, sqrtRatioNextX96, liquidity, true);
        amountOut = max && !exactIn
            ? amountOut
            : SqrtPriceMath.getAmount0Delta(sqrtRatioCurrentX96, sqrtRatioNextX96, liquidity, false);
    }

    // cap the output amount to not exceed the remaining output amount
    if (!exactIn && amountOut > uint256(-amountRemaining)) {
        amountOut = uint256(-amountRemaining);
    }

    if (exactIn && sqrtRatioNextX96 != sqrtRatioTargetX96) {
        // we didn't reach the target, so take the remainder of the maximum input as fee
        feeAmount = uint256(amountRemaining) - amountIn;
    } else {
        feeAmount = FullMath.mulDivRoundingUp(amountIn, feePips, 1e6 - feePips);
    }
}

/// @notice Computes the result of swapping some amount in, or amount out, given the parameters of the swap
/// @dev The fee, plus the amount in, will never exceed the amount remaining if the swap's `amountSpecified` is positive
/// @param sqrtRatioCurrentX96 The current sqrt price of the pool
/// @param sqrtRatioTargetX96 The price that cannot be exceeded, from which the direction of the swap is inferred
/// @param liquidity The usable liquidity
/// @param amountRemaining How much input or output amount is remaining to be swapped in/out
/// @param feePips The fee taken from the input amount, expressed in hundredths of a bip
/// @return sqrtRatioNextX96 The price after swapping the amount in/out, not to exceed the price target
/// @return amountIn The amount to be swapped in, of either token0 or token1, based on the direction of the swap
/// @return amountOut The amount to be received, of either token0 or token1, based on the direction of the swap
/// @return feeAmount The amount of input that will be taken as a fee