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Outline

• interface IValueLiquidFormula
•    - function getReserveAndWeights(address ...
•    - function getFactoryReserveAndWeights(
•    - function getAmountIn(
•    - function getPairAmountIn(
•    - function getAmountOut(
•    - function getPairAmountOut(
•    - function getAmountsIn(
•    - function getFactoryAmountsIn(
•    - function getAmountsOut(
•    - function getFactoryAmountsOut(
•    - function ensureConstantValue(
•    - function getReserves(
•    - function getOtherToken(address pair, ...
•    - function quote(
•    - function sortTokens(address tokenA, a ...
•    - function mintLiquidityFee(
• interface IValueLiquidPair
•    - function name()
•    - function symbol()
•    - function decimals()
•    - function totalSupply()
•    - function balanceOf(address owner)
•    - function allowance(address owner, add ...
•    - function approve(address spender, uin ...
•    - function transfer(address to, uint256 ...
•    - function transferFrom(
•    - function DOMAIN_SEPARATOR()
•    - function PERMIT_TYPEHASH()
•    - function nonces(address owner)
•    - function permit(
•    - function MINIMUM_LIQUIDITY()
•    - function factory()
•    - function token0()
•    - function token1()
•    - function getReserves()
•    - function getCollectedFees()
•    - function getTokenWeights()
•    - function getSwapFee()
•    - function price0CumulativeLast()
•    - function price1CumulativeLast()
•    - function mint(address to)
•    - function burn(address to)
•    - function swap(
•    - function skim(address to)
•    - function sync()
•    - function initialize(
• interface IValueLiquidFactory
•    - function feeTo()
•    - function formula()
•    - function protocolFee()
•    - function feeToSetter()
•    - function getPair(
•    - function allPairs(uint256)
•    - function isPair(address)
•    - function allPairsLength()
•    - function createPair(
•    - function getWeightsAndSwapFee(address ...
•    - function setFeeTo(address)
•    - function setFeeToSetter(address)
•    - function setProtocolFee(uint256)
• library SafeMath
•    - function add(uint256 x, uint256 y)
•    - function sub(uint256 x, uint256 y)
•    - function mul(uint256 x, uint256 y)
•    - function div(uint256 a, uint256 b)
•  contract ValueLiquidFormula is IVa ... *
•    - function initMaxExpArray()
•    - function power(
•    - function generalLog(uint256 x)
•    - function floorLog2(uint256 _n)
•    - function findPositionInMaxExpArray(ui ...
•    - function generalExp(uint256 _x, uint8 ...
•    - function optimalLog(uint256 x)
•    - function optimalExp(uint256 x)
•    - function getReserveAndWeights(address ...
•    - function getFactoryReserveAndWeights(
•    - function getAmountOut(
•    - function getAmountIn(
•    - function getAmountsOut(
•    - function getFactoryAmountsOut(
•    - function getPairAmountOut(
•    - function getAmountsIn(
•    - function getFactoryAmountsIn(
•    - function getPairAmountIn(
•    - function getWeightsAndSwapFee(address ...
•    - function getFactoryWeightsAndSwapFee( ...
•    - function ensureConstantValue(
•    - function sortTokens(address tokenA, a ...
•    - function getReserves(
•    - function getOtherToken(address pair, ...
•    - function quote(
•    - function mintLiquidityFee(

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/**
 *Submitted for verification at BscScan.com on 2021-02-17
*/

// SPDX-License-Identifier: SEE LICENSE IN LICENSE

pragma solidity >=0.7.6;

/*
    Bancor Formula interface
*/
interface IValueLiquidFormula {
    function getReserveAndWeights(address pair, address tokenA)
    external
    view
    returns (
        address tokenB,
        uint256 reserveA,
        uint256 reserveB,
        uint32 tokenWeightA,
        uint32 tokenWeightB,
        uint32 swapFee
    );

    function getFactoryReserveAndWeights(
        address factory,
        address pair,
        address tokenA
    )
    external
    view
    returns (
        address tokenB,
        uint256 reserveA,
        uint256 reserveB,
        uint32 tokenWeightA,
        uint32 tokenWeightB,
        uint32 swapFee
    );

    function getAmountIn(
        uint256 amountOut,
        uint256 reserveIn,
        uint256 reserveOut,
        uint32 tokenWeightIn,
        uint32 tokenWeightOut,
        uint32 swapFee
    ) external view returns (uint256 amountIn);

    function getPairAmountIn(
        address pair,
        address tokenIn,
        uint256 amountOut
    ) external view returns (uint256 amountIn);

    function getAmountOut(
        uint256 amountIn,
        uint256 reserveIn,
        uint256 reserveOut,
        uint32 tokenWeightIn,
        uint32 tokenWeightOut,
        uint32 swapFee
    ) external view returns (uint256 amountOut);

    function getPairAmountOut(
        address pair,
        address tokenIn,
        uint256 amountIn
    ) external view returns (uint256 amountOut);

    function getAmountsIn(
        address tokenIn,
        address tokenOut,
        uint256 amountOut,
        address[] calldata path
    ) external view returns (uint256[] memory amounts);

    function getFactoryAmountsIn(
        address factory,
        address tokenIn,
        address tokenOut,
        uint256 amountOut,
        address[] calldata path
    ) external view returns (uint256[] memory amounts);

    function getAmountsOut(
        address tokenIn,
        address tokenOut,
        uint256 amountIn,
        address[] calldata path
    ) external view returns (uint256[] memory amounts);

    function getFactoryAmountsOut(
        address factory,
        address tokenIn,
        address tokenOut,
        uint256 amountIn,
        address[] calldata path
    ) external view returns (uint256[] memory amounts);

    function ensureConstantValue(
        uint256 reserve0,
        uint256 reserve1,
        uint256 balance0Adjusted,
        uint256 balance1Adjusted,
        uint32 tokenWeight0
    ) external view returns (bool);

    function getReserves(
        address pair,
        address tokenA,
        address tokenB
    ) external view returns (uint256 reserveA, uint256 reserveB);

    function getOtherToken(address pair, address tokenA) external view returns (address tokenB);

    function quote(
        uint256 amountA,
        uint256 reserveA,
        uint256 reserveB
    ) external pure returns (uint256 amountB);

    function sortTokens(address tokenA, address tokenB) external pure returns (address token0, address token1);

    function mintLiquidityFee(
        uint256 totalLiquidity,
        uint112 reserve0,
        uint112 reserve1,
        uint32 tokenWeight0,
        uint32 tokenWeight1,
        uint112 collectedFee0,
        uint112 collectedFee1
    ) external view returns (uint256 amount);
}

interface IValueLiquidPair {
    event Approval(address indexed owner, address indexed spender, uint256 value);
    event Transfer(address indexed from, address indexed to, uint256 value);

    function name() external view returns (string memory);

    function symbol() external view returns (string memory);

    function decimals() external pure returns (uint8);

    function totalSupply() external view returns (uint256);

    function balanceOf(address owner) external view returns (uint256);

    function allowance(address owner, address spender) external view returns (uint256);

    function approve(address spender, uint256 value) external returns (bool);

    function transfer(address to, uint256 value) external returns (bool);

    function transferFrom(
        address from,
        address to,
        uint256 value
    ) external returns (bool);

    function DOMAIN_SEPARATOR() external view returns (bytes32);

    function PERMIT_TYPEHASH() external pure returns (bytes32);

    function nonces(address owner) external view returns (uint256);

    function permit(
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external;

    event PaidProtocolFee(uint112 collectedFee0, uint112 collectedFee1);
    event Mint(address indexed sender, uint256 amount0, uint256 amount1);
    event Burn(address indexed sender, uint256 amount0, uint256 amount1, address indexed to);
    event Swap(address indexed sender, uint256 amount0In, uint256 amount1In, uint256 amount0Out, uint256 amount1Out, address indexed to);
    event Sync(uint112 reserve0, uint112 reserve1);

    function MINIMUM_LIQUIDITY() external pure returns (uint256);

    function factory() external view returns (address);

    function token0() external view returns (address);

    function token1() external view returns (address);

    function getReserves()
    external
    view
    returns (
        uint112 reserve0,
        uint112 reserve1,
        uint32 blockTimestampLast
    );

    function getCollectedFees() external view returns (uint112 _collectedFee0, uint112 _collectedFee1);

    function getTokenWeights() external view returns (uint32 tokenWeight0, uint32 tokenWeight1);

    function getSwapFee() external view returns (uint32);

    function price0CumulativeLast() external view returns (uint256);

    function price1CumulativeLast() external view returns (uint256);

    function mint(address to) external returns (uint256 liquidity);

    function burn(address to) external returns (uint256 amount0, uint256 amount1);

    function swap(
        uint256 amount0Out,
        uint256 amount1Out,
        address to,
        bytes calldata data
    ) external;

    function skim(address to) external;

    function sync() external;

    function initialize(
        address,
        address,
        uint32,
        uint32
    ) external;
}

interface IValueLiquidFactory {
    event PairCreated(address indexed token0, address indexed token1, address pair, uint32 tokenWeight0, uint32 swapFee, uint256);

    function feeTo() external view returns (address);

    function formula() external view returns (address);

    function protocolFee() external view returns (uint256);

    function feeToSetter() external view returns (address);

    function getPair(
        address tokenA,
        address tokenB,
        uint32 tokenWeightA,
        uint32 swapFee
    ) external view returns (address pair);

    function allPairs(uint256) external view returns (address pair);

    function isPair(address) external view returns (bool);

    function allPairsLength() external view returns (uint256);

    function createPair(
        address tokenA,
        address tokenB,
        uint32 tokenWeightA,
        uint32 swapFee
    ) external returns (address pair);

    function getWeightsAndSwapFee(address pair)
    external
    view
    returns (
        uint32 tokenWeight0,
        uint32 tokenWeight1,
        uint32 swapFee
    );

    function setFeeTo(address) external;

    function setFeeToSetter(address) external;

    function setProtocolFee(uint256) external;
}

// a library for performing overflow-safe math, courtesy of DappHub (https://github.com/dapphub/ds-math)
library SafeMath {
    function add(uint256 x, uint256 y) internal pure returns (uint256 z) {
        require((z = x + y) >= x, "ds-math-add-overflow");
    }

    function sub(uint256 x, uint256 y) internal pure returns (uint256 z) {
        require((z = x - y) <= x, "ds-math-sub-underflow");
    }

    function mul(uint256 x, uint256 y) internal pure returns (uint256 z) {
        require(y == 0 || (z = x * y) / y == x, "ds-math-mul-overflow");
    }

    function div(uint256 a, uint256 b) internal pure returns (uint256 c) {
        require(b > 0, "ds-math-division-by-zero");
        c = a / b;
    }
}

contract ValueLiquidFormula is IValueLiquidFormula {
    using SafeMath for uint256;

    uint256 private constant ONE = 1;
    uint8 private constant MIN_PRECISION = 32;
    uint8 private constant MAX_PRECISION = 127;

    uint256 private constant FIXED_1 = 0x080000000000000000000000000000000;
    uint256 private constant FIXED_2 = 0x100000000000000000000000000000000;
    uint256 private constant MAX_NUM = 0x200000000000000000000000000000000;

    uint256 private constant LN2_NUMERATOR = 0x3f80fe03f80fe03f80fe03f80fe03f8;
    uint256 private constant LN2_DENOMINATOR = 0x5b9de1d10bf4103d647b0955897ba80;

    uint256 private constant OPT_LOG_MAX_VAL = 0x15bf0a8b1457695355fb8ac404e7a79e3;
    uint256 private constant OPT_EXP_MAX_VAL = 0x800000000000000000000000000000000;

    uint256 private constant LAMBERT_CONV_RADIUS = 0x002f16ac6c59de6f8d5d6f63c1482a7c86;
    uint256 private constant LAMBERT_POS2_SAMPLE = 0x0003060c183060c183060c183060c18306;
    uint256 private constant LAMBERT_POS2_MAXVAL = 0x01af16ac6c59de6f8d5d6f63c1482a7c80;
    uint256 private constant LAMBERT_POS3_MAXVAL = 0x6b22d43e72c326539cceeef8bb48f255ff;

    uint256 private constant MAX_UNF_WEIGHT = 0x10c6f7a0b5ed8d36b4c7f34938583621fafc8b0079a2834d26fa3fcc9ea9;

    uint256[128] private maxExpArray;

    function initMaxExpArray() internal {
        maxExpArray[32] = 0x1c35fedd14ffffffffffffffffffffffff;
        maxExpArray[33] = 0x1b0ce43b323fffffffffffffffffffffff;
        maxExpArray[34] = 0x19f0028ec1ffffffffffffffffffffffff;
        maxExpArray[35] = 0x18ded91f0e7fffffffffffffffffffffff;
        maxExpArray[36] = 0x17d8ec7f0417ffffffffffffffffffffff;
        maxExpArray[37] = 0x16ddc6556cdbffffffffffffffffffffff;
        maxExpArray[38] = 0x15ecf52776a1ffffffffffffffffffffff;
        maxExpArray[39] = 0x15060c256cb2ffffffffffffffffffffff;
        maxExpArray[40] = 0x1428a2f98d72ffffffffffffffffffffff;
        maxExpArray[41] = 0x13545598e5c23fffffffffffffffffffff;
        maxExpArray[42] = 0x1288c4161ce1dfffffffffffffffffffff;
        maxExpArray[43] = 0x11c592761c666fffffffffffffffffffff;
        maxExpArray[44] = 0x110a688680a757ffffffffffffffffffff;
        maxExpArray[45] = 0x1056f1b5bedf77ffffffffffffffffffff;
        maxExpArray[46] = 0x0faadceceeff8bffffffffffffffffffff;
        maxExpArray[47] = 0x0f05dc6b27edadffffffffffffffffffff;
        maxExpArray[48] = 0x0e67a5a25da4107fffffffffffffffffff;
        maxExpArray[49] = 0x0dcff115b14eedffffffffffffffffffff;
        maxExpArray[50] = 0x0d3e7a392431239fffffffffffffffffff;
        maxExpArray[51] = 0x0cb2ff529eb71e4fffffffffffffffffff;
        maxExpArray[52] = 0x0c2d415c3db974afffffffffffffffffff;
        maxExpArray[53] = 0x0bad03e7d883f69bffffffffffffffffff;
        maxExpArray[54] = 0x0b320d03b2c343d5ffffffffffffffffff;
        maxExpArray[55] = 0x0abc25204e02828dffffffffffffffffff;
        maxExpArray[56] = 0x0a4b16f74ee4bb207fffffffffffffffff;
        maxExpArray[57] = 0x09deaf736ac1f569ffffffffffffffffff;
        maxExpArray[58] = 0x0976bd9952c7aa957fffffffffffffffff;
        maxExpArray[59] = 0x09131271922eaa606fffffffffffffffff;
        maxExpArray[60] = 0x08b380f3558668c46fffffffffffffffff;
        maxExpArray[61] = 0x0857ddf0117efa215bffffffffffffffff;
        maxExpArray[62] = 0x07ffffffffffffffffffffffffffffffff;
        maxExpArray[63] = 0x07abbf6f6abb9d087fffffffffffffffff;
        maxExpArray[64] = 0x075af62cbac95f7dfa7fffffffffffffff;
        maxExpArray[65] = 0x070d7fb7452e187ac13fffffffffffffff;
        maxExpArray[66] = 0x06c3390ecc8af379295fffffffffffffff;
        maxExpArray[67] = 0x067c00a3b07ffc01fd6fffffffffffffff;
        maxExpArray[68] = 0x0637b647c39cbb9d3d27ffffffffffffff;
        maxExpArray[69] = 0x05f63b1fc104dbd39587ffffffffffffff;
        maxExpArray[70] = 0x05b771955b36e12f7235ffffffffffffff;
        maxExpArray[71] = 0x057b3d49dda84556d6f6ffffffffffffff;
        maxExpArray[72] = 0x054183095b2c8ececf30ffffffffffffff;
        maxExpArray[73] = 0x050a28be635ca2b888f77fffffffffffff;
        maxExpArray[74] = 0x04d5156639708c9db33c3fffffffffffff;
        maxExpArray[75] = 0x04a23105873875bd52dfdfffffffffffff;
        maxExpArray[76] = 0x0471649d87199aa990756fffffffffffff;
        maxExpArray[77] = 0x04429a21a029d4c1457cfbffffffffffff;
        maxExpArray[78] = 0x0415bc6d6fb7dd71af2cb3ffffffffffff;
        maxExpArray[79] = 0x03eab73b3bbfe282243ce1ffffffffffff;
        maxExpArray[80] = 0x03c1771ac9fb6b4c18e229ffffffffffff;
        maxExpArray[81] = 0x0399e96897690418f785257fffffffffff;
        maxExpArray[82] = 0x0373fc456c53bb779bf0ea9fffffffffff;
        maxExpArray[83] = 0x034f9e8e490c48e67e6ab8bfffffffffff;
        maxExpArray[84] = 0x032cbfd4a7adc790560b3337ffffffffff;
        maxExpArray[85] = 0x030b50570f6e5d2acca94613ffffffffff;
        maxExpArray[86] = 0x02eb40f9f620fda6b56c2861ffffffffff;
        maxExpArray[87] = 0x02cc8340ecb0d0f520a6af58ffffffffff;
        maxExpArray[88] = 0x02af09481380a0a35cf1ba02ffffffffff;
        maxExpArray[89] = 0x0292c5bdd3b92ec810287b1b3fffffffff;
        maxExpArray[90] = 0x0277abdcdab07d5a77ac6d6b9fffffffff;
        maxExpArray[91] = 0x025daf6654b1eaa55fd64df5efffffffff;
        maxExpArray[92] = 0x0244c49c648baa98192dce88b7ffffffff;
        maxExpArray[93] = 0x022ce03cd5619a311b2471268bffffffff;
        maxExpArray[94] = 0x0215f77c045fbe885654a44a0fffffffff;
        maxExpArray[95] = 0x01ffffffffffffffffffffffffffffffff;
        maxExpArray[96] = 0x01eaefdbdaaee7421fc4d3ede5ffffffff;
        maxExpArray[97] = 0x01d6bd8b2eb257df7e8ca57b09bfffffff;
        maxExpArray[98] = 0x01c35fedd14b861eb0443f7f133fffffff;
        maxExpArray[99] = 0x01b0ce43b322bcde4a56e8ada5afffffff;
        maxExpArray[100] = 0x019f0028ec1fff007f5a195a39dfffffff;
        maxExpArray[101] = 0x018ded91f0e72ee74f49b15ba527ffffff;
        maxExpArray[102] = 0x017d8ec7f04136f4e5615fd41a63ffffff;
        maxExpArray[103] = 0x016ddc6556cdb84bdc8d12d22e6fffffff;
        maxExpArray[104] = 0x015ecf52776a1155b5bd8395814f7fffff;
        maxExpArray[105] = 0x015060c256cb23b3b3cc3754cf40ffffff;
        maxExpArray[106] = 0x01428a2f98d728ae223ddab715be3fffff;
        maxExpArray[107] = 0x013545598e5c23276ccf0ede68034fffff;
        maxExpArray[108] = 0x01288c4161ce1d6f54b7f61081194fffff;
        maxExpArray[109] = 0x011c592761c666aa641d5a01a40f17ffff;
        maxExpArray[110] = 0x0110a688680a7530515f3e6e6cfdcdffff;
        maxExpArray[111] = 0x01056f1b5bedf75c6bcb2ce8aed428ffff;
        maxExpArray[112] = 0x00faadceceeff8a0890f3875f008277fff;
        maxExpArray[113] = 0x00f05dc6b27edad306388a600f6ba0bfff;
        maxExpArray[114] = 0x00e67a5a25da41063de1495d5b18cdbfff;
        maxExpArray[115] = 0x00dcff115b14eedde6fc3aa5353f2e4fff;
        maxExpArray[116] = 0x00d3e7a3924312399f9aae2e0f868f8fff;
        maxExpArray[117] = 0x00cb2ff529eb71e41582cccd5a1ee26fff;
        maxExpArray[118] = 0x00c2d415c3db974ab32a51840c0b67edff;
        maxExpArray[119] = 0x00bad03e7d883f69ad5b0a186184e06bff;
        maxExpArray[120] = 0x00b320d03b2c343d4829abd6075f0cc5ff;
        maxExpArray[121] = 0x00abc25204e02828d73c6e80bcdb1a95bf;
        maxExpArray[122] = 0x00a4b16f74ee4bb2040a1ec6c15fbbf2df;
        maxExpArray[123] = 0x009deaf736ac1f569deb1b5ae3f36c130f;
        maxExpArray[124] = 0x00976bd9952c7aa957f5937d790ef65037;
        maxExpArray[125] = 0x009131271922eaa6064b73a22d0bd4f2bf;
        maxExpArray[126] = 0x008b380f3558668c46c91c49a2f8e967b9;
        maxExpArray[127] = 0x00857ddf0117efa215952912839f6473e6;
    }

    constructor() {
        initMaxExpArray();
    }

    /**
     * @dev General Description:
     *     Determine a value of precision.
     *     Calculate an integer approximation of (_baseN / _baseD) ^ (_expN / _expD) * 2 ^ precision.
     *     Return the result along with the precision used.
     *
     * Detailed Description:
     *     Instead of calculating "base ^ exp", we calculate "e ^ (log(base) * exp)".
     *     The value of "log(base)" is represented with an integer slightly smaller than "log(base) * 2 ^ precision".
     *     The larger "precision" is, the more accurately this value represents the real value.
     *     However, the larger "precision" is, the more bits are required in order to store this value.
     *     And the exponentiation function, which takes "x" and calculates "e ^ x", is limited to a maximum exponent (maximum value of "x").
     *     This maximum exponent depends on the "precision" used, and it is given by "maxExpArray[precision] >> (MAX_PRECISION - precision)".
     *     Hence we need to determine the highest precision which can be used for the given input, before calling the exponentiation function.
     *     This allows us to compute "base ^ exp" with maximum accuracy and without exceeding 256 bits in any of the intermediate computations.
     *     This functions assumes that "_expN < 2 ^ 256 / log(MAX_NUM - 1)", otherwise the multiplication should be replaced with a "safeMul".
     *     Since we rely on unsigned-integer arithmetic and "base < 1" ==> "log(base) < 0", this function does not support "_baseN < _baseD".
     */
    function power(
        uint256 _baseN,
        uint256 _baseD,
        uint32 _expN,
        uint32 _expD
    ) internal view returns (uint256, uint8) {
        require(_baseN < MAX_NUM);

        uint256 baseLog;
        uint256 base = (_baseN * FIXED_1) / _baseD;
        if (base < OPT_LOG_MAX_VAL) {
            baseLog = optimalLog(base);
        } else {
            baseLog = generalLog(base);
        }

        uint256 baseLogTimesExp = (baseLog * _expN) / _expD;
        if (baseLogTimesExp < OPT_EXP_MAX_VAL) {
            return (optimalExp(baseLogTimesExp), MAX_PRECISION);
        } else {
            uint8 precision = findPositionInMaxExpArray(baseLogTimesExp);
            return (generalExp(baseLogTimesExp >> (MAX_PRECISION - precision), precision), precision);
        }
    }

    /**
     * @dev computes log(x / FIXED_1) * FIXED_1.
     * This functions assumes that "x >= FIXED_1", because the output would be negative otherwise.
     */
    function generalLog(uint256 x) internal pure returns (uint256) {
        uint256 res = 0;

        // If x >= 2, then we compute the integer part of log2(x), which is larger than 0.
        if (x >= FIXED_2) {
            uint8 count = floorLog2(x / FIXED_1);
            x >>= count;
            // now x < 2
            res = count * FIXED_1;
        }

        // If x > 1, then we compute the fraction part of log2(x), which is larger than 0.
        if (x > FIXED_1) {
            for (uint8 i = MAX_PRECISION; i > 0; --i) {
                x = (x * x) / FIXED_1;
                // now 1 < x < 4
                if (x >= FIXED_2) {
                    x >>= 1;
                    // now 1 < x < 2
                    res += ONE << (i - 1);
                }
            }
        }

        return (res * LN2_NUMERATOR) / LN2_DENOMINATOR;
    }

    /**
     * @dev computes the largest integer smaller than or equal to the binary logarithm of the input.
     */
    function floorLog2(uint256 _n) internal pure returns (uint8) {
        uint8 res = 0;

        if (_n < 256) {
            // At most 8 iterations
            while (_n > 1) {
                _n >>= 1;
                res += 1;
            }
        } else {
            // Exactly 8 iterations
            for (uint8 s = 128; s > 0; s >>= 1) {
                if (_n >= (ONE << s)) {
                    _n >>= s;
                    res |= s;
                }
            }
        }

        return res;
    }

    /**
     * @dev the global "maxExpArray" is sorted in descending order, and therefore the following statements are equivalent:
     * - This function finds the position of [the smallest value in "maxExpArray" larger than or equal to "x"]
     * - This function finds the highest position of [a value in "maxExpArray" larger than or equal to "x"]
     */
    function findPositionInMaxExpArray(uint256 _x) internal view returns (uint8) {
        uint8 lo = MIN_PRECISION;
        uint8 hi = MAX_PRECISION;

        while (lo + 1 < hi) {
            uint8 mid = (lo + hi) / 2;
            if (maxExpArray[mid] >= _x) lo = mid;
            else hi = mid;
        }

        if (maxExpArray[hi] >= _x) return hi;
        if (maxExpArray[lo] >= _x) return lo;

        revert();
    }

    /**
     * @dev this function can be auto-generated by the script 'PrintFunctionGeneralExp.py'.
     * it approximates "e ^ x" via maclaurin summation: "(x^0)/0! + (x^1)/1! + ... + (x^n)/n!".
     * it returns "e ^ (x / 2 ^ precision) * 2 ^ precision", that is, the result is upshifted for accuracy.
     * the global "maxExpArray" maps each "precision" to "((maximumExponent + 1) << (MAX_PRECISION - precision)) - 1".
     * the maximum permitted value for "x" is therefore given by "maxExpArray[precision] >> (MAX_PRECISION - precision)".
     */
    function generalExp(uint256 _x, uint8 _precision) internal pure returns (uint256) {
        uint256 xi = _x;
        uint256 res = 0;

        xi = (xi * _x) >> _precision;
        res += xi * 0x3442c4e6074a82f1797f72ac0000000;
        // add x^02 * (33! / 02!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x116b96f757c380fb287fd0e40000000;
        // add x^03 * (33! / 03!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x045ae5bdd5f0e03eca1ff4390000000;
        // add x^04 * (33! / 04!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x00defabf91302cd95b9ffda50000000;
        // add x^05 * (33! / 05!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x002529ca9832b22439efff9b8000000;
        // add x^06 * (33! / 06!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x00054f1cf12bd04e516b6da88000000;
        // add x^07 * (33! / 07!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x0000a9e39e257a09ca2d6db51000000;
        // add x^08 * (33! / 08!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x000012e066e7b839fa050c309000000;
        // add x^09 * (33! / 09!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x000001e33d7d926c329a1ad1a800000;
        // add x^10 * (33! / 10!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x0000002bee513bdb4a6b19b5f800000;
        // add x^11 * (33! / 11!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x00000003a9316fa79b88eccf2a00000;
        // add x^12 * (33! / 12!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x0000000048177ebe1fa812375200000;
        // add x^13 * (33! / 13!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x0000000005263fe90242dcbacf00000;
        // add x^14 * (33! / 14!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x000000000057e22099c030d94100000;
        // add x^15 * (33! / 15!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x0000000000057e22099c030d9410000;
        // add x^16 * (33! / 16!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x00000000000052b6b54569976310000;
        // add x^17 * (33! / 17!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x00000000000004985f67696bf748000;
        // add x^18 * (33! / 18!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x000000000000003dea12ea99e498000;
        // add x^19 * (33! / 19!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x00000000000000031880f2214b6e000;
        // add x^20 * (33! / 20!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x000000000000000025bcff56eb36000;
        // add x^21 * (33! / 21!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x000000000000000001b722e10ab1000;
        // add x^22 * (33! / 22!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x0000000000000000001317c70077000;
        // add x^23 * (33! / 23!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x00000000000000000000cba84aafa00;
        // add x^24 * (33! / 24!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x00000000000000000000082573a0a00;
        // add x^25 * (33! / 25!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x00000000000000000000005035ad900;
        // add x^26 * (33! / 26!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x000000000000000000000002f881b00;
        // add x^27 * (33! / 27!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x0000000000000000000000001b29340;
        // add x^28 * (33! / 28!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x00000000000000000000000000efc40;
        // add x^29 * (33! / 29!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x0000000000000000000000000007fe0;
        // add x^30 * (33! / 30!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x0000000000000000000000000000420;
        // add x^31 * (33! / 31!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x0000000000000000000000000000021;
        // add x^32 * (33! / 32!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x0000000000000000000000000000001;
        // add x^33 * (33! / 33!)

        return res / 0x688589cc0e9505e2f2fee5580000000 + _x + (ONE << _precision);
        // divide by 33! and then add x^1 / 1! + x^0 / 0!
    }

    /**
     * @dev computes log(x / FIXED_1) * FIXED_1
     * Input range: FIXED_1 <= x <= OPT_LOG_MAX_VAL - 1
     * Auto-generated via 'PrintFunctionOptimalLog.py'
     * Detailed description:
     * - Rewrite the input as a product of natural exponents and a single residual r, such that 1 < r < 2
     * - The natural logarithm of each (pre-calculated) exponent is the degree of the exponent
     * - The natural logarithm of r is calculated via Taylor series for log(1 + x), where x = r - 1
     * - The natural logarithm of the input is calculated by summing up the intermediate results above
     * - For example: log(250) = log(e^4 * e^1 * e^0.5 * 1.021692859) = 4 + 1 + 0.5 + log(1 + 0.021692859)
     */
    function optimalLog(uint256 x) internal pure returns (uint256) {
        uint256 res = 0;

        uint256 y;
        uint256 z;
        uint256 w;

        if (x >= 0xd3094c70f034de4b96ff7d5b6f99fcd8) {
            res += 0x40000000000000000000000000000000;
            x = (x * FIXED_1) / 0xd3094c70f034de4b96ff7d5b6f99fcd8;
        }
        // add 1 / 2^1
        if (x >= 0xa45af1e1f40c333b3de1db4dd55f29a7) {
            res += 0x20000000000000000000000000000000;
            x = (x * FIXED_1) / 0xa45af1e1f40c333b3de1db4dd55f29a7;
        }
        // add 1 / 2^2
        if (x >= 0x910b022db7ae67ce76b441c27035c6a1) {
            res += 0x10000000000000000000000000000000;
            x = (x * FIXED_1) / 0x910b022db7ae67ce76b441c27035c6a1;
        }
        // add 1 / 2^3
        if (x >= 0x88415abbe9a76bead8d00cf112e4d4a8) {
            res += 0x08000000000000000000000000000000;
            x = (x * FIXED_1) / 0x88415abbe9a76bead8d00cf112e4d4a8;
        }
        // add 1 / 2^4
        if (x >= 0x84102b00893f64c705e841d5d4064bd3) {
            res += 0x04000000000000000000000000000000;
            x = (x * FIXED_1) / 0x84102b00893f64c705e841d5d4064bd3;
        }
        // add 1 / 2^5
        if (x >= 0x8204055aaef1c8bd5c3259f4822735a2) {
            res += 0x02000000000000000000000000000000;
            x = (x * FIXED_1) / 0x8204055aaef1c8bd5c3259f4822735a2;
        }
        // add 1 / 2^6
        if (x >= 0x810100ab00222d861931c15e39b44e99) {
            res += 0x01000000000000000000000000000000;
            x = (x * FIXED_1) / 0x810100ab00222d861931c15e39b44e99;
        }
        // add 1 / 2^7
        if (x >= 0x808040155aabbbe9451521693554f733) {
            res += 0x00800000000000000000000000000000;
            x = (x * FIXED_1) / 0x808040155aabbbe9451521693554f733;
        }
        // add 1 / 2^8

        z = y = x - FIXED_1;
        w = (y * y) / FIXED_1;
        res += (z * (0x100000000000000000000000000000000 - y)) / 0x100000000000000000000000000000000;
        z = (z * w) / FIXED_1;
        // add y^01 / 01 - y^02 / 02
        res += (z * (0x0aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa - y)) / 0x200000000000000000000000000000000;
        z = (z * w) / FIXED_1;
        // add y^03 / 03 - y^04 / 04
        res += (z * (0x099999999999999999999999999999999 - y)) / 0x300000000000000000000000000000000;
        z = (z * w) / FIXED_1;
        // add y^05 / 05 - y^06 / 06
        res += (z * (0x092492492492492492492492492492492 - y)) / 0x400000000000000000000000000000000;
        z = (z * w) / FIXED_1;
        // add y^07 / 07 - y^08 / 08
        res += (z * (0x08e38e38e38e38e38e38e38e38e38e38e - y)) / 0x500000000000000000000000000000000;
        z = (z * w) / FIXED_1;
        // add y^09 / 09 - y^10 / 10
        res += (z * (0x08ba2e8ba2e8ba2e8ba2e8ba2e8ba2e8b - y)) / 0x600000000000000000000000000000000;
        z = (z * w) / FIXED_1;
        // add y^11 / 11 - y^12 / 12
        res += (z * (0x089d89d89d89d89d89d89d89d89d89d89 - y)) / 0x700000000000000000000000000000000;
        z = (z * w) / FIXED_1;
        // add y^13 / 13 - y^14 / 14
        res += (z * (0x088888888888888888888888888888888 - y)) / 0x800000000000000000000000000000000;
        // add y^15 / 15 - y^16 / 16

        return res;
    }

    /**
     * @dev computes e ^ (x / FIXED_1) * FIXED_1
     * input range: 0 <= x <= OPT_EXP_MAX_VAL - 1
     * auto-generated via 'PrintFunctionOptimalExp.py'
     * Detailed description:
     * - Rewrite the input as a sum of binary exponents and a single residual r, as small as possible
     * - The exponentiation of each binary exponent is given (pre-calculated)
     * - The exponentiation of r is calculated via Taylor series for e^x, where x = r
     * - The exponentiation of the input is calculated by multiplying the intermediate results above
     * - For example: e^5.521692859 = e^(4 + 1 + 0.5 + 0.021692859) = e^4 * e^1 * e^0.5 * e^0.021692859
     */
    function optimalExp(uint256 x) internal pure returns (uint256) {
        uint256 res = 0;

        uint256 y;
        uint256 z;

        z = y = x % 0x10000000000000000000000000000000;
        // get the input modulo 2^(-3)
        z = (z * y) / FIXED_1;
        res += z * 0x10e1b3be415a0000;
        // add y^02 * (20! / 02!)
        z = (z * y) / FIXED_1;
        res += z * 0x05a0913f6b1e0000;
        // add y^03 * (20! / 03!)
        z = (z * y) / FIXED_1;
        res += z * 0x0168244fdac78000;
        // add y^04 * (20! / 04!)
        z = (z * y) / FIXED_1;
        res += z * 0x004807432bc18000;
        // add y^05 * (20! / 05!)
        z = (z * y) / FIXED_1;
        res += z * 0x000c0135dca04000;
        // add y^06 * (20! / 06!)
        z = (z * y) / FIXED_1;
        res += z * 0x0001b707b1cdc000;
        // add y^07 * (20! / 07!)
        z = (z * y) / FIXED_1;
        res += z * 0x000036e0f639b800;
        // add y^08 * (20! / 08!)
        z = (z * y) / FIXED_1;
        res += z * 0x00000618fee9f800;
        // add y^09 * (20! / 09!)
        z = (z * y) / FIXED_1;
        res += z * 0x0000009c197dcc00;
        // add y^10 * (20! / 10!)
        z = (z * y) / FIXED_1;
        res += z * 0x0000000e30dce400;
        // add y^11 * (20! / 11!)
        z = (z * y) / FIXED_1;
        res += z * 0x000000012ebd1300;
        // add y^12 * (20! / 12!)
        z = (z * y) / FIXED_1;
        res += z * 0x0000000017499f00;
        // add y^13 * (20! / 13!)
        z = (z * y) / FIXED_1;
        res += z * 0x0000000001a9d480;
        // add y^14 * (20! / 14!)
        z = (z * y) / FIXED_1;
        res += z * 0x00000000001c6380;
        // add y^15 * (20! / 15!)
        z = (z * y) / FIXED_1;
        res += z * 0x000000000001c638;
        // add y^16 * (20! / 16!)
        z = (z * y) / FIXED_1;
        res += z * 0x0000000000001ab8;
        // add y^17 * (20! / 17!)
        z = (z * y) / FIXED_1;
        res += z * 0x000000000000017c;
        // add y^18 * (20! / 18!)
        z = (z * y) / FIXED_1;
        res += z * 0x0000000000000014;
        // add y^19 * (20! / 19!)
        z = (z * y) / FIXED_1;
        res += z * 0x0000000000000001;
        // add y^20 * (20! / 20!)
        res = res / 0x21c3677c82b40000 + y + FIXED_1;
        // divide by 20! and then add y^1 / 1! + y^0 / 0!

        if ((x & 0x010000000000000000000000000000000) != 0) res = (res * 0x1c3d6a24ed82218787d624d3e5eba95f9) / 0x18ebef9eac820ae8682b9793ac6d1e776;
        // multiply by e^2^(-3)
        if ((x & 0x020000000000000000000000000000000) != 0) res = (res * 0x18ebef9eac820ae8682b9793ac6d1e778) / 0x1368b2fc6f9609fe7aceb46aa619baed4;
        // multiply by e^2^(-2)
        if ((x & 0x040000000000000000000000000000000) != 0) res = (res * 0x1368b2fc6f9609fe7aceb46aa619baed5) / 0x0bc5ab1b16779be3575bd8f0520a9f21f;
        // multiply by e^2^(-1)
        if ((x & 0x080000000000000000000000000000000) != 0) res = (res * 0x0bc5ab1b16779be3575bd8f0520a9f21e) / 0x0454aaa8efe072e7f6ddbab84b40a55c9;
        // multiply by e^2^(+0)
        if ((x & 0x100000000000000000000000000000000) != 0) res = (res * 0x0454aaa8efe072e7f6ddbab84b40a55c5) / 0x00960aadc109e7a3bf4578099615711ea;
        // multiply by e^2^(+1)
        if ((x & 0x200000000000000000000000000000000) != 0) res = (res * 0x00960aadc109e7a3bf4578099615711d7) / 0x0002bf84208204f5977f9a8cf01fdce3d;
        // multiply by e^2^(+2)
        if ((x & 0x400000000000000000000000000000000) != 0) res = (res * 0x0002bf84208204f5977f9a8cf01fdc307) / 0x0000003c6ab775dd0b95b4cbee7e65d11;
        // multiply by e^2^(+3)

        return res;
    }

    function getReserveAndWeights(address pair, address tokenA)
    public
    view
    override
    returns (
        address tokenB,
        uint256 reserveA,
        uint256 reserveB,
        uint32 tokenWeightA,
        uint32 tokenWeightB,
        uint32 swapFee
    )
    {
        address token0 = IValueLiquidPair(pair).token0();
        (uint256 reserve0, uint256 reserve1, ) = IValueLiquidPair(pair).getReserves();
        uint32 tokenWeight0;
        uint32 tokenWeight1;
        (tokenWeight0, tokenWeight1, swapFee) = getWeightsAndSwapFee(pair);

        if (tokenA == token0) {
            (tokenB, reserveA, reserveB, tokenWeightA, tokenWeightB) = (IValueLiquidPair(pair).token1(), reserve0, reserve1, tokenWeight0, tokenWeight1);
        } else {
            (tokenB, reserveA, reserveB, tokenWeightA, tokenWeightB) = (token0, reserve1, reserve0, tokenWeight1, tokenWeight0);
        }
    }

    function getFactoryReserveAndWeights(
        address factory,
        address pair,
        address tokenA
    )
    public
    view
    override
    returns (
        address tokenB,
        uint256 reserveA,
        uint256 reserveB,
        uint32 tokenWeightA,
        uint32 tokenWeightB,
        uint32 swapFee
    )
    {
        address token0 = IValueLiquidPair(pair).token0();
        (uint256 reserve0, uint256 reserve1, ) = IValueLiquidPair(pair).getReserves();
        uint32 tokenWeight0;
        uint32 tokenWeight1;
        (tokenWeight0, tokenWeight1, swapFee) = getFactoryWeightsAndSwapFee(factory, pair);

        if (tokenA == token0) {
            (tokenB, reserveA, reserveB, tokenWeightA, tokenWeightB) = (IValueLiquidPair(pair).token1(), reserve0, reserve1, tokenWeight0, tokenWeight1);
        } else {
            (tokenB, reserveA, reserveB, tokenWeightA, tokenWeightB) = (token0, reserve1, reserve0, tokenWeight1, tokenWeight0);
        }
    }

    /**
     * @dev given an input amount of an asset and pair reserves, returns the maximum output amount of the other asset,
     *
     * Formula:
     * return = reserveOut * (1 - (reserveIn / (reserveIn + amountIn * (1000 - swapFee))) ^ (tokenWeightIn / tokenWeightOut))
     *
     * @param amountIn                  source reserve amount
     * @param reserveIn    source reserve balance
     * @param reserveOut    target reserve balance
     * @param tokenWeightIn     source reserve weight, represented in ppm (2-98)
     * @param tokenWeightOut     target reserve weight, represented in ppm (2-98)
     * @param swapFee                  swap fee of the conversion
     *
     * @return amountOut
     */
    function getAmountOut(
        uint256 amountIn,
        uint256 reserveIn,
        uint256 reserveOut,
        uint32 tokenWeightIn,
        uint32 tokenWeightOut,
        uint32 swapFee
    ) public view override returns (uint256 amountOut) {
        // validate input
        require(amountIn > 0, "ValueFormula: INSUFFICIENT_INPUT_AMOUNT");
        require(reserveIn > 0 && reserveOut > 0, "ValueFormula: INSUFFICIENT_LIQUIDITY");
        uint256 amountInWithFee = amountIn.mul(1000 - swapFee);
        // special case for equal weights
        if (tokenWeightIn == tokenWeightOut) {
            return reserveOut.mul(amountInWithFee) / (reserveIn.mul(1000).add(amountInWithFee));
        }

        uint256 result;
        uint8 precision;
        uint256 baseN = reserveIn.mul(1000).add(amountInWithFee);
        (result, precision) = power(baseN, reserveIn.mul(1000), tokenWeightIn, tokenWeightOut);

        uint256 temp1 = reserveOut.mul(result);
        uint256 temp2 = reserveOut << precision;
        return (temp1 - temp2) / result;
    }

    /**
     * @dev given an output amount of an asset and pair reserves, returns a required input amount of the other asset
     *
     * Formula:
     * return = reserveIn * ( (reserveOut / (reserveOut - amountOut)) ^ (tokenWeightOut / tokenWeightIn) - 1) * (1000/ (1000 - swapFee)
     *
     * @param amountOut     target reserve amount
     * @param reserveIn    source reserve balance
     * @param reserveOut    target reserve balance
     * @param tokenWeightIn     source reserve weight, represented in ppm (2-98)
     * @param tokenWeightOut     target reserve weight, represented in ppm (2-98)
     * @param swapFee                  swap fee of the conversion
     *
     * @return amountIn
     */
    function getAmountIn(
        uint256 amountOut,
        uint256 reserveIn,
        uint256 reserveOut,
        uint32 tokenWeightIn,
        uint32 tokenWeightOut,
        uint32 swapFee
    ) public view override returns (uint256 amountIn) {
        // validate input
        require(amountOut > 0, "ValueFormula: INSUFFICIENT_OUTPUT_AMOUNT");
        require(reserveIn > 0 && reserveOut > 0, "ValueFormula: INSUFFICIENT_LIQUIDITY");
        // special case for equal weights
        if (tokenWeightIn == tokenWeightOut) {
            uint256 numerator = reserveIn.mul(amountOut).mul(1000);
            uint256 denominator = reserveOut.sub(amountOut).mul(1000 - swapFee);
            return (numerator / denominator).add(1);
        }

        uint256 result;
        uint8 precision;
        uint256 baseD = reserveOut.sub(amountOut);
        (result, precision) = power(reserveOut, baseD, tokenWeightOut, tokenWeightIn);
        uint256 baseReserveIn = reserveIn.mul(1000);
        uint256 temp1 = baseReserveIn.mul(result);
        uint256 temp2 = baseReserveIn << precision;
        return (((temp1 - temp2) >> precision) / (1000 - swapFee)).add(1);
    }

    // performs chained getAmountOut calculations on any number of pairs
    function getAmountsOut(
        address tokenIn,
        address tokenOut,
        uint256 amountIn,
        address[] calldata path
    ) external view override returns (uint256[] memory amounts) {
        require(path.length > 0, "ValueFormula: INVALID_PATH");
        amounts = new uint256[](path.length + 1);
        amounts[0] = amountIn;
        address currentTokenIn = tokenIn;
        for (uint256 i = 0; i < path.length; i++) {
            (address currentTokenOut, uint256 reserveIn, uint256 reserveOut, uint32 tokenWeightIn, uint32 tokenWeightOut, uint32 swapFee) =
            getReserveAndWeights(path[i], currentTokenIn);
            amounts[i + 1] = getAmountOut(amounts[i], reserveIn, reserveOut, tokenWeightIn, tokenWeightOut, swapFee);
            currentTokenIn = currentTokenOut;
        }
        require(currentTokenIn == tokenOut, "ValueFormula: INVALID_TOKEN_OUT_PATH");
    }

    function getFactoryAmountsOut(
        address factory,
        address tokenIn,
        address tokenOut,
        uint256 amountIn,
        address[] calldata path
    ) external view override returns (uint256[] memory amounts) {
        require(path.length > 0, "ValueFormula: INVALID_PATH");
        amounts = new uint256[](path.length + 1);
        amounts[0] = amountIn;
        address currentTokenIn = tokenIn;
        for (uint256 i = 0; i < path.length; i++) {
            (address currentTokenOut, uint256 reserveIn, uint256 reserveOut, uint32 tokenWeightIn, uint32 tokenWeightOut, uint32 swapFee) =
            getFactoryReserveAndWeights(factory, path[i], currentTokenIn);
            amounts[i + 1] = getAmountOut(amounts[i], reserveIn, reserveOut, tokenWeightIn, tokenWeightOut, swapFee);
            currentTokenIn = currentTokenOut;
        }
        require(currentTokenIn == tokenOut, "ValueFormula: INVALID_TOKEN_OUT_PATH");
    }

    function getPairAmountOut(
        address pair,
        address tokenIn,
        uint256 amountIn
    ) external view override returns (uint256 amountOut) {
        (, uint256 reserveIn, uint256 reserveOut, uint32 tokenWeightIn, uint32 tokenWeightOut, uint32 swapFee) =
        getReserveAndWeights(pair, tokenIn);
        amountOut = getAmountOut(amountIn, reserveIn, reserveOut, tokenWeightIn, tokenWeightOut, swapFee);
    }

    // performs chained getAmountIn calculations on any number of pairs
    function getAmountsIn(
        address tokenIn,
        address tokenOut,
        uint256 amountOut,
        address[] calldata path
    ) external view override returns (uint256[] memory amounts) {
        require(path.length > 0, "ValueFormula: INVALID_PATH");
        amounts = new uint256[](path.length + 1);
        amounts[amounts.length - 1] = amountOut;
        address currentTokenIn = tokenOut;
        for (uint256 i = path.length; i > 0; i--) {
            (address currentTokenOut, uint256 reserveIn, uint256 reserveOut, uint32 tokenWeightIn, uint32 tokenWeightOut, uint32 swapFee) =
            getReserveAndWeights(path[i - 1], currentTokenIn);
            amounts[i - 1] = getAmountIn(amounts[i], reserveOut, reserveIn, tokenWeightOut, tokenWeightIn, swapFee);
            currentTokenIn = currentTokenOut;
        }
        require(currentTokenIn == tokenIn, "ValueFormula: INVALID_TOKEN_IN_PATH");
    }

    function getFactoryAmountsIn(
        address factory,
        address tokenIn,
        address tokenOut,
        uint256 amountOut,
        address[] calldata path
    ) external view override returns (uint256[] memory amounts) {
        require(path.length > 0, "ValueFormula: INVALID_PATH");
        amounts = new uint256[](path.length + 1);
        amounts[amounts.length - 1] = amountOut;
        address currentTokenIn = tokenOut;
        for (uint256 i = path.length; i > 0; i--) {
            (address currentTokenOut, uint256 reserveIn, uint256 reserveOut, uint32 tokenWeightIn, uint32 tokenWeightOut, uint32 swapFee) =
            getFactoryReserveAndWeights(factory, path[i - 1], currentTokenIn);
            amounts[i - 1] = getAmountIn(amounts[i], reserveOut, reserveIn, tokenWeightOut, tokenWeightIn, swapFee);
            currentTokenIn = currentTokenOut;
        }
        require(currentTokenIn == tokenIn, "ValueFormula: INVALID_TOKEN_IN_PATH");
    }

    function getPairAmountIn(
        address pair,
        address tokenIn,
        uint256 amountOut
    ) external view override returns (uint256 amountIn) {
        (, uint256 reserveIn, uint256 reserveOut, uint32 tokenWeightIn, uint32 tokenWeightOut, uint32 swapFee) =
        getReserveAndWeights(pair, tokenIn);
        amountIn = getAmountIn(amountOut, reserveOut, reserveIn, tokenWeightOut, tokenWeightIn, swapFee);
    }

    function getWeightsAndSwapFee(address pair)
    public
    view
    returns (
        uint32 tokenWeight0,
        uint32 tokenWeight1,
        uint32 swapFee
    )
    {
    try IValueLiquidPair(pair).getTokenWeights() returns (uint32 _tokenWeight0, uint32 _tokenWeight1) {
    return (_tokenWeight0, _tokenWeight1, IValueLiquidPair(pair).getSwapFee());
    } catch Error(string memory reason) {
    revert(reason);
    } catch (
    bytes memory /*lowLevelData*/
    ) {
    return (50, 50, 3);
    }
    }

    function getFactoryWeightsAndSwapFee(address factory, address pair)
    public
    view
    returns (
        uint32 tokenWeight0,
        uint32 tokenWeight1,
        uint32 swapFee
    )
    {
        return IValueLiquidFactory(factory).getWeightsAndSwapFee(pair);
    }

    // Ensure constant value reserve0^(tokenWeight0/50) * reserve1^((100 - tokenWeight0)/50) <= balance0Adjusted^(tokenWeight0/50) * balance1Adjusted^((100 - tokenWeight0)/50)
    //  1 <= (balance0Adjusted / reserve0 )^(tokenWeight0/50) * (balance1Adjusted/reserve1)^((100 - tokenWeight0)/50)
    //  (reserve0 / balance0Adjusted) ^ (tokenWeight0/50) <=  (balance1Adjusted / reserve1) ^ ((100 - tokenWeight0)/50)
    function ensureConstantValue(
        uint256 reserve0,
        uint256 reserve1,
        uint256 balance0Adjusted,
        uint256 balance1Adjusted,
        uint32 tokenWeight0
    ) external view override returns (bool) {
        if (tokenWeight0 == 50) {
            return balance0Adjusted.mul(balance1Adjusted) >= reserve0.mul(reserve1);
        }
        if (balance0Adjusted >= reserve0 && balance1Adjusted >= reserve1) {
            return true;
        }
        if ((balance0Adjusted == reserve0 && balance1Adjusted < reserve1) || (balance0Adjusted < reserve0 && balance1Adjusted == reserve1)) {
            return false;
        }
        uint32 w0 = tokenWeight0;
        uint32 w1 = 100 - w0;

        uint256 r0;
        uint256 p0;
        uint256 r1;
        uint256 p1;
        if (balance0Adjusted >= reserve0) {
            (r0, p0) = power(reserve1, balance1Adjusted, w1, 50);
            (r1, p1) = power(balance0Adjusted, reserve0, w0, 50);
        } else {
            (r0, p0) = power(reserve0, balance0Adjusted, w0, 50);
            (r1, p1) = power(balance1Adjusted, reserve1, w1, 50);
        }
        uint256 minP = p0 < p1 ? p0 : p1;
        p0 = p0 - minP;
        p1 = p1 - minP;
        return (r0 >> p0) <= (r1 >> p1);
    }

    function sortTokens(address tokenA, address tokenB) public pure override returns (address token0, address token1) {
        require(tokenA != tokenB, "ValueFormula: IDENTICAL_ADDRESSES");
        (token0, token1) = tokenA < tokenB ? (tokenA, tokenB) : (tokenB, tokenA);
        require(token0 != address(0), "ValueFormula: ZERO_ADDRESS");
    }

    function getReserves(
        address pair,
        address tokenA,
        address tokenB
    ) external view override returns (uint256 reserveA, uint256 reserveB) {
        (address token0, ) = sortTokens(tokenA, tokenB);
        (uint256 reserve0, uint256 reserve1, ) = IValueLiquidPair(pair).getReserves();
        (reserveA, reserveB) = tokenA == token0 ? (reserve0, reserve1) : (reserve1, reserve0);
    }

    function getOtherToken(address pair, address tokenA) external view override returns (address tokenB) {
        address token0 = IValueLiquidPair(pair).token0();
        address token1 = IValueLiquidPair(pair).token1();
        tokenB = token0 == tokenA ? token1 : token0;
    }

    // given some amount of an asset and pair reserves, returns an equivalent amount of the other asset
    function quote(
        uint256 amountA,
        uint256 reserveA,
        uint256 reserveB
    ) external pure override returns (uint256 amountB) {
        require(amountA > 0, "ValueFormula: INSUFFICIENT_AMOUNT");
        require(reserveA > 0 && reserveB > 0, "ValueFormula: INSUFFICIENT_LIQUIDITY");
        amountB = amountA.mul(reserveB) / reserveA;
    }

    function mintLiquidityFee(
        uint256 totalLiquidity,
        uint112 reserve0,
        uint112 reserve1,
        uint32 tokenWeight0,
        uint32 tokenWeight1,
        uint112 collectedFee0,
        uint112 collectedFee1
    ) external view override returns (uint256 amount) {
        if (collectedFee0 > 0) {
            (uint256 r0, uint256 p0) = power(uint256(collectedFee0).add(reserve0), reserve0, tokenWeight0, 100);
            amount = amount.add(totalLiquidity.mul(r0) >> p0).sub(totalLiquidity);
        }
        if (collectedFee1 > 0) {
            (uint256 r1, uint256 p1) = power(uint256(collectedFee1).add(reserve1), reserve1, tokenWeight1, 100);
            amount = amount.add(totalLiquidity.mul(r1) >> p1).sub(totalLiquidity);
        }
    }
}

• No Contract Security Audit Submitted- Submit Audit Here

[{"inputs":[],"stateMutability":"nonpayable","type":"constructor"},{"inputs":[{"internalType":"uint256","name":"reserve0","type":"uint256"},{"internalType":"uint256","name":"reserve1","type":"uint256"},{"internalType":"uint256","name":"balance0Adjusted","type":"uint256"},{"internalType":"uint256","name":"balance1Adjusted","type":"uint256"},{"internalType":"uint32","name":"tokenWeight0","type":"uint32"}],"name":"ensureConstantValue","outputs":[{"internalType":"bool","name":"","type":"bool"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"uint256","name":"amountOut","type":"uint256"},{"internalType":"uint256","name":"reserveIn","type":"uint256"},{"internalType":"uint256","name":"reserveOut","type":"uint256"},{"internalType":"uint32","name":"tokenWeightIn","type":"uint32"},{"internalType":"uint32","name":"tokenWeightOut","type":"uint32"},{"internalType":"uint32","name":"swapFee","type":"uint32"}],"name":"getAmountIn","outputs":[{"internalType":"uint256","name":"amountIn","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"uint256","name":"amountIn","type":"uint256"},{"internalType":"uint256","name":"reserveIn","type":"uint256"},{"internalType":"uint256","name":"reserveOut","type":"uint256"},{"internalType":"uint32","name":"tokenWeightIn","type":"uint32"},{"internalType":"uint32","name":"tokenWeightOut","type":"uint32"},{"internalType":"uint32","name":"swapFee","type":"uint32"}],"name":"getAmountOut","outputs":[{"internalType":"uint256","name":"amountOut","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"tokenIn","type":"address"},{"internalType":"address","name":"tokenOut","type":"address"},{"internalType":"uint256","name":"amountOut","type":"uint256"},{"internalType":"address[]","name":"path","type":"address[]"}],"name":"getAmountsIn","outputs":[{"internalType":"uint256[]","name":"amounts","type":"uint256[]"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"tokenIn","type":"address"},{"internalType":"address","name":"tokenOut","type":"address"},{"internalType":"uint256","name":"amountIn","type":"uint256"},{"internalType":"address[]","name":"path","type":"address[]"}],"name":"getAmountsOut","outputs":[{"internalType":"uint256[]","name":"amounts","type":"uint256[]"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"factory","type":"address"},{"internalType":"address","name":"tokenIn","type":"address"},{"internalType":"address","name":"tokenOut","type":"address"},{"internalType":"uint256","name":"amountOut","type":"uint256"},{"internalType":"address[]","name":"path","type":"address[]"}],"name":"getFactoryAmountsIn","outputs":[{"internalType":"uint256[]","name":"amounts","type":"uint256[]"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"factory","type":"address"},{"internalType":"address","name":"tokenIn","type":"address"},{"internalType":"address","name":"tokenOut","type":"address"},{"internalType":"uint256","name":"amountIn","type":"uint256"},{"internalType":"address[]","name":"path","type":"address[]"}],"name":"getFactoryAmountsOut","outputs":[{"internalType":"uint256[]","name":"amounts","type":"uint256[]"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"factory","type":"address"},{"internalType":"address","name":"pair","type":"address"},{"internalType":"address","name":"tokenA","type":"address"}],"name":"getFactoryReserveAndWeights","outputs":[{"internalType":"address","name":"tokenB","type":"address"},{"internalType":"uint256","name":"reserveA","type":"uint256"},{"internalType":"uint256","name":"reserveB","type":"uint256"},{"internalType":"uint32","name":"tokenWeightA","type":"uint32"},{"internalType":"uint32","name":"tokenWeightB","type":"uint32"},{"internalType":"uint32","name":"swapFee","type":"uint32"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"factory","type":"address"},{"internalType":"address","name":"pair","type":"address"}],"name":"getFactoryWeightsAndSwapFee","outputs":[{"internalType":"uint32","name":"tokenWeight0","type":"uint32"},{"internalType":"uint32","name":"tokenWeight1","type":"uint32"},{"internalType":"uint32","name":"swapFee","type":"uint32"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"pair","type":"address"},{"internalType":"address","name":"tokenA","type":"address"}],"name":"getOtherToken","outputs":[{"internalType":"address","name":"tokenB","type":"address"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"pair","type":"address"},{"internalType":"address","name":"tokenIn","type":"address"},{"internalType":"uint256","name":"amountOut","type":"uint256"}],"name":"getPairAmountIn","outputs":[{"internalType":"uint256","name":"amountIn","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"pair","type":"address"},{"internalType":"address","name":"tokenIn","type":"address"},{"internalType":"uint256","name":"amountIn","type":"uint256"}],"name":"getPairAmountOut","outputs":[{"internalType":"uint256","name":"amountOut","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"pair","type":"address"},{"internalType":"address","name":"tokenA","type":"address"}],"name":"getReserveAndWeights","outputs":[{"internalType":"address","name":"tokenB","type":"address"},{"internalType":"uint256","name":"reserveA","type":"uint256"},{"internalType":"uint256","name":"reserveB","type":"uint256"},{"internalType":"uint32","name":"tokenWeightA","type":"uint32"},{"internalType":"uint32","name":"tokenWeightB","type":"uint32"},{"internalType":"uint32","name":"swapFee","type":"uint32"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"pair","type":"address"},{"internalType":"address","name":"tokenA","type":"address"},{"internalType":"address","name":"tokenB","type":"address"}],"name":"getReserves","outputs":[{"internalType":"uint256","name":"reserveA","type":"uint256"},{"internalType":"uint256","name":"reserveB","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"pair","type":"address"}],"name":"getWeightsAndSwapFee","outputs":[{"internalType":"uint32","name":"tokenWeight0","type":"uint32"},{"internalType":"uint32","name":"tokenWeight1","type":"uint32"},{"internalType":"uint32","name":"swapFee","type":"uint32"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"uint256","name":"totalLiquidity","type":"uint256"},{"internalType":"uint112","name":"reserve0","type":"uint112"},{"internalType":"uint112","name":"reserve1","type":"uint112"},{"internalType":"uint32","name":"tokenWeight0","type":"uint32"},{"internalType":"uint32","name":"tokenWeight1","type":"uint32"},{"internalType":"uint112","name":"collectedFee0","type":"uint112"},{"internalType":"uint112","name":"collectedFee1","type":"uint112"}],"name":"mintLiquidityFee","outputs":[{"internalType":"uint256","name":"amount","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"uint256","name":"amountA","type":"uint256"},{"internalType":"uint256","name":"reserveA","type":"uint256"},{"internalType":"uint256","name":"reserveB","type":"uint256"}],"name":"quote","outputs":[{"internalType":"uint256","name":"amountB","type":"uint256"}],"stateMutability":"pure","type":"function"},{"inputs":[{"internalType":"address","name":"tokenA","type":"address"},{"internalType":"address","name":"tokenB","type":"address"}],"name":"sortTokens","outputs":[{"internalType":"address","name":"token0","type":"address"},{"internalType":"address","name":"token1","type":"address"}],"stateMutability":"pure","type":"function"}]

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