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• library XNum
•    - function btoi(uint256 a)
•    - function bfloor(uint256 a)
•    - function badd(uint256 a, uint256 b)
•    - function bsub(uint256 a, uint256 b)
•    - function bsubSign(uint256 a, uint256 ...
•    - function bmul(uint256 a, uint256 b)
•    - function bdiv(uint256 a, uint256 b)
•    - function bpowi(uint256 a, uint256 n)
•    - function bpow(uint256 base, uint256 e ...
•    - function bpowApprox(
• library XMath
•    - function calcSpotPrice(
•    - function calcOutGivenIn(
•    - function calcInGivenOut(
•    - function calcPoolOutGivenSingleIn(
•    - function calcSingleOutGivenPoolIn(

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/**
 *Submitted for verification at Etherscan.io on 2021-03-13
*/

// File: contracts/lib/XNum.sol

pragma solidity 0.5.17;

library XNum {
    uint256 public constant BONE = 10**18;
    uint256 public constant MIN_BPOW_BASE = 1 wei;
    uint256 public constant MAX_BPOW_BASE = (2 * BONE) - 1 wei;
    uint256 public constant BPOW_PRECISION = BONE / 10**10;

    function btoi(uint256 a) internal pure returns (uint256) {
        return a / BONE;
    }

    function bfloor(uint256 a) internal pure returns (uint256) {
        return btoi(a) * BONE;
    }

    function badd(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        require(c >= a, "ERR_ADD_OVERFLOW");
        return c;
    }

    function bsub(uint256 a, uint256 b) internal pure returns (uint256) {
        (uint256 c, bool flag) = bsubSign(a, b);
        require(!flag, "ERR_SUB_UNDERFLOW");
        return c;
    }

    function bsubSign(uint256 a, uint256 b)
        internal
        pure
        returns (uint256, bool)
    {
        if (a >= b) {
            return (a - b, false);
        } else {
            return (b - a, true);
        }
    }

    function bmul(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c0 = a * b;
        require(a == 0 || c0 / a == b, "ERR_MUL_OVERFLOW");
        uint256 c1 = c0 + (BONE / 2);
        require(c1 >= c0, "ERR_MUL_OVERFLOW");
        uint256 c2 = c1 / BONE;
        return c2;
    }

    function bdiv(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b != 0, "ERR_DIV_ZERO");
        uint256 c0 = a * BONE;
        require(a == 0 || c0 / a == BONE, "ERR_DIV_INTERNAL"); // bmul overflow
        uint256 c1 = c0 + (b / 2);
        require(c1 >= c0, "ERR_DIV_INTERNAL"); //  badd require
        uint256 c2 = c1 / b;
        return c2;
    }

    // DSMath.wpow
    function bpowi(uint256 a, uint256 n) internal pure returns (uint256) {
        uint256 z = n % 2 != 0 ? a : BONE;

        for (n /= 2; n != 0; n /= 2) {
            a = bmul(a, a);

            if (n % 2 != 0) {
                z = bmul(z, a);
            }
        }
        return z;
    }

    // Compute b^(e.w) by splitting it into (b^e)*(b^0.w).
    // Use `bpowi` for `b^e` and `bpowK` for k iterations
    // of approximation of b^0.w
    function bpow(uint256 base, uint256 exp) internal pure returns (uint256) {
        require(base >= MIN_BPOW_BASE, "ERR_BPOW_BASE_TOO_LOW");
        require(base <= MAX_BPOW_BASE, "ERR_BPOW_BASE_TOO_HIGH");

        uint256 whole = bfloor(exp);
        uint256 remain = bsub(exp, whole);

        uint256 wholePow = bpowi(base, btoi(whole));

        if (remain == 0) {
            return wholePow;
        }

        uint256 partialResult = bpowApprox(base, remain, BPOW_PRECISION);
        return bmul(wholePow, partialResult);
    }

    function bpowApprox(
        uint256 base,
        uint256 exp,
        uint256 precision
    ) internal pure returns (uint256) {
        // term 0:
        uint256 a = exp;
        (uint256 x, bool xneg) = bsubSign(base, BONE);
        uint256 term = BONE;
        uint256 sum = term;
        bool negative = false;

        // term(k) = numer / denom
        //         = (product(a - i + 1, i=1-->k) * x^k) / (k!)
        // each iteration, multiply previous term by (a-(k-1)) * x / k
        // continue until term is less than precision
        for (uint256 i = 1; term >= precision; i++) {
            uint256 bigK = i * BONE;
            (uint256 c, bool cneg) = bsubSign(a, bsub(bigK, BONE));
            term = bmul(term, bmul(c, x));
            term = bdiv(term, bigK);
            if (term == 0) break;

            if (xneg) negative = !negative;
            if (cneg) negative = !negative;
            if (negative) {
                sum = bsub(sum, term);
            } else {
                sum = badd(sum, term);
            }
        }

        return sum;
    }
}

// File: contracts/lib/XMath.sol

// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

pragma solidity 0.5.17;


library XMath {
    using XNum for uint256;

    uint256 public constant BONE = 10**18;
    uint256 public constant EXIT_ZERO_FEE = 0;

    /**********************************************************************************************
    // calcSpotPrice                                                                             //
    // sP = spotPrice                                                                            //
    // bI = tokenBalanceIn                ( bI / wI )         1                                  //
    // bO = tokenBalanceOut         sP =  -----------  *  ----------                             //
    // wI = tokenWeightIn                 ( bO / wO )     ( 1 - sF )                             //
    // wO = tokenWeightOut                                                                       //
    // sF = swapFee                                                                              //
    **********************************************************************************************/
    function calcSpotPrice(
        uint256 tokenBalanceIn,
        uint256 tokenWeightIn,
        uint256 tokenBalanceOut,
        uint256 tokenWeightOut,
        uint256 swapFee
    ) public pure returns (uint256 spotPrice) {
        uint256 numer = tokenBalanceIn.bdiv(tokenWeightIn);
        uint256 denom = tokenBalanceOut.bdiv(tokenWeightOut);
        uint256 ratio = numer.bdiv(denom);
        uint256 scale = BONE.bdiv(BONE.bsub(swapFee));
        return (spotPrice = ratio.bmul(scale));
    }

    /**********************************************************************************************
    // calcOutGivenIn                                                                            //
    // aO = tokenAmountOut                                                                       //
    // bO = tokenBalanceOut                                                                      //
    // bI = tokenBalanceIn              /      /            bI             \    (wI / wO) \      //
    // aI = tokenAmountIn    aO = bO * |  1 - | --------------------------  | ^            |     //
    // wI = tokenWeightIn               \      \ ( bI + ( aI * ( 1 - sF )) /              /      //
    // wO = tokenWeightOut                                                                       //
    // sF = swapFee                                                                              //
    **********************************************************************************************/
    function calcOutGivenIn(
        uint256 tokenBalanceIn,
        uint256 tokenWeightIn,
        uint256 tokenBalanceOut,
        uint256 tokenWeightOut,
        uint256 tokenAmountIn,
        uint256 swapFee
    ) public pure returns (uint256 tokenAmountOut) {
        uint256 weightRatio;
        if (tokenWeightIn == tokenWeightOut) {
            weightRatio = 1 * BONE;
        } else if (tokenWeightIn >> 1 == tokenWeightOut) {
            weightRatio = 2 * BONE;
        } else {
            weightRatio = tokenWeightIn.bdiv(tokenWeightOut);
        }
        uint256 adjustedIn = BONE.bsub(swapFee);
        adjustedIn = tokenAmountIn.bmul(adjustedIn);
        uint256 y = tokenBalanceIn.bdiv(tokenBalanceIn.badd(adjustedIn));
        uint256 foo;
        if (tokenWeightIn == tokenWeightOut) {
            foo = y;
        } else if (tokenWeightIn >> 1 == tokenWeightOut) {
            foo = y.bmul(y);
        } else {
            foo = y.bpow(weightRatio);
        }
        uint256 bar = BONE.bsub(foo);
        tokenAmountOut = tokenBalanceOut.bmul(bar);
        return tokenAmountOut;
    }

    /**********************************************************************************************
    // calcInGivenOut                                                                            //
    // aI = tokenAmountIn                                                                        //
    // bO = tokenBalanceOut               /  /     bO      \    (wO / wI)      \                 //
    // bI = tokenBalanceIn          bI * |  | ------------  | ^            - 1  |                //
    // aO = tokenAmountOut    aI =        \  \ ( bO - aO ) /                   /                 //
    // wI = tokenWeightIn           --------------------------------------------                 //
    // wO = tokenWeightOut                          ( 1 - sF )                                   //
    // sF = swapFee                                                                              //
    **********************************************************************************************/
    function calcInGivenOut(
        uint256 tokenBalanceIn,
        uint256 tokenWeightIn,
        uint256 tokenBalanceOut,
        uint256 tokenWeightOut,
        uint256 tokenAmountOut,
        uint256 swapFee
    ) public pure returns (uint256 tokenAmountIn) {
        uint256 weightRatio;
        if (tokenWeightOut == tokenWeightIn) {
            weightRatio = 1 * BONE;
        } else if (tokenWeightOut >> 1 == tokenWeightIn) {
            weightRatio = 2 * BONE;
        } else {
            weightRatio = tokenWeightOut.bdiv(tokenWeightIn);
        }
        uint256 diff = tokenBalanceOut.bsub(tokenAmountOut);
        uint256 y = tokenBalanceOut.bdiv(diff);
        uint256 foo;
        if (tokenWeightOut == tokenWeightIn) {
            foo = y;
        } else if (tokenWeightOut >> 1 == tokenWeightIn) {
            foo = y.bmul(y);
        } else {
            foo = y.bpow(weightRatio);
        }
        foo = foo.bsub(BONE);
        tokenAmountIn = BONE.bsub(swapFee);
        tokenAmountIn = tokenBalanceIn.bmul(foo).bdiv(tokenAmountIn);
        return tokenAmountIn;
    }

    /**********************************************************************************************
    // calcPoolOutGivenSingleIn                                                                  //
    // pAo = poolAmountOut         /                                              \              //
    // tAi = tokenAmountIn        ///      /     //    wI \      \\       \     wI \             //
    // wI = tokenWeightIn        //| tAi *| 1 - || 1 - --  | * sF || + tBi \    --  \            //
    // tW = totalWeight     pAo=||  \      \     \\    tW /      //         | ^ tW   | * pS - pS //
    // tBi = tokenBalanceIn      \\  ------------------------------------- /        /            //
    // pS = poolSupply            \\                    tBi               /        /             //
    // sF = swapFee                \                                              /              //
    **********************************************************************************************/
    function calcPoolOutGivenSingleIn(
        uint256 tokenBalanceIn,
        uint256 tokenWeightIn,
        uint256 poolSupply,
        uint256 totalWeight,
        uint256 tokenAmountIn,
        uint256 swapFee
    ) public pure returns (uint256 poolAmountOut) {
        // Charge the trading fee for the proportion of tokenAi
        ///  which is implicitly traded to the other pool tokens.
        // That proportion is (1- weightTokenIn)
        // tokenAiAfterFee = tAi * (1 - (1-weightTi) * poolFee);
        uint256 normalizedWeight = tokenWeightIn.bdiv(totalWeight);
        uint256 zaz = BONE.bsub(normalizedWeight).bmul(swapFee);
        uint256 tokenAmountInAfterFee = tokenAmountIn.bmul(BONE.bsub(zaz));

        uint256 newTokenBalanceIn = tokenBalanceIn.badd(tokenAmountInAfterFee);
        uint256 tokenInRatio = newTokenBalanceIn.bdiv(tokenBalanceIn);

        // uint newPoolSupply = (ratioTi ^ weightTi) * poolSupply;
        uint256 poolRatio = tokenInRatio.bpow(normalizedWeight);
        uint256 newPoolSupply = poolRatio.bmul(poolSupply);
        poolAmountOut = newPoolSupply.bsub(poolSupply);
        return poolAmountOut;
    }

    /**********************************************************************************************
    // calcSingleOutGivenPoolIn                                                                  //
    // tAo = tokenAmountOut            /      /                                             \\   //
    // bO = tokenBalanceOut           /      // pS - (pAi * (1 - eF)) \     /    1    \      \\  //
    // pAi = poolAmountIn            | bO - || ----------------------- | ^ | --------- | * b0 || //
    // ps = poolSupply                \      \\          pS           /     \(wO / tW)/      //  //
    // wI = tokenWeightIn      tAo =   \      \                                             //   //
    // tW = totalWeight                    /     /      wO \       \                             //
    // sF = swapFee                    *  | 1 - |  1 - ---- | * sF  |                            //
    // eF = exitFee                        \     \      tW /       /                             //
    **********************************************************************************************/
    function calcSingleOutGivenPoolIn(
        uint256 tokenBalanceOut,
        uint256 tokenWeightOut,
        uint256 poolSupply,
        uint256 totalWeight,
        uint256 poolAmountIn,
        uint256 swapFee
    ) public pure returns (uint256 tokenAmountOut) {
        uint256 normalizedWeight = tokenWeightOut.bdiv(totalWeight);
        // charge exit fee on the pool token side
        // pAiAfterExitFee = pAi*(1-exitFee)
        uint256 poolAmountInAfterExitFee =
            poolAmountIn.bmul(BONE.bsub(EXIT_ZERO_FEE));
        uint256 newPoolSupply = poolSupply.bsub(poolAmountInAfterExitFee);
        uint256 poolRatio = newPoolSupply.bdiv(poolSupply);

        // newBalTo = poolRatio^(1/weightTo) * balTo;
        uint256 tokenOutRatio = poolRatio.bpow(BONE.bdiv(normalizedWeight));
        uint256 newTokenBalanceOut = tokenOutRatio.bmul(tokenBalanceOut);

        uint256 tokenAmountOutBeforeSwapFee =
            tokenBalanceOut.bsub(newTokenBalanceOut);

        // charge swap fee on the output token side
        //uint tAo = tAoBeforeSwapFee * (1 - (1-weightTo) * swapFee)
        uint256 zaz = BONE.bsub(normalizedWeight).bmul(swapFee);
        tokenAmountOut = tokenAmountOutBeforeSwapFee.bmul(BONE.bsub(zaz));
        return tokenAmountOut;
    }
}

• No Contract Security Audit Submitted- Submit Audit Here

[{"constant":true,"inputs":[],"name":"BONE","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"payable":false,"stateMutability":"view","type":"function"},{"constant":true,"inputs":[],"name":"EXIT_ZERO_FEE","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"payable":false,"stateMutability":"view","type":"function"},{"constant":true,"inputs":[{"internalType":"uint256","name":"tokenBalanceIn","type":"uint256"},{"internalType":"uint256","name":"tokenWeightIn","type":"uint256"},{"internalType":"uint256","name":"tokenBalanceOut","type":"uint256"},{"internalType":"uint256","name":"tokenWeightOut","type":"uint256"},{"internalType":"uint256","name":"tokenAmountOut","type":"uint256"},{"internalType":"uint256","name":"swapFee","type":"uint256"}],"name":"calcInGivenOut","outputs":[{"internalType":"uint256","name":"tokenAmountIn","type":"uint256"}],"payable":false,"stateMutability":"pure","type":"function"},{"constant":true,"inputs":[{"internalType":"uint256","name":"tokenBalanceIn","type":"uint256"},{"internalType":"uint256","name":"tokenWeightIn","type":"uint256"},{"internalType":"uint256","name":"tokenBalanceOut","type":"uint256"},{"internalType":"uint256","name":"tokenWeightOut","type":"uint256"},{"internalType":"uint256","name":"tokenAmountIn","type":"uint256"},{"internalType":"uint256","name":"swapFee","type":"uint256"}],"name":"calcOutGivenIn","outputs":[{"internalType":"uint256","name":"tokenAmountOut","type":"uint256"}],"payable":false,"stateMutability":"pure","type":"function"},{"constant":true,"inputs":[{"internalType":"uint256","name":"tokenBalanceIn","type":"uint256"},{"internalType":"uint256","name":"tokenWeightIn","type":"uint256"},{"internalType":"uint256","name":"poolSupply","type":"uint256"},{"internalType":"uint256","name":"totalWeight","type":"uint256"},{"internalType":"uint256","name":"tokenAmountIn","type":"uint256"},{"internalType":"uint256","name":"swapFee","type":"uint256"}],"name":"calcPoolOutGivenSingleIn","outputs":[{"internalType":"uint256","name":"poolAmountOut","type":"uint256"}],"payable":false,"stateMutability":"pure","type":"function"},{"constant":true,"inputs":[{"internalType":"uint256","name":"tokenBalanceOut","type":"uint256"},{"internalType":"uint256","name":"tokenWeightOut","type":"uint256"},{"internalType":"uint256","name":"poolSupply","type":"uint256"},{"internalType":"uint256","name":"totalWeight","type":"uint256"},{"internalType":"uint256","name":"poolAmountIn","type":"uint256"},{"internalType":"uint256","name":"swapFee","type":"uint256"}],"name":"calcSingleOutGivenPoolIn","outputs":[{"internalType":"uint256","name":"tokenAmountOut","type":"uint256"}],"payable":false,"stateMutability":"pure","type":"function"},{"constant":true,"inputs":[{"internalType":"uint256","name":"tokenBalanceIn","type":"uint256"},{"internalType":"uint256","name":"tokenWeightIn","type":"uint256"},{"internalType":"uint256","name":"tokenBalanceOut","type":"uint256"},{"internalType":"uint256","name":"tokenWeightOut","type":"uint256"},{"internalType":"uint256","name":"swapFee","type":"uint256"}],"name":"calcSpotPrice","outputs":[{"internalType":"uint256","name":"spotPrice","type":"uint256"}],"payable":false,"stateMutability":"pure","type":"function"}]

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