library Pairing {
    struct G1Point {
        uint256 X;
        uint256 Y;
    }
    // Encoding of field elements is: X[0] * z + X[1]
    struct G2Point {
        uint256[2] X;
        uint256[2] Y;
    }

    /// @return the generator of G1
    function P1() internal pure returns (G1Point memory) {
        return G1Point(1, 2);
    }

    /// @return the generator of G2
    function P2() internal pure returns (G2Point memory) {
        // Original code point
        return
            G2Point(
                [
                    11559732032986387107991004021392285783925812861821192530917403151452391805634,
                    10857046999023057135944570762232829481370756359578518086990519993285655852781
                ],
                [
                    4082367875863433681332203403145435568316851327593401208105741076214120093531,
                    8495653923123431417604973247489272438418190587263600148770280649306958101930
                ]
            );

        /*
        // Changed by Jordi point
        return G2Point(
            [10857046999023057135944570762232829481370756359578518086990519993285655852781,
             11559732032986387107991004021392285783925812861821192530917403151452391805634],
            [8495653923123431417604973247489272438418190587263600148770280649306958101930,
             4082367875863433681332203403145435568316851327593401208105741076214120093531]
        );
*/
    }

    /// @return r the negation of p, i.e. p.addition(p.negate()) should be zero.
    function negate(G1Point memory p) internal pure returns (G1Point memory r) {
        // The prime q in the base field F_q for G1
        uint256 q = 21888242871839275222246405745257275088696311157297823662689037894645226208583;
        if (p.X == 0 && p.Y == 0) return G1Point(0, 0);
        return G1Point(p.X, q - (p.Y % q));
    }

    /// @return r the sum of two points of G1
    function addition(G1Point memory p1, G1Point memory p2)
        internal
        view
        returns (G1Point memory r)
    {
        uint256[4] memory input;
        input[0] = p1.X;
        input[1] = p1.Y;
        input[2] = p2.X;
        input[3] = p2.Y;
        bool success;
        // solium-disable-next-line security/no-inline-assembly
        assembly {
            success := staticcall(sub(gas(), 2000), 6, input, 0xc0, r, 0x60)
            // Use "invalid" to make gas estimation work
            switch success
            case 0 {
                invalid()
            }
        }
        require(success, "pairing-add-failed");
    }

    /// @return r the product of a point on G1 and a scalar, i.e.
    /// p == p.scalar_mul(1) and p.addition(p) == p.scalar_mul(2) for all points p.
    function scalar_mul(G1Point memory p, uint256 s)
        internal
        view
        returns (G1Point memory r)
    {
        uint256[3] memory input;
        input[0] = p.X;
        input[1] = p.Y;
        input[2] = s;
        bool success;
        // solium-disable-next-line security/no-inline-assembly
        assembly {
            success := staticcall(sub(gas(), 2000), 7, input, 0x80, r, 0x60)
            // Use "invalid" to make gas estimation work
            switch success
            case 0 {
                invalid()
            }
        }
        require(success, "pairing-mul-failed");
    }

    /// @return the result of computing the pairing check
    /// e(p1[0], p2[0]) *  .... * e(p1[n], p2[n]) == 1
    /// For example pairing([P1(), P1().negate()], [P2(), P2()]) should
    /// return true.
    function pairing(G1Point[] memory p1, G2Point[] memory p2)
        internal
        view
        returns (bool)
    {
        require(p1.length == p2.length, "pairing-lengths-failed");
        uint256 elements = p1.length;
        uint256 inputSize = elements * 6;
        uint256[] memory input = new uint256[](inputSize);
        for (uint256 i = 0; i < elements; i++) {
            input[i * 6 + 0] = p1[i].X;
            input[i * 6 + 1] = p1[i].Y;
            input[i * 6 + 2] = p2[i].X[0];
            input[i * 6 + 3] = p2[i].X[1];
            input[i * 6 + 4] = p2[i].Y[0];
            input[i * 6 + 5] = p2[i].Y[1];
        }
        uint256[1] memory out;
        bool success;
        // solium-disable-next-line security/no-inline-assembly
        assembly {
            success := staticcall(
                sub(gas(), 2000),
                8,
                add(input, 0x20),
                mul(inputSize, 0x20),
                out,
                0x20
            )
            // Use "invalid" to make gas estimation work
            switch success
            case 0 {
                invalid()
            }
        }
        require(success, "pairing-opcode-failed");
        return out[0] != 0;
    }

    /// Convenience method for a pairing check for two pairs.
    function pairingProd2(
        G1Point memory a1,
        G2Point memory a2,
        G1Point memory b1,
        G2Point memory b2
    ) internal view returns (bool) {
        G1Point[] memory p1 = new G1Point[](2);
        G2Point[] memory p2 = new G2Point[](2);
        p1[0] = a1;
        p1[1] = b1;
        p2[0] = a2;
        p2[1] = b2;
        return pairing(p1, p2);
    }

    /// Convenience method for a pairing check for three pairs.
    function pairingProd3(
        G1Point memory a1,
        G2Point memory a2,
        G1Point memory b1,
        G2Point memory b2,
        G1Point memory c1,
        G2Point memory c2
    ) internal view returns (bool) {
        G1Point[] memory p1 = new G1Point[](3);
        G2Point[] memory p2 = new G2Point[](3);
        p1[0] = a1;
        p1[1] = b1;
        p1[2] = c1;
        p2[0] = a2;
        p2[1] = b2;
        p2[2] = c2;
        return pairing(p1, p2);
    }

    /// Convenience method for a pairing check for four pairs.
    function pairingProd4(
        G1Point memory a1,
        G2Point memory a2,
        G1Point memory b1,
        G2Point memory b2,
        G1Point memory c1,
        G2Point memory c2,
        G1Point memory d1,
        G2Point memory d2
    ) internal view returns (bool) {
        G1Point[] memory p1 = new G1Point[](4);
        G2Point[] memory p2 = new G2Point[](4);
        p1[0] = a1;
        p1[1] = b1;
        p1[2] = c1;
        p1[3] = d1;
        p2[0] = a2;
        p2[1] = b2;
        p2[2] = c2;
        p2[3] = d2;
        return pairing(p1, p2);
    }
}
function pairing(G1Point[] memory p1, G2Point[] memory p2)
    internal
    view
    returns (bool)
{
    require(p1.length == p2.length, "pairing-lengths-failed");
    uint256 elements = p1.length;
    uint256 inputSize = elements * 6;
    uint256[] memory input = new uint256[](inputSize);
    for (uint256 i = 0; i < elements; i++) {
        input[i * 6 + 0] = p1[i].X;
        input[i * 6 + 1] = p1[i].Y;
        input[i * 6 + 2] = p2[i].X[0];
        input[i * 6 + 3] = p2[i].X[1];
        input[i * 6 + 4] = p2[i].Y[0];
        input[i * 6 + 5] = p2[i].Y[1];
    }
    uint256[1] memory out;
    bool success;
    // solium-disable-next-line security/no-inline-assembly
    assembly {
        success := staticcall(
            sub(gas(), 2000),
            8,
            add(input, 0x20),
            mul(inputSize, 0x20),
            out,
            0x20
        )
        // Use "invalid" to make gas estimation work
        switch success
        case 0 {
            invalid()
        }
    }
    require(success, "pairing-opcode-failed");
    return out[0] != 0;
}

/// @return the result of computing the pairing check
/// e(p1[0], p2[0]) *  .... * e(p1[n], p2[n]) == 1
/// For example pairing([P1(), P1().negate()], [P2(), P2()]) should
/// return true.