library Utils {

    /* @notice      Convert the bytes array to bytes32 type, the bytes array length must be 32
    *  @param _bs   Source bytes array
    *  @return      bytes32
    */
    function bytesToBytes32(bytes memory _bs) internal pure returns (bytes32 value) {
        require(_bs.length == 32, "bytes length is not 32.");
        assembly {
            // load 32 bytes from memory starting from position _bs + 0x20 since the first 0x20 bytes stores _bs length
            value := mload(add(_bs, 0x20))
        }
    }

    /* @notice      Convert bytes to uint256
    *  @param _b    Source bytes should have length of 32
    *  @return      uint256
    */
    function bytesToUint256(bytes memory _bs) internal pure returns (uint256 value) {
        require(_bs.length == 32, "bytes length is not 32.");
        assembly {
            // load 32 bytes from memory starting from position _bs + 32
            value := mload(add(_bs, 0x20))
        }
        require(value <= 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff, "Value exceeds the range");
    }

    /* @notice      Convert uint256 to bytes
    *  @param _b    uint256 that needs to be converted
    *  @return      bytes
    */
    function uint256ToBytes(uint256 _value) internal pure returns (bytes memory bs) {
        require(_value <= 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff, "Value exceeds the range");
        assembly {
            // Get a location of some free memory and store it in result as
            // Solidity does for memory variables.
            bs := mload(0x40)
            // Put 0x20 at the first word, the length of bytes for uint256 value
            mstore(bs, 0x20)
            //In the next word, put value in bytes format to the next 32 bytes
            mstore(add(bs, 0x20), _value)
            // Update the free-memory pointer by padding our last write location to 32 bytes
            mstore(0x40, add(bs, 0x40))
        }
    }

    /* @notice      Convert bytes to address
    *  @param _bs   Source bytes: bytes length must be 20
    *  @return      Converted address from source bytes
    */
    function bytesToAddress(bytes memory _bs) internal pure returns (address addr)
    {
        require(_bs.length == 20, "bytes length does not match address");
        assembly {
            // for _bs, first word store _bs.length, second word store _bs.value
            // load 32 bytes from mem[_bs+20], convert it into Uint160, meaning we take last 20 bytes as addr (address).
            addr := mload(add(_bs, 0x14))
        }

    }

    /* @notice      Convert address to bytes
    *  @param _addr Address need to be converted
    *  @return      Converted bytes from address
    */
    function addressToBytes(address _addr) internal pure returns (bytes memory bs){
        assembly {
            // Get a location of some free memory and store it in result as
            // Solidity does for memory variables.
            bs := mload(0x40)
            // Put 20 (address byte length) at the first word, the length of bytes for uint256 value
            mstore(bs, 0x14)
            // logical shift left _a by 12 bytes, change _a from right-aligned to left-aligned
            mstore(add(bs, 0x20), shl(96, _addr))
            // Update the free-memory pointer by padding our last write location to 32 bytes
            mstore(0x40, add(bs, 0x40))
       }
    }

    /* @notice          Do hash leaf as the multi-chain does
    *  @param _data     Data in bytes format
    *  @return          Hashed value in bytes32 format
    */
    function hashLeaf(bytes memory _data) internal pure returns (bytes32 result)  {
        result = sha256(abi.encodePacked(byte(0x0), _data));
    }

    /* @notice          Do hash children as the multi-chain does
    *  @param _l        Left node
    *  @param _r        Right node
    *  @return          Hashed value in bytes32 format
    */
    function hashChildren(bytes32 _l, bytes32  _r) internal pure returns (bytes32 result)  {
        result = sha256(abi.encodePacked(bytes1(0x01), _l, _r));
    }

    /* @notice              Compare if two bytes are equal, which are in storage and memory, seperately
                            Refer from https://github.com/summa-tx/bitcoin-spv/blob/master/solidity/contracts/BytesLib.sol#L368
    *  @param _preBytes     The bytes stored in storage
    *  @param _postBytes    The bytes stored in memory
    *  @return              Bool type indicating if they are equal
    */
    function equalStorage(bytes storage _preBytes, bytes memory _postBytes) internal view returns (bool) {
        bool success = true;

        assembly {
            // we know _preBytes_offset is 0
            let fslot := sload(_preBytes_slot)
            // Arrays of 31 bytes or less have an even value in their slot,
            // while longer arrays have an odd value. The actual length is
            // the slot divided by two for odd values, and the lowest order
            // byte divided by two for even values.
            // If the slot is even, bitwise and the slot with 255 and divide by
            // two to get the length. If the slot is odd, bitwise and the slot
            // with -1 and divide by two.
            let slength := div(and(fslot, sub(mul(0x100, iszero(and(fslot, 1))), 1)), 2)
            let mlength := mload(_postBytes)

            // if lengths don't match the arrays are not equal
            switch eq(slength, mlength)
            case 1 {
                // fslot can contain both the length and contents of the array
                // if slength < 32 bytes so let's prepare for that
                // v. http://solidity.readthedocs.io/en/latest/miscellaneous.html#layout-of-state-variables-in-storage
                // slength != 0
                if iszero(iszero(slength)) {
                    switch lt(slength, 32)
                    case 1 {
                        // blank the last byte which is the length
                        fslot := mul(div(fslot, 0x100), 0x100)

                        if iszero(eq(fslot, mload(add(_postBytes, 0x20)))) {
                            // unsuccess:
                            success := 0
                        }
                    }
                    default {
                        // cb is a circuit breaker in the for loop since there's
                        //  no said feature for inline assembly loops
                        // cb = 1 - don't breaker
                        // cb = 0 - break
                        let cb := 1

                        // get the keccak hash to get the contents of the array
                        mstore(0x0, _preBytes_slot)
                        let sc := keccak256(0x0, 0x20)

                        let mc := add(_postBytes, 0x20)
                        let end := add(mc, mlength)

                        // the next line is the loop condition:
                        // while(uint(mc < end) + cb == 2)
                        for {} eq(add(lt(mc, end), cb), 2) {
                            sc := add(sc, 1)
                            mc := add(mc, 0x20)
                        } {
                            if iszero(eq(sload(sc), mload(mc))) {
                                // unsuccess:
                                success := 0
                                cb := 0
                            }
                        }
                    }
                }
            }
            default {
                // unsuccess:
                success := 0
            }
        }

        return success;
    }

    /* @notice              Slice the _bytes from _start index till the result has length of _length
                            Refer from https://github.com/summa-tx/bitcoin-spv/blob/master/solidity/contracts/BytesLib.sol#L246
    *  @param _bytes        The original bytes needs to be sliced
    *  @param _start        The index of _bytes for the start of sliced bytes
    *  @param _length       The index of _bytes for the end of sliced bytes
    *  @return              The sliced bytes
    */
    function slice(
        bytes memory _bytes,
        uint _start,
        uint _length
    )
        internal
        pure
        returns (bytes memory)
    {
        require(_bytes.length >= (_start + _length));

        bytes memory tempBytes;

        assembly {
            switch iszero(_length)
            case 0 {
                // Get a location of some free memory and store it in tempBytes as
                // Solidity does for memory variables.
                tempBytes := mload(0x40)

                // The first word of the slice result is potentially a partial
                // word read from the original array. To read it, we calculate
                // the length of that partial word and start copying that many
                // bytes into the array. The first word we copy will start with
                // data we don't care about, but the last `lengthmod` bytes will
                // land at the beginning of the contents of the new array. When
                // we're done copying, we overwrite the full first word with
                // the actual length of the slice.
                // lengthmod <= _length % 32
                let lengthmod := and(_length, 31)

                // The multiplication in the next line is necessary
                // because when slicing multiples of 32 bytes (lengthmod == 0)
                // the following copy loop was copying the origin's length
                // and then ending prematurely not copying everything it should.
                let mc := add(add(tempBytes, lengthmod), mul(0x20, iszero(lengthmod)))
                let end := add(mc, _length)

                for {
                    // The multiplication in the next line has the same exact purpose
                    // as the one above.
                    let cc := add(add(add(_bytes, lengthmod), mul(0x20, iszero(lengthmod))), _start)
                } lt(mc, end) {
                    mc := add(mc, 0x20)
                    cc := add(cc, 0x20)
                } {
                    mstore(mc, mload(cc))
                }

                mstore(tempBytes, _length)

                //update free-memory pointer
                //allocating the array padded to 32 bytes like the compiler does now
                mstore(0x40, and(add(mc, 31), not(31)))
            }
            //if we want a zero-length slice let's just return a zero-length array
            default {
                tempBytes := mload(0x40)

                mstore(0x40, add(tempBytes, 0x20))
            }
        }

        return tempBytes;
    }
    /* @notice              Check if the elements number of _signers within _keepers array is no less than _m
    *  @param _keepers      The array consists of serveral address
    *  @param _signers      Some specific addresses to be looked into
    *  @param _m            The number requirement paramter
    *  @return              True means containment, false meansdo do not contain.
    */
    function containMAddresses(address[] memory _keepers, address[] memory _signers, uint _m) internal pure returns (bool){
        uint m = 0;
        for(uint i = 0; i < _signers.length; i++){
            for (uint j = 0; j < _keepers.length; j++) {
                if (_signers[i] == _keepers[j]) {
                    m++;
                    delete _keepers[j];
                }
            }
        }
        return m >= _m;
    }

    /* @notice              TODO
    *  @param key
    *  @return
    */
    function compressMCPubKey(bytes memory key) internal pure returns (bytes memory newkey) {
         require(key.length >= 67, "key lenggh is too short");
         newkey = slice(key, 0, 35);
         if (uint8(key[66]) % 2 == 0){
             newkey[2] = byte(0x02);
         } else {
             newkey[2] = byte(0x03);
         }
         return newkey;
    }

    /**
     * @dev Returns true if `account` is a contract.
     *      Refer from https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/utils/Address.sol#L18
     *
     * This test is non-exhaustive, and there may be false-negatives: during the
     * execution of a contract's constructor, its address will be reported as
     * not containing a contract.
     *
     * IMPORTANT: It is unsafe to assume that an address for which this
     * function returns false is an externally-owned account (EOA) and not a
     * contract.
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies in extcodesize, which returns 0 for contracts in
        // construction, since the code is only stored at the end of the
        // constructor execution.

        // According to EIP-1052, 0x0 is the value returned for not-yet created accounts
        // and 0xc5d2460186f7233c927e7db2dcc703c0e500b653ca82273b7bfad8045d85a470 is returned
        // for accounts without code, i.e. `keccak256('')`
        bytes32 codehash;
        bytes32 accountHash = 0xc5d2460186f7233c927e7db2dcc703c0e500b653ca82273b7bfad8045d85a470;
        // solhint-disable-next-line no-inline-assembly
        assembly { codehash := extcodehash(account) }
        return (codehash != 0x0 && codehash != accountHash);
    }
}
function addressToBytes(address _addr) internal pure returns (bytes memory bs){
        assembly {
            // Get a location of some free memory and store it in result as
            // Solidity does for memory variables.
            bs := mload(0x40)
            // Put 20 (address byte length) at the first word, the length of bytes for uint256 value
            mstore(bs, 0x14)
            // logical shift left _a by 12 bytes, change _a from right-aligned to left-aligned
            mstore(add(bs, 0x20), shl(96, _addr))
            // Update the free-memory pointer by padding our last write location to 32 bytes
            mstore(0x40, add(bs, 0x40))
       }
    }
/* @notice      Convert address to bytes
 *  @param _addr Address need to be converted
 *  @return      Converted bytes from address
 */