library SafeMath {
  /**
   * @dev Returns the addition of two unsigned integers, reverting on
   * overflow.
   *
   * Counterpart to Solidity's `+` operator.
   *
   * Requirements:
   *
   * - Addition cannot overflow.
   */
  function add(uint256 a, uint256 b) internal pure returns (uint256) {
    uint256 c = a + b;
    require(c >= a, "SafeMath: addition overflow");

    return c;
  }

  /**
   * @dev Returns the subtraction of two unsigned integers, reverting on
   * overflow (when the result is negative).
   *
   * Counterpart to Solidity's `-` operator.
   *
   * Requirements:
   *
   * - Subtraction cannot overflow.
   */
  function sub(uint256 a, uint256 b) internal pure returns (uint256) {
    return sub(a, b, "SafeMath: subtraction overflow");
  }

  /**
   * @dev Returns the subtraction of two unsigned integers, reverting with custom message on
   * overflow (when the result is negative).
   *
   * Counterpart to Solidity's `-` operator.
   *
   * Requirements:
   *
   * - Subtraction cannot overflow.
   */
  function sub(
    uint256 a,
    uint256 b,
    string memory errorMessage
  ) internal pure returns (uint256) {
    require(b <= a, errorMessage);
    uint256 c = a - b;

    return c;
  }

  /**
   * @dev Returns the multiplication of two unsigned integers, reverting on
   * overflow.
   *
   * Counterpart to Solidity's `*` operator.
   *
   * Requirements:
   *
   * - Multiplication cannot overflow.
   */
  function mul(uint256 a, uint256 b) internal pure returns (uint256) {
    // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
    // benefit is lost if 'b' is also tested.
    // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
    if (a == 0) {
      return 0;
    }

    uint256 c = a * b;
    require(c / a == b, "SafeMath: multiplication overflow");

    return c;
  }

  /**
   * @dev Returns the integer division of two unsigned integers. Reverts on
   * division by zero. The result is rounded towards zero.
   *
   * Counterpart to Solidity's `/` operator. Note: this function uses a
   * `revert` opcode (which leaves remaining gas untouched) while Solidity
   * uses an invalid opcode to revert (consuming all remaining gas).
   *
   * Requirements:
   *
   * - The divisor cannot be zero.
   */
  function div(uint256 a, uint256 b) internal pure returns (uint256) {
    return div(a, b, "SafeMath: division by zero");
  }

  /**
   * @dev Returns the integer division of two unsigned integers. Reverts with custom message on
   * division by zero. The result is rounded towards zero.
   *
   * Counterpart to Solidity's `/` operator. Note: this function uses a
   * `revert` opcode (which leaves remaining gas untouched) while Solidity
   * uses an invalid opcode to revert (consuming all remaining gas).
   *
   * Requirements:
   *
   * - The divisor cannot be zero.
   */
  function div(
    uint256 a,
    uint256 b,
    string memory errorMessage
  ) internal pure returns (uint256) {
    require(b > 0, errorMessage);
    uint256 c = a / b;
    // assert(a == b * c + a % b); // There is no case in which this doesn't hold

    return c;
  }

  /**
   * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
   * Reverts when dividing by zero.
   *
   * Counterpart to Solidity's `%` operator. This function uses a `revert`
   * opcode (which leaves remaining gas untouched) while Solidity uses an
   * invalid opcode to revert (consuming all remaining gas).
   *
   * Requirements:
   *
   * - The divisor cannot be zero.
   */
  function mod(uint256 a, uint256 b) internal pure returns (uint256) {
    return mod(a, b, "SafeMath: modulo by zero");
  }

  /**
   * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
   * Reverts with custom message when dividing by zero.
   *
   * Counterpart to Solidity's `%` operator. This function uses a `revert`
   * opcode (which leaves remaining gas untouched) while Solidity uses an
   * invalid opcode to revert (consuming all remaining gas).
   *
   * Requirements:
   *
   * - The divisor cannot be zero.
   */
  function mod(
    uint256 a,
    uint256 b,
    string memory errorMessage
  ) internal pure returns (uint256) {
    require(b != 0, errorMessage);
    return a % b;
  }

  // babylonian method (https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method)
  function sqrrt(uint256 a) internal pure returns (uint256 c) {
    if (a > 3) {
      c = a;
      uint256 b = add(div(a, 2), 1);
      while (b < c) {
        c = b;
        b = div(add(div(a, b), b), 2);
      }
    } else if (a != 0) {
      c = 1;
    }
  }

  /*
   * Expects percentage to be trailed by 00,
   */
  function percentageAmount(uint256 total_, uint8 percentage_)
    internal
    pure
    returns (uint256 percentAmount_)
  {
    return div(mul(total_, percentage_), 1000);
  }

  /*
   * Expects percentage to be trailed by 00,
   */
  function substractPercentage(uint256 total_, uint8 percentageToSub_)
    internal
    pure
    returns (uint256 result_)
  {
    return sub(total_, div(mul(total_, percentageToSub_), 1000));
  }

  function percentageOfTotal(uint256 part_, uint256 total_)
    internal
    pure
    returns (uint256 percent_)
  {
    return div(mul(part_, 100), total_);
  }

  /**
   * Taken from Hypersonic https://github.com/M2629/HyperSonic/blob/main/Math.sol
   * @dev Returns the average of two numbers. The result is rounded towards
   * zero.
   */
  function average(uint256 a, uint256 b) internal pure returns (uint256) {
    // (a + b) / 2 can overflow, so we distribute
    return (a / 2) + (b / 2) + (((a % 2) + (b % 2)) / 2);
  }

  function quadraticPricing(uint256 payment_, uint256 multiplier_)
    internal
    pure
    returns (uint256)
  {
    return sqrrt(mul(multiplier_, payment_));
  }

  function bondingCurve(uint256 supply_, uint256 multiplier_)
    internal
    pure
    returns (uint256)
  {
    return mul(multiplier_, supply_);
  }
}
/**
 * @dev Wrappers over Solidity's arithmetic operations with added overflow
 * checks.
 *
 * Arithmetic operations in Solidity wrap on overflow. This can easily result
 * in bugs, because programmers usually assume that an overflow raises an
 * error, which is the standard behavior in high level programming languages.
 * `SafeMath` restores this intuition by reverting the transaction when an
 * operation overflows.
 *
 * Using this library instead of the unchecked operations eliminates an entire
 * class of bugs, so it's recommended to use it always.
 */
function average(uint256 a, uint256 b) internal pure returns (uint256) {
  // (a + b) / 2 can overflow, so we distribute
  return (a / 2) + (b / 2) + (((a % 2) + (b % 2)) / 2);
}

/**
 * Taken from Hypersonic https://github.com/M2629/HyperSonic/blob/main/Math.sol
 * @dev Returns the average of two numbers. The result is rounded towards
 * zero.
 */