bitwise multiplication to reduce gas cost

Question

This is the multiplication method from the SafeMath library.

/**
* @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;
}

Could this be done using the shift operators in Solidity to reduce the amount of gas consumed?

If yes, what would the necessary changes look like?