Q: I've been replacing multiplications and divisions with shift operators, because shifting is more efficient.
A: This is an excellent example of a potentially risky and usually unnecessary optimization. Any compiler worthy of the name can replace a constant, power-of-two multiplication with a left shift, or a similar division of an unsigned quantity with a right shift. (Ritchie's original PDP-11 compiler, though it ran in less than 64K of memory and omitted several features now considered mandatory, performed both of these optimizations, without even turning on its optional optimization pass.) Furthermore, a compiler will make these optimizations only when they're correct; many programmers overlook the fact that shifting a negative value to the right is not equivalent to division. (Therefore, when you need to make sure that these optimizations are performed, you may have to declare relevant variables as unsigned.)