If you need to know
exactly which operations are performed when the modulus operator is used
then I would suggest you are "doing it wrong".
Modulus may be different depending on OS and underlying architecture. It may vary or it may not, but if you need to rely on the implementation, it is likely that your time could best be spent elsewhere. The implementation is not guaranteed to stay the same, or to be consistent across different machines.
Why do you believe modulus to be a major source of computation? Regardless of its implementation, the operation is very likely to be a constant - i.e, if it is operating within an algorithm which has big-O greater than constant time, optimize the algorithm first.
Ask yourself why you need to optimize. Is the computation taking (significantly) longer than expected?
Then ask yourself where 90 - 99% of the computation is being spent. Try using a profiler to get numbers, even if you think you know where time is being spent. It may give you a clue or shed light on a bug.
与恶龙缠斗过久,自身亦成为恶龙;凝视深渊过久,深渊将回以凝视…