What is the difference between instruction pipelining and arithmetic pipelining?

Arithmetic pipelines differ from instruction pipelines in some important ways. They are generally synchronous. This means that each stage executes in a fixed number of clock cycles. In a synchronous pipeline, moreover, no buffering between stages is provided. Each stage must be ready to accept the data passed from a previous stage when that data is produced.

Another important difference is that an arithmetic pipeline may be nonlinear. The "stages" in this type of pipeline are associated with key processing components such as adders, shifters, etc. Instead of a steady progression through a fixed sequence of stages, a task in a nonlinear pipeline may use more than one stage at a time, or may return to the same stage at several points in processing.