Is the floating point unit a regular pipeline

The floating point units are not pipelines in and of themselves, but are rather one of the several execution units in the pipeline.

Here's a diagram from Wikipedia of the Nehalem microarchitecture:

The pipeline is essentially all of the boxes except for the four on the right side. Instructions travel down through the pipeline from top to bottom. The floating-point units are the orange boxes labelled SSE, FP, ADD, MUL, etc.

Similar threads