Efficient 4×4 matrix vector multiplication with SSE: horizontal add and dot product – what’s the point?

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Horizontal add and dot product instructions are complex: they are decomposed into multiple simpler microoperations which are executed by processor just like simple instructions. The exact decomposition of horizontal add and dot product instructions into microoperations is processor-specific, but for recent Intel processors horizontal add is decomposed into 2 SHUFFLE + 1 ADD microoperations, and dot product is decomposed into 1 MUL + 1 SHUFFLE + 2 ADD microoperations. Besides a larger number of microoperations, this instructions also stress the instruction decoder in the processor pipeline: Intel processors can decode only one such complex instruction per cycle (compared to 4 simple instructions). On AMD Bulldozer the relative cost of these complex instructions is even higher.

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