Optimizing matrix multiply using PHiPAC: a portable, high-performance, ANSI C coding methodology

PHiPAC was an early attempt to improve software performance by searching in a large design space of possible implementations to find the best one. At the time, in the early 1990s, the most efficient numerical linear algebra libraries were carefully hand tuned for specific microarchitectures and compilers, and were often written in assembly language. This allowed very precise tuning of an algorithm to the specifics of a current platform, and provided great opportunity for high efficiency. The prevailing thought at the time was that such an approach was necessary to produce near-peak performance. On the other hand, this approach was brittle, and required great human effort to try each code variant, and so only a tiny subset of the possible code design points could be explored. Worse, given the combined complexities of the compiler and microarchitecture, it was difficult to predict which code variants would be worth the implementation effort. PHiPAC circumvented this effort by using code generators that could easily generate a vast assortment of very different points within a design space, and even across very different design spaces altogether. By following a set of carefully crafted coding guidelines, the generated code was reasonably efficient for any point in the design space. To search the design space, PHiPAC took a rather naive but effective approach. Due to the human-designed and deterministic nature of computing systems, one might reasonably think that smart modeling of the microprocessor and compiler would be sufficient to predict, without performing any timing, the optimal point for a given algorithm. But the combination of an optimizing compiler and a dynamically scheduled mi-