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Is there actually a BLAS implementation that uses strassen? I don’t think it’s accurate that only trivial implementations use the direct o(n^3) algorithm. AFAI

• chessgecko 2y ago
  I remember reading that it’s too hard to get good memory bandwidth/l2 utilization in the fancy algorithms, you need to read contiguous blocks and be able to use them repeatedly. But I also haven’t looked at the gpu blas implementations directly.
• jcranmer 2y ago
  AIUI, Strassen gets used moderately commonly with non-floating-point datatypes, where numerical stability is less of a concern and multiplications are more useful to minimize than memory traffic. But from what I can tell, every floating-point BLAS library eschews Strassen, despite a steady trickle of papers saying "hey, there might be some small wins if we go to Strassen!"
  • chillee 2y ago
    The big issue with Strassen isn't performance - it's numerical stability.
• leecarraher 2y ago
  BLAS is just the library definition and not the implementation, so BLAS implementations could implement GEMM anyway they want. But in practice the triple loop method (n^3) is the most common, despite Strassen's and the more numerically stable, Winograd methods being well known and available for decades. But with most things involving real computing hardware, memory access patterns and locality tend to be more important for performance than operation counts