Why is BLAS so much faster than custom matrix multiplication implementations?

How BLAS Achieves Exceptional Performance

Impressive Speed Discrepancy

A comparison between a custom matrix multiplication implementation and BLAS reveals a remarkable performance disparity. BLAS leverages highly optimized techniques to outpace custom implementations significantly.

Levels of BLAS Optimization

BLAS is structured into three levels based on the scope of operations:

Level 1: Vector operations that benefit from vectorization and SIMD capabilities.

Level 2: Matrix-vector operations that can leverage multiprocessor architectures and shared memory.

Level 3: Matrix-matrix operations that perform a high number of operations on a comparatively small amount of data. This level employs cache optimization, significantly enhancing performance.

Implementation and Compiler Impact

Contrary to popular belief, most high-performance BLAS implementations are not written in Fortran. Libraries like ATLAS and OpenBLAS utilize C or even assembler for performance-critical components. Fortran is used primarily for the reference implementation and interfacing with LAPACK.

Why Custom Implementations Fall Short

Custom implementations typically lack the sophisticated optimization techniques employed by BLAS. Specifically, they often fail to leverage cache optimization, which contributes significantly to BLAS's exceptional performance.

Innovative BLIS Papers

Recent advancements in this field are highlighted in the groundbreaking BLIS papers. These papers provide insights into the intricacies of BLAS optimization and present a concise implementation of a matrix-matrix product. Variants utilizing intrinsics and assembler code further enhance performance.

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