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About this paper
Faizan A Khattak, Mantas Mikaitis, Carlo J. Graziani
A systematic characterization of AMD CDNA 1, CDNA 2, and CDNA 3 matrix cores reveals architecture- and format-specific accumulation, rounding, subnormal, and exceptional-value behavior that is not captured by generic IEEE-style models. The resulting MATLAB/Octave models matched GPU outputs across randomized tests with up to 20 million cases per format and were used to examine numerical effects in high-precision matrix multiplication and signal-processing workloads.
Key insights
- AMD CDNA generations differ substantially: CDNA 1 retains full-precision products in several paths, CDNA 2 often converts products to FP32 and flushes subnormals, while CDNA 3 introduces denormalized accumulation and multiple alignment and rounding stages.
- The effective multi-product accumulation size depends on both architecture and input format, ranging from sequential FMA behavior to groups of 2, 4, 8, or 16 products.
- Final output rounding alone does not describe matrix-core arithmetic; intermediate truncation, normalization, overflow, and the timing of the addend can affect results and reproducibility.
Summary by alphaXiv.
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