Abstract
It is universally known that caching is critical to attain high-performance implementations: In many situations, data locality (in space and time) plays a bigger role than optimizing the (number of) arithmetic floating point operations. In this paper, we show evidence that at least for linear algebra algorithms, caching is also a crucial factor for accurate performance modeling and performance prediction.
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Notes
- 1.
With \(n = 1{,}568 = 2^5 \cdot 7^2\), we choose a matrix size that is not a power of \(2\) to avoid performance artifacts due to the specific problem size.
- 2.
The subscripts R through U are the values of the flag arguments side, uplo, trans, and diag; they distinguish the form of the operation performed by the kernel.
- 3.
Read from the CPU’s time stamp counter through the assembly instruction rdtsc.
- 4.
The system fluctuations cause variations of the dgeqrf timings of 0.057 % on average. With the exception of the tiny dcopy s, these fluctuations are not significant.
- 5.
By “touching”, we mean a simple read+write access to the data, e.g.
. - 6.
The length of the list can be safely restricted to the number of kernel calls per iteration of the blocked algorithm.
- 7.
For \(n = 2400\), the upper triangular portion of the matrix is about twice as large as the cache size.
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Acknowledgments
Financial support from the Deutsche Forschungsgemeinschaft (DFG) through grant GSC 111 and the Deutsche Telekom Stiftung is gratefully acknowledged.
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Peise, E., Bientinesi, P. (2015). A Study on the Influence of Caching: Sequences of Dense Linear Algebra Kernels. In: Daydé, M., Marques, O., Nakajima, K. (eds) High Performance Computing for Computational Science -- VECPAR 2014. VECPAR 2014. Lecture Notes in Computer Science(), vol 8969. Springer, Cham. https://doi.org/10.1007/978-3-319-17353-5_21
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DOI: https://doi.org/10.1007/978-3-319-17353-5_21
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