Adaptive Precision Sparse Matrix–Vector Product and Its Application to Krylov Solvers

Graillat, Stef; Jézéquel, Fabienne; Mary, Theo; Molina, Roméo

doi:10.1137/22m1522619

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2024

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Cited by 2 publications

References 26 publications

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Reduced-Precision and Reduced-Exponent Formats for Accelerating Adaptive Precision Sparse Matrix–Vector Product

Graillat,

Jézéquel,

Mary

et al. 2024

Lecture Notes in Computer Science

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Reduced-Precision and Reduced-Exponent Formats for Accelerating Adaptive Precision Sparse Matrix–Vector Product

Graillat,

Jézéquel,

Mary

et al. 2024

Lecture Notes in Computer Science

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pSpMv: precision-based sparse matrix partition and SpMV optimization

Liu,

Wang,

Gao

et al. 2024

CCF Trans. HPC

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The new generation of computing devices tends to support multiple floating-point formats and different computing precision. Besides single and double precision, half precision is embraced and widely supported by new computing devices. Low-precision representations have compact memory size and lightweight computing strength, and they also bring opportunities to the optimization of BLAS routines. This paper proposes a new sparse matrix partition approach based on IEEE 754 standard floating-point format. An input sparse matrix in double precision is partitioned and transformed into several sub-matrices in different precision without loss of accuracy. Most non-zero elements can be stored in half or single precision, if the most significant bits of exponent and the least significant bits of mantissa are zeros in double-precision representation. Based on this mixed-precision representation of sparse matrix, we also present a new SpMV algorithm pSpMV for GPU devices. pSpMV not only reduces the memory access overhead, but also reduces the computing strength of floating-point numbers. Experimental results on two GPU devices show that pSpMV achieves a geometric mean speedup of 1.39x on Tesla V100 and 1.45x on Tesla P100 over double-precision SpMV for 2,554 sparse matrices.

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Adaptive Precision Sparse Matrix–Vector Product and Its Application to Krylov Solvers

Cited by 2 publications

References 26 publications

Reduced-Precision and Reduced-Exponent Formats for Accelerating Adaptive Precision Sparse Matrix–Vector Product

Reduced-Precision and Reduced-Exponent Formats for Accelerating Adaptive Precision Sparse Matrix–Vector Product

pSpMv: precision-based sparse matrix partition and SpMV optimization

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