Multi-Stage Memory Efficient Strassen's Matrix Multiplication on GPU

Prior implementations of Strassen's matrix multiplication algorithm on GPUs traded additional workspace in the form of global memory or registers for time. Although Strassen's algorithm offers a reduction in computational complexity as compared to the classical algorithm, the memory overhe...

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Vydáno v:Proceedings - International Conference on High Performance Computing s. 212 - 221
Hlavní autoři: Krishnan, Arjun Gopala, Goswami, Dhrubajyoti
Médium: Konferenční příspěvek
Jazyk:angličtina
Vydáno: IEEE 01.12.2021
Témata:
Conferences
fast matrix multiplication on GPU
Graphics processing units
High performance computing
Memory management
memory optimization on GPU
Parallel processing
Processor scheduling
Scheduling
Strassen's matrix multiplication algorithm
task scheduling for enhanced parallelism
ISSN:2640-0316
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Shrnutí:Prior implementations of Strassen's matrix multiplication algorithm on GPUs traded additional workspace in the form of global memory or registers for time. Although Strassen's algorithm offers a reduction in computational complexity as compared to the classical algorithm, the memory overhead associated with the algorithm limits its practical utility. While there were past attempts at reducing the memory footprint of Strassen's algorithm by compromising parallelism, no prior implementation, to our knowledge, was able to hide the workspace requirement successfully. This paper presents an implementation of Strassen's matrix multiplication in eUDA, titled Multi-Stage Memory Efficient Strassen (MSMES), that eliminates additional workspace requirements by reusing and recovering input matrices. MSMES organizes the steps involved in Strassen's algorithm into five stages where multiple steps in the same stage can be executed in parallel. Two additional stages are also discussed in the paper that allows the recovery of the input matrices. Unlike previous works, MSMES has no additional memory requirements irrespective of the level of recursion of Strassen's algorithm. Experiments performed with MSMES (with the recovery stages) on NVIDIA Tesla V100 GPU and NVIDIA GTX 1660ti GPU yielded higher compute performance and lower memory requirements as compared to the NVIDIA library function for double precision matrix multiplication, cublasDgemm.
ISSN:2640-0316
DOI:10.1109/HiPC53243.2021.00035