Acceleration of Multiple Precision Matrix Multiplication Based on Multi-component Floating-Point Arithmetic Using AVX2
Acceleration of Multiple Precision Matrix Multiplication Based on Multi-component Floating-Point Arithmetic Using AVX2
复制标题
基于AVX2的多分量浮点运算的多精度矩阵乘法加速
DOI：
10.1007/978-3-030-86976-2_14
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Kouya Tomonori
中科院分区：
文献类型：
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作者：
Habib Md. Ahsan;Md. Rokibul Alam Kazi;Morimoto Yasuhiko;大瀧脩人，照井章，三河正彦;Kouya Tomonori
本文报道了用AVX2加速多二进制64型多精度块和Strassen矩阵乘法的结果。我们的目标是使用某些类型的无误差变换(EFT)算法设计的双倍(DD)、三倍(TD)和四倍(QD)精度算法。此外，我们在x86_计算环境上实现了同时计算四个二进制64位数的SIMD化EFT函数，并利用它们开发了SIMD化的DD、TD和QD加法和乘法。此外，采用了AVX2的加载/存储功能，有效地加快了矩阵元素在存储器中的读取和存储速度。由于这些技术的结合，我们实现的多精度矩阵乘法的速度比非加速的快了三倍以上。我们的加速矩阵乘法使用OpenMP修改了并行化性能。
In this paper, we report the results obtained from the acceleration of multi-binary64-type multiple precision block and Strassen matrix multiplications with AVX2. We target double-double (DD), triple-double (TD), and quad-double (QD) precision arithmetic designed using certain types of error-free transformation (EFT) arithmetic. Furthermore, we implement SIMDized EFT functions, which simultaneously compute with four binary64 numbers on x86_64 computing environment, and by using help of them, we also develop SIMDized DD, TD, and QD additions and multiplications. In addition, AVX2 load/store functions were adopted to efficiently speed up reading and storing matrix elements from/to memory. Owing to these combined techniques, our implemented multiple precision matrix multiplications were accelerated more than three times compared with non-accelerated ones. Our accelerated matrix multiplication modifies parallelization performance with OpenMP.