Computation of the 100 quadrillionth hexadecimal digit of π on a cluster of Intel Xeon Phi processors

被引：8
|
作者：
Takahashi, Daisuke [1 ]
机构：
[1] Univ Tsukuba, Ctr Computat Sci, 1-1-1 Tennodai, Tsukuba, Ibaraki 3058577, Japan
来源：
PARALLEL COMPUTING | 2018年 / 75卷
关键词：
BBP-type formula; Modular exponentiation; Cluster of Intel Xeon Phi processors; MULTIPLICATION;
D O I：
10.1016/j.parco.2018.02.002
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
This paper presents the computation of a specific hexadecimal digit of 7 by using a Bailey-Borwein-Plouffe (BBP)-type formula on a cluster of Intel Xeon Phi processors. The BBP-type formula can be computed using modular exponentiation. We use Montgomery multiplication for the modular multiplication, which is the most time-consuming part of the modular exponentiation. We vectorize multiple modular exponentiations and multiple integer divisions by using Intel Advanced Vector Extensions 512 (Intel AVX-512) instructions. A parallel implementation of the BBP-type formula is presented. The 100 quadrillionth hexadecimal digit of it was computed on a 512-node cluster of Intel Xeon Phi processors with an elapsed time of 641 h 29 min that includes the time required for verification. (C) 2018 Elsevier B.V. All rights reserved.
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页码：1 / 10
页数：10
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