Abstract
Locality is an algorithm characteristic describing a usage level of fast access memory. For example, in case of distributed memory computers we focus on memory of each computational node. To achieve the high performance of algorithm implementation one should choose the best possible locality option. Studying the parallel algorithm locality is to estimate the number and volume of data communications. In this work, we formulate and prove the statements for computers with distributed memory that allow us to estimate the asymptotic volume of data communication operations. These estimation results are useful while comparing alternative versions of parallel algorithms during data communication cost analysis.
Highlights
Locality is an algorithm characteristic describing a usage level of fast access memory
In case of distributed memory computers we focus on memory of each computational node
We formulate and prove the statements for computers with distributed memory that allow us to estimate the asymptotic volume of data communication operations
Summary
Реализующего двухшаговую разностную схему продольно-поперечной прогонки, можно представить в следующем виде (циклы, итерации которых можно выполнять независимо, записаны как dopar): do j =1, j0 dopar i2= 1, N2 – 1 do i1= 1, N1 – 1. S6: y(2) (i1, N 2= - i2 ) alpha(N 2 - i2 + 1) y(2) (i1, N 2 - i2 + 1) + beta(N 2 - i2 + 1). Здесь alpha(i) и beta(i) – коэффициенты прогонок, возникающих при решении промежуточных систем линейных алгебраических уравнений. Приведем функции истинных зависимостей алгоритма продольно-поперечной прогонки (найти их можно исходя из определения зависимостей или методом работы [4]): Φ1,1( j, i2 , i1) =. Перестановкой и распределением циклов алгоритм преобразуется таким образом, чтобы глобальные циклы были внешними по отношению к локальным
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