Abstract
Algorithms designed for implementation on parallel computers with distributed memory consist of computational macro operations (calculation grains) and communication operations specifying the data arrays exchange between computing nodes. The major difficulty is how to find an efficient way to organize the data exchange. To solve this problem, it is first necessary to identify information dependences between macro operations and then to generate the communication operations caused by these dependences. To automate and simplify the process of code generation, it is necessary to formalize communication operations. The formalization is known for the case of homogeneous information dependences. Such formalization uses the vectors of global dependences as a representation of dependences between the calculation grains. Also, there is a way that makes it possible to obtain the data arrays exchange, but it requires the usage of tools to work with polyhedra and does not formalize communication operations. This article presents a formalization method and a method of inclusion of communication operations into the algorithm structure (receiving and sending data arrays) in case of a parallel algorithm with affine dependences. The usage of functions determining the relationship between macro operations allowed obtaining explicit representations of communication operations. This work is a generalization of the formalization of the operations of sending data in a parallel algorithm, where operations are not divided into macro operations, as well as a generalization of some aspects of obtaining the communication operation method.
Highlights
Algorithms designed for implementation on parallel computers with distributed memory consist of compu tational macro operations and communication operations specifying the data arrays exchange between computing nodes
It is first necessary to identify information dependences between macro operations and to generate the communication operations caused by these dependences
The formalization is known for the case of homogeneous information dependences
Summary
Для каждого набора операторов имеется столько локальных циклов, сколько r1θ,..., rnθθ превосходят единицу. Граф рассматриваемого алгоритма с очертаниями тайлов изображен на рис. Формализуем множества информационно зависимых операций тайлов, порождающие глобальные зависимости: θβ ,inm J gl ,a,β подмножество итераций. При выполнении которых на вхождении ( ) (a,Sβ,q) используются результаты операций тайла. изображен граф зависимостей уровня тайлов, порождаемых функциями глобальных зависимостей gl . 2. Граф глобальных зависимостей, порождаемых зависимостями между операциями S3(i,j) (Q1 = Q2 = 4) Fig. 2. изображены очертания тайлов операций S3(i,j), отмечены множества зависимых операций тайлов и соответствующие векторы глобальных зависимостей. 3. Схема тайлов, множеств информационно зависимых операций тайлов, глобальных зависимостей (r1 = r2 = 3, Q1 = Q2 = 3) Fig. 3. Перейдем непосредственно к формализации коммуникационных операций получения и отправки массивов данных в параллельном зернистом алгоритме с аффинными зависимостями, который предназначен для реализации на компьютере с распределенной памятью.
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