并行计算时间与存储空间关系研究
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摘要
作为解决大规模计算问题的重要手段,高性能计算被越来越广泛的应用到科学与工程的各个领域,人们对其效率的要求也越来越高。面对庞大、复杂且对时效性要求极高的计算任务,如何优化并行程序设计,提高系统性能是高性能计算领域有待突破的重点和难点问题。要解决此类问题,首先需要解决的就是高性能计算中的性能评价。
并行程序的设计与优化是个非常复杂的过程。在并行程序的开发过程中,时间需求和存储需求是其中必须要考虑的重要问题;进一步合理解决计算时间和存储空间的关系,也是并行程序性能优化的有效途径。本文结合“飞行器RCS(Radar Cross-Section)精确数值计算并行化研究及实现”项目,紧紧围绕并行计算时间与存储空间关系这一主题,对时间与空间评测标准、时间与空间之间的关系、并行程序时间开销及其处理器规模的计算方法进行了深入研究。本文的主要工作包括:
1、提出时间加速模型与空间加速模型
针对并行程序特点,调整了加速比性能定律,并称为时间加速模型。该模型论证了并行计算中时间加速的存在性,在时间加速比中加入了空间因素。同时,分析了时间效率和计算时间在并行程序优化后的变化规律。
分析了并行计算中存储空间的变化特点,提出了空间加速模型,确定了存储空间在并行计算中的基本特征。为了获取空间加速模型中所需的空间参数,提出了两种空间统计策略。一种用于统计并行程序运行时对总存储空间需求量的峰值,一种用于统计节点内对存储空间需求量的峰值。
2、提出时间与空间关系模型及其预测方法
分析了时间与空间之间的四种关系,并给出相应的时间效率和空间效率关系图。通过时空效率关系图,寻找即能充分发挥系统计算能力又能缩短计算时间的平衡点。
提出用空间表示时间的计算模型。该模型采用了相对简单的方法,能够付出较小的代价计算出具体处理器规模下关键存储空间的处理时间,用于研究关键存储空间对并行程序整体性能的影响,为预测时空关系提供了可能性。
3、提出并行程序时间开销模型及其处理器规模计算方法
针对分布存储、共享存储、分布式共享存储并行处理机的体系结构,研究了MPI、OpenMP和MPI+OpenMP并行程序的时间开销模型。尤其是对MPI+OpenMP程序时间开销的研究,揭示了混合编程模型的时间开销来源和各时间开销之间的关系。
分析了OpenMP程序特点,指出使用OpenMP进行编程时,需要重新考虑其处理器规模的确定方法。根据采用并行计算后程序规模的膨胀情况,提出OpenMP程序和MPI+OpenMP程序处理器规模的计算方法。为在分布存储、共享存储、分布式共享存储体系结构下研究时空问题,分析了三者的主要差异。
High performance computing (HPC) is widely used in science and engineering fields to solve large scale computing problems. The demand for promoting its performance has rapidly increased. Facing huge, complex and time-critical computing tasks, how to optimize parallel program designing to improve parallel system performance efficiency is still an important and difficult problem in high performance computing, which remains to be broken through. To solve such problem, the performance evaluation of high performance computing is the one, which should be solved firstly.
It is a complicated process to develop and optimize parallel program. Time requirement and storage requirement are two important aspects that should be taken into consideration during the programming process. Refining the relationship between time and storage space is also an efficient method to optimize parallel program. In this dissertation, the relationship between time requirement and storage requirement is deeply analyzed. The theories on this topic, such as evaluation metric for time and space, the relationship between time and space, and the overhead model of parallel program and its computing processor scale’s calculating method are studied. The actual practice of these theories and analyze are carried out in the project-‘the study and implementation of aircrafts RCS exact parallel computing’. The main contributions of this dissertation are as follows.
1. The time speedup model and space speedup model are raised.
Based on the parallel program’s characteristics, the speedup is adjusted, and renamed as time speedup model. In this model, the existence of the time speedup in parallel computing is discussed, and the spatial factor is placed into it. Meanwhile, the changing trends of time efficiency and computing time after parallel program optimization are analyzed.
The changing regularity of storage requirement in parallel computing is analyzed, and the space speedup model is proposed. In this model, the primary characteristic of storage requirement in parallel computing is identified. And in order to obtain the parameters used in the space speedup model, two storage space statistics are proposed. One can be used to survey the total storage requirement of a parallel program, and another to census the storage requirement in a certain node.
2. The relationship model between time and space and the relationship prediction method are proposed.
Four kinds of time and space’s relationship are analyzed, and the relative time efficiency and space efficiency diagrams are given. Using the time efficiency and space efficiency diagram, the equilibrium point to make effective use of system resources and shorten the calculating time can be found.
A calculating model to use space to express time is presented. Using a relatively simple way, the processing time of the key storage space under certain parallel processor scale can be calculated with little overhead. It can be used to study the key storage space’s effect on parallel program’s whole performance and to provide the possibility to predict the relationship between time and space.
3. The overhead model of parallel program and its processor scale’s calculating method are raised.
In view of the distributed memory, shared memory and distributed shared memory systems’structures, the overhead models of MPI program, OpenMP program and MPI+OpenMP program are studied. Especially, the MPI+OpenMP program’s overhead model reveals the mixed program’s overhead sources and the relationship between them.
The characteristic of OpenMP program is analyzed, pointing out that the method to determine processor scale, when using OpenMP to develop programs, should be reconsidered. The strategies to calculate the processor scales of OpenMP program and MPI+OpenMP program are proposed, making use of the expansion condition of program size. Thus, the main difference in discussing the time and space problem under distributed memory, shared memory and distributed shared memory systems is analyzed.
并行程序的设计与优化是个非常复杂的过程。在并行程序的开发过程中,时间需求和存储需求是其中必须要考虑的重要问题;进一步合理解决计算时间和存储空间的关系,也是并行程序性能优化的有效途径。本文结合“飞行器RCS(Radar Cross-Section)精确数值计算并行化研究及实现”项目,紧紧围绕并行计算时间与存储空间关系这一主题,对时间与空间评测标准、时间与空间之间的关系、并行程序时间开销及其处理器规模的计算方法进行了深入研究。本文的主要工作包括:
1、提出时间加速模型与空间加速模型
针对并行程序特点,调整了加速比性能定律,并称为时间加速模型。该模型论证了并行计算中时间加速的存在性,在时间加速比中加入了空间因素。同时,分析了时间效率和计算时间在并行程序优化后的变化规律。
分析了并行计算中存储空间的变化特点,提出了空间加速模型,确定了存储空间在并行计算中的基本特征。为了获取空间加速模型中所需的空间参数,提出了两种空间统计策略。一种用于统计并行程序运行时对总存储空间需求量的峰值,一种用于统计节点内对存储空间需求量的峰值。
2、提出时间与空间关系模型及其预测方法
分析了时间与空间之间的四种关系,并给出相应的时间效率和空间效率关系图。通过时空效率关系图,寻找即能充分发挥系统计算能力又能缩短计算时间的平衡点。
提出用空间表示时间的计算模型。该模型采用了相对简单的方法,能够付出较小的代价计算出具体处理器规模下关键存储空间的处理时间,用于研究关键存储空间对并行程序整体性能的影响,为预测时空关系提供了可能性。
3、提出并行程序时间开销模型及其处理器规模计算方法
针对分布存储、共享存储、分布式共享存储并行处理机的体系结构,研究了MPI、OpenMP和MPI+OpenMP并行程序的时间开销模型。尤其是对MPI+OpenMP程序时间开销的研究,揭示了混合编程模型的时间开销来源和各时间开销之间的关系。
分析了OpenMP程序特点,指出使用OpenMP进行编程时,需要重新考虑其处理器规模的确定方法。根据采用并行计算后程序规模的膨胀情况,提出OpenMP程序和MPI+OpenMP程序处理器规模的计算方法。为在分布存储、共享存储、分布式共享存储体系结构下研究时空问题,分析了三者的主要差异。
High performance computing (HPC) is widely used in science and engineering fields to solve large scale computing problems. The demand for promoting its performance has rapidly increased. Facing huge, complex and time-critical computing tasks, how to optimize parallel program designing to improve parallel system performance efficiency is still an important and difficult problem in high performance computing, which remains to be broken through. To solve such problem, the performance evaluation of high performance computing is the one, which should be solved firstly.
It is a complicated process to develop and optimize parallel program. Time requirement and storage requirement are two important aspects that should be taken into consideration during the programming process. Refining the relationship between time and storage space is also an efficient method to optimize parallel program. In this dissertation, the relationship between time requirement and storage requirement is deeply analyzed. The theories on this topic, such as evaluation metric for time and space, the relationship between time and space, and the overhead model of parallel program and its computing processor scale’s calculating method are studied. The actual practice of these theories and analyze are carried out in the project-‘the study and implementation of aircrafts RCS exact parallel computing’. The main contributions of this dissertation are as follows.
1. The time speedup model and space speedup model are raised.
Based on the parallel program’s characteristics, the speedup is adjusted, and renamed as time speedup model. In this model, the existence of the time speedup in parallel computing is discussed, and the spatial factor is placed into it. Meanwhile, the changing trends of time efficiency and computing time after parallel program optimization are analyzed.
The changing regularity of storage requirement in parallel computing is analyzed, and the space speedup model is proposed. In this model, the primary characteristic of storage requirement in parallel computing is identified. And in order to obtain the parameters used in the space speedup model, two storage space statistics are proposed. One can be used to survey the total storage requirement of a parallel program, and another to census the storage requirement in a certain node.
2. The relationship model between time and space and the relationship prediction method are proposed.
Four kinds of time and space’s relationship are analyzed, and the relative time efficiency and space efficiency diagrams are given. Using the time efficiency and space efficiency diagram, the equilibrium point to make effective use of system resources and shorten the calculating time can be found.
A calculating model to use space to express time is presented. Using a relatively simple way, the processing time of the key storage space under certain parallel processor scale can be calculated with little overhead. It can be used to study the key storage space’s effect on parallel program’s whole performance and to provide the possibility to predict the relationship between time and space.
3. The overhead model of parallel program and its processor scale’s calculating method are raised.
In view of the distributed memory, shared memory and distributed shared memory systems’structures, the overhead models of MPI program, OpenMP program and MPI+OpenMP program are studied. Especially, the MPI+OpenMP program’s overhead model reveals the mixed program’s overhead sources and the relationship between them.
The characteristic of OpenMP program is analyzed, pointing out that the method to determine processor scale, when using OpenMP to develop programs, should be reconsidered. The strategies to calculate the processor scales of OpenMP program and MPI+OpenMP program are proposed, making use of the expansion condition of program size. Thus, the main difference in discussing the time and space problem under distributed memory, shared memory and distributed shared memory systems is analyzed.
引文
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