Computer-aided design and execution of effective programs for numerical algorithms

Designing effective parallel programs for multiprocessor architectures is difficult because there are no clear formal rules to follow. The concept of the $Q$-determinant can be applied to solve this problem when implementing numerical algorithms. This theory allows for automated analysis of the algorithm parallelism resource, automated comparison of the parallelism resources of algorithms solving the same algorithmic problem. In addition, it makes it possible to design effective programs for the implementation of numerical algorithms using a specially developed design method, improve the efficiency of the implementation of numerical methods and algorithmic problems. The results obtained on the basis of the $Q$-determinant concept are one of the options for solving the problem of effective implementation of numerical algorithms, methods and algorithmic problems on parallel computing systems. However, the fundamental problem of computer-aided design and execution for any numerical algorithm of a program that implements the algorithm effectively remains unresolved. The paper describes the development of a software system for designing and executing $Q$-effective programs that is unified for numerical algorithms. A $Q$-effective program is an effective program designed using the concept of a $Q$-determinant. The system is intended for use on parallel computing systems with shared memory. It consists of a compiler and a virtual machine. The compiler converts the representation of the algorithm in the form of a $Q$-determinant into an executable program that uses the algorithm's parallelism resource completely. The virtual machine executes the program generated by the compiler. The paper also provides an experimental study of the created software system using the SUSU Tornado supercomputer.