SOFTWARE COMPLEXITY METRICS FOR HIGH-PRECISION COMPUTATIONS IN DISTRIBUTED SYSTEMS

Abstract

Modern software systems increasingly rely on numerical algorithms that require high or arbitrary precision, especially in scientific computing, numerical modeling, optimization, and data analysis. The use of high-precision arithmetic significantly affects the computational behavior of programs, since the cost of arithmetic and transcendental operations depends on the precision level of numerical data representation. In such conditions, predicting program execution time and estimating computational complexity become non-trivial tasks, particularly in distributed computing environments.

This paper presents an analysis of existing software complexity metrics with respect to their applicability to programs performing high-precision computations in distributed systems. Classical software metrics, including size metrics, control flow complexity metrics, and data flow complexity metrics, are considered and systematized. Their main limitations are identified in the context of high-precision arithmetic, where the assumption of constant-time arithmetic operations is no longer valid.

It is shown that classical complexity metrics do not account for the dependence of computational cost on the mantissa length of numerical variables and the actual cost of arithmetic operations. As a result, programs with relatively simple control structures but intensive high-precision computations may require significantly more computational resources than programs with complex control logic implemented using standard floating-point arithmetic.

The study substantiates the necessity of extending existing complexity evaluation approaches by incorporating parameters related to numerical precision and operation cost. The computational complexity of a program is proposed to be considered as a function of the types of arithmetic operations, their execution frequency, and the mantissa length of numerical data. Such an approach allows for a more accurate estimation of execution time and resource consumption, which is especially important for programs executed in distributed computing systems where communication overhead and data transfer costs play a significant role.

The obtained results can be used for preliminary performance estimation, rational resource allocation, and the selection of appropriate parallelization strategies for high-precision numerical software in distributed environments.