A new advance on dimensional-aware scalar, vector and matrix operations in C++

TL;DR

This paper introduces Univec, a C++ library that enables dimensional-aware scalar, vector, and matrix operations, supporting complex number systems and improving scientific computing accuracy.

Contribution

The paper presents Univec, a novel C++ library that enhances dimensional-aware computations for various mathematical objects and compares its performance with existing solutions.

Findings

Univec supports complex, quaternion, octonion, and sedenion operations.

Performance benchmarks show advantages over existing solutions.

The library improves accuracy and safety in scientific computations.

Abstract

We review the dimensional check problem of the high-level programming languages, discuss the existing solutions, and come up with a new solution suited for scientific and engineering computations. Then, we introduce Univec, our C++ library designed to make scalar, vector, and matrix operations using units of measurement. Moreover, Univec supports dimensional-aware operations for complex numbers, quaternions, octonions, and sedenions. We provide tables of the relevant functions and operators implemented. Our library was compared with several existing solutions, and the results are shown in the performance section. Finally, we present our future plans for improving the current implementation.