A C++11 implementation of arbitrary-rank tensors for high-performance computing

TL;DR

This paper presents an efficient C++11 implementation of arbitrary-rank tensors, enabling high-performance computing with a flexible Array class and expression templates, tested on CPU and GPU.

Contribution

It introduces a versatile tensor class template with expression templates for high-performance algebraic computations in C++11.

Findings

Efficient tensor operations achieved on CPU and GPU.

Flexible and high-level tensor algebra in C++11.

Maintains performance without sacrificing abstraction.

Abstract

This article discusses an efficient implementation of tensors of arbitrary rank by using some of the idioms introduced by the recently published C++ ISO Standard (C++11). With the aims at providing a basic building block for high-performance computing, a single Array class template is carefully crafted, from which vectors, matrices, and even higher-order tensors can be created. An expression template facility is also built around the array class template to provide convenient mathematical syntax. As a result, by using templates, an extra high-level layer is added to the C++ language when dealing with algebraic objects and their operations, without compromising performance. The implementation is tested running on both CPU and GPU.