Efficient representation of higher-dimensional arrays by dimension transformations

Array operations are important for large number of scientific and engineering applications. Two-dimensional array operations are prominent in these applications because of their simplicity and good performance. But in practical applications, the number of dimension is large and hence efficient design of multidimensional array operation is an important research issue. In this paper, we propose and evaluate a new data layout to represent a multidimensional array into a two-dimensional array, namely generalized 2-dimensional array (G2A) by dimension transformations. The G2A transforms an n-dimensional array into a two-dimensional array. Hence, it is possible to design less complicated algorithms that improve the data locality. We design efficient algorithms for matrix–matrix addition/subtraction and multiplication using G2A. Both theoretical analysis and experimental results show that the proposed scheme outperforms the traditional multidimensional array-based algorithms. This is because of the efficient index computation and improved data locality of G2A for better cache performance.