A High Efficient In-place Transposition Scheme for Multidimensional Arrays

This paper presents a in-place cycle-reducing method for multidimensional arrays transposition in local memory to reduce the memory R/W operations. The resulting method can significantly reduce the number of subcycles (also called following-cycles) and that of memory operations for square arrays. Taking square array 256 by 256 for example, the number of subcycles used by current available best algorithm can be reduced from 32894 to only 574, using our new method, and the memory operation number can be reduced by about 32.58%, from 98430 to 66366. Taking advantage of this new method, the elapsed time can be reduced as a result. The number of cycles and operations can also be reduced for 2D rectangle arrays with 2^m rows and 2ⁿ column stored in column-major, especially n=2m, even though the improvement is not as significant as that for square arrays. The improved 2D in-place algorithm has been extended to 3D arrays, and some theoretic and numerical results are also provided. Furthermore, we develop a new in-place 3D arrays transposition algorithm. This algorithm is very important for a deep research for multidimensional arrays. Experimental results show that our algorithm can improve efficiency significantly, compared to some other 3D array transposition schemes.