ROM table reduction techniques for computing the squaring operation using modular arithmetic

Modular arithmetic is necessary when using the residue number system, which is suitable for high-speed signal processing, due to its carry-free and parallel nature. The author presents techniques for minimizing the size of the look-up table ROMs used for computing the squaring operation, when arithmetic modulo m is performed. Such squaring operations are necessary when implementing the quarter squared and the one over eight squared algorithms. These squared-law algorithms are useful in computing multiplicative intensive operations, such as convolutions, correlations and complex multiplications. The memory compression schemes presented can result in significant ROM savings, with the only extra cost of a small overhead