Title :
Incremental computation of squares and sums of squares
Author_Institution :
Dept. of Electr. Eng., Edinburgh Univ., UK
Abstract :
An incremental algorithm for computation of sums of squares is presented that is suitable for both most-significant-bit- (MSB-)first and least-significant-bit- (LSB-)first bit-sequential operation. By exploiting symmetry properties of numerical values and evaluation times in the bit-product matrix, it is shown how incremental multipliers can be converted to perform squaring at reduced hardware cost, and sum of squaring at a hardware cost to that of scalar multiplication. By the elimination of redundant computation, existing hardware modules are either reduced in size or assigned to the evaluation of a second squaring computation. The corresponding hardware architectures are derived from a simple conversion of existing incremental scalar multipliers. This conversion process is less practical on standard serial/parallel or serial-pipeline multipliers. A digit-on-line algorithm is outlined for magnitude extraction operations on plane vectors.<>
Keywords :
digital arithmetic; bit-sequential operation; digit-on-line algorithm; hardware architectures; hardware modules; incremental algorithm; incremental multipliers; magnitude extraction operations; plane vectors; scalar multiplication; sums of squares; symmetry properties; Automata; Clocks; Computer architecture; Councils; Counting circuits; Digital arithmetic; Hardware; Iterative algorithms; Pipelines; Symmetric matrices;
Journal_Title :
Computers, IEEE Transactions on