Research and Advances

Speeding up an overrelaxation method of division in Radix-2n machine

For normalized floating point division, digital computers can take advantage of a division process that uses an iterative multiplying operation instead of repeated subtractions. An improvement of this division process by using accelerating constants in the overrelaxation has previously been proposed. Multiplication by a chosen accelerating constant accelerates the process of generating accurate digits of a quotient in division. We propose a further improvement by generalizing the accelerating constants in the overrelaxation method. Two benefits resulting from this improvement promise to yield faster division in digital computers.

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Research and Advances

An overrelaxation for a numerical inverse of a constant

When division is performed by a power series implementation with additions, subtractions, digit shifts, and multiplications, the convergence rate of the power series is important in practical application. Particularly if the rate of the power series is close to one, the convergence is slow and therefore a special method to accelerate the convergence is needed. Without such an acceleration, the power series implementation is less attractive. An acceleration method is proposed for the slow convergence rate. First, the worst case convergence rate of the power series is determined for a given appropriate acceleration factor. Next, a simple way to choose the appropriate acceleration factor is presented.

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