For arbitrary precision numbers, reciprocal computing algorithms based on Newton iteration is asymptotically the fastest. In this work we provide a refined a lgorithm based on the Newton reciprocal algorithm by Brent ...
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For arbitrary precision numbers, reciprocal computing algorithms based on Newton iteration is asymptotically the fastest. In this work we provide a refined a lgorithm based on the Newton reciprocal algorithm by Brent and Zimmermann in their MCA book. The key techniques used in the refinement are D1 balancing, clear specification, r emainder o peration, and economical multiplication. The refined algorithm is more general,and gives exact and unique result. Numerical results show that these improvements are made without the cost of time *** is still the potential to further improve the efficiency by utilizing a short multiplication algorithm.
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