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Automatic Computation of Exponentials, Logarithms, Ratios and Square Roots

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1 Author(s)
Chen, T.C. ; IBM San Jose Research Laboratory, California 95114, USA

It is shown how a relatively simple device can evaluate exponentials, logarithms, ratios and square roots for fraction arguments, employing only shifts, adds, high-speed table lookups, and bit counting. The scheme is based on the cotransformation of a number pair (x,y) such that the F(x,y) = f(x0) is invariant; when x is driven towards a known value xω , y is driven towards the result. For an N-bit fraction about N/4 iterations are required, each involving two or three adds; then a termination algorithm, based on an add and an abbreviated multiply, completes the process, for a total cost of about one conventional multiply time. Convergence, errors and simulation using APL are discussed.

Note: The Institute of Electrical and Electronics Engineers, Incorporated is distributing this Article with permission of the International Business Machines Corporation (IBM) who is the exclusive owner. The recipient of this Article may not assign, sublicense, lease, rent or otherwise transfer, reproduce, prepare derivative works, publicly display or perform, or distribute the Article.  

Published in:

IBM Journal of Research and Development  (Volume:16 ,  Issue: 4 )