Fast Evaluation of Arithmetic Functions

CMU-CS-85-169

Andreas Nowatzyk

September 1985

Only addition, subtraction and multiplication can be realized efficiently by combinational logic circuits. Other arithmetic functions such as division, square root, logarithm, etc. must resort to slower and/or more expansive iterative hardware for high performance applications. Iterations, such as the Newton method, frequently start with a table look-up operation for an initial estimate. This paper describes the use of interpolation methods to improve the precision of the table look-up operation to eliminate the need for subsequent iterations. The resulting scheme can be pipelined easily because it does not use any feedback data paths. Look-up table based interpolation units can be integrated to supplement high performance floating point chips.

18 pages

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