This paper presents a general theory for developing new Svoboda-Tung (or simply NST) division algorithms not suffering the drawbacks of the "classical" Svoboda-Tung (or simply ST) method. NST avoids the drawbacks of ST by proper receding of the two most significant digits of the residual before selecting the most significant digit of this receded residual as the quotient-digit. NST relies on the divisor being in the range [1, 1 + •), where • is a positive fraction depending upon: 1) the radix, 2) the signed-digit set used to represent the residual, and 3) the receding conditions of the two most significant digits of the residual. If the operands belong to the IEEE-Std range [1, 2), they have to be conveniently prescaled. In that case, NST produces the correct quotient but the final residual is scaled by the same factor as the operands, therefore, NST is not useful in applications where the unsealed residual is necessary. An analysis of NST shows that previously published algorithms can be derived from the general theory proposed in this paper. Moreover, NST reveals a spectrum of new possibilities for the design of alternative division units. For a given radix-b, the number of different algorithms of this kind is b 2/4.
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The authors would like to thank the anonymous reviewers for their valuable comments and suggestions. Luis Montalvo would also like to express his gratitude to Prof. Peter Kornerup for his many comments on this work. This research was supported in part by the U.S. Office of Naval Research under contract number N00014-91-J-1008.
- Computer arithmetic
- Digit-recurrence division
- Operand prescaling
- Redundant number system
- Svoboda-Tung method