Abstract—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 recoding of the two most
significant digits of the residual before selecting the most significant
digit of this recoded residual as the quotient-digit. NST relies on the
δ), where δ is a positive fraction
divisor being in the range [1, 1 +
depending upon: 1) the radix, 2) the signed-digit set used to represent
the residual, and 3) the recoding 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 unscaled 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
2
b, the number of different algorithms of this kind is b/4.
radix-