New Svoboda-Tung Division

This paper presents a general theory for developing new Svoboda-Tung (or simply NST) division algorithms not suuering the drawbacks of the \classical" Svoboda-Tung (or simply ST) method. NST avoids the drawbacks of ST, by means of a proper recoding of the two most signiicant digits of the residual before selecting the most signiicant digit of this recoded 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 recoding conditions of the two most signiicant digits of the residual. If the operands belong to the IEEE-Std range 1; 2), they have to be conveniently pre-scaled. In that case, NST produces the correct quotient but the nal 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 radix b, the number of diierent algorithms of this kind is b 2 =4.