New Svoboda-Tung division

The 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 divisor being in the range [1, 1+δ), where δ 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 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 the 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 b²/4