Procesadores aritméticos especializados: computación racional exacta

Resumo

This doctoral dissertation presents a model of specialized arithmetic processor from the scratch to precisely calculate numbers and which also allows further precision adjustment to be made on it. It describes not only expression but flexible processing methods together with an implementation proposal. It is hoped that its outcome will provide a deeper insight when building high performance processors. The number representation format takes advantage of the fact that the positional fractional expression of any rational number is made up of a finite amount of significant digits. Taking the floating point representation as a starting point, a representation function of any ? element can be obtained through the addition of one mantissa that codifies the periodic part, given the flexibility the format shows in length. The operators on this numerical representation system maintain the operational capacity and incorporate characteristics of precision adjustment required by each problem. The variable precision processing discussed is the primitive identity, addition and multiplication operations. The operating process is supported by definitions and theorems on the rational number calculation expressed in positional fractional notation. The development of the methods rests on two basic pillars: iterative design frames, which enable processing to account for all the operand digits and the use of memories containing pre-calculated results, ensuring robust structures parallel designs and further re-use. The integration of these calculation methods accomplishes a specialized arithmetic processor that incorporates the additional elements for the correct management of the precision of operands and results. A precision control unit will determine the degree of proximity the exact result for each operation and, a flexible memory unit will get adequate structure to lodge the data variable in length. The experiments validate diverse aspects of the methods used and the results obtained. The capacity of these operators to deliver an exact result is taken as base for comparison to measure the deviation shown by conventional calculation method processing and to value its use in solving critical problems.