Mixed Arithmetics : Introduction and Design
نویسندگان
چکیده
CAD tools for special purpose architecture usually use conventional radix 2 number system to represent integers. However, DSP designer expertise shows that redundant number systems improve the delay of arithmetic operations. In this paper, we come to the conclusion that arithmetic operator outputs have to be redundant whereas inputs have not. Therefore, an optimal design has to use mixed arithmetic (using both conventional and redundant number systems). Moreover, the selection of the number system for each operand is not trivial, as the inputs of operations are often the outputs of other operations. Therefore, we propose a design strategy to automatically realize this task. R esum e Les outils de CAO d'architectures int egr ees utilisent g en eralement un syst eme conven-tionnel en base 2 pour repr esenter les entiers. Cependant, l'exp erience des concepteurs de circuits de traitement du signal montre que l'utilisation d'arithm etiques redondantes am eliorent le d elai des op erateurs arithm etiques. Dans cet article, nous montrons que les sorties des op erateurs doivent ^ etre redondantes, alors que les entr ees doivent ^ etre non redondantes. Ainsi, l'id eal est l'utilisation d'une arithm etique mixte (utilisant a la fois des repr esentations redondantes et conventionnelles des nombres). Cependant, la s election du syst eme de repr esentation de chaque op erande n'est pas evidente, puisque les entr ees d'op erateurs sont souvent les sorties d'autres op erateurs. Nous proposons donc une strat egie visant a r ealiser cette t^ ache automatiquement.
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