A How E . F . Rent ’ s decades - old rule and its implications

was formulated in the 1960s and published worldwide in 1971, it took until the end of the 1990s before its value became clearly apparent, leading to the creation of an entire research field on a priori wire length predictions. Even when the rule itself became quite popular, its inventor, E.F. Rent, stayed in the background: who the man actually was remained a mystery. It was as if Mr. Rent stayed in the prompter’s box while others took the stage and spread the word on his findings. In this article, I will show that Rent’s rule can be viewed as a fundamental law of nature with respect to electronic circuits. As there are many interpretations of the rule, this article will shed some light on the core of Rent’s rule and the research that has been built on it. The scaling of computer technology has been driven by Moore’s law, which states that the number of transistors on a chip doubles with every technology generation. (In the 1970s, the number of transistors doubled every 18 months; later, this was every two years, and over the last decade it has been every three years.) In the 20th century, Moore’s law also meant an increase in the clock frequency with every technology generation (Figure 1). This currently is no longer the case, however: clock frequencies are now staying almost the same with each new technology generation. Few people are aware of it, but the reason for this has its basis in Rent’s rule. Although there are many interpretations, Rent’s rule basically states that, in a chip design, the number of wires emanating from a region containing B logic blocks (the basic computational elements on chips) grows faster than the perimeter length increase when B grows (Figure 2). Note that this is explicitly a scaling argument and, in principle, assumes an infinitely large circuit. With some calculations, one can deduce from this that the average length of an interconnection on chip must increase with a growing number of Dirk Stroobandt