Rent's rule

Rent's rule pertains to the organization of computing logic, specifically the relationship between the number of external signal connections to a logic block (i.e., the number of "pins") with the number of logic gates in the logic block, and has been applied to circuits ranging from small digital circuits to mainframe computers.

In the 1960s, E. F. Rent, an IBM employee, found a remarkable trend between the number of pins (terminals, T) at the boundaries of integrated circuit designs at IBM and the number of internal components (g), such as logic gates or standard cells. On a log–log plot, these datapoints were on a straight line, implying a power-law relation ${\displaystyle T=tg^{p}}$, where t and p are constants (p < 1.0, and generally 0.5 < p < 0.8).

Rent disclosed his findings in IBM-internal memoranda that were published in the IBM Journal of Research and Development in 2005, but the relation was described in 1971 by Landman and Russo. They performed a hierarchical circuit partitioning in such a way that at each hierarchical level (top-down) the least number of interconnections had to be cut to partition the circuit (in more or less equal parts). At each partitioning step, they noted the number of terminals and the number of components in each partition and then partitioned the sub-partitions further. They found the power-law rule applied to the resulting T versus g plot and named it "Rent's rule".

Rent's rule is an empirical result based on observations of existing designs, and therefore it is less applicable to the analysis of non-traditional circuit architectures. However, it provides a useful framework with which to compare similar architectures.

Christie and Stroobandt later derived Rent's rule theoretically for homogeneous systems and pointed out that the amount of optimization achieved in placement is reflected by the parameter ${\displaystyle p}$, the "Rent exponent", which also depends on the circuit topology. In particular, values ${\displaystyle p<1}$ correspond to a greater fraction of short interconnects. The constant ${\displaystyle t}$ in Rent's rule can be viewed as the average number of terminals required by a single logic block, since ${\displaystyle T=t}$ when ${\displaystyle g=1}$.

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