Put simply, it states that there is a simple power law relationship between these two values (pins and gates).
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
Rent's findings in IBM-internal memoranda were published in the IBM Journal of Research and Development in 2005,[1] but the relation was described in 1971 by Landman and Russo.
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.
Christie and Stroobandt[3] 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
in Rent's rule can be viewed as the average number of terminals required by a single logic block, since
Larger values are impossible, since the maximal number of terminals for any region containing g logic components in a homogeneous system is given by
Lower bounds on p depend on the interconnection topology, since it is generally impossible to make all wires short.
is often called the "intrinsic Rent exponent", a notion first introduced by Hagen et al.[4] It can be used to characterize optimal placements and also measure the interconnection complexity of a circuit.
Rent's rule has been shown to apply among the regions of the brain of Drosophila fruit fly, using synapses instead of gates, and neurons which extend both inside and outside the region as pins.
[6] To estimate Rent's exponent, one can use top-down partitioning, as used in min-cut placement.
[2] A similar deviation also exists for small partitions and has been found by Stroobandt,[8] who called it "Region III".
The resulting wirelength estimates have been improved significantly since then and are now used for "technology exploration".
[12] The use of Rent's rule allows to perform such estimates a priori (i.e., before actual placement) and thus predict the properties of future technologies (clock frequencies, number of routing layers needed, area, power) based on limited information about future circuits and technologies.
A comprehensive overview of work based on Rent's rule has been published by Stroobandt.