1330 IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS, VOL. 12, NO. 12, DECEMBER 2004 Interpretation of Rent’s Rule for Ultralarge-Scale Integrated Circuit Designs, With an Application to Wirelength Distribution Models Mary Yvonne Lanzerotti, Member, IEEE, Giovanni Fiorenza, Member, IEEE, and R. A. Rand Abstract—Computer hardware components have changed sig- nificantly since the 1960s, 1970s, 1980s, and even since the early 1990s. Work concerning Rent’s memos prior to the present paper has been based on a 1971 interpretation of two unpublished mem- oranda written in 1960 by E. F. Rent while working at IBM, even though today’s computer components are significantly different from those in 1960 and 1971. However, because of the significant changes in the design and implementation of computer hardware components since 1960 and 1971, a new interpretation of Rent’s memos is needed for today’s components. We have obtained copies of Rent’s two memos. In these memos, Rent describes the method that he used to obtain an empirical relationship between proper- ties of the computer hardware components of the IBM 1401 and the IBM 1410 computers. We have studied these memos carefully in order to understand Rent’s original intent. Based on our careful reading of these two memos, the personal knowledge of one of us with the 1401 and 1410 computers, and our experience designing ultralarge-scale integrated (ULSI) circuits for high-performance microprocessors, we have derived an historically equivalent inter- pretation of Rent’s memos suitable for today’s computer compo- nents. The purpose of this paper is to present a new interpretation of the memos and to present an application to wirelength distribu- tions of real ULSI circuitry. In this paper, we will: 1) describe the contents of the memos and Rent’s method; 2) provide an histori- cally-equivalent interpretation of Rent’s memos for today’s com- puter components; and 3) apply this new interpretation to real ULSI control logic circuitry in the 1.3-GHz IBM POWER4 micro- processor. In this paper, we will show that this new interpretation of the two memos provides improved wirelength distribution models with better qualitative agreement with measurements and more accurate estimates of wirelength distributions and wirelength re- quirements for real ULSI designs compared with prior methods. Index Terms—Circuit, Rent, ultralarge-scale integration (ULSI), very large scale integration (VLSI), wirelength distribution. I. INTRODUCTION B ECAUSE significant changes have occurred in the design and implementation of computer hardware components since the 1960s, on through the 1970s, 1980s and even since the 1990s [1], [2], a new interpretation of empirical rules such as Rent’s rule—described by E. F. Rent in two 1960 memos [3] and first interpreted in 1971 [4]—is needed for today’s computer components. All of the prior extensive work concerning Rent’s memos, including for example [5]–[20], has been based on the 1971 interpretation of two unpublished memoranda written in Manuscript received July 22, 2003; revised April 23, 2004. The authors are with the IBM T. J. Watson Research Center, Yorktown Heights, NY 10598 USA (e-mail: myl@us.ibm.com; gfiorenz@us.ibm.com; rarand@us.ibm.com). Digital Object Identifier 10.1109/TVLSI.2004.837990 1960 by E. F. Rent at IBM, even though today’s computer com- ponents differ significantly from the components in 1960 to 1971. Since significant differences exist between the compo- nents discussed in Rent’s original work and today’s computer components, a new interpretation of Rent’s memos that is suit- able for today’s ultralarge-scale integrated (ULSI) designs is therefore required. We have obtained copies of both of Rent’s IBM memoranda [3] in which he describes an analysis of the IBM 1401 and 1410 computers. The two memos are dated November 28, 1960, and December 12, 1960, and we have studied these memos in order to understand the method that Rent employed to analyze the characteristics of the 1401 and 1410 computers. In these memos, Rent describes his method to deduce an empirical re- lationship between the properties of computer hardware com- ponents. Based on our careful reading of these two memos, the personal knowledge of R. A. Rand regarding the 1401 and 1410 computers, and our experience in the design and wiring of ULSI circuitry in high-performance microprocessors, we have derived an historically-equivalent interpretation of Rent’s memos that is suitable for today’s computer components. In this paper, the phrase historically-equivalent refers to our mapping of each computer component described by Rent to a functionally-equiv- alent computer component that exists in today’s computers. This mapping is described later in the text. In this paper, we present an historically-equivalent interpreta- tion of Rent’s memos that is suitable for today’s ULSI circuitry designs. The contributions of this paper are: 1) a description of the contents of the two memoranda and Rent’s method; 2) an historically-equivalent interpretation of Rent’s memos that is suitable for today’s computer components; and 3) application of this interpretation to real ULSI control logic circuit designs in the POWER4 microprocessor. The first application is to ex- tract historically-equivalent empirical values of Rent’s parame- ters for these designs. The second application is to evaluate ex- isting wirelength distribution models and existing expressions for average wirelength as functions of these new empirical pa- rameters. We will then compare these distributions and average wirelength estimates with measured distributions and average wirelength measurements in real chip designs. The designs se- lected for this study are all (100) of the control logic designs in the IBM POWER4 core, which is currently incorporated in the IBM Enterprise Server pSeries 680 and pSeries 690 [21], [22]. Together, the control designs occupy approximately 40% of the core area [22]. 1063-8210/04$20.00 © 2004 IEEE