Web Extra Appendix: Implications of Historical Trends in the Electrical Efficiency of Computing

Data and Methods

Our goal for this analysis is an accurate general overview of trends in compute capabilities and power use over time, and for this purpose, the metric of computations per kWh is a reasonable one. We calculate this metric for dozens of different computers, ranging from laptop PCs to mainframes and integrated supercomputers. We rely on long-term performance trends developed in a consistent fashion as well as measured electricity use data for historical computers. The data and results from the analysis are summarized in Tables S1, S2, and S3 .

Summary of methods

Analyzing long-term trends is a tricky business. Ideally we'd have performance and energy use data for all types of computers in all applications since 1946. In practice, such data simply do not exist, so we compiled available data in a consistent way to piece together the long-term trends.

To estimate computations per kWh we focused on the full load computational capacity and the active power for each machine, dividing the number of computations possible per hour at full load by the number of kWh consumed over that same hour. This metric says nothing about the power used by computers when they are idle or running at less than full load but it is a well-defined measure of the electrical efficiency of this technology, and it is one that can show how the technology has changed over time.

Measuring computing performance has always been controversial, and this article will not settle those issues. The most sophisticated and comprehensive historical analysis of computing performance over time is the work by Nordhaus (2007), which builds on the work of McCallum (2002), Moravec (1998), Knight (1963, 1966, 1968), SPEC <http://www.spec.org>, and others. We relied on Nordhaus's benchmark of millions of computations per second (MCPS), to be consistent with his long-term trends. His analysis combined synthetic benchmarks in an attempt to mimic the increase over time in complexity of computing tasks.

Nordhaus estimated performance data for more than 200 different computers in the modern era (since 1946) ranging from the first vacuum tube machines, to the first identifiable personal computer (the Altair 8800), to the Cray 1 supercomputer, to modern day PCs and servers. Whenever possible we attached measured active power data to computers on Nordhaus's list, but where such data did not exist we did not attempt to estimate power use. Instead, we located or performed power measurements for computers not on Nordhaus's list and then estimated performance of those machines in MCPS by scaling using other published performance benchmarks, such as theoretical FLOPS, Composite Theoretical Performance (CTP), or the SPEC benchmarks associated with these machines. Following Nordhaus, we used SPEC benchmarks for scaling when data were available, but only half a dozen machines for which we had power data also had SPEC benchmarks associated with them. As discussed below, using CTP instead would have resulted in estimates for MCPS that were modestly different (between 8% smaller and 20% larger).

We chose to only include measured power data because the uncertainty associated with estimating power use is much greater than the uncertainties introduced by scaling the performance estimates. ¹ The main sources for measured power data were Weik (1955, 1961, 1964) for computers from 1946 through the early 1960s, Russell (1978) for the Cray 1 supercomputer, Roberson et al. (2002), Harris et al. (1988), and Lovins (1993) for PCs, and Koomey et al. (2009) for servers. We also conducted new measurements for recent desktops and two laptops and compiled additional measured data from researchers in the technology industry (these data are presented and described in Tables S2 and S3 and in the final complete analysis spreadsheets downloadable at <http://www.mediafire.com/file/az2h7b9q6puvaka/koomeycomputertrendsreleaseversion-v36.xlsx>.

Computations per kWh

To estimate computations per kWh we focus on the full load computational capacity and the active power for each machine, dividing the number of computations per hour by the number of kWh consumed over that same hour. That requires estimates of peak...