2016 ExponentialLawsofComputingGrowt

(Denning & Lewis, 2016) ⇒ Peter J. Denning, and Ted G. Lewis. (2016). “Exponential Laws of Computing Growth.” In: Communications of the ACM Journal, 60(1). doi:10.1145/2976758

Subject Headings: Moore's Law, Exponential IT Growth.

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Abstract

Moore's Law is one small component in an exponentially growing planetary computing ecosystem.

Key Insights

Exponential growth seems to be unique to computing and information technologies and their markets, stimulating continued economic, social, and political disruptions.
Exponential growth occurs simultaneously at all levels of the computing ecosystem - chips, systems, adopting communities.
Technology jumping sustains exponential growth as companies switch to new technologies when the current ones reach their points of diminishing return.

Introduction

In a forecasting exercise, Gordon Earle Moore, co-founder of Intel, plotted data on the number of components — transistors, resistors, and capacitors — in chips made from 1959 to 1965. He saw an approximate straight line on log paper (see Figure 1). Extrapolating the line, he speculated that the number of components would grow from 26 in 1965 to 216 in 1975, doubling every year. His 1965–1975 forecast came true. In 1975, with more data, he revised the estimate of the doubling period to two years. In those days, doubling components also doubled chip speed because the greater number of components could perform more powerful operations and smaller circuits allowed faster clock speeds. Later, Moore's Intel colleague David House claimed the doubling time for speed should be taken as 18 months because of increasing clock speed, whereas Moore maintained that the doubling time for components was 24 months. But clock speed stabilized around 2000 because faster speeds caused more heat dissipation than chips could withstand. Since then, the faster speeds are achieved with multi-core chips at the same clock frequency.

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The three kinds of exponential growth, as noted — doubling of components, speeds, and technology adoptions — have all been lumped under the heading of Moore's Law. Because the original Moore's Law applies only to components on chips, not to systems or families of technologies, other phenomena must be at work. We will use the term "Moore's Law" for the component-doubling rule Moore proposed and "exponential growth" for all the other performance measures that plot as straight lines on log paper. What drives the exponential growth effect? Can we continue to expect exponential growth in the computational power of our technologies?

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Conclusion

The original 1965 Moore's Law was an empirical observation that component density on a computer chip doubled every two years. Similar doubling rates have been observed in chip speeds, computer speeds, and computations per unit of energy. However, the durability of these technology forecasts suggests deeper phenomena.

We have argued that exponential growth would not have succeeded without sustained exponential growth at three levels of the computing ecosystem — chip, system, and adopting community. Growth (progress) feeds on itself up to the inflection point. Diminishing returns then set in, signaling the need to jump to another technology, system design, or class of application or community.

At the chip level, there are strong economic motivations for chip companies and their engineers to feed on previous improvements, building faster chips that grow exponentially up to the inflection point. The first significant technology path for exponential chip growth appeared in the form of Dennard scaling, which showed how to reduce component dimension without increasing power density. Dennard scaling reached an inflection point in the 1990s due to heat-dissipation problems that limited clock speed to approximately 3.5Ghz. Engineers responded with a technology jump to multicore chips, which gave speedup through parallelism. This jump has been enormously effective. Cloud platforms and supercomputers achieve high computation rates through massive parallelism among many chips.

A major technology barrier to chip growth has been the distribution of clock signals to all components on a chip. The theoretically most efficient distribution mechanism is the space-filling fractal H-tree that reaches diminishing returns when the tree itself starts to consume most of the physical space on the chip. Engineers are experimenting with hybrids that feature subsystems (such as cores) with their own clocks interacting via asynchronous signaling. Some engineers have been exploring the design of all-asynchronous circuits (no clocks), but these systems cannot yet compete in speed with clocked systems.

Engineers have been systematically examining the barriers that prevent the continuation of Moore's Law for CMOS technologies. As alternatives mature, it will be feasible to jump to the new technologies and continue the exponential growth. Although there is controversy about how successful some of the alternatives may be, there is considerable optimism that some will work out and exponential growth can continue with new base technologies.

When chips and other components are assembled into complete computer systems, engineers have located and relieved technology bottlenecks that would prevent the systems from scaling up in speed as fast as their component chips scale. Koomey's Laws document exponential growth of computations per computer and per unit of energy from 1946 to 2009. Koomey's Law for computations per unit of energy is especially important throughout an energy-constrained industry. Additionally, the technology jump from algorithm parallelism to data parallelism further assures us we can grow systems performance as long as the workloads have sufficient parallelism, which has turned out to be the case for cloud and supercomputing systems.

Finally, we demonstrated that simple assumptions about adoption process lead to the S-curve model in which adoptions grow exponentially until an inflection point and then slow down because of market saturation. Business leaders use the S-curve model to guide them in jumping to new technologies when the older ones start to encounter their limits. Exponential growth in sales through ever-expanding applications and communities provides the financial stimulus to advance the chip-and system-level technologies (Rock's Law). It is a complete cycle.

These analyses show that the conditions exist at all three levels of the computing ecosystem to sustain exponential growth. They support the optimism of many engineers that many additional years of exponential growth are likely. Moore's Law was sustained for five decades. Exponential growth is likely to be sustained for many more.

References

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	Author	volume	Date Value	title	type	journal	titleUrl	doi	note	year
2016 ExponentialLawsofComputingGrowt	Peter J. Denning Ted G. Lewis			Exponential Laws of Computing Growth				10.1145/2976758		2016