Koomey's law describes a trend in the

history of computing hardware The history of computing hardware covers the developments from early simple devices to aid calculation to modern day computers. Before the 20th century, most calculations were done by humans. The first aids to computation were purely mechan ...

: for about a half-century, the number of computations per

joule The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force applied ...

of energy dissipated doubled about every 1.57 years. Professor Jonathan Koomey described the trend in a 2010 paper in which he wrote that "at a fixed computing load, the amount of battery you need will fall by a factor of two every year and a half.". This trend had been remarkably stable since the 1950s ( ''R''² of over 98%). But in 2011, Koomey re-examined this data and found that after 2000, the doubling slowed to about once every 2.6 years. This is related to the slowing of

Moore's law Moore's law is the observation that the number of transistors in a dense integrated circuit (IC) doubles about every two years. Moore's law is an observation and projection of a historical trend. Rather than a law of physics, it is an empir ...

, the ability to build smaller transistors; and the end around 2005 of

Dennard scaling Dennard scaling, also known as MOSFET scaling, is a scaling law which states roughly that, as transistors get smaller, their power density stays constant, so that the power use stays in proportion with area; both voltage and current scale (downward) ...

, the ability to build smaller transistors with constant

power density Power density is the amount of power (time rate of energy transfer) per unit volume. In energy transformers including batteries, fuel cells, motors, power supply units etc., power density refers to a volume, where it is often called volume p ...

. "The difference between these two growth rates is substantial. A doubling every year and a half results in a 100-fold increase in efficiency every decade. A doubling every two and a half years yields just a 16-fold increase", Koomey wrote.

Implications

The implications of Koomey's law are that the amount of battery needed for a fixed computing load will fall by a factor of 100 every decade. As computing devices become smaller and more mobile, this trend may be even more important than improvements in raw processing power for many applications. Furthermore, energy costs are becoming an increasing factor in the economics of data centers, further increasing the importance of Koomey's law. The slowing of Koomey's law has implications for energy use in information and communications technology. However, because computers do not run at peak output continuously, the effect of this slowing may not be seen for a decade or more. Koomey writes that "as with any exponential trend, this one will eventually end...in a decade or so, energy use will once again be dominated by the power consumed when a computer is active. And that active power will still be hostage to the physics behind the slowdown in Moore's Law."

History

Koomey was the lead author of the article in ''

IEEE Annals of the History of Computing The ''IEEE Annals of the History of Computing'' is a quarterly peer-reviewed academic journal published by the IEEE Computer Society. It covers the history of computing, computer science, and computer hardware. It was founded in 1979 by the AFIPS ...

'' that first documented the trend. At about the same time, Koomey published a short piece about it in ''

IEEE Spectrum ''IEEE Spectrum'' is a magazine edited by the Institute of Electrical and Electronics Engineers. The first issue of ''IEEE Spectrum'' was published in January 1964 as a successor to ''Electrical Engineering''. The magazine contains peer-revie ...

''. It was further discussed in ''

MIT Technology Review ''MIT Technology Review'' is a bimonthly magazine wholly owned by the Massachusetts Institute of Technology, and editorially independent of the university. It was founded in 1899 as ''The Technology Review'', and was re-launched without "The" in ...

,'' and in a post by

Erik Brynjolfsson Erik Brynjolfsson (born 1962) is an American academic, author and inventor. He is the Jerry Yang and Akiko Yamazaki Professor and a Senior Fellow at Stanford University where he directs thDigital Economy Labat the Stanford Institute for Human-Cen ...

on the "Economics of Information" blog, and at ''

The Economist ''The Economist'' is a British weekly newspaper printed in demitab format and published digitally. It focuses on current affairs, international business, politics, technology, and culture. Based in London, the newspaper is owned by The Econo ...

online''. The trend was previously known for

digital signal processor A digital signal processor (DSP) is a specialized microprocessor chip, with its architecture optimized for the operational needs of digital signal processing. DSPs are fabricated on MOS integrated circuit chips. They are widely used in audio si ...

s, and it was then named "Gene's law". The name came from Gene Frantz, an electrical engineer at

Texas Instruments Texas Instruments Incorporated (TI) is an American technology company headquartered in Dallas, Texas, that designs and manufactures semiconductors and various integrated circuits, which it sells to electronics designers and manufacturers globall ...

. Frantz had documented that power dissipation in DSPs had been reduced by half every 18 months, over a 25-year period.

Slowing and end of Koomey's law

Latest studies indicate that Koomey's Law has slowed to doubling every 2.6 years. This rate is a statistical average over many technologies and many years, but there are exceptions. For example in 2020 AMD reported that, since 2014, the company has managed to improve the efficiency of its mobile processors by a factor of 31.7, which is a doubling rate of 1.2 years. In June 2020, Koomey responded to the report, writing, "I have reviewed the data and can report that AMD exceeded the 25×20 goal it set in 2014 through improved design, superior optimization, and a laser-like focus on energy efficiency." By the

second law of thermodynamics The second law of thermodynamics is a physical law based on universal experience concerning heat and Energy transformation, energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects ( ...

and

Landauer's principle Landauer's principle is a physical principle pertaining to the lower theoretical limit of energy consumption of computation. It holds that "any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two ...

, irreversible computing cannot continue to be made more energy efficient forever. Assuming that the energy efficiency of computing will continue to double every 2.6 years, and taking the most efficient super computer as of 2022, the Landauer bound will be reached around 2080. Thus, after this point, Koomey's law can no longer hold. Landauer's principle, however, does not constrain the efficiency of

reversible computing Reversible computing is any model of computation where the computational process, to some extent, is time-reversible. In a model of computation that uses deterministic transitions from one state of the abstract machine to another, a necessary c ...

. This, in conjunction with other ''beyond CMOS'' computing technologies, could permit continued advances in efficiency.

Implications

History

Slowing and end of Koomey's law

See also

References

Further reading