Koomey's law describes a trend in the

history of computing hardware The history of computing hardware spans the developments from early devices used for simple calculations to today's complex computers, encompassing advancements in both analog and digital technology. The first aids to computation were purely mec ...

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

joule The joule ( , or ; symbol: J) is the unit of energy in the International System of Units (SI). In terms of SI base units, one joule corresponds to one kilogram- metre squared per second squared One joule is equal to the amount of work d ...

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 Transistor count, number of transistors in an integrated circuit (IC) doubles about every two years. Moore's law is an observation and Forecasting, projection of a historical trend. Rather than a law of ...

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

Dennard scaling In semiconductor electronics, 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 vol ...

, the ability to build smaller transistors with constant

power density Power density, defined as the amount of power (the time rate of energy transfer) per unit volume, is a critical parameter used across a spectrum of scientific and engineering disciplines. This metric, typically denoted in watts per cubic meter ...

. "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 Ame ...

'' 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 and published 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''. In 2010, ''IEEE Spe ...

''. It was further discussed in ''

MIT Technology Review ''MIT Technology Review'' is a bimonthly magazine wholly owned by the Massachusetts Institute of Technology. It was founded in 1899 as ''The Technology Review'', and was re-launched without "''The''" in its name on April 23, 1998, under then pu ...

,'' and in a post by

Erik Brynjolfsson Erik Brynjolfsson 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 the Digital Economy Lab at the Stanford Institute for Human-Centered AI ...

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

The Economist ''The Economist'' is a British newspaper published weekly in printed magazine format and daily on Electronic publishing, digital platforms. It publishes stories on topics that include economics, business, geopolitics, technology and culture. M ...

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 metal–oxide–semiconductor (MOS) integrated circuit chips. ...

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 multinational semiconductor company headquartered in Dallas, Texas. It is one of the top 10 semiconductor companies worldwide based on sales volume. The company's focus is on developing analog ...

. 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 Energy efficiency may refer to: * Energy efficiency (physics), the ratio between the useful output and input of an energy conversion process ** Electrical efficiency, useful power output per electrical power consumed ** Mechanical efficiency, a rat ...

." By the

second law of thermodynamics The second law of thermodynamics is a physical law based on Universal (metaphysics), universal empirical observation concerning heat and Energy transformation, energy interconversions. A simple statement of the law is that heat always flows spont ...

and

Landauer's principle Landauer's principle is a physical principle pertaining to a lower theoretical limit of energy consumption of computation. It holds that an irreversible change in information stored in a computer, such as merging two computational paths, dissipa ...

, 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 every step of the process is time-reversible. This means that, given the output of a computation, it's possible to perfectly reconstruct the input. In systems that progress deterministica ...

. This, in conjunction with other

Beyond CMOS Beyond CMOS refers to the possible future digital logic technologies beyond the scaling limits of CMOS technology. which limits device density and speeds due to heating effects. ''Beyond CMOS'' is the name of one of the 7 focus groups in ITRS 2 ...

computing technologies, could permit continued advances in efficiency.

Implications

History

Slowing and end of Koomey's law

See also

References

Further reading