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Space and time trade-offs in advanced computing

Posted: 22 Mar 2013 ?? ?Print Version ?Bookmark and Share

Keywords:personal computing? 3D transistors? FinFETs? electronic keys?

On the supply side, battery technology has been improving slowly; Lithium-ion and lithium-ion-polymer technologies continue to be the choice for most portable electronics, due to advantages in energy density (weight), high voltage, no memory effect, and flexibility of manufacturing in custom sizes. But energy capacity has improved slowly over time, around 8% year over year, which is nearly constant compared to the exponential growth in microelectronics capacities and performance seen through Moore's Law. As a result, the major advances that have enabled today's mobile computers have been on the "demand" sidedoing more with less.

"Low power design"building integrated circuits that consume far less energy, has been a focus in the chip design industry for only about a decade, but the results have been spectacular. From advancements in architectural design, to logical and physical implementation optimisations, all the way to fundamental changes in device fabrication, including recent moves to 3D transistors, or FinFETs, power-efficient design and verification techniques have rippled through every facet of integrated circuit design.

Limits of optimisation
Whether it's space (volume or memory), time (performance), power, or communications, for every parameter that we optimise, the question that arises is, "how much is enough?" Can we build a chip (or an app) that is too fast or too small? Probably not, but any given application requires a certain amount of processing, and at some point additional speed is wasted (this is the law of diminishing returns).

For example, digital audio standards developed 30 years ago were defined based on the limits of human hearing, and even though we could easily increase both the sampling rate and resolution today, attempts to do so have largely failed commercially, indicating that the original solution was complete, and well-defined. In fact, most music today is stored in compressed form (mp3), indicating that storage space is still at a premium compared to the incremental audio fidelity.

Similarly, the march towards "smallness" for smartphones seems to already have reached its inflection point. Given the applications that have become requirements for our latest personal computers such as web browsing and movie watching, a 3.5" to 4" screen seems to be the minimum acceptable size, and some "size rebound" has already begun, which is heating up the market for small tablets as well.

On the digital video side, however, we are just getting to the point where "high-definition" video and "retina displays" challenge our ability to discern the incremental quality level. And given the enormous amount of storage required to store high-resolution video, this application will be on the optimisation target list for some time.

Note that in each of these cases, the practical limit of optimisation is related to the human interface; there's no need to produce better audio than can be heard, nor higher resolution video than can be seen. Similarly, web browsers must respond at a humanly acceptable rate; and interactive programs and games must refresh fast enough for feedback to human input, but faster than that doesn't get any extra credit.

In Computer Science, time and space are the classic trade-off. We can compute a complex result each time it's needed, or store the result for instant access on successive computations. This basic idea can be used to improve the speed of algorithms for everything from computer system design (memory caching), integrated circuit design optimisation (synthesis), to searching and indexing the internet itself.

For today's mobile computers, time and space are just the beginning. With the additional parameter of power, plus the requirement of wireless communication, which also has a significant and sometimes dominant impact on power, te solution space is multi-dimensional, and extremely complex.

Watching a movie on a tablet is a simple, common application. In a simple experiment, viewing a locally stored, 2GB movie (2.1 hours) used about 11.9Wh of energy on a 3rd generation iPad with retina display. Streaming the same movie from the cloud required 14.9Wh of energy, but the quality of the video in the 138MB version was only "adequate". To get to a "nice" level of video, the file size was increased to 1.1GB, and streaming the movie now required 17.4Wh of energy (and also required an average data transmission rate of over 1.2Mbps). So, to save 2GB of local storage on the device, the energy cost is 550mWh for each viewing, plus the dollar cost of transmitting 1.1GB of data. Over a cellular connection, the transmission cost itself nearly justifies the cost of additional storage, but in the case of a WiFi connection the incremental cost is much smaller.

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