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{{Infobox scientist
[[image:systolic array.jpg|thumb|240px|A systolic array network in which each data processing unit (DPU) receives data from one or more input streams and/or other DPUs and sends data to one or more output streams and/or other DPUs]]
|name              = Ronald N. Bracewell
|image            =
|image_size      =
|caption          =
|birth_date        = {{Birth date|1921|07|22}}
|birth_place      = [[Sydney, New South Wales|Sydney]], [[New South Wales]], [[Australia]]
|death_date        = {{Death date and age|2007|08|12|1921|07|22}}
|death_place      = [[Stanford, California|Stanford]], [[California]], [[United States of America|USA]]
|residence        =
|citizenship      =
|nationality      = [[Australia]]n
|ethnicity        =
|field            = [[Physics|Physicist]]<br />[[Mathematics|Mathematician]]<br />[[Radio astronomy|Radio astronomer]]
|work_institutions = [[Commonwealth Scientific and Industrial Research Organisation|CSIRO]]<br />[[University of California, Berkeley]]<br />[[Stanford University]]
|alma_mater        = [[University of Sydney]]<br />[[University of Cambridge]] [[Sydney Boys High School]]
|doctoral_advisor  =
|doctoral_students =
|known_for        =
|author_abbrev_bot =
|author_abbrev_zoo =
|influences        =
|influenced        =
|prizes            = [[IEEE Heinrich Hertz Medal]] (1994)<br />Officer of the [[Order of Australia]] (1998)
|religion          =
|footnotes        =
}}
'''Ronald Newbold Bracewell''' [[Order of Australia|AO]] (July 22, 1921 &ndash; August 12, 2007) was the [[Lewis M. Terman]] Professor of Electrical Engineering, Emeritus of the Space, Telecommunications and Radioscience Laboratory at [[Stanford University]].


== Education ==
In [[computer architecture]], a '''systolic array''' is a pipe network arrangement of [[Data processing system|processing units]] called cells. It is a specialized form of [[parallel computing]], where cells (i.e. processors), compute data and store it independently of each other.


Bracewell was born in [[Sydney]], [[Australia]], in 1921, and educated at [[Sydney Boys High School]]. He graduated from the [[University of Sydney]] in 1941 with the B.Sc. degree in mathematics and physics, later receiving the degrees of B.E. (1943), and M.E. (1948) with first class honours, and while working in the Engineering Department became the President of the Oxometrical Society. During [[World War II]] he designed and developed microwave radar equipment in the Radiophysics Laboratory of the Commonwealth Scientific and Industrial Research Organisation, Sydney under the direction of [[Joseph Lade Pawsey|Joseph L. Pawsey]] and [[Edward George Bowen|Edward G. Bowen]] and from 1946 to 1949 was a research student at [[Sidney Sussex College]], [[Cambridge]], engaged in [[ionosphere|ionospheric]] research in the [[Cavendish Laboratory]], where he received his Ph.D. degree in physics under [[J. A. Ratcliffe]].
==Description==
A systolic array is composed of matrix-like rows of data processing units called cells. Data processing units ([[Data processing system|DPU]]s) are similar to [[central processing unit]]s ([[CPU]])s, (except for the usual lack of a [[program counter]],<ref>The Paracel GeneMatcher series of systolic array processors do have a program counter. More complicated algorithms are implemented as a series of simple steps, with shifts specified in the instructions.</ref> since operation is [[transport triggered architecture|transport-triggered]], i.e., by the arrival of a data object). Each cell shares the information with its neighbours immediately after processing. The systolic array is often rectangular where data flows across the array between neighbour DPUs, often with different data flowing in different directions. The data streams entering and leaving the ports of the array are generated by [[auto-sequencing memory]] units, ASMs. Each ASM includes a [[data counter]]. In [[embedded system]]s a data stream may also be input from and/or output to an external source.


== Career ==
An example of a systolic [[algorithm]] might be designed for [[matrix multiplication]]. One [[matrix (math)|matrix]] is fed in a row at a time from the top of the array and is passed down the array, the other matrix is fed in a column at a time from the left hand side of the array and passes from left to right. Dummy values are then passed in until each processor has seen one whole row and one whole column. At this point, the result of the multiplication is stored in the array and can now be output a row or a column at a time, flowing down or across the array.<ref>[http://web.cecs.pdx.edu/~mperkows/temp/May22/0020.Matrix-multiplication-systolic.pdf Systolic Array Matrix Multiplication]</ref>


From October 1949 to September 1954 Dr. Bracewell was a Senior Research Officer at the Radiophysics Laboratory of the [[CSIRO]], Sydney, concerned with very long wave propagation and [[radio astronomy]]. He then lectured in radio astronomy at the Astronomy Department of the [[University of California, Berkeley]] from September 1954 to June 1955 at the invitation of [[Otto Struve]], and at Stanford University during the summer of 1955, and joined the Electrical Engineering faculty at Stanford in December 1955.  
Systolic arrays are arrays of DPUs which are connected to a small number of nearest neighbour DPUs in a mesh-like topology. DPUs perform a sequence of operations on data that flows between them. Because the traditional systolic array synthesis methods have been practiced by algebraic algorithms, only uniform arrays with only linear pipes can be obtained, so that the architectures are the same in all DPUs. The consequence is, that only applications with regular data dependencies can be implemented on classical systolic arrays. Like [[SIMD]] machines, clocked systolic arrays compute in "lock-step" with each processor undertaking alternate  compute | communicate
phases. But systolic arrays with asynchronous handshake between DPUs are called ''wavefront arrays''.
One well-known systolic array is Carnegie Mellon University's [[iWarp]] processor, which has been manufactured by Intel. An iWarp system has a linear array processor connected by data buses going in both directions.


In 1974 he was appointed the first Lewis M. Terman Professor and Fellow in Electrical Engineering (1974–1979).  Though he retired in 1979, he continued to be active until his death.
==History==
The systolic array paradigm, data-stream-driven by data counters, is the counterpart of the [[von Neumann architecture|von Neumann paradigm]], instruction-stream-driven by a program counter. Because a systolic array usually sends and receives multiple data streams, and multiple data counters are needed to generate these data streams, it supports [[data parallelism]]. [[Systole (medicine)|The name]] derives from analogy with the regular pumping of blood by the heart.


== Contributions and honours ==
[[H. T. Kung]] and [[Charles E. Leiserson]] published the first paper describing systolic arrays in 1978; however, the first machine known to have used a similar technique was the [[Colossus computer|Colossus Mark II]] in 1944.


Professor Bracewell was a Fellow of the [[Royal Astronomical Society]] (1950), Fellow and life member of the [[Institute of Electrical and Electronic Engineers]] (1961), Fellow of the [[American Association for the Advancement of Science]] (1989), and was a Fellow with other significant societies and organisations.
==Applications==
''An application Example - Polynomial Evaluation''


For experimental contributions to the study of the ionosphere by means of very low frequency waves, Dr. Bracewell received the  Duddell Premium of the Institution of Electrical Engineers, London in 1952. In 1992 he was elected to foreign associate membership of the Institute of Medicine of the U.S. [[United States National Academy of Sciences|National Academy of Sciences]] (1992), the first Australian to achieve that distinction, for fundamental contributions to medical imaging. He was one of Sydney University's three honourees when alumni awards were instituted in 1992, with a citation for brain scanning, and was the 1994 recipient of the Institute of Electrical and Electronic Engineers' Heinrich Hertz medal for pioneering work in antenna [[aperture synthesis]] and image reconstruction as applied to radio astronomy and to computer-assisted tomography. In 1998 Dr. Bracewell was named Officer of the [[Order of Australia]] (AO) for service to science in the fields of radio astronomy and image reconstruction.
[[Horner's rule]] for evaluating a polynomial is:


At CSIRO Radiophysics Laboratory, work that in 1942-1945 was classified appeared in a dozen reports. Activities included design, construction, and demonstration of voice-modulation equipment for a 10&nbsp;cm magnetron (July 1943), a microwave triode oscillator at 25&nbsp;cm using cylindrical cavity resonators, equipment designed for microwave radar in field use (wavemeter, echo box, thermistor power meter, etc.) and microwave measurement technique. Experience with numerical computation of fields in cavities led, after the war, to a Master of Engineering degree (1948) and the definitive publication on step discontinuities in radial transmission lines (1954).
<math>
y = ( ... ( ( (a_n*x + a_{n-1})*x + a_{n-2})*x + a_{n-3})*x + ... + a_1)*x + a_0
</math>


While at the Cavendish Laboratory, Cambridge (1946–1950) Bracewell worked on observation and theory of upper atmospheric ionisation, contributing to experimental technique (1948), explaining solar effects (1949), and distinguishing two layers below the E-layer (1952), work recognised by the Duddell Premium.
A linear systolic array in which the processors are arranged in pairs:
one multiplies its input by <math>x</math> and passes the result to the right,
the next adds <math>a_j</math> and passes the result to the right:


At Stanford Professor Bracewell constructed a microwave spectroheliograph (1961), a large and complex radio telescope which produced daily temperature maps of the sun reliably for eleven years, the duration of a solar cycle.  The first [[radio telescope]] to give output automatically in printed form, and therefore capable of worldwide dissemination by teleprinter, its daily solar weather maps received acknowledgement from [[NASA]] for support of the first manned landing on the moon.
==Advantages and Disadvantages==
Pros
*Faster
*Scalable
Cons
*Expensive
*Highly specialized for particular applications
*Difficult to build


Many fundamental papers on restoration (1954–1962), [[interferometry]] (1958–1974) and reconstruction (1956–1961) appeared along with instrumental and observational papers. By 1961 the radio-interferometer calibration techniques developed for the [[spectroheliograph]] first allowed an antenna system, with 52" fan beam, to equal the angular resolution of the human eye in one observation. With this beam the components of [[Cygnus A]], spaced 100", were put directly in evidence without the need for repeated observations with variable spacing [[aperture synthesis]] interferometry.
==Implementations==
[[Cisco]] PXF network processor is internally organized as systolic array.<ref>http://www.cisco.com/en/US/prod/collateral/routers/ps133/prod_white_paper09186a008008902a.html</ref>


The nucleus of the extragalactic source [[Centaurus A]] was resolved into two separate components whose right ascensions were accurately determined with a 2.3-minute fan beam at 9.1&nbsp;cm.  Knowing that Centaurus A was composite, Bracewell used the 6.7-minute beam of the [[Parkes Observatory]] 64 m [[radiotelescope]] at 10&nbsp;cm to determine the separate declinations of the components and in so doing was the first to observe strong polarisation in an extragalactic source (1962), a discovery of fundamental significance for the structure and role of astrophysical magnetic fields. Subsequent observations made at Parkes by other observers with a 14-minute and wider beams at [[21 cm line|21 cm]] and longer wavelengths, though not resolving the components, were compatible with the <math>\lambda^2</math> dependence expected from Faraday rotation if magnetic fields were the polarising agent.
==See also==
*[[iWarp]] - Systolic Array Computer, VLSI, Intel/CMU
*[[WARP (systolic array)]] - Systolic Array Computer, GE/CMU


A second major radiotelescope (1971) employing advanced concepts to achieve an angular resolution of 18 seconds of arc was designed and built at Stanford and applied to both solar and galactic studies. The calibration techniques for this leading-edge resolution passed into general use in radio interferometry via the medium of alumni.
==Notes==
 
<references/>
Upon the discovery of the [[cosmic microwave background radiation|cosmic background radiation]]:
* a remarkable observational limit of 1.7 millikelvins, with considerable theoretical significance for cosmology, was set on the anisotropy in collaboration with Ph. D. student [[E.K. Conklin]] (1967), and was not improved on for many years
* the correct theory of a relativistic observer in a blackbody enclosure (1968) was given in the first of several papers by various authors obtaining the same result
* the absolute motion of the [[Sun]] at 308&nbsp;km/s through the cosmic background radiation was measured by Conklin in 1969, some years before independent confirmation.
 
With the advent of the space age, Bracewell became interested in [[celestial mechanics]], made observations of the radio emission from [[Sputnik 1]], and supplied the press with accurate charts predicting the path of Soviet satellites, which were perfectly visible, if you knew when and where to look. Following the puzzling performance of [[Explorer I]] in orbit, he published the first explanation (1958-9) of the observed spin instability of satellites, in terms of the Poinsot motion of a non-rigid body with internal friction. He recorded the signals from Sputniks I, II and III and discussed them in terms of the satellite spin, antenna polarisation, and propagation effects of the ionised medium, especially Faraday effect.
 
Later (1978, 1979) he invented a spinning, [[Nuller|nulling]], two-element infrared interferometer suitable for space-shuttle launching into an orbit near [[Jupiter]], with milliarcsecond resolution, that could lead to the discovery of [[Extrasolar planet|planets around stars other than the sun]].  This concept was elaborated in 1995 by Angel and Woolf, whose space-station version with four-element double nulling became the [[Terrestrial Planet Finder]] (TPF), NASA's candidate for imaging planetary configurations of other stars.<ref>''Scientific American'', April 1996</ref>
 
Imaging in astronomy led to participation in development of computer assisted x-ray tomography, where commercial scanners reconstruct tomographic images using the algorithm developed by Bracewell for radioastronomical reconstruction from fan-beam scans. This corpus of work has been recognized by the Institute of Medicine, an award by the [[University of Sydney]], and the Heinrich Hertz medal. Service on the founding editorial board of the ''Journal for Computer-Assisted Tomography'', to which he also contributed publications, and on the scientific advisory boards of medical instrumentation companies maintained Bracewell's interest in medical imaging, which became an important part of his regular graduate lectures on imaging, and forms an important part of his 1995 text on imaging.
 
Experience with the optics, mechanics and control of radiotelescopes led to involvement with solar thermophotovoltaic energy at the time of the energy crisis, including the fabrication of low-cost solid and perforated paraboloidal reflectors by hydraulic inflation.
 
Bracewell is also known for being the first to propose the use of autonomous [[interstellar]] [[space probes]] for communication between alien civilisations as an alternative to [[radio]] transmission dialogs. This hypothetical concept has been dubbed the [[Bracewell probe]] after its inventor.
 
=== Fourier analysis ===
 
As a consequence of relating images to [[Fourier analysis]], in 1983 he discovered a [[Discrete Hartley transform|new factorisation of the discrete Fourier transform]] matrix leading to a fast algorithm for spectral analysis. This method, which has advantages over the fast Fourier algorithm, especially for images, is treated in [[Hartley transform|The Hartley Transform]] (1986), in U.S. Patent 4,646,256 (1987, now in the public domain), and in over 200 technical papers by various authors that were stimulated by the discovery. Analogue methods of creating a Hartley transform plane first with light and later with microwaves were demonstrated in the laboratory and permitted the determination of electromagnetic phase by the use of square-law detectors.  A new elementary signal representation, the [[Chirplet transform]], was discovered (1991) that complements the Gabor elementary signal representations used in dynamic spectral analysis (with the property of meeting the bandwidth-duration minimum associated with the [[uncertainty principle]]). This advance opened a new field of adaptive dynamic spectra with wide application in information analysis.
 
=== Other interests ===
 
Professor Bracewell was interested in conveying an appreciation of the role of science in society to the public, in mitigating the effects of scientific illiteracy on public decision making through contact with alumni groups, and in liberal undergraduate education within the framework of the Astronomy Course Program and the Western Culture program in Values, Technology, Science and Society, in both of which he taught for some years.  He gave the 1996 Bunyan Lecture on ''The Destiny of Man''.
 
He was also interested in the trees of Stanford's campus and published a book about them. He also taught an undergraduate seminar titled I Dig Trees.<ref>{{cite web|url=http://trees.stanford.edu/ |title=Trees of Stanford |publisher=Trees.stanford.edu |date= |accessdate=2012-04-19}}</ref><ref>{{cite web|url=http://news-service.stanford.edu/news/2005/march30/trees-033005.html |title=More than 350 tree species on campus cataloged by professor in new book |publisher=News-service.stanford.edu |date=2005-03-30 |accessdate=2012-04-19}}</ref>
 
Bracewell was also a designer and builder of [[sundial]]s. He built one on the South side of the Terman Engineering Building. He built one at the home of his son, Mark Bracewell. He built another on the deck of professor John Linvill's house.
 
As his seminar "I Dig Trees" indicated, Dr. Bracewell was known for having a tremendously keen, intelligent sense of wry, science-infused humor.  One of his treasured family photos showed him sitting on the ground, legs akimbo, with a beer bottle in front of him that he had neatly balanced on one of its bottom edges—his proof that even that thin edge had 3 balance points.
 
==Selected publications==
 
*Bracewell, R.N. and Pawsey, J.L., ''Radio Astronomy'' (Oxford, 1955) ''(also translated into Russian and reprinted in China)''
*Bracewell, R.N., ''Radio Interferometry of Discrete Sources'' (Proceedings of the IRE, January 1958)
*Bracewell, Ronald N., ed., ''Paris Symposium on Radio Astronomy, IAU Symposium no. 9 and URSI Symposium no. 1, held 30 July 1958 &ndash; 6 August 1958'' (Stanford Univ. Press, Stanford, CA, 1959) ''(also translated into Russian)''
*Professor Bracewell translated ''Radio Astronomy'', by J.L. Steinberg and J. Lequeux, (McGraw-Hill, 1963) from French
*Bracewell, R.N., ''The Fourier Transform and Its Applications'' (McGraw-Hill, 1965, 2nd ed. 1978, revised 1986) ''(also translated into Japanese and Polish)''
*Bracewell, R.N., ''Trees on the Stanford Campus'' (Stanford: Samizdat, 1973)
*Bracewell, R.N., ''The Galactic Club: Intelligent Life in Outer Space'' (Portable Stanford: Alumni Association, 1974) ''(also translated into Dutch, Japanese, and Italian)''
*Bracewell, R.N., ''The Hartley Transform'' (Oxford University Press, 1986) ''(also translated into German and Russian)''
*Bracewell, R.N., ''Two-Dimensional Imaging'' (Prentice-Hall, 1995)
*Bracewell, R.N., ''Fourier Analysis and Imaging'' (Plenum, 2004)
 
*Bracewell, R.N., ''Trees of Stanford and Environs'' (Stanford Historical Society, 2005)
 
==Chapter contributions==
Bracewell has contributed chapters to:
 
*Textbook of Radar ''Microwave Transmission and Cavity Resonator Theory,'' ed. E.G. Bowen, 1946
*Advances in Astronautical Sciences ''Satellite Rotation,'' ed.  H. Jacobs, 1959
*The Radio Noise Spectrum ''Correcting Noise Maps for Beamwidth,'' ed. D.H. Menzel, 1960
*Modern Physics for the Engineer ''Radio Astronomy,'' ed. L. Ridenour and [[William Nierenberg|W. Nierenberg]], 1960
*Statistical methods in Radio Wave Propagation ''Antenna Tolerance Theory,'' ed. W.C. Hoffman, 1960
*Advances in Geophysics ''Satellite Studies of the Ionization in Space by Radio,'' ed. H.E. Landsberg, 1961 (O.K. Garriott and R.N.  Bracewell)
*Handbuch der Physik ''Radio Astronomy Techniques,'' ed. S. Flugge, 1962
*Encyclopedia of Electronics ''Extraterrestrial Radio Noise'', ed. C. Susskind, 1962
*Stars and Galaxies ''Radio Broadcasts from the Depths of Space,'' ed. T.L Page, 1962
*Radio Waves and Circuits ''Aerials and Data Processing,'' ed. S. Silver, 1963
*Light and Life in the Universe ''Life in the Galaxy,'' ed. S.T. Butler and H. Messel, 1964
*Encyclopædia Britannica ''Telescope, Radio'', 1967
*Vistas in Science ''The Microwave Sky,'' ed. David L. Arm, 1968
*Man in Inner and Outer Space ''The Sun (Five Chapters),'' ed. H. Messel and S.T. Butler, 1968
*Image Reconstruction from Projections: Implementation and Applications ''Image Reconstruction in Radio Astronomy,'' ed. G. Hermann, 1979
*Annual Review of Astronomy and Astrophysics ''Computer Image Processing,'' ed. G. Burbidge et al., 1979
*Energy for Survival ''How It All Began,'' ''Man the Lazy Animal,'' and ''Energy from Sunlight,'' ed. H. Messel, 1979
*Life in the Universe ''Manifestations of Advanced Civilizations,'' ed. J. Billingham, 1981
*Extraterrestrials: Where Are They? ''Preemption of the Galaxy by the First Advanced Civilization,'' ed. M.H. Hart and B. Zuckerman, 1982, 1995
*Transformations in Optical Signal Processing ''Fourier Inversion of Deficient Data,'' ed. W.T. Rhodes, J.R. Fienup and B.E.A. Saleh, 1984
*The Early Years of Radio Astronomy ''Early Work on Imaging Theory in Radio Astronomy,'' ed. W.T. Sullivan, III, 1984
*Indirect Imaging ''Inversion of Nonplanar Visibilities,'' ed. J.A. Roberts, 1984
*Fourier Techniques and Applications ''The Life of Joseph Fourier'' and ''Fourier Techniques and Applications,'' ed. J.F. Price, 1985
*Yearbook of Science and Technology ''Wavelets,'' 1996
*Encyclopedia of Applied Physics ''Fourier and Other Mathematical Transforms'' 1997
*[[Cornelius Lanczos]]&mdash;Collected Published Papers with Commentaries ''The Fast Fourier Transform'' and''Smoothing Data by Analysis and by Eye'' ed. W.R. Davis et al., 1999


==References==
==References==
{{reflist}}
{{More footnotes|date=April 2011}}
*H. T. Kung, C. E. Leiserson: Algorithms for VLSI processor arrays; in: C. Mead, L. Conway (eds.): Introduction to VLSI Systems; Addison-Wesley, 1979
*S. Y. Kung: VLSI Array Processors; Prentice-Hall, Inc., 1988
*N. Petkov: Systolic Parallel Processing; North Holland Publishing Co, 1992


==External links==
==External links==
*[http://www-star.stanford.edu/people/bracewell.html Stanford Web Profile]
*[http://www.iti.fh-flensburg.de/lang/papers/isa/index.htm ''Instruction Systolic Array (ISA)'']
*[http://news-service.stanford.edu/pr/2007/pr-bracewell-082207.html Stanford Death Notice]
* [http://ieeexplore.ieee.org/iel5/92/4292150/04292156.pdf 'A VLSI Architecture for Image Registration in Real Time' (Based on systolic array), Vol. 15, September 2007]
 
{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
| NAME              = Bracewell, Ronald
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION =
| DATE OF BIRTH    = 1921-07-22
| PLACE OF BIRTH    = [[Sydney, New South Wales|Sydney]], [[New South Wales]], [[Australia]]
| DATE OF DEATH    = 2007-08-12
| PLACE OF DEATH    = [[Stanford, California|Stanford]], [[California]], [[United States of America|USA]]
}}
{{DEFAULTSORT:Bracewell, Ronald}}
[[Category:1921 births]]
[[Category:2007 deaths]]
[[Category:Stanford University School of Engineering faculty]]
[[Category:Australian astronomers]]
[[Category:Australian physicists]]
[[Category:Officers of the Order of Australia]]
[[Category:Fellows of St Catherine's College, Oxford]]
[[Category:Fellows of the American Association for the Advancement of Science]]
[[Category:Fellow Members of the IEEE]]
[[Category:20th-century astronomers]]
[[Category:Alumni of Sidney Sussex College, Cambridge]]
[[Category:Search for extraterrestrial intelligence]]
[[Category:People educated at Sydney Boys High School]]


[[fr:Ronald Bracewell]]
{{DEFAULTSORT:Systolic Array}}
[[Category:Parallel computing]]
[[Category:Reconfigurable computing]]

Revision as of 14:29, 11 August 2014

A systolic array network in which each data processing unit (DPU) receives data from one or more input streams and/or other DPUs and sends data to one or more output streams and/or other DPUs

In computer architecture, a systolic array is a pipe network arrangement of processing units called cells. It is a specialized form of parallel computing, where cells (i.e. processors), compute data and store it independently of each other.

Description

A systolic array is composed of matrix-like rows of data processing units called cells. Data processing units (DPUs) are similar to central processing units (CPU)s, (except for the usual lack of a program counter,[1] since operation is transport-triggered, i.e., by the arrival of a data object). Each cell shares the information with its neighbours immediately after processing. The systolic array is often rectangular where data flows across the array between neighbour DPUs, often with different data flowing in different directions. The data streams entering and leaving the ports of the array are generated by auto-sequencing memory units, ASMs. Each ASM includes a data counter. In embedded systems a data stream may also be input from and/or output to an external source.

An example of a systolic algorithm might be designed for matrix multiplication. One matrix is fed in a row at a time from the top of the array and is passed down the array, the other matrix is fed in a column at a time from the left hand side of the array and passes from left to right. Dummy values are then passed in until each processor has seen one whole row and one whole column. At this point, the result of the multiplication is stored in the array and can now be output a row or a column at a time, flowing down or across the array.[2]

Systolic arrays are arrays of DPUs which are connected to a small number of nearest neighbour DPUs in a mesh-like topology. DPUs perform a sequence of operations on data that flows between them. Because the traditional systolic array synthesis methods have been practiced by algebraic algorithms, only uniform arrays with only linear pipes can be obtained, so that the architectures are the same in all DPUs. The consequence is, that only applications with regular data dependencies can be implemented on classical systolic arrays. Like SIMD machines, clocked systolic arrays compute in "lock-step" with each processor undertaking alternate compute | communicate phases. But systolic arrays with asynchronous handshake between DPUs are called wavefront arrays. One well-known systolic array is Carnegie Mellon University's iWarp processor, which has been manufactured by Intel. An iWarp system has a linear array processor connected by data buses going in both directions.

History

The systolic array paradigm, data-stream-driven by data counters, is the counterpart of the von Neumann paradigm, instruction-stream-driven by a program counter. Because a systolic array usually sends and receives multiple data streams, and multiple data counters are needed to generate these data streams, it supports data parallelism. The name derives from analogy with the regular pumping of blood by the heart.

H. T. Kung and Charles E. Leiserson published the first paper describing systolic arrays in 1978; however, the first machine known to have used a similar technique was the Colossus Mark II in 1944.

Applications

An application Example - Polynomial Evaluation

Horner's rule for evaluating a polynomial is:

A linear systolic array in which the processors are arranged in pairs: one multiplies its input by and passes the result to the right, the next adds and passes the result to the right:

Advantages and Disadvantages

Pros

  • Faster
  • Scalable

Cons

  • Expensive
  • Highly specialized for particular applications
  • Difficult to build

Implementations

Cisco PXF network processor is internally organized as systolic array.[3]

See also

Notes

  1. The Paracel GeneMatcher series of systolic array processors do have a program counter. More complicated algorithms are implemented as a series of simple steps, with shifts specified in the instructions.
  2. Systolic Array Matrix Multiplication
  3. http://www.cisco.com/en/US/prod/collateral/routers/ps133/prod_white_paper09186a008008902a.html

References

Template:More footnotes

  • H. T. Kung, C. E. Leiserson: Algorithms for VLSI processor arrays; in: C. Mead, L. Conway (eds.): Introduction to VLSI Systems; Addison-Wesley, 1979
  • S. Y. Kung: VLSI Array Processors; Prentice-Hall, Inc., 1988
  • N. Petkov: Systolic Parallel Processing; North Holland Publishing Co, 1992

External links