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[[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]]
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.


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.
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==Description==
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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.


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>
'''MathML'''
:<math forcemathmode="mathml">E=mc^2</math>


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
<!--'''PNG''' (currently default in production)
phases. But systolic arrays with asynchronous handshake between DPUs are called ''wavefront arrays''.
:<math forcemathmode="png">E=mc^2</math>
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==
'''source'''
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.
:<math forcemathmode="source">E=mc^2</math> -->


[[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.
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].


==Applications==
==Demos==
''An application Example - Polynomial Evaluation''


[[Horner's rule]] for evaluating a polynomial is:
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:


<math>
y = ( ... ( ( (a_n*x + a_{n-1})*x + a_{n-2})*x + a_{n-3})*x + ... + a_1)*x + a_0
</math>


A linear systolic array in which the processors are arranged in pairs:
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one multiplies its input by <math>x</math> and passes the result to the right,
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
the next adds <math>a_j</math> and passes the result to the right:
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


==Advantages and Disadvantages==
==Test pages ==
Pros
*Faster
*Scalable
Cons
*Expensive
*Highly specialized for particular applications
*Difficult to build


==Implementations==
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
[[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>
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*[[Help:Formula]]


==See also==
*[[Inputtypes|Inputtypes (private Wikis only)]]
*[[iWarp]] - Systolic Array Computer, VLSI, Intel/CMU
*[[Url2Image|Url2Image (private Wikis only)]]
*[[WARP (systolic array)]] - Systolic Array Computer, GE/CMU
==Bug reporting==
 
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .
==Notes==
<references/>
 
==References==
{{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==
*[http://www.iti.fh-flensburg.de/lang/papers/isa/index.htm ''Instruction Systolic Array (ISA)'']
* [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]
 
{{DEFAULTSORT:Systolic Array}}
[[Category:Parallel computing]]
[[Category:Reconfigurable computing]]

Latest revision as of 22:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML

E=mc2


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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