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      <title>By thiamchunkoh</title>
      <description><![CDATA[ parallelism without really knowing what they're talking about. I can't tell you how many articles and books I've read on parallel computing that use the term over and over without ever defining it. Many of these “authoritative” sources cite Amdahl's Law (1), originally proffered by Gene Amdahl in 1967, but they seem blissfully unaware of the more general and precise quantification of parallelism provided by theoretical computer science.  Amdahl's Law and see what it says and what it doesn't say. Amdahl made what amounts to the following observation. Suppose that 50% of a computation can be parallelized and 50% can't. Then, even if the 50% that is parallel took no time at all to execute, the total time is cut at most in half, leaving a speedup of less than 2. In general, if a fraction p of a computation can be run in parallel and the rest must run serially, Amdahl's Law upper-bounds the speedup by 1/(1–p).  We can use the dag model for multithreading...The dag model views the execution of a multithreaded program as a set of instructions (the vertices of the dag) with graph edges indicating dependences between instructions. We say that an instruction x precedes an instruction y, sometimes denoted x ? y, if x must complete before y can begin. In a diagram for the dag, x ? y means that there is a positive-length path from x to y. If neither x ? y nor y ? x, we say the instructions are in parallel, denoted x ? y. The Work Law holds, because in our model, each processor executes at most 1 instruction per unit time, and hence P processors can execute at most P instructions per unit time. Thus, to do all the work on P processors, it must take at least T1/P time.
We can interpret the Work Law in terms of speedup. Using our notation, the speedup on P processors is just T1/TP, which is how much faster the application runs on P processors than on 1 processor. Rewriting the Work Law, we obtain T1/TP = P, which is to say that the speedup on P processors can be at most P. If the application obtains speedup proportional to P, we say that the speedup is linear. If it obtains speedup exactly P (which is the best we can do in our model), we say that the application exhibits perfect linear speedup. If the application obtains speedup greater than P (which can't happen in our model due to the work bound, but can happen in models that incorporate caching and other processor effects), we say that the application exhibits superlinear speedup.
This path is sometimes called the critical path of the dag, and span is sometimes referred to in the literature as critical-path length. Since the span is the theoretically fastest time the dag could be executed on a computer with an infinite number of processors (assuming no overheads for communication, scheduling, etc.), we denote it by T8. 
Like work, Law on P-processor execution time
is given above and refrences to it as a computational models. ]]></description>
      <link>http://software.intel.com/en-us/articles/what-the-is-parallelism-anyhow-1/#comment-37659</link>
      <pubDate>Sun, 03 Jan 2010 17:56:24 -0800</pubDate>
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    <item>
      <title>By Projection programming, the future of software development? &amp;laquo; Idémaskinen</title>
      <description><![CDATA[ n/a ]]></description>
      <link>http://software.intel.com/en-us/articles/what-the-is-parallelism-anyhow-1/#comment-47655</link>
      <pubDate>Thu, 19 Aug 2010 15:10:49 -0700</pubDate>
      <guid isPermaLink="true">http://software.intel.com/en-us/articles/what-the-is-parallelism-anyhow-1/#comment-47655</guid>
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      <title>By Quel est le futur des logiciels ? Une explosion encore croissante ? | Simply GreenIT</title>
      <description><![CDATA[ n/a ]]></description>
      <link>http://software.intel.com/en-us/articles/what-the-is-parallelism-anyhow-1/#comment-54444</link>
      <pubDate>Wed, 05 Jan 2011 04:20:22 -0800</pubDate>
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    <item>
      <title>By Aater Suleman</title>
      <description><![CDATA[ Nice blog. I particularly enjoyed the Span and Work. 

As far as Amdahl's law is concerned, there are a lot of issues with the law. It is too simplistic to be useful. I would live with it if the real models were super complicated bu t they are not. Like Patrick points out, it wasn't created by Amdahl's himself. 
 ]]></description>
      <link>http://software.intel.com/en-us/articles/what-the-is-parallelism-anyhow-1/#comment-61136</link>
      <pubDate>Sun, 26 Jun 2011 01:18:58 -0700</pubDate>
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