parallprefix.html

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<H1>parallel prefix computation</H1>
<P>
(algorithm)

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<strong>Definition:</strong>
Calculate a function, f, on all prefixes of an n-element array, that is, s[0], f(s[0], s[1]), f(s[0], f(s[1], s[2])),  ..., f(s[0],  ... f(s[n-2], s[n-1]) ...),  using <a href="theta.html" tppabs="http://hissa.nist.gov/dads/HTML/theta.html"><em> <img src="Theta-1.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/Theta.gif"  border=0 height=10 width=8  alt="Capital Theta">(n)</em></a> processors in  <img src="Theta-1.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/Theta.gif"  border=0 height=10 width=8  alt="Capital Theta">( log n) time. The algorithm is <br> for j := 0 to lg(n-1) do <br> &nbsp;&nbsp;&nbsp;&nbsp;for i := 2<sup>j</sup> to n-1 parallel-do<br> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; s[i] := f(s[i-2<sup>j</sup>], s[i]) <br> where lg is the logarithm base 2, and parallel-do does the innermost computations in parallel.  The function must be <a href="associative.html" tppabs="http://hissa.nist.gov/dads/HTML/associative.html"><em>associative</em></a>.
<P><em>Note:
In particular, this calculates any associative function, such as sum, maximum, or concatenate, over a list of values in <a href="logarithmic.html" tppabs="http://hissa.nist.gov/dads/HTML/logarithmic.html"><em>logarithmic</em></a> time.  Since this overwrites the initial values, the n processors can copy input values to a working array in parallel in one additional step.<br> From Yair Tuaff (r56409@email.sps.mot.com), 29 December 1999.</em>
<P>Author: <a href="terms.html#authorPEB" tppabs="http://hissa.nist.gov/dads/terms.html#authorPEB">PEB</a>

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Entry modified Wed Dec 29 14:01:48 1999.<BR>
HTML page formatted Wed Dec 29 14:02:13 1999.

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