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📁 Design and building parallel program
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<B> Next:</B> <A NAME=tex2html3450 HREF="node122.html" tppabs="http://www.dit.hcmut.edu.vn/books/system/par_anl/node122.html"> Chapter Notes</A>
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<H1><A NAME=SECTION04250000000000000000> Exercises</A></H1>
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An application running on <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img1110.gif" tppabs="http://www.dit.hcmut.edu.vn/books/system/par_anl/img1110.gif"> processors consumes <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img1111.gif" tppabs="http://www.dit.hcmut.edu.vn/books/system/par_anl/img1111.gif"> random
numbers per second per processor.  For how long can the application
execute before it exhausts all available numbers, assuming that the
leapfrog method is applied to the linear congruential generator of
Equation <A HREF="node117.html#eqrand2" tppabs="http://www.dit.hcmut.edu.vn/books/system/par_anl/node117.html#eqrand2">10.3</A> on a 32-bit machine?  A 64-bit machine?
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A Monte Carlo simulation must perform <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img1112.gif" tppabs="http://www.dit.hcmut.edu.vn/books/system/par_anl/img1112.gif"> independent trials.  How
many random numbers can be employed in each trial without duplication,
assuming that the modified leapfrog method is applied to the linear
congruential generator of Equation <A HREF="node117.html#eqrand" tppabs="http://www.dit.hcmut.edu.vn/books/system/par_anl/node117.html#eqrand">10.1</A> on a 32-bit machine?
A 64 bit machine?
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Monte Carlo integration techniques are sometimes to compute integrals
of high dimension. They approximate the <b>r</b>-dimensional integral
<P><IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img1113.gif" tppabs="http://www.dit.hcmut.edu.vn/books/system/par_anl/img1113.gif"><P>
of a function <b>f</b> as
<P><IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img1114.gif" tppabs="http://www.dit.hcmut.edu.vn/books/system/par_anl/img1114.gif"><P>
where each <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img1115.gif" tppabs="http://www.dit.hcmut.edu.vn/books/system/par_anl/img1115.gif"> is an <em> r</em>
-vector of random values.  Design
and implement a parallel algorithm for this method, and use it to
compute the one-dimensional integral
<P><IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img1116.gif" tppabs="http://www.dit.hcmut.edu.vn/books/system/par_anl/img1116.gif"><P>
Measure and account for the performance of the parallel program as a
function of <em> N</em>
 and P.
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<B> Next:</B> <A NAME=tex2html3450 HREF="node122.html" tppabs="http://www.dit.hcmut.edu.vn/books/system/par_anl/node122.html"> Chapter Notes</A>
<B>Up:</B> <A NAME=tex2html3448 HREF="node116.html" tppabs="http://www.dit.hcmut.edu.vn/books/system/par_anl/node116.html">10 Random Numbers</A>
<B> Previous:</B> <A NAME=tex2html3442 HREF="node120.html" tppabs="http://www.dit.hcmut.edu.vn/books/system/par_anl/node120.html">10.4 Summary</A>
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<I>&#169 Copyright 1995 by <A href="msgs0.htm#6" tppabs="http://www.dit.hcmut.edu.vn/books/system/par_anl/tppmsgs/msgs0.htm#6">Ian Foster</a></I>
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