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\begin{document}

Name: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

Directions: {\bf \Large Work only on this sheet} (on both sides, if
needed); do not turn in any supplementary sheets of paper. There is
actually plenty of room for your answers, as long as you organize
yourself BEFORE starting writing.

{\bf \Large Unless otherwise stated, give numerical answers as
expressions, e.g. $\frac{2}{3} \times 6 - 1.8$.  Do NOT use
calculators.}

{\bf 1.} Consider a six-dimensional hypercube $D$, subdivided into two
five-dimensional hypercubes $D_0$ and $D_1$.

\begin{itemize}

\item [(a)] () What is the node number of the partner of node 23?

\item [(b)] () What is the node number of the root in $D_1$?

\item [(c)] () Suppose our algorithm requires partners in the two
5-cubes to exchange their values of an {\bf int} variable {\bf x}.
What would be the best MPI function for this purpose?

\end{itemize}

{\bf 2.} Consider the program on pp.85-87.

\begin{itemize}

\item [(a)] () Suppose that while running the program, someone runs the
shell commands {\bf ps} and {\bf gdb}.  At this point, the likely line
number on which the program is running (at all nodes) is
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.

\item [(b)] () Fill in the table regarding the actions of lines 107 and
108 and the array {\bf overallmin}, at a given node.  Mark an entry R if the
array is read, W if it is RW if both, and N if neither:

\begin{tabular}{|r|r|r|}
\hline
node number & 107 & 108 \\ \hline 
0 & \  & \  \\ \hline 
$\neq$ 0 & \  & \  \\ \hline 
\end{tabular}

\item [(c)] () This example program is somewhat artificial, in that each
node generates its data matrix {\bf ohd}.  Instead, say that node 0 has
the matrix, say by reading it from disk, and wishes to distribute it to
the other nodes.  Give a single line of code that would replace lines
57-64, that would accomplish this distribution.

\end{itemize}

{\bf Solutions:}

{\bf 1a.}  23 + 32 = 55

{\bf 1b.} 100000, i.e. 32

{\bf 1c.} {\bf  MPI\_Sendrecv() }

{\bf 2a.} 70

{\bf 2b.}

\begin{tabular}{|r|r|r|}
\hline
node number & 107 & 108 \\ \hline 
0 & W & R \\ \hline 
$\neq$ 0 & N & W \\ \hline 
\end{tabular}

{\bf 2c.}

\begin{Verbatim}[fontsize=\relsize{-2}]
MPI_Bcast(ohd,nv*nv,MPI_INT,0,MPI_COMM_WORLD);
\end{Verbatim}

\end{document}