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Generalize team split 2D example for any # of PEs #13

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Generalize team split 2D example for any # of PEs #13

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100 changes: 48 additions & 52 deletions content/shmem_team_split_2d.tex
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Expand Up @@ -146,100 +146,96 @@
\apicexample
{The following example demonstrates the use of 2D Cartesian split in a
\Cstd[11] program. This example shows how multiple 2D splits can be used
to generate a 3D Cartesian split. This method can be extrapolated to
generate splits of any number of dimensions.}
to generate a 3D Cartesian split.}
{./example_code/shmem_team_split_2D.c}
{
The example above splits \LibHandleRef{SHMEM\_TEAM\_WORLD} into a 3D team
with dimensions 3x4xN. For example, if \VAR{npes} = 16, \VAR{xdim} = 3,
and \VAR{ydim} = 4, then the final dimensions are 3x4x2. In this case, the
first split of \LibHandleRef{SHMEM\_TEAM\_WORLD} results in 6 \VAR{xteams}
and 3 \VAR{yzteams}:
with dimensions \VAR{xdim}, \VAR{ydim}, and \VAR{zdim}, where each
dimension is calculated using the functions, \FUNC{find\_xy\_dims} and
\FUNC{find\_xyz\_dims}. When running with 12 \acp{PE}, the dimensions
are 3x2x2, respectively, and the first split of
\LibHandleRef{SHMEM\_TEAM\_WORLD} results in 4 \VAR{xteams} and 3
\VAR{yzteams}:

\begin{center}
\begin{tabular}{|l|l|l|l|l|}
\hline
\multicolumn{2}{|c|}{} & \multicolumn{3}{c|}{\VAR{yzteam}} \\ \cline{3-5}
\multicolumn{2}{|c|}{} & \VAR{x} = 0 & \VAR{x} = 1 & \VAR{x} = 2 \\ \hline
\multirow{6}{*}{\VAR{xteam}} & \VAR{yz} = 0 & 0 & 1 & 2 \\ \cline{2-5}
\multirow{4}{*}{\VAR{xteam}} & \VAR{yz} = 0 & 0 & 1 & 2 \\ \cline{2-5}
& \VAR{yz} = 1 & 3 & 4 & 5 \\ \cline{2-5}
& \VAR{yz} = 2 & 6 & 7 & 8 \\ \cline{2-5}
& \VAR{yz} = 3 & 9 & 10 & 11 \\ \cline{2-5}
& \VAR{yz} = 4 & 12 & 13 & 14 \\ \cline{2-5}
& \VAR{yz} = 5 & 15 \\
& \VAR{yz} = 3 & 9 & 10 & 11 \\ \cline{2-5}
\cline{0-2}
\end{tabular}
\end{center}

The second split of \VAR{yzteam} for \VAR{x} = 0, \VAR{ydim} = 4 results in 2
\VAR{yteams} and 4 \VAR{zteams}:
The second split of \VAR{yzteam} for \VAR{x} = 0, \VAR{ydim} = 2 results in 2
\VAR{yteams} and 2 \VAR{zteams}:


\begin{center}
\begin{tabular}{|l|l|l|l|l|l|}
\begin{tabular}{|l|l|l|l|}
\hline
\multicolumn{2}{|c|}{} & \multicolumn{4}{c|}{\VAR{zteam}} \\ \cline{3-6}
\multicolumn{2}{|c|}{} & \VAR{y} = 0 & \VAR{y} = 1 & \VAR{y} = 2 & \VAR{y} = 3 \\ \hline
\multirow{2}{*}{\VAR{yteam}} & \VAR{z} = 0 & 0 & 3 & 6 & 9 \\ \cline{2-6}
& \VAR{z} = 1 & 12 & 15 \\
\multicolumn{2}{|c|}{} & \multicolumn{2}{c|}{\VAR{zteam}} \\ \cline{3-4}
\multicolumn{2}{|c|}{} & \VAR{y} = 0 & \VAR{y} = 1 \\ \hline
\multirow{2}{*}{\VAR{yteam}} & \VAR{z} = 0 & 0 & 3 \\ \cline{2-4}
& \VAR{z} = 1 & 6 & 9 \\
\cline{0-3}
\end{tabular}
\end{center}

The second split of \VAR{yzteam} for \VAR{x} = 1, \VAR{ydim} = 4 results in
2 \VAR{yteams} and 4 \VAR{zteams}:
The second split of \VAR{yzteam} for \VAR{x} = 1, \VAR{ydim} = 2 results in
2 \VAR{yteams} and 2 \VAR{zteams}:

\begin{center}
\begin{tabular}{|l|l|l|l|l|l|}
\begin{tabular}{|l|l|l|l|}
\hline
\multicolumn{2}{|c|}{} & \multicolumn{4}{c|}{\VAR{zteam}} \\ \cline{3-6}
\multicolumn{2}{|c|}{} & \VAR{y} = 0 & \VAR{y} = 1 & \VAR{y} = 2 & \VAR{y} = 3 \\ \hline
\multirow{2}{*}{\VAR{yteam}} & \VAR{z} = 0 & 1 & 4 & 7 & 10 \\ \cline{2-6}
& \VAR{z} = 1 & 13 \\
\cline{0-2}
\multicolumn{2}{|c|}{} & \multicolumn{2}{c|}{\VAR{zteam}} \\ \cline{3-4}
\multicolumn{2}{|c|}{} & \VAR{y} = 0 & \VAR{y} = 1 \\ \hline
\multirow{2}{*}{\VAR{yteam}} & \VAR{z} = 0 & 1 & 4 \\ \cline{2-4}
& \VAR{z} = 1 & 7 & 10 \\
\cline{0-3}
\end{tabular}
\end{center}

The second split of \VAR{yzteam} for \VAR{x} = 2, \VAR{ydim} = 4 results in
2 \VAR{yteams} and 4 \VAR{zteams}:
The second split of \VAR{yzteam} for \VAR{x} = 2, \VAR{ydim} = 2 results in
2 \VAR{yteams} and 2 \VAR{zteams}:

\begin{center}
\begin{tabular}{|l|l|l|l|l|l|}
\begin{tabular}{|l|l|l|l|}
\hline
\multicolumn{2}{|c|}{} & \multicolumn{4}{c|}{\VAR{zteam}} \\ \cline{3-6}
\multicolumn{2}{|c|}{} & \VAR{y} = 0 & \VAR{y} = 1 & \VAR{y} = 2 & \VAR{y} = 3 \\ \hline
\multirow{2}{*}{\VAR{yteam}} & \VAR{z} = 0 & 2 & 5 & 8 & 11 \\ \cline{2-6}
& \VAR{z} = 1 & 14 \\
\cline{0-2}
\multicolumn{2}{|c|}{} & \multicolumn{2}{c|}{\VAR{zteam}} \\ \cline{3-4}
\multicolumn{2}{|c|}{} & \VAR{y} = 0 & \VAR{y} = 1 \\ \hline
\multirow{2}{*}{\VAR{yteam}} & \VAR{z} = 0 & 2 & 5 \\ \cline{2-4}
& \VAR{z} = 1 & 8 & 11 \\
\cline{0-3}
\end{tabular}
\end{center}

The final number of teams for each dimension are:
\begin{itemize}
\item 6 \VAR{xteams}: these are teams where (\VAR{z},\VAR{y}) is fixed and \VAR{x} varies.
\item 4 \VAR{xteams}: these are teams where (\VAR{z},\VAR{y}) is fixed and \VAR{x} varies.
\item 6 \VAR{yteams}: these are teams where (\VAR{x},\VAR{z}) is fixed and \VAR{y} varies.
\item 12 \VAR{zteams}: these are teams where (\VAR{x},\VAR{y}) is fixed and \VAR{z} varies.
\item 6 \VAR{zteams}: these are teams where (\VAR{x},\VAR{y}) is fixed and \VAR{z} varies.
\end{itemize}

The expected output is: \\
The expected output with 12 \acp{PE} is: \\
\begin{small}
\texttt{
(0, 0, 0) is me = 0 \\
(1, 0, 0) is me = 1 \\
(2, 0, 0) is me = 2 \\
(0, 1, 0) is me = 3 \\
(1, 1, 0) is me = 4 \\
(2, 1, 0) is me = 5 \\
(0, 2, 0) is me = 6 \\
(1, 2, 0) is me = 7 \\
(2, 2, 0) is me = 8 \\
(0, 3, 0) is me = 9 \\
(1, 3, 0) is me = 10 \\
(2, 3, 0) is me = 11 \\
(0, 0, 1) is me = 12 \\
(1, 0, 1) is me = 13 \\
(2, 0, 1) is me = 14 \\
(0, 1, 1) is me = 15
xdim = 3, ydim = 2, zdim = 2 \\
(0, 0, 0) is mype = 0 \\
(1, 0, 0) is mype = 1 \\
(2, 0, 0) is mype = 2 \\
(0, 1, 0) is mype = 3 \\
(1, 1, 0) is mype = 4 \\
(2, 1, 0) is mype = 5 \\
(0, 0, 1) is mype = 6 \\
(1, 0, 1) is mype = 7 \\
(2, 0, 1) is mype = 8 \\
(0, 1, 1) is mype = 9 \\
(1, 1, 1) is mype = 10 \\
(2, 1, 1) is mype = 11 \\
}
\end{small}
}
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33 changes: 26 additions & 7 deletions example_code/shmem_team_split_2D.c
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Original file line number Diff line number Diff line change
@@ -1,20 +1,39 @@
#include <shmem.h>
#include <stdio.h>
#include <math.h>

/* Find x and y such that x * y == npes and abs(x - y) is minimized. */
void find_xy_dims(int npes, int *x, int *y) {
for(int divider = ceil(sqrt(npes)); divider >= 1; divider--)
if (npes % divider == 0) {
*x = divider;
*y = npes / divider;
return;
}
}

/* Find x, y, and z such that x * y * z == npes and
* abs(x - y) + abs(x - z) + abs(y - z) is minimized. */
void find_xyz_dims(int npes, int *x, int *y, int *z) {
for(int divider = ceil(cbrt(npes)); divider >= 1; divider--)
if (npes % divider == 0) {
*x = divider;
find_xy_dims(npes / divider, y, z);
return;
}
}

int main(void) {
int xdim = 3;
int ydim = 4;
int xdim, ydim, zdim;

shmem_init();
int mype = shmem_my_pe();
int npes = shmem_n_pes();

if (npes < (xdim * ydim)) {
printf("Not enough PEs to create 4x3xN layout\n");
exit(1);
}
find_xyz_dims(npes, &xdim, &ydim, &zdim);

if (shmem_my_pe() == 0) printf("xdim = %d, ydim = %d, zdim = %d\n", xdim, ydim, zdim);

int zdim = (npes / (xdim * ydim)) + (((npes % (xdim * ydim)) > 0) ? 1 : 0);
shmem_team_t xteam, yzteam, yteam, zteam;

shmem_team_split_2d(SHMEM_TEAM_WORLD, xdim, NULL, 0, &xteam, NULL, 0, &yzteam);
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