This example shows how to generate CUDA® kernels for stencil type operations by implementing "Game of Life" by John H. Conway.

"Game of Life" is a zero-player `cellular automaton`

game that consists of a collection of cells (`population`

) in a rectangular grid (`universe`

). The cells evolve at discrete time steps known as `generations`

. A set of mathematical rules applied to the cells and its neighbors control their life, death, and reproduction. This "Game of Life" implementation is based on the example provided in the e-book *Experiments in MATLAB* by Cleve Moler. It follows a few simple rules:

Cells are arranged in a 2-D grid

At each step, the vitality of the eight nearest neighbors of each cell determines its fate

Any cell with exactly three live neighbors comes to life at the next step

A live cell with exactly two live neighbors remains alive at the next step

All other cells (including those with more than three neighbors) die at the next step or remain empty

Here are some examples of how a cell is updated:

Many array operations can be expressed as a `stencil`

operation, where each element of the output array depends on a small region of the input array. The stencil in the example shown is therefore the 3x3 region around each cell. Finite differences, convolution, median filtering, and finite-element methods are examples of other operations that stencil processing can perform.

CUDA enabled NVIDIA® GPU with compute capability 3.2 or higher.

NVIDIA CUDA toolkit.

Environment variables for the compilers and libraries. For information on the supported versions of the compilers and libraries, see Third-party Products. For setting up the environment variables, see Setting Up the Prerequisite Products.

Use the `coder.checkGpuInstall`

function and verify that the compilers and libraries needed for running this example are set up correctly.

```
envCfg = coder.gpuEnvConfig('host');
envCfg.BasicCodegen = 1;
envCfg.Quiet = 1;
coder.checkGpuInstall(envCfg);
```

Being zero-player, the evolution of the game is determined by its initial state. For this example, an initial population of cells is created on a two-dimensional grid with roughly 25% of the locations alive.

gridSize = 500; numGenerations = 100; initialGrid = (rand(gridSize,gridSize) > .75); % Draw the initial grid imagesc(initialGrid); colormap([1 1 1;0 0.5 0]); title('Initial Grid');

The gameoflife_orig.m function is a fully vectorized implementation of "Game of Life". The function updates all cells on the grid in one pass per generation.

```
type gameoflife_orig
```

%% MATLAB vectorized implementation function grid = gameoflife_orig(initialGrid) numGenerations = 100; grid = initialGrid; [gridSize,~] = size(initialGrid); % Loop through each generation updating the grid and displaying it for generation = 1:numGenerations grid = updateGrid(grid, gridSize); imagesc(grid); colormap([1 1 1;0 0.5 0]); title(['Grid at Iteration ',num2str(generation)]); drawnow; end function X = updateGrid(X, N) % Index vectors increase or decrease the centered index by one % thereby accessing neighbors to the left,right,up,down p = [1 1:N-1]; q = [2:N N]; % Count how many of the eight neighbors are alive. neighbors = X(:,p) + X(:,q) + X(p,:) + X(q,:) + ... X(p,p) + X(q,q) + X(p,q) + X(q,p); % A live cell with two live neighbors, or any cell with % three live neighbors, is alive at the next step. X = (X & (neighbors == 2)) | (neighbors == 3); end end

Now play the game by calling the `gameoflife_orig`

function with an initial population. The game iterates through 100 generations and displays the population at each generation.

gameoflife_orig(initialGrid);

Looking at the calculations in the `updateGrid`

function, it is apparent that the same operations are applied at each grid location independently. However, each cell must know about its eight neighbors. The modified gameoflife_stencil.m function uses the `gpucoder.stencilKernel`

pragma to compute a 3x3 region around each cell. The GPU Coder™ implementation of the stencil kernel, computes one element of the grid in each thread and uses shared memory to improve memory bandwidth and data locality.

```
type gameoflife_stencil
```

function grid = gameoflife_stencil(initialGrid) %#codegen numGenerations = 100; grid = initialGrid; % Loop through each generation updating the grid for generation = 1:numGenerations grid = gpucoder.stencilKernel(@updateElem, grid, [3,3], 'same'); end end function X = updateElem(window) [winH, winW] = size(window); neighbors = 0; for ww = 1:winW for wh = 1:winH neighbors = window(1,1) + window(1,2) + window(1,3) ... + window(2,1) + window(2,3) ... + window(3,1) + window(3,2) + window(3,3); end end X = (window(2,2) & (neighbors == 2)) | (neighbors == 3); end

To generate CUDA MEX for the `gameoflife_stencil`

function, create a code GPU code configuration object and use the `codegen`

function.

cfg = coder.gpuConfig('mex'); evalc('codegen -config cfg -args {initialGrid} gameoflife_stencil');

Run generated `gameoflife_stencil_mex`

with the random initial population.

gridGPU = gameoflife_stencil_mex(initialGrid); % Draw the grid after 100 generations imagesc(gridGPU); colormap([1 1 1;0 0.5 0]); title('Final Grid - CUDA MEX');

In this example, CUDA code was generated for a simple stencil operation - Conway's "Game of Life". Implementation was accomplished by using the `gpucoder.stencilKernel`

pragma. This technique demonstrated in this example can be used to implement a range of stencil operations including finite-element algorithms, convolutions, and filters.