This sample shows the Game of Life CPU code converted to a PGI accelerator directive version. Please direct any questions or comments to help@nccs.gov

## GOL.c

#include <stdio.h> #include <stdlib.h> #define SRAND_VALUE 1985 int main(int argc, char* argv[]) { int i,j,iter; // Linear game grid dimension excluding ghost cells int dim = 1024; // Number of game iterations int maxIter = 1<<10; // Allocate square grid of (dim+2)^2 elements, 2 added for ghost cells int **restrict grid = (int**) malloc( sizeof(int*) * (dim+2) ); grid[0] = (int*) malloc(sizeof(int) * (dim+2)*(dim+2)); for(i = 1; i < dim+2; i++) grid[i] = grid[i-1]+(dim+2); // Allocate newGrid int **restrict newGrid = (int**) malloc( sizeof(int*) * (dim+2) ); newGrid[0] = (int*) malloc(sizeof(int) * (dim+2)*(dim+2)); for(i = 1; i < dim+2; i++) newGrid[i] = newGrid[i-1]+(dim+2); // Assign initial population randomly srand(SRAND_VALUE); for(i = 1; i <= dim; i++) { for(j = 1; j <= dim; j++) { grid[i][j] = rand() % 2; } } #pragma acc region copy(grid[0:dim+1][0:dim+1]) local(newGrid[0:dim+1][0:dim+1]) { // Main game loop for (iter = 0; iter<maxIter; iter++) { // Left-Right columns for (i = 1; i <= dim; i++) { grid[i][0] = grid[i][dim]; //Copy first real column to right ghost column grid[i][dim+1] = grid[i][1]; //Copy last real column to left ghost column } // Top-Bottom rows for (j = 0; j <= dim+1; j++) { grid[0][j] = grid[dim][j]; //Copy first real row to bottom ghost row grid[dim+1][j] = grid[1][j]; //Copy last real row to top ghost row } // Now we loop over all cells and determine their fate for (i = 1; i <= dim; i++) { for (j = 1; j <= dim; j++) { // Get the number of neighbors for a given grid point int numNeighbors = grid[i+1][j] + grid[i-1][j] //upper lower + grid[i][j+1] + grid[i][j-1] //right left + grid[i+1][j+1] + grid[i-1][j-1] //diagonals + grid[i-1][j+1] + grid[i+1][j-1]; // Here we have explicitly all of the game rules if (grid[i][j] == 1 && numNeighbors < 2) newGrid[i][j] = 0; else if (grid[i][j] == 1 && (numNeighbors == 2 || numNeighbors == 3)) newGrid[i][j] = 1; else if (grid[i][j] == 1 && numNeighbors > 3) newGrid[i][j] = 0; else if (grid[i][j] == 0 && numNeighbors == 3) newGrid[i][j] = 1; else newGrid[i][j] = grid[i][j]; } } // Can't switch pointers so we mannually have to copy array over for(i = 1; i <= dim; i++) { for(j = 1; j <= dim; j++) { grid[i][j] = newGrid[i][j]; } } } }//end Acc region // Sum up alive cells and print results int total = 0; for (i = 1; i <= dim; i++) { for (j = 1; j <= dim; j++) { total += grid[i][j]; } } printf("Total Alive: %d\n", total); // Release memory free(grid); free(newGrid); return 0; }

### Changes to GOL.c

// Allocate square grid of (dim+2)^2 elements, 2 added for ghost cells int **restrict grid = (int**) malloc( sizeof(int*) * (dim+2) ); grid[0] = (int*) malloc(sizeof(int) * (dim+2)*(dim+2)); for(i = 1; i < dim+2; i++) grid[i] = grid[i-1]+(dim+2); // Allocate newGrid int **restrict newGrid = (int**) malloc( sizeof(int*) * (dim+2) ); newGrid[0] = (int*) malloc(sizeof(int) * (dim+2)*(dim+2)); for(i = 1; i < dim+2; i++) newGrid[i] = newGrid[i-1]+(dim+2);

Memory transfers between host and device can be very costly and so optimizing memory transfers in any way possible is highly recommended. One way to possibly speed this transfer up is to allocate multidimensional arrays in a contiguous chunk of memory, as shown here. As discussed in the vector addition example our pointers must have **restrict** qualifier as a guarantee to the compiler that we are not aliasing our pointers.

#pragma acc region copy(grid[0:dim+1][0:dim+1]) local(newGrid[0:dim+1][0:dim+1])

We start the **acc region** before our main game loop starts even though we can not parallelize this loop. If we were to place the **acc region** inside of the main game loop the game grids would be copied back and forth between the host and device each iteration of the loop. We let the compiler know that **grid** is to be copied *to* the device at the start of the directive and *from* the device at the end of the directive. **newGrid** can reside solely on the device and so we specify it to be **local**. Another way to approach this is the **data region** approach looked at below.

// Get the number of neighbors for a given grid point int numNeighbors = grid[i+1][j] + grid[i-1][j] //upper lower + grid[i][j+1] + grid[i][j-1] //right left + grid[i+1][j+1] + grid[i-1][j-1] //diagonals + grid[i-1][j+1] + grid[i+1][j-1];

In the CUDA programming model all functions must be effectively inlined. Here we manually inline our function to calculate the number of alive neighbors a cell has.

// Can't switch pointers so we mannually have to copy array over for(i = 1; i <= dim; i++) { for(j = 1; j <= dim; j++) { grid[i][j] = newGrid[i][j]; } }

This modification is **very** important, device pointers are not accessible inside of the **acc region**. If you leave the pointer swap in place from the cpu code the compiler will not complain, the code will run, and you will get incorrect results. This is not a limitation of GPU programming as you will see in the CUDA GOL example but of the PGI directive framework. The easiest way to fix this is to replace the pointer swap with a copy operation as we have done. The cost of this operation and possible workarounds are investigated below.

}//end Acc region

At the end of our **acc region** the game grid is copied back to the host via DMA.

### Compiling GOL.c

We add the **time** option to the target accelerator flag. This flag will print out GPU timing information at runtime. We will also specify the option **cc13** to tell the compiler to only generate code for compute capability 1.3, this will make the output slightly more digestible.

$ module load cudatoolkit $ cc -ta=nvidia,time,cc20 -Minfo GOL.c -o GOL.out

**Output**:

main: 31, Generating local(newGrid[:dim+1][:dim+1]) Generating copy(grid[:dim+1][:dim+1]) Generating compute capability 1.3 binary

The memory transfer between the host and accelerator, as well as the compute capability, has been explicitly stated by us.

34, Loop carried dependence due to exposed use of 'grid[0:1023][1:1025]' prevents parallelization ... Loop carried dependence due to exposed use of 'grid[1:1024][1:1024]' prevents parallelization Loop carried dependence due to exposed use of 'newGrid[1:1024][1:1024]' prevents parallelization Sequential loop scheduled on host

In the current version we wrap the **acc region** directive around the entire game loop even though the game loop must be executed serially. The compiler correctly identifies it can not parallelize this loop.

36, Loop is parallelizable Accelerator kernel generated 36, #pragma acc for parallel, vector(32) Non-stride-1 accesses for array 'grid' CC 1.3 : 4 registers; 24 shared, 116 constant, 0 local memory bytes; 25 occupancy 41, Loop is parallelizable Accelerator kernel generated 41, #pragma acc for parallel, vector(256) CC 1.3 : 6 registers; 24 shared, 116 constant, 0 local memory bytes; 100 occupancy

To copy over the ghost cells our two loops get converted into two accelerator kernels. We notice that for the first loop we get the line **Non-stride-1 accesses for array ‘grid’**, indicating that our memory access is not accessed in the best possible way. By starting our loop index at 1 instead of 0 we get non coalesced memory access which degrades performance. Coalescing requirements are dependent on compute capability and can be found in **Appendix G** of the **CUDA_C_Programming_guide**.

47, Loop is parallelizable 48, Loop is parallelizable Accelerator kernel generated 47, #pragma acc for parallel, vector(16) 48, #pragma acc for parallel, vector(16) Cached references to size [18x18] block of 'grid' Using register for 'newGrid' CC 1.3 : 20 registers; 1328 shared, 140 constant, 0 local memory bytes; 75 occupancy

The main computation takes place here. The nested loops are mapped onto 16×16 thread blocks. A software managed cache is used to minimize global memory access of **grid**, this is particularly important in devices with compute capability less than 2.0, as they do not have a global memory cache.

68, Loop is parallelizable 69, Loop is parallelizable Accelerator kernel generated 68, #pragma acc for parallel, vector(16) 69, #pragma acc for parallel, vector(16) CC 1.3 : 7 registers; 28 shared, 120 constant, 0 local memory bytes; 100 occupancy

Lastly we see the kernel is generated for the **grid**/**newGrid** switch. Not being able to switch pointers is a limitation of the current PGI accelerate implimentation and not inherent of CUDA, we will measure the impact this extra memory transfer has below.

## GOL.f90

program main implicit none integer :: i,j,iter,seed(8),numNeighbors,total real :: randm ! Linear game grid dimension integer :: dim = 1024 ! Number of game iterations integer :: maxIter = 2**10 ! Game grid pointers integer,dimension(:,:),allocatable :: grid, newGrid ! Allocate square grid of (dim+2)^2 elements, 2 added for ghost cells allocate(grid(dim+2,dim+2)) allocate(newGrid(dim+2,dim+2)) ! Assign initial population randomly seed = (/1985, 2011, 2012, 500, 24, 15, 99, 8/) call random_seed(PUT=seed) do j=1,dim do i=1,dim call random_number(randm) grid(i,j) = nint(randm) enddo enddo ! Main game loop !$acc region copy(grid(1:dim+2,1:dim+2)) local(newGrid(1:dim+2,1:dim+2)) do iter=1,maxIter ! Top-Bottom ghost rows do j=2,dim+1 grid(1,j) = grid(dim+1,j) !Copy first game grid row to bottom ghost row grid(dim+2,j) = grid(2,j) !Copy first game grid row to top ghost row enddo ! Left-Right ghost columns do i=1,dim+2 grid(i,1) = grid(i, dim+1) !Copy first game grid column to right ghost column grid(i,dim+2) = grid(i,2) !Copy last game grid column to left ghost column enddo ! Now we loop over all cells and determine their fate !$acc do independent do j=2,dim+1 !$acc do independent do i=2,dim+1 ! Get the number of neighbors for a given grid point numNeighbors = grid(i,j+1) + grid(i,j-1)& !left & right + grid(i+1,j) + grid(i-1,j)& !upper & lower + grid(i+1,j+1) + grid(i-1,j-1)& !diagonals + grid(i-1,j+1) + grid(i+1,j-1) ! Here we have explicitly all of the game rules if(grid(i,j) == 1 .AND. numNeighbors < 2) then newGrid(i,j) = 0 elseif(grid(i,j) == 1 .AND. (numNeighbors == 2 .OR. numNeighbors == 3)) then newGrid(i,j) = 1 elseif(grid(i,j) == 1 .AND. numNeighbors > 3) then newGrid(i,j) = 0 elseif(grid(i,j) == 0 .AND. numNeighbors == 3) then newGrid(i,j) = 1 else newGrid(i,j) = grid(i,j) endif enddo enddo ! Can't switch pointers so we mannually have to copy array over !$acc do independent do j=2,dim+1 !$acc do independent do i=2,dim+1 grid(i,j) = newGrid(i,j) enddo enddo enddo!end main game loop !$acc end region ! Sum up alive cells and print results total = 0 do j=2,dim+1 do i=2,dim+1 total = total + grid(i,j) enddo enddo print *, "Total Alive", total ! Release memory deallocate(grid) deallocate(newGrid) end program

### Changes to GOL.f90

! Game grid pointers integer,dimension(:,:),allocatable :: grid, newGrid

The pointer attribute found in the CPU version is changed to **allocatable**, we will see that we can not use pointers as we desire on the device.

!$acc region copy(grid(1:dim+2,1:dim+2)) local(newGrid(1:dim+2,1:dim+2))

We start the acc region before our main game loop starts even though we can not parallelize this loop. If we were to place the acc region inside of the main game loop the game grids would be copied back and forth between the host and device each iteration of the loop. We let the compiler know that grid is to be copied to the device at the start of the directive and from the device at the end of the directive. newGrid can reside solely on the device and so we specify it to be local. Another way to approach this is the data region approach looked at below.

!$acc do independent do j=2,dim+1 !$acc do independent do i=2,dim+1

!$acc do independent do j=2,dim+1 !$acc do independent do i=2,dim+1

The **acc do** directive applies only to the loop immediately following it and is used, with additional instructions, to guide the compiler in mapping the code to the target accelerator. In our case we specify that each iteration of the do loop is **independent** of one another. Without these guiding directives the compiler will complain that grid and newGrid carry a dependency that prevents parallelization, we the programmer know this is not true however. The game grid is only updated at the end of each game iteration and so the specified loop iterations are independent.

! Get the number of neighbors for a given grid point numNeighbors = grid(i,j+1) + grid(i,j-1)& !left & right + grid(i+1,j) + grid(i-1,j)& !upper & lower + grid(i+1,j+1) + grid(i-1,j-1)& !diagonals + grid(i-1,j+1) + grid(i+1,j-1)

In the CUDA programming model all functions must be effectively inlined. Here we manually inline our function to calculate the number of alive neighbors a cell has.

!$acc end region

At the end of our **acc region** the game grid is copied back to the host via DMA.

### Compiling GOL.f90

We add the **time** option to the target accelerator flag. This flag will print out GPU timing information at runtime. We will also specify the option **cc13** to tell the compiler to only generate code for compute capability 1.3, this will make the output slightly more digestible.

$ module load cudatoolkit $ ftn -ta=nvidia,time,cc20 -Minfo GOL.f90 -o GOL.out

**Output**:

main: 30, Generating local(newgrid(1:dim+2,1:dim+2)) Generating copy(grid(1:dim+2,1:dim+2)) Generating compute capability 1.3 binary

The memory transfer between the host and accelerator, as well as the compute capability, has been explicitly stated by us.

31, Loop carried dependence due to exposed use of 'grid(1:dim+2,2)' prevents parallelization ... Loop carried dependence due to exposed use of 'grid(1:dim+2,dim+1)' prevents parallelization Loop carried dependence due to exposed use of 'newgrid(1:dim,1:dim)' prevents parallelization

In the current version we wrap the acc region directive around the entire game loop even though the game loop must be executed serially. The compiler correctly identifies it can not parallelize this loop.

33, Loop is parallelizable Accelerator kernel generated 33, !$acc do parallel, vector(32) Non-stride-1 accesses for array 'grid' CC 1.3 : 5 registers; 24 shared, 148 constant, 0 local memory bytes; 25 occupancy 39, Loop is parallelizable Accelerator kernel generated 39, !$acc do parallel, vector(256) CC 1.3 : 8 registers; 24 shared, 148 constant, 0 local memory bytes; 100 occupancy

To copy over the ghost cells our two loops get converted into two accelerator kernels. We notice that for the first loop we get the line Non-stride-1 accesses for array ‘grid’, indicating that our memory access is not accessed in the best possible way. By starting our loop index at 1 instead of 0 we get non coalesced memory access which degrades performance. Coalescing requirements are dependent on compute capability and can be found in Appendix G of the CUDA_C_Programming_guide.

47, Loop is parallelizable 49, Loop is parallelizable Accelerator kernel generated 47, !$acc do parallel, vector(16) 49, !$acc do parallel, vector(16) Cached references to size [18x18] block of 'grid' Using register for 'newgrid' CC 1.3 : 20 registers; 1328 shared, 140 constant, 0 local memory bytes; 75 occupancy

The main computation takes place here. The nested loops are mapped onto 16×16 thread blocks via the **vector(16)** directive and done in **parallel** on the GPU. We could specify our own block size in the same way if we chose to change it. A software managed cache is used to minimize global memory access of grid, this is particularly important in devices with compute capability less than 2.0, as they do not have a global memory cache.

72, Loop is parallelizable 74, Loop is parallelizable Accelerator kernel generated 72, !$acc do parallel, vector(16) 74, !$acc do parallel, vector(16) CC 1.3 : 7 registers; 28 shared, 120 constant, 0 local memory bytes; 100 occupancy

Lastly we see the kernel is generated for the grid/newGrid switch. Not being able to switch pointers is a limitation of the current PGI accelerate implimentation and not inherent of CUDA, we will measure the impact this extra memory transfer has below.

### Running GOL.f90

$ aprun gol.out

**Output**

The following timings were computed on a NVIDIA Tesla C2070.

Total Alive: 45224 Accelerator Kernel Timing data GOL.c main 32: region entered 1 time time(us): total=4460133 init=3498235 region=961898 kernels=752537 data=4349 w/o init: total=961898 max=961898 min=961898 avg=961898

The overall timing data is listed first, giving various timings in microseconds. The **min**, **max**, and **av**era**g**e timings for the region. Since our region is only entered once **min**, **max** and **avg** are all the same.

37: kernel launched 1024 times grid: [32] block: [32] time(us): total=12357 max=34 min=10 avg=12 42: kernel launched 1024 times grid: [5] block: [256] time(us): total=5579 max=7 min=5 avg=5

The kernels generated to copy our ghost cells do not require much time. this is because there is not much to copy and that it is a device to device trasfer. We do notice that the uncoelesced kernel takes approximately twice as long to run as the coelesced. This is expected as **Appendix G** of the **CUDA_C_Programming_guide** states for compute capability 2.0 GPUs that for a sequential but misaligned request to global memory, as we have in the non coalesced kernel, each memory transaction will be broken into two seperate requests.

49: kernel launched 1024 times grid: [64x64] block: [16x16] time(us): total=523002 max=604 min=496 avg=510

Our main computation takes place here and we see it takes the majority of the time.

71: kernel launched 1024 times grid: [64x64] block: [16x16] time(us): total=211599 max=210 min=200 avg=206

Nearly half of the GPUs computational time is spent doing this memory transfer that replaced our pointer switch. Currently the only way to get rid of this kernel and still use the PGI accelerate directives is to slightly rewrite our algorithm. See if you can figure out how to rewrite the above using minimal modifcations so that we can remove the memory copy kernel, One solution is given below.

## GOL-Try2.c

In this version we will remove the memory copy kernel that we needed to use since PGI accelerate does not currently suppoort device pointers. As an added bonus we will also take a look at the **acc data region** directive.

#include <stdio.h> #include <stdlib.h> #define SRAND_VALUE 1985 int main(int argc, char* argv[]) { int i,j,iter,numNeighbors; int dim = 1024; // Number of game iterations int maxIter = 1<<15; // Allocate square grid of (dim+2)^2 elements, 2 added for ghost cells int **restrict grid = (int**) malloc( sizeof(int*) * (dim+2) ); grid[0] = (int*) malloc(sizeof(int*) * (dim+2)*(dim+2)); for(i = 1; i<dim+2; i++) grid[i] = grid[i-1]+(dim+2); // Allocate newGrid int **restrict newGrid = (int**) malloc( sizeof(int*) * (dim+2) ); newGrid[0] = (int*) malloc(sizeof(int*) * (dim+2)*(dim+2)); for(i = 1; i<dim+2; i++) newGrid[i] = newGrid[i-1]+(dim+2); srand(SRAND_VALUE); // Assign initial population randomly for(i = 1; i<=dim; i++) { for(j = 1; j<=dim; j++) { grid[i][j] = (int)rand() % 2; } } #pragma acc data region copy(grid[0:dim+1][0:dim+1]) local(newGrid[0:dim+1][0:dim+1]) { // Main game loop for (iter = 0; iter<maxIter; iter++) { if(iter%2==0) { #pragma acc region { // Left-Right columns for (i = 1; i<=dim; i++) { grid[i][0] = grid[i][dim]; //Copy first real column to right ghost column grid[i][dim+1] = grid[i][1]; //Copy last real column to left ghost column } // Note the o to dim+1 to accounts for the "corners" // Top-Bottom rows for (j = 0; j<=dim+1; j++) { grid[0][j] = grid[dim][j]; //Copy first real row to bottom ghost row grid[dim+1][j] = grid[1][j]; //Copy last real row to top ghost row } // Now we loop over all cells and determine their fate for (i = 1; i<=dim; i++) { for (j = 1; j<=dim; j++) { // Get the number of neighbors for a given grid point numNeighbors = grid[i+1][j] + grid[i-1][j] //upper lower + grid[i][j+1] + grid[i][j-1] //right left + grid[i+1][j+1] + grid[i-1][j-1] //diagonals + grid[i-1][j+1] + grid[i+1][j-1]; // Here we have explicitly all of the game rules if (grid[i][j] == 1 && numNeighbors < 2) newGrid[i][j] = 0; else if (grid[i][j] == 1 && (numNeighbors == 2 || numNeighbors == 3)) newGrid[i][j] = 1; else if (grid[i][j] == 1 && numNeighbors > 3) newGrid[i][j] = 0; else if (grid[i][j] == 0 && numNeighbors == 3) newGrid[i][j] = 1; else newGrid[i][j] = grid[i][j]; } } }//end acc region }//end if else { #pragma acc region { // Left-Right columns for (i = 1; i<=dim; i++) { newGrid[i][0] = newGrid[i][dim]; //Copy first real column to right ghost column newGrid[i][dim+1] = newGrid[i][1]; //Copy last real column to left ghost column } // Note the o to dim+1 to accounts for the "corners" // Top-Bottom rows for (j = 0; j<=dim+1; j++) { newGrid[0][j] = newGrid[dim][j]; //Copy first real row to bottom ghost row newGrid[dim+1][j] = newGrid[1][j]; //Copy last real row to top ghost row } // Now we loop over all cells and determine their fate for (i = 1; i<=dim; i++) { for (j = 1; j<=dim; j++) { // Get the number of neighbors for a given grid point numNeighbors = newGrid[i+1][j] + newGrid[i-1][j] //upper lower + newGrid[i][j+1] + newGrid[i][j-1] //right left + newGrid[i+1][j+1] + newGrid[i-1][j-1] //diagonals + newGrid[i-1][j+1] + newGrid[i+1][j-1]; // Here we have explicitly all of the game rules if (newGrid[i][j] == 1 && numNeighbors < 2) grid[i][j] = 0; else if (newGrid[i][j] == 1 && (numNeighbors == 2 || numNeighbors == 3)) grid[i][j] = 1; else if (newGrid[i][j] == 1 && numNeighbors > 3) grid[i][j] = 0; else if (newGrid[i][j] == 0 && numNeighbors == 3) grid[i][j] = 1; else grid[i][j] = newGrid[i][j]; } } }//end acc region }//end else }//end iter loop }//end data region // Sum up alive cells and print results int total = 0; for (i = 1; i<=dim; i++) { for (j = 1; j<=dim; j++) { total += grid[i][j]; } } printf("Total Alive: %d\n", total); free(grid); free(newGrid); return 0; }

### Changes in GOL-Try2.c

#pragma acc data region copy(grid[0:dim+1][0:dim+1]) local(newGrid[0:dim+1][0:dim+1]) {

}//end data region

Although it is not neccesary to use in this program the **acc data region** is an important aspect of the PGI accelerate directives. When such a directive is encountered data is copied over to the device where it persists until the data region is exited. This directive can take the same options as the **acc region** in terms of tuning data transfers. While inside of a data region any number of **acc region**s can be encountered that make use of the data already on the device. This allows the programmer greater control over host to device and device to host data transfers.

**Lines 37-121**

if(iter%2==0) { #pragma acc region { // Left-Right columns for (i = 1; i<=dim; i++) { grid[i][0] = grid[i][dim]; //Copy first real column to right ghost column grid[i][dim+1] = grid[i][1]; //Copy last real column to left ghost column } // Note the o to dim+1 to accounts for the "corners" // Top-Bottom rows for (j = 0; j<=dim+1; j++) { grid[0][j] = grid[dim][j]; //Copy first real row to bottom ghost row grid[dim+1][j] = grid[1][j]; //Copy last real row to top ghost row } // Now we loop over all cells and determine their fate for (i = 1; i<=dim; i++) { for (j = 1; j<=dim; j++) { // Get the number of neighbors for a given grid point numNeighbors = grid[i+1][j] + grid[i-1][j] //upper lower + grid[i][j+1] + grid[i][j-1] //right left + grid[i+1][j+1] + grid[i-1][j-1] //diagonals + grid[i-1][j+1] + grid[i+1][j-1]; // Here we have explicitly all of the game rules if (grid[i][j] == 1 && numNeighbors < 2) newGrid[i][j] = 0; else if (grid[i][j] == 1 && (numNeighbors == 2 || numNeighbors == 3)) newGrid[i][j] = 1; else if (grid[i][j] == 1 && numNeighbors > 3) newGrid[i][j] = 0; else if (grid[i][j] == 0 && numNeighbors == 3) newGrid[i][j] = 1; else newGrid[i][j] = grid[i][j]; } } }//end acc region }//end if else { #pragma acc region { // Left-Right columns for (i = 1; i<=dim; i++) { newGrid[i][0] = newGrid[i][dim]; //Copy first real column to right ghost column newGrid[i][dim+1] = newGrid[i][1]; //Copy last real column to left ghost column } // Note the o to dim+1 to accounts for the "corners" // Top-Bottom rows for (j = 0; j<=dim+1; j++) { newGrid[0][j] = newGrid[dim][j]; //Copy first real row to bottom ghost row newGrid[dim+1][j] = newGrid[1][j]; //Copy last real row to top ghost row } // Now we loop over all cells and determine their fate for (i = 1; i<=dim; i++) { for (j = 1; j<=dim; j++) { // Get the number of neighbors for a given grid point numNeighbors = newGrid[i+1][j] + newGrid[i-1][j] //upper lower + newGrid[i][j+1] + newGrid[i][j-1] //right left + newGrid[i+1][j+1] + newGrid[i-1][j-1] //diagonals + newGrid[i-1][j+1] + newGrid[i+1][j-1]; // Here we have explicitly all of the game rules if (newGrid[i][j] == 1 && numNeighbors < 2) grid[i][j] = 0; else if (newGrid[i][j] == 1 && (numNeighbors == 2 || numNeighbors == 3)) grid[i][j] = 1; else if (newGrid[i][j] == 1 && numNeighbors > 3) grid[i][j] = 0; else if (newGrid[i][j] == 0 && numNeighbors == 3) grid[i][j] = 1; else grid[i][j] = newGrid[i][j]; } } }//end acc region }//end else

The major change to our code has been to get rid of the grid/newGrid switching kernel. We have explicitly coded the two cases and use the modulus of the main iteration variable to switch between the two pieces of code. This increases the code complexity but does get around the costly memory transfer.

## GOL-Try2.f90

program main implicit none integer :: i,j,iter,seed(8),numNeighbors,total real :: randm ! Linear game grid dimension integer :: dim = 1024 ! Number of game iterations integer :: maxIter = 2**10 ! Game grid pointers integer,dimension(:,:),allocatable :: grid, newGrid, tmpGrid ! Allocate square grid of (dim+2)^2 elements, 2 added for ghost cells allocate(grid(dim+2,dim+2)) allocate(newGrid(dim+2,dim+2)) ! Assign initial population randomly seed = (/1985, 2011, 2012, 500, 24, 15, 99, 8/) call random_seed(PUT=seed) do j=1,dim do i=1,dim call random_number(randm) grid(i,j) = nint(randm) enddo enddo ! Main game loop !$acc data region copy(grid(1:dim+2,1:dim+2)) local(newGrid(1:dim+2,1:dim+2)) do iter=1,maxITer if(MOD(iter,2) == 1) then !$acc region ! Top-Bottom ghost rows do j=2,dim+1 grid(1,j) = grid(dim+1,j) !Copy first game grid row to bottom ghost row grid(dim+2,j) = grid(2,j) !Copy first game grid row to top ghost row enddo ! Left-Right ghost columns do i=1,dim+2 grid(i,1) = grid(i, dim+1) !Copy first game grid column to right ghost column grid(i,dim+2) = grid(i,2) !Copy last game grid column to left ghost column enddo ! Now we loop over all cells and determine their fate !$acc do independent do j=2,dim+1 !$acc do independent do i=2,dim+1 ! Get the number of neighbors for a given grid point numNeighbors = grid(i,j+1) + grid(i,j-1)& !left & right + grid(i+1,j) + grid(i-1,j)& !upper & lower + grid(i+1,j+1) + grid(i-1,j-1)& !diagonals + grid(i-1,j+1) + grid(i+1,j-1) ! Here we have explicitly all of the game rules if(grid(i,j) == 1 .AND. numNeighbors < 2) then newGrid(i,j) = 0 elseif(grid(i,j) == 1 .AND. (numNeighbors == 2 .OR. numNeighbors == 3)) then newGrid(i,j) = 1 elseif(grid(i,j) == 1 .AND. numNeighbors > 3) then newGrid(i,j) = 0 elseif(grid(i,j) == 0 .AND. numNeighbors == 3) then newGrid(i,j) = 1 else newGrid(i,j) = grid(i,j) endif enddo enddo !$acc end region else !$acc region ! Top-Bottom ghost rows do j=2,dim+1 newGrid(1,j) = newGrid(dim+1,j) !Copy first game grid row to bottom ghost row newGrid(dim+2,j) = newGrid(2,j) !Copy first game grid row to top ghost row enddo ! Left-Right ghost columns do i=1,dim+2 newGrid(i,1) = newGrid(i,dim+1) !Copy first game grid column to right ghost col newGrid(i,dim+2) = newGrid(i,2) !Copy last game grid column to left ghost col enddo ! Now we loop over all cells and determine their fate !$acc do independent do j=2,dim+1 !$acc do independent do i=2,dim+1 !Get the number of neighbors for a given grid point numNeighbors = newGrid(i,j+1) + newGrid(i,j-1)& !left and right + newGrid(i+1,j) + newGrid(i-1,j)& !upper and lower + newGrid(i+1,j+1) + newGrid(i-1,j-1)& !diagonals + newGrid(i-1,j+1) + newGrid(i+1,j-1) !Here we have explicitly all of the game rules if(newGrid(i,j) == 1 .AND. numNeighbors < 2) then grid(i,j) = 0 elseif(newGrid(i,j)==1 .AND. (numNeighbors==2 .OR. numNeighbors==3)) then grid(i,j) = 1 elseif(newGrid(i,j) == 1 .AND. numNeighbors > 3) then grid(i,j) = 0 elseif(newGrid(i,j) == 0 .AND. numNeighbors == 3) then grid(i,j) = 1 else grid(i,j) = newGrid(i,j) endif enddo enddo !$acc end region endif !end grid newGrid switch enddo!end main game loop !$acc end data region ! Sum up alive cells and print results total = 0 do j=2,dim+1 do i=2,dim+1 total = total + grid(i,j) enddo enddo print *, "Total Alive", total ! Release memory deallocate(grid) deallocate(newGrid) end program