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#include "mpi.h"
#include <cmath>
#include <cassert>
#include <cstdlib>
#include <cstdio>
#include <ctime>
#define LIN(x, y, dimX) ((x) + (y)*(dimX))
#define LIN2(x,y,dimX) (LIN(x+1,y+1,dimX+2))
#define CYCLIN(x, y, dimX, dimY) LIN((x+dimX) % (dimX), (y+dimY) % (dimY), (dimX))
static double ks = 1.0;
class Grid {
private:
double *myGridPrev_, *myGridCurr_, *myGridNext_;
double *leftEdgeIn_, *leftEdgeOut_, *rightEdgeIn_, *rightEdgeOut_;
int numGridsX_, numGridsY_, dimX_, dimY_;
int myGridX_, myGridY_;
public:
Grid(int dimX, int dimY, int numGridsX, int numGridsY, int numInitialPerturbations)
: dimX_(dimX), dimY_(dimY), numGridsX_(numGridsX), numGridsY_(numGridsY) {
myGridPrev_ = new double[(dimX+2)*(2+dimY)]();
myGridCurr_ = new double[(dimX+2)*(2+dimY)]();
myGridNext_ = new double[(dimX+2)*(2+dimY)]();
leftEdgeIn_ = new double[dimY];
rightEdgeIn_ = new double[dimY];
leftEdgeOut_ = new double[dimY];
rightEdgeOut_ = new double[dimY];
int myRank;
MPI_Comm_rank(MPI_COMM_WORLD, &myRank);
myGridX_ = myRank % numGridsX_;
myGridY_ = myRank / numGridsX_;
initGrid(numInitialPerturbations);
}
~Grid() {
delete[] myGridPrev_;
delete[] myGridCurr_;
delete[] myGridNext_;
delete[] leftEdgeIn_;
delete[] rightEdgeIn_;
delete[] leftEdgeOut_;
delete[] rightEdgeOut_;
}
void doIterations(int numIterations) {
for (int i = 0; i < numIterations; ++i) {
exchangeEdges();
doOneIteration();
double *tmp = myGridPrev_;
myGridPrev_ = myGridCurr_;
myGridCurr_ = myGridNext_;
myGridNext_ = tmp;
}
}
private:
void initGrid(int numInitialPerturbations) {
for(int s = 0; s < numInitialPerturbations; s++){
// Determine where to place a circle within the interior of the 2-d domain
int radius = 20+rand() % 30;
int xcenter = radius + rand() % (dimX_*numGridsX_ - 2*radius);
int ycenter = radius + rand() % (dimY_*numGridsY_ - 2*radius);
// Draw the circle
for(int x = 1; x < dimX_; x++){
for(int y = 1; y < dimY_; y++){
// The coordinate in the global data array (not just in this rank's portion)
int globalx = myGridX_*dimX_ + x;
int globaly = myGridY_*dimY_ + y;
double distanceToCenter = sqrt((globalx-xcenter)*(globalx-xcenter)
+ (globaly-ycenter)*(globaly-ycenter));
if (distanceToCenter < radius) {
// ranges from 0 to 3pi/2
double rscaled = (distanceToCenter/radius) * 3.0 * 3.14159/2.0;
// Range won't exceed -700 to 700
double t = 700.0 * cos(rscaled);
myGridCurr_[LIN2(x,y,dimX_)] = myGridPrev_[LIN2(x,y,dimX_)] = t;
}
}
}
}
}
void doOneIteration() {
for (int x = 0; x < dimX_; ++x) {
for (int y = 0; y < dimY_; ++y) {
myGridNext_[LIN2(x,y,dimX_)] =
ks * (myGridCurr_[LIN2(x+1,y,dimX_)] + myGridCurr_[LIN2(x-1,y,dimX_)]
+ myGridCurr_[LIN2(x,y+1,dimX_)] + myGridCurr_[LIN2(x,y-1,dimX_)]
- myGridCurr_[LIN2(x,y,dimX_)] * 4)
- myGridPrev_[LIN2(x,y,dimX_)] + 2*myGridCurr_[LIN2(x,y,dimX_)];
}
}
}
void exchangeEdges() {
MPI_Request reqs[4];
MPI_Status stats[4];
int topRank = CYCLIN(myGridX_, myGridY_+1, numGridsX_, numGridsY_);
int leftRank = CYCLIN(myGridX_-1, myGridY_, numGridsX_, numGridsY_);
int rightRank = CYCLIN(myGridX_+1, myGridY_, numGridsX_, numGridsY_);
int bottomRank = CYCLIN(myGridX_, myGridY_-1, numGridsX_, numGridsY_);
/*************** Recv ***************/
// Top.
MPI_Irecv(&(myGridCurr_[LIN(1,0,dimX_+2)]), dimX_, MPI_DOUBLE, topRank, 0, MPI_COMM_WORLD, &reqs[0]);
// Bottom.
MPI_Irecv(&(myGridCurr_[LIN(1,dimY_+1,dimX_+2)]), dimX_, MPI_DOUBLE,
bottomRank, 0, MPI_COMM_WORLD, &reqs[1]);
// Left.
MPI_Irecv(leftEdgeIn_, dimY_, MPI_DOUBLE, leftRank, 0, MPI_COMM_WORLD, &reqs[2]);
// Right.
MPI_Irecv(rightEdgeIn_, dimY_, MPI_DOUBLE, rightRank, 0, MPI_COMM_WORLD, &reqs[3]);
/*************** Send ***************/
// Top.
MPI_Send(&(myGridCurr_[LIN2(0,0,dimX_)]), dimX_, MPI_DOUBLE, topRank, 0, MPI_COMM_WORLD);
// Bottom.
MPI_Send(&(myGridCurr_[LIN2(0,dimY_-1,dimX_)]), dimX_, MPI_DOUBLE, bottomRank, 0, MPI_COMM_WORLD);
// Left.
// A bit more annoying, since the data is not stored contiguously.
for (int i = 0; i < dimY_; ++i) leftEdgeOut_[i] = myGridCurr_[LIN2(0, i, dimX_)];
MPI_Send(leftEdgeOut_, dimY_, MPI_DOUBLE, leftRank, 0, MPI_COMM_WORLD);
// Right.
for (int i = 0; i < dimY_; ++i) rightEdgeOut_[i] = myGridCurr_[LIN2(dimX_-1, i, dimX_)];
MPI_Send(rightEdgeOut_, dimY_, MPI_DOUBLE, rightRank, 0, MPI_COMM_WORLD);
/*************** Update ***************/
// Wait for all messages to be sent/received.
MPI_Waitall(4, reqs, stats);
for (int y = 0; y < dimY_; ++y) {
myGridCurr_[LIN(0, y+1, dimX_+2)] = leftEdgeIn_[y];
myGridCurr_[LIN(dimX_+1, y+1, dimX_+2)] = rightEdgeIn_[y];
}
}
};
int main(int argc, char *argv[])
{
// Initialize MPI stuff.
int nprocs, myRank;
MPI_Init(&argc, &argv);
MPI_Comm_size(MPI_COMM_WORLD, &nprocs);
MPI_Comm_rank(MPI_COMM_WORLD, &myRank);
// Seed the RNG.
int seed;
if (myRank == 0) seed = time(NULL);
MPI_Bcast(&seed, 1, MPI_INT, 0, MPI_COMM_WORLD);
srand(seed);
// Complain if we're missing arguments.
assert(argc >= 6);
// Get dimensionality information from the command line.
// FIXME?: Number of ranks cannot be prime.
int myDimX = atoi(argv[1]), myDimY = atoi(argv[2]);
int numGridsX = atoi(argv[3]), numGridsY = atoi(argv[4]);
int numInitPerturbations = atoi(argv[5]);
// Make sure those dimensions are right before moving on.
assert(numGridsX * numGridsY == nprocs);
Grid grid(myDimX, myDimY, numGridsX, numGridsY, numInitPerturbations);
grid.doIterations(100);
MPI_Finalize();
return 0;
}
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