Multiply matrices using dgemv and multithreads in c - multithreading

I have a problem in my code. I want to multiply 2 matrices using dgemv from cblas, but I want to share the operations to the threads I have. I have also used dgemv to multiply the matrices in a previous exercise where there was no parallelism needed. Is there any idea of what I should do?
The code:
for (it = 0; it < itime; it++) {
cblas_dgemv(CblasColMajor,CblasNoTrans,n,n, 1 , sigma, n, u , 1, 0.0 , d, 1);
#pragma omp parallel for private(i,j,sum) schedule(static)
for (i = 0; i < n; i++) {
sum = 0.0;
uplus[i] = u[i] + dtmu - dt * u[i];
#pragma omp simd reduction(+:sum)
for (j = 0; j < n; j++) {
sum += sigma[i*n+j]*u[j];
}
sum = sum - u[i]*m[i];
uplus[i] += dtdiv * sum;
if (uplus[i] > uth) {
uplus[i] = 0.0;
if (it >= ttransient) {
omega1[i] += 1.0;
}
}
}
t = u;
u = uplus;
uplus = t;
}
I want to get the dgemv function into the parallel region and share somehow the multiplications to the threads I have.

Related

Is Implement of operators in one instruction really faster than implement operators in separated instructions?

I tried to measure the speed of a simple code as below. The purpose is to find out which method will be faster (1 instruction x[j] = j * 2.0 + 1.0; OR 2 separated instructions x[j] = j * 2.0; x[j] += 1.0; ?)
int main(int argc, char* argv[])
{
int x[100000];
std::clock_t start;
start = std::clock();
for (int i = 0; i < 10000; i++) {
for (int j = 0; j < 100000; j++) {
x[j] = j * 2.0 + 1.0;
//x[j] = j * 2.0;
//x[j] += 1.0;
}
}
std::cout << (std::clock() - start) / (double)(CLOCKS_PER_SEC / 1000) << std::endl;
getchar();
return 0;
}
The results showed that with only 1 instruction (x[j] = j * 2.0 + 1.0;), it took me around 3.5(s). However, with 2 separated instructions (x[j] = j * 2.0; x[j] += 1.0;), it took me 8(s).
Could anyone explain why the difference of time is so big like that? Thanks in advance all.

Modifying a matrix in groovy with multiple threads

I have a multi-threading problem in which I should multiply 2 random matrices. The problem is that after I finish the execution the matrix is empty although if I print the element that is inserted into the matrix it is displayed right. The matrices to be multiplied are not empty.
import java.util.Random
p1 = 500
p2 = 500
threads = 4
def giveTasks(int workers, int tasks) {
int[] taskArray = new int[workers + 1]
taskArray[0] = 0
for (i = 1; i <= workers; i++) {
taskArray[i] = taskArray[i - 1] + tasks / workers + Math.max(tasks % workers - i + 1, 0)
}
return taskArray
}
class Matrix {
public int[][] table
public Matrix(int p1, int p2) {
table = new int[p1][p2]
}
public Matrix(int[][] matrix) {
table = matrix
}
}
def createMatrix(int lines, int columns) {
int[][] matrix = new int[lines][columns]
Random rn = new Random()
for (i = 0; i < lines; i++)
for (j = 0; j < columns; j++)
matrix[i][j] = rn.nextInt(100)
return matrix
}
Matrix matrix1 = new Matrix(createMatrix(p1, p2))
Matrix matrix2 = new Matrix(createMatrix(p2, p1))
Matrix matrix = new Matrix(p1, p2)
int[] taskArray = giveTasks(threads, p1)
def thread
int tn = 0
for (int i = 1; i < threads + 1; i++) {
start = taskArray[i - 1]
stop = taskArray[i]
thread = Thread.start {
for (int job = start; job < stop; job++) { //line for matrix1
int sum = 0
for (int j = 0; j < p1; j++) {
for (int k = 0; k < p1; k++)
sum += matrix1.table[job][k] + matrix2.table[k][j]
matrix.table[job][j] = sum
}
}
tn += 1
println "Thread " + tn + "finished"
}
}
thread.join()
print matrix.table
There is one major thing wrongly understood by you in the code you have shown us - you overwrite thread variable inside for-loop and after you spawn all 4 threads you wait only for the last one to finish execution.
Instead you should store a list of all spawned threads and you would have to join them all in the end of the script. Something like:
def queue = []
int tn = 0
for (int i = 1; i < threads + 1; i++) {
start = taskArray[i - 1]
stop = taskArray[i]
def thread = Thread.start {
for (int job = start; job < stop; job++) { //line for matrix1
int sum = 0
for (int j = 0; j < p1; j++) {
for (int k = 0; k < p1; k++)
sum += matrix1.table[job][k] + matrix2.table[k][j]
matrix.table[job][j] = sum
}
}
tn += 1
println "Thread " + tn + "finished"
}
queue << thread
}
queue*.join()
matrix.table.each { println it }
You can see that in the end of the script it does:
queue*.join()
It uses Groovy's spread operator to call join() method on all elements collected in the list. And we add every spawned thread to the queue list using left shift operator:
queue << thread
This is an equivalent of queue.add(thread).
I have run your program with p1=16 and p2=16 with those changes applied and I got an output like:
Thread 3finished
Thread 4finished
Thread 1finished
Thread 2finished
[1470, 2794, 4343, 5924, 7388, 9015, 10533, 12064, 13713, 15672, 17354, 18916, 20524, 22086, 23370, 24982]
[1464, 2782, 4325, 5900, 7358, 8979, 10491, 12016, 13659, 15612, 17288, 18844, 20446, 22002, 23280, 24886]
[1629, 3112, 4820, 6560, 8183, 9969, 11646, 13336, 15144, 17262, 19103, 20824, 22591, 24312, 25755, 27526]
[1466, 2786, 4331, 5908, 7368, 8991, 10505, 12032, 13677, 15632, 17310, 18868, 20472, 22030, 23310, 24918]
[1487, 2828, 4394, 5992, 7473, 9117, 10652, 12200, 13866, 15842, 17541, 19120, 20745, 22324, 23625, 25254]
[1570, 2994, 4643, 6324, 7888, 9615, 11233, 12864, 14613, 16672, 18454, 20116, 21824, 23486, 24870, 26582]
[1345, 2544, 3968, 5424, 6763, 8265, 9658, 11064, 12588, 14422, 15979, 17416, 18899, 20336, 21495, 22982]
[1622, 3098, 4799, 6532, 8148, 9927, 11597, 13280, 15081, 17192, 19026, 20740, 22500, 24214, 25650, 27414]
[1557, 2968, 4604, 6272, 7823, 9537, 11142, 12760, 14496, 16542, 18311, 19960, 21655, 23304, 24675, 26374]
[1477, 2808, 4364, 5952, 7423, 9057, 10582, 12120, 13776, 15742, 17431, 19000, 20615, 22184, 23475, 25094]
[1447, 2748, 4274, 5832, 7273, 8877, 10372, 11880, 13506, 15442, 17101, 18640, 20225, 21764, 23025, 24614]
[1473, 2800, 4352, 5936, 7403, 9033, 10554, 12088, 13740, 15702, 17387, 18952, 20563, 22128, 23415, 25030]
[1727, 3308, 5114, 6952, 8673, 10557, 12332, 14120, 16026, 18242, 20181, 22000, 23865, 25684, 27225, 29094]
[1483, 2820, 4382, 5976, 7453, 9093, 10624, 12168, 13830, 15802, 17497, 19072, 20693, 22268, 23565, 25190]
[1575, 3004, 4658, 6344, 7913, 9645, 11268, 12904, 14658, 16722, 18509, 20176, 21889, 23556, 24945, 26662]
[1474, 2802, 4355, 5940, 7408, 9039, 10561, 12096, 13749, 15712, 17398, 18964, 20576, 22142, 23430, 25046]
Hope it helps.

OpenMP in Biham-Middleton-Levine BML model

I've got a serial version of BML and I'm trying to write a parallel one with OpenMP. Basically my code works with a main witin a loop calling two functions for horizontal and vertical moves. Like that:
for (s = 0; s < nmovss; s++) {
horizontal_movs(grid, N);
copy_sides(grid, N);
cur = 1-cur;
vertical_movs(grid, N);
copy_sides(grid, N);
cur = 1-cur;
}
Where cur is the current grid. Then horizontal and vertical functions are similar and have a nested loop:
for(i = 1; i <= n; i++) {
for(j = 1; j <= n+1; j++) {
if(grid[cur][i][j-1] == LR && grid[cur][i][j] == EMPTY) {
grid[1-cur][i][j-1] = EMPTY;
grid[1-cur][i][j] = LR;
}
else {
grid[1-cur][i][j] = grid[cur][i][j];
}
}
}
The code produces a ppm image at every step, and whit a certain input the serial version produce an output that we can suppose good. But using #pragma omp parallel for inside the two functions H and V, the ppm file results splitted in such zones as the number of threads(i.e. 4):
I suppose the problem is that every thread should be doing both functions in sequence before termitate because movememnts are strictcly connected. I don't know how to do that. If I set pragma at a highter level like before main loop, there is no speed-up. Obviously the ppm file has to be not sliced like the image.
Goin'on I tried this solution that gives me an identical result as the serial code, but I don't excatly understand why
# pragma omp parallel num_threads(thread_count) default(none) \
shared(grid, n, cur) private(i, j)
for(i = 1; i <= n+1; i++) {
# pragma omp for
for(j = 1; j <= n; j++) {
if(grid[cur][i-1][j] == TB && grid[cur][i][j] == EMPTY) {
grid[1-cur][i-1][j] = EMPTY;
grid[1-cur][i][j] = TB;
}
else {
grid[1-cur][i][j] = grid[cur][i][j];
}
}
}
}
Therefore, if i use just one thread more than available cores(4), the execution time "explodes" instead of remain barely the same.

Hybrid MPI+OpenMP Vs MPI Performance

I am converting a 3-D Jacobi solver from pure MPI to Hybrid MPI+OpenMP. I have a 192x192x192 array which is divided among 24 processes in Pure MPI in 1-D decomposition i.e. each process has 192/24 x 192 x 192 = 8 x 192 x 192 slab of data. Now I do :
for(i=0 ; i <= 7; i++)
for(j=0; j<= 191; j++)
for(k=0; k<= 191; k++)
{
unew[i][j][k] = 1/6.0 * (u[i+1][j][k]+u[i-1][j][k]+
u[i][j+1][k]+u[i][j-1][k]+
u[i][j][k+1]+u[i][j][k-1]);
}
This update takes around 60 seconds for each process.
Now with Hybrid MPI, I run two processes (1 process per socket --bind-to socket --map-by socket and OMP_PROC_PLACES=coreswith OMP_PROC_BIND=close). I create 12 threads per MPI Process (i.e. 12 threads per socket or processor). Now each MPI process has an array of size : 192/2 x 192 x 192 = 96x192x192 elements. Each thread works on 96/12 x 192 x 192 = 8 x 192 x 192 portion of the array owned by each process. I do the same triple loop update using threads but the time is approximately 76 seconds for each thread. The load balance is perfect in both the problems. What could be the possible causes of performance degradation ? Is is False Sharing because threads could be invalidating the cache lines close to each other's chunk of data ? If yes, then how do I reduce this performance degradation ? (I have purposefully not mentioned ghost data but initially I am NOT overlapping communication with computation.)
In response to the comments below, am posting the code. Apologies for the long MWE but you can very safely ignore (1) Header files declaration (2) Variable Declaration (3) Memory allocation routine (4) Formation of Cartesian Topology (5) Setting boundary conditions in parallel using OpenMP parallel region (6) Declaration of MPI_Type_subarray datatype (7) MPI_Isend() and MPI_Irecv() calls and just concentrate on (a) INDEPENDENT UPDATE OpenMP parallel region (b) independent_update(...) routine being called from here.
/* IGNORE THIS PORTION */
#include<mpi.h>
#include<omp.h>
#include<stdio.h>
#include<stdlib.h>
#include<math.h>
#define MIN(a,b) (a < b ? a : b)
#define Tol 0.00001
/* IGNORE THIS ROUTINE */
void input(int *X, int *Y, int *Z)
{
int a=193, b=193, c=193;
*X = a;
*Y = b;
*Z = c;
}
/* IGNORE THIS ROUTINE */
float*** allocate_mem(int X, int Y, int Z)
{
int i,j;
float ***matrix;
float *arr;
arr = (float*)calloc(X*Y*Z, sizeof(float));
matrix = (float***)calloc(X, sizeof(float**));
for(i = 0 ; i<= X-1; i++)
matrix[i] = (float**)calloc(Y, sizeof(float*));
for(i = 0 ; i <= X-1; i++)
for(j=0; j<= Y-1; j++)
matrix[i][j] = &(arr[i*Y*Z + j*Z]);
return matrix ;
}
/* THIS ROUTINE IS IMPORTANT */
float independent_update(float ***old, float ***new, int NX, int NY, int NZ, int tID, int chunk)
{
int i,j,k, start, end;
float error = 0.0;
float diff;
start = tID * chunk + 1;
end = MIN( (tID+1)*chunk, NX-2 );
for(i = start; i <= end ; i++)
{
for(j = 1; j<= NY-2; j++)
{
#pragma omp simd
for(k = 1; k<= NZ-2; k++)
{
new[i][j][k] = (1/6.0) *(old[i-1][j][k] + old[i+1][j][k] + old[i][j-1][k] + old[i][j+1][k] + old[i][j][k-1] + old[i][j][k+1] );
diff = 1.0 - new[i][j][k];
diff = (diff > 0 ? diff : -1.0 * diff );
if(diff > error)
error = diff;
}
}
}
return error;
}
int main(int argc, char *argv[])
{
/* IGNORE VARIABLE DECLARATION */
int size, rank; //Size of old_comm and rank of process
int i, j, k,l; //General loop variables
MPI_Comm old_comm, new_comm; //MPI_COMM_WORLD handle and for MPI_Cart_create()
int N[3]; //For taking input of size of matrix from user
int P; //Represent number of processes i.e. same as size
int dims[3]; //For dimensions of Cartesian topology
int PX, PY, PZ; //X dim, Y dim, Z dim of each process
float ***old, ***new, ***temp; //Matrices for results dimensions is (Px+2)*(PY+2)*(PZ+2)
int period[3]; //Periodicity for each dimension
int reorder; //Whether processes should be reordered in new cartesian topology
int ndims; //Number of dimensions (which is 3)
int Z_TOWARDS_U, Z_AWAY_U; //Z neighbour towards you and away from you (Z const)
int X_DOWN, X_UP; //Below plane and above plane (X const)
int Y_LEFT, Y_RIGHT; //Left plane and right plane (Y const)
int coords[3]; //Finding coordinates of processes
int dimension; //Used in MPI_Cart_shift() , values = 0, 1,2
int displacement; //Used in MPI_Cart_shift(), values will be +1 to find immediate neighbours
float l_max_err; //Local maximum error on process
float l_max_err_new; //For dependent faces.
float G_max_err = 1.0; //Maximum error for stopping criterion
int iterations = 0 ; //Counting number of iterations
MPI_Request send[6], recv[6]; //For MPI_Isend and MPI_Irecv
int start[3]; //Start will be defined in MPI_Isend() and MPI_Irecv()
int gsize[3]; //Defining global size of subarray
MPI_Datatype x_subarray; //For sending X_UP and X_DOWN
int local_x[3]; //Defining local plane size for X_UP/X_DOWN
MPI_Datatype y_subarray; //For sending Y_LEFT and Y_RIGHT
int local_y[3]; //Defining local plane for Y_LEFT/Y_RIGHT
MPI_Datatype z_subarray; //For sending Z_TOWARDS_U and Z_AWAY_U
int local_z[3]; //Defining local plan size for XY plane i.e. where Z=0
double strt, end; //For measuring time
double strt1, end1, delta1; //For measuring trivial time 1
double strt2, end2, delta2; //For measuring trivial time 2
double t_i_strt, t_i_end, t_i_sum=0; //Time for independent computational kernel
double t_up_strt, t_up_end, t_up_sum=0; //Time for X_UP
double t_down_strt, t_down_end, t_down_sum=0; //Time for X_DOWN
double t_left_strt, t_left_end, t_left_sum=0; //Time for Y_LEFT
double t_right_strt, t_right_end, t_right_sum=0; //Time for Y_RIGHT
double t_towards_strt, t_towards_end, t_towards_sum=0; //For Z_TOWARDS_U
double t_away_strt, t_away_end, t_away_sum=0; //For Z_AWAY_U
double t_comm_strt, t_comm_end, t_comm_sum=0; //Time comm + independent update (need to subtract to get comm time)
double t_setup_strt,t_setup_end; //Set-up start and end time
double t_allred_strt,t_allred_end,t_allred_total=0.0; //Measuring Allreduce time separately.
int threadID; //ID of a thread
int nthreads; //Total threads in OpenMP region
int chunk; //chunk - used to calculate iterations of a thread
/* IGNORE MPI STARTUP ETC */
MPI_Init(&argc, &argv);
t_setup_strt = MPI_Wtime();
old_comm = MPI_COMM_WORLD;
MPI_Comm_size(old_comm, &size);
MPI_Comm_rank(old_comm, &rank);
P = size;
if(rank == 0)
{
input(&N[0], &N[1], &N[2]);
}
MPI_Bcast(N, 3, MPI_INT, 0, old_comm);
dims[0] = 0;
dims[1] = 0;
dims[2] = 0;
period[0] = period[1] = period[2] = 0; //All dimensions aperiodic
reorder = 0 ; //No reordering of ranks in new_comm
ndims = 3;
MPI_Dims_create(P,ndims,dims);
MPI_Cart_create(old_comm, ndims, dims, period, reorder, &new_comm);
if( (N[0]-1) % dims[0] == 0 && (N[1]-1) % dims[1] == 0 && (N[2]-1) % dims[2] == 0 )
{
PX = (N[0]-1)/dims[0]; //Rows of unknowns each process gets
PY = (N[1]-1)/dims[1]; //Columns of unknowns each process gets
PZ = (N[2]-1)/dims[2]; //Depth of unknowns each process gets
}
old = allocate_mem(PX+2, PY+2, PZ+2); //3D arrays with ghost points
new = allocate_mem(PX+2, PY+2, PZ+2); //3D arrays with ghost points
dimension = 0;
displacement = 1;
MPI_Cart_shift(new_comm, dimension, displacement, &X_UP, &X_DOWN); //Find UP and DOWN neighbours
dimension = 1;
MPI_Cart_shift(new_comm, dimension, displacement, &Y_LEFT, &Y_RIGHT); //Find UP and DOWN neighbours
dimension = 2;
MPI_Cart_shift(new_comm, dimension, displacement, &Z_TOWARDS_U, &Z_AWAY_U); //Find UP and DOWN neighbours
/* IGNORE BOUNDARY SETUPS FOR PDE */
#pragma omp parallel for default(none) shared(old,new,PX,PY,PZ) private(i,j,k) schedule(static)
for(i = 0; i <= PX+1; i++)
{
for(j = 0; j <= PY+1; j++)
{
for(k = 0; k <= PZ+1; k++)
{
old[i][j][k] = 0.0;
new[i][j][k] = 0.0;
}
}
}
#pragma omp parallel default(none) shared(X_DOWN,X_UP,Y_LEFT,Y_RIGHT,Z_TOWARDS_U,Z_AWAY_U,old,new,PX,PY,PZ) private(i,j,k,threadID,nthreads)
{
threadID = omp_get_thread_num();
nthreads = omp_get_num_threads();
if(threadID == 0)
{
if(X_DOWN == MPI_PROC_NULL) //X is constant here, this is YZ upper plane
{
for(j = 1 ; j<= PY ; j++)
for(k = 1 ; k<= PZ ; k++)
{
old[0][j][k] = 1;
new[0][j][k] = 1; //Set boundaries in new also
}
}
}
if(threadID == (nthreads-1))
{
if(X_UP == MPI_PROC_NULL) //YZ lower plane
{
for(j = 1 ; j<= PY ; j++)
for(k = 1; k<= PZ ; k++)
{
old[PX+1][j][k] = 1;
new[PX+1][j][k] = 1;
}
}
}
if(Y_LEFT == MPI_PROC_NULL) //Y is constant, this is left XZ plane, possibly can use collapse(2)
{
#pragma omp for schedule(static)
for(i = 1 ; i<= PX ; i++)
for(k = 1; k<= PZ; k++)
{
old[i][0][k] = 1;
new[i][0][k] = 1;
}
}
if(Y_RIGHT == MPI_PROC_NULL) //XZ right plane, again collapse(2) potential
{
#pragma omp for schedule(static)
for(i = 1 ; i<= PX; i++)
for(k = 1; k<= PZ ; k++)
{
old[i][PY+1][k] = 1;
new[i][PY+1][k] = 1;
}
}
if(Z_TOWARDS_U == MPI_PROC_NULL) //Z is constant here, towards you XY plane, collapse(2)
{
#pragma omp for schedule(static)
for(i = 1 ; i<= PX ; i++)
for(j = 1; j<= PY ; j++)
{
old[i][j][0] = 1;
new[i][j][0] = 1;
}
}
if(Z_AWAY_U == MPI_PROC_NULL) //Away from you XY plane, collapse(2)
{
#pragma omp for schedule(static)
for(i = 1 ; i<= PX; i++)
for(j = 1; j<= PY ; j++)
{
old[i][j][PZ+1] = 1;
new[i][j][PZ+1] = 1;
}
}
}
/* IGNORE SUBARRAY DECLARATION */
gsize[0] = PX+2; //Global sizes of 3-D cubes for each process
gsize[1] = PY+2;
gsize[2] = PZ+2;
start[0] = 0; //Will specify starting location while sending/receiving
start[1] = 0;
start[2] = 0;
local_x[0] = 1;
local_x[1] = PY;
local_x[2] = PZ;
MPI_Type_create_subarray(ndims, gsize, local_x, start, MPI_ORDER_C, MPI_FLOAT, &x_subarray);
MPI_Type_commit(&x_subarray);
local_y[0] = PX;
local_y[1] = 1;
local_y[2] = PZ;
MPI_Type_create_subarray(ndims, gsize, local_y, start, MPI_ORDER_C, MPI_FLOAT, &y_subarray);
MPI_Type_commit(&y_subarray);
local_z[0] = PX;
local_z[1] = PY;
local_z[2] = 1;
MPI_Type_create_subarray(ndims, gsize, local_z, start, MPI_ORDER_C, MPI_FLOAT, &z_subarray);
MPI_Type_commit(&z_subarray);
t_setup_end = MPI_Wtime();
strt = MPI_Wtime();
while(G_max_err > Tol) //iterations < ITERATIONS)
{
iterations++ ;
t_comm_strt = MPI_Wtime();
/* IGNORE MPI COMMUNICATION */
MPI_Irecv(&old[0][1][1], 1, x_subarray, X_DOWN, 10, new_comm, &recv[0]);
MPI_Irecv(&old[PX+1][1][1], 1, x_subarray, X_UP, 20, new_comm, &recv[1]);
MPI_Irecv(&old[1][PY+1][1], 1, y_subarray, Y_RIGHT, 30, new_comm, &recv[2]);
MPI_Irecv(&old[1][0][1], 1, y_subarray, Y_LEFT, 40, new_comm, &recv[3]);
MPI_Irecv(&old[1][1][PZ+1], 1, z_subarray, Z_AWAY_U, 50, new_comm, &recv[4]);
MPI_Irecv(&old[1][1][0], 1, z_subarray, Z_TOWARDS_U, 60, new_comm, &recv[5]);
MPI_Isend(&old[PX][1][1], 1, x_subarray, X_UP, 10, new_comm, &send[0]);
MPI_Isend(&old[1][1][1], 1, x_subarray, X_DOWN, 20, new_comm, &send[1]);
MPI_Isend(&old[1][1][1], 1, y_subarray, Y_LEFT, 30, new_comm, &send[2]);
MPI_Isend(&old[1][PY][1], 1, y_subarray, Y_RIGHT, 40, new_comm, &send[3]);
MPI_Isend(&old[1][1][1], 1, z_subarray, Z_TOWARDS_U, 50, new_comm, &send[4]);
MPI_Isend(&old[1][1][PZ], 1, z_subarray, Z_AWAY_U, 60, new_comm, &send[5]);
MPI_Waitall(6, send, MPI_STATUSES_IGNORE);
MPI_Waitall(6, recv, MPI_STATUSES_IGNORE);
t_comm_end = MPI_Wtime();
t_comm_sum = t_comm_sum + (t_comm_end - t_comm_strt);
/* Use threads in Independent update */
t_i_strt = MPI_Wtime();
l_max_err = 0.0; //Very important, Reduction result is combined with this !
/* THIS IS THE IMPORTANT REGION */
#pragma omp parallel default(none) shared(old,new,PX,PY,PZ,chunk) private(threadID,nthreads) reduction(max:l_max_err)
{
nthreads = omp_get_num_threads();
threadID = omp_get_thread_num();
chunk = (PX-1+1) / nthreads ;
l_max_err = independent_update(old, new, PX+2, PY+2, PZ+2, threadID, chunk);
}
t_i_end = MPI_Wtime();
t_i_sum = t_i_sum + (t_i_end - t_i_strt) ;
/* IGNORE THE REMAINING CODE */
t_allred_strt = MPI_Wtime();
MPI_Allreduce(&l_max_err, &G_max_err, 1, MPI_FLOAT, MPI_MAX, new_comm);
t_allred_end = MPI_Wtime();
t_allred_total = t_allred_total + (t_allred_end - t_allred_strt);
temp = new ;
new = old;
old = temp;
}
MPI_Barrier(new_comm);
end = MPI_Wtime();
if( rank == 0)
{
printf("\nIterations = %d, G_max_err = %f", iterations, G_max_err);
printf("\nThe total SET-UP time for MPI and boundary conditions is %lf", (t_setup_end-t_setup_strt));
printf("\nThe total time for SOLVING is %lf", (end-strt));
printf("\nThe total time for INDEPENDENT COMPUTE %lf", t_i_sum);
printf("\nThe total time for COMMUNICATION OVERHEAD is %lf", t_comm_sum);
printf("\nThe total time for MPI_ALLREDUCE() is %lf", t_allred_total);
}
MPI_Type_free(&x_subarray);
MPI_Type_free(&y_subarray);
MPI_Type_free(&z_subarray);
free(&old[0][0][0]);
free(&new[0][0][0]);
MPI_Finalize();
return 0;
}
P.S. : I am almost sure that the cost of spawning/waking the threads is not the reason for such a huge difference in the timing.
Please find attached Scalasca snapshot for INDEPENDENT COMPUTE of the Hybrid Program.
Using loop simd construct
#pragma omp parallel default(none) shared(old,new,PX,PY,PZ,l_max_err) private(i,j,k,diff)
{
#pragma omp for simd schedule(static) reduction(max:l_max_err)
for(i = 1; i <= PX ; i++)
{
for(j = 1; j<= PY; j++)
{
for(k = 1; k<= PZ; k++)
{
new[i][j][k] = (1/6.0) *(old[i-1][j][k] + old[i+1][j][k] + old[i][j-1][k] + old[i][j+1][k] + old[i][j][k-1] + old[i][j][k+1] );
diff = 1.0 - new[i][j][k];
diff = (diff > 0 ? diff : -1.0 * diff );
if(diff > l_max_err)
l_max_err = diff;
}
}
}
}
You frequently get memory access and cache issues when you just do one MPI process per socket on a CPU with multiple memory controllers. It can be on either the read or the write side, so you can't really say which. This is especially an issue when doing thread-parallel execution with lightweight compute tasks (e.g. math on arrays). One MPI process per socket in this case tends to fare significantly worse than pure MPI.
In your BIOS, set up whatever the maximal NUMA per socket option is
Use one MPI process per NUMA node.
Try some different parameter values in schedule(static). I've rarely found the default to be best.
Essentially what this will do is ensure each bundle of threads only works on a single pool of memory.

Errors with repeated FFTW calls

I'm having a strange issue that I can't resolve. I made this as a simple example that demonstrates the problem. I have a sine wave defined between [0, 2*pi]. I take the Fourier transform using FFTW. Then I have a for loop where I repeatedly take the inverse Fourier transform. In each iteration, I take the average of my solution and print the results. I expect that the average stays the same with each iteration because there is no change to solution, y. However, when I pick N = 256 and other even values of N, I note that the average grows as if there are numerical errors. However, if I choose, say, N = 255 or N = 257, this is not the case and I get what is expect (avg = 0.0 for each iteration).
Code:
#include <stdio.h>
#include <stdlib.h>
#include <fftw3.h>
#include <math.h>
int main(void)
{
int N = 256;
double dx = 2.0 * M_PI / (double)N, dt = 1.0e-3;
double *x, *y;
x = (double *) malloc (sizeof (double) * N);
y = (double *) malloc (sizeof (double) * N);
// initial conditions
for (int i = 0; i < N; i++) {
x[i] = (double)i * dx;
y[i] = sin(x[i]);
}
fftw_complex yhat[N/2 + 1];
fftw_plan fftwplan, fftwplan2;
// forward plan
fftwplan = fftw_plan_dft_r2c_1d(N, y, yhat, FFTW_ESTIMATE);
fftw_execute(fftwplan);
// set N/2th mode to zero if N is even
if (N % 2 < 1.0e-13) {
yhat[N/2][0] = 0.0;
yhat[N/2][1] = 0.0;
}
// backward plan
fftwplan2 = fftw_plan_dft_c2r_1d(N, yhat, y, FFTW_ESTIMATE);
for (int i = 0; i < 50; i++) {
// yhat to y
fftw_execute(fftwplan2);
// rescale
for (int j = 0; j < N; j++) {
y[j] = y[j] / (double)N;
}
double avg = 0.0;
for (int j = 0; j < N; j++) {
avg += y[j];
}
printf("%.15f\n", avg/N);
}
fftw_destroy_plan(fftwplan);
fftw_destroy_plan(fftwplan2);
void fftw_cleanup(void);
free(x);
free(y);
return 0;
}
Output for N = 256:
0.000000000000000
0.000000000000000
0.000000000000000
-0.000000000000000
0.000000000000000
0.000000000000022
-0.000000000000007
-0.000000000000039
0.000000000000161
-0.000000000000314
0.000000000000369
0.000000000004775
-0.000000000007390
-0.000000000079126
-0.000000000009457
-0.000000000462023
0.000000000900855
-0.000000000196451
0.000000000931323
-0.000000009895302
0.000000039348379
0.000000133179128
0.000000260770321
-0.000003233551979
0.000008285045624
-0.000016331672668
0.000067450106144
-0.000166893005371
0.001059055328369
-0.002521514892578
0.005493164062500
-0.029907226562500
0.093383789062500
-0.339111328125000
1.208251953125000
-3.937500000000000
13.654296875000000
-43.812500000000000
161.109375000000000
-479.250000000000000
1785.500000000000000
-5369.000000000000000
19376.000000000000000
-66372.000000000000000
221104.000000000000000
-753792.000000000000000
2387712.000000000000000
-8603776.000000000000000
29706240.000000000000000
-96833536.000000000000000
Any ideas?
libfftw has the odious habit of modifying its inputs. Back up yhat if you want to do repeated inverse transforms.
OTOH, it's perverse, but why are you repeating the same operation if you don't expect it give different results? (Despite this being the case)
As indicated in comments: "if you want to keep the input data unchanged, use the FFTW_PRESERVE_INPUT flag. Per http://www.fftw.org/doc/Planner-Flags.html"
For example:
// backward plan
fftwplan2 = fftw_plan_dft_c2r_1d(N, yhat, y, FFTW_ESTIMATE | FFTW_PRESERVE_INPUT);

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