# Worksharing Constructs(others)

Most of the time, we end up having more than one loop, a nested loop, where two or three loops will be next to each other. OpenMP provides a clause for handling this kind of situation with collapse. To understand this, we will now study Matrix multiplication, which involves a nested loop. Again, most of the time, we might do computation with a nested loop. Therefore, studying this example would be good practice for solving the nested loop in the future.

#### Collapse¶

The collapse clause can be used for the nested loop; an entire part of the iteration will be divided by an available number of threads. If the outer loop is equal to the available threads, then the outer loop will be divided number of threads. The figure below shows an example of not using the collapse clause. Therefore, only the outer loop is parallelised; each outer loop index will have N number of inner loop iterations.

This is not what we want. Instead, with the available threads, we would like to parallelise the loops as efficiently as we could. Moreover, most of the time, we might have more threads available on a machine; for example, on MeluXina, we can have up to 256 threads. Therefore, when adding the collapse clause, we notice that the available threads execute every single iteration, as seen in the figure below.

Collapse
#pragma omp parallel
#pragma omp for collapse(2)
for(int i = 0; i < N; i++)
{
for(int j = 0; j < N; j++)
{
cout << " Thread id" << " " << omp_get_thread_num() << endl;
}
}

// Or

#pragma omp parallel for collapse(2)
for(int i = 0; i < N; i++)
{
for(int j = 0; j < N; j++)
{
cout << " Thread id" << " " << omp_get_thread_num() << endl;
}
}
!$omp parallel !$omp do collapse(2)
do i = 1, n
do j = 1, n
end do
end do
!$omp end do !$omp end parallel

!! Or

!$omp parallel do collapse(2) do i = 1, n do j = 1, n print*, 'Thread id', omp_get_thread_num() end do end do !$omp end parallel do
Examples and Questions: Collapse
#include <iostream>
#include <omp.h>

using namespace std;

int main()
{
int N=5;

#pragma omp parallel
#pragma omp for collapse(2)
for(int i = 0; i < N; i++)
{
for(int j = 0; j < N; j++)
{
cout << "Outer loop id " << i << " Inner loop id "<< j << " Thread id" << " " << omp_get_thread_num() << endl;
}
}

return 0;
}
program main
use omp_lib
implicit none

integer :: n, i, j
n=5

!$omp parallel !$omp do collapse(2)
do i = 1, n
do j = 1, n
print*, 'Outer loop id ', i , 'Inner loop id ', j , 'Thread id', omp_get_thread_num()
end do
end do
!$omp end do !$omp end parallel

end program main
Outer loop id            4 Inner loop id            2 Thread id          16
Outer loop id            1 Inner loop id            4 Thread id           3
Outer loop id            5 Inner loop id            1 Thread id          20
Outer loop id            4 Inner loop id            1 Thread id          15
Outer loop id            2 Inner loop id            1 Thread id           5
Outer loop id            3 Inner loop id            1 Thread id          10
Outer loop id            3 Inner loop id            4 Thread id          13
Outer loop id            4 Inner loop id            4 Thread id          18
Outer loop id            4 Inner loop id            3 Thread id          17
Outer loop id            3 Inner loop id            3 Thread id          12
Outer loop id            1 Inner loop id            2 Thread id           1
Outer loop id            2 Inner loop id            3 Thread id           7
Outer loop id            1 Inner loop id            5 Thread id           4
Outer loop id            2 Inner loop id            2 Thread id           6
Outer loop id            3 Inner loop id            2 Thread id          11
Outer loop id            2 Inner loop id            5 Thread id           9
Outer loop id            3 Inner loop id            5 Thread id          14
Outer loop id            5 Inner loop id            3 Thread id          22
Outer loop id            5 Inner loop id            4 Thread id          23
Outer loop id            5 Inner loop id            5 Thread id          24
Outer loop id            2 Inner loop id            4 Thread id           8
Outer loop id            1 Inner loop id            3 Thread id           2
Outer loop id            4 Inner loop id            5 Thread id          19
Outer loop id            1 Inner loop id            1 Thread id           0
Outer loop id            5 Inner loop id            2 Thread id          21
• Can you add here any of the scheduling clauses, for example, static, dynamic, etc?
• Is it really necessary to them when you use the collapse, or is it dependent on other factors, such as the nature of the computation and available threads?

#### Reduction¶

The reduction clauses are data-sharing attribute clauses that can be used to perform some forms of repetition calculations in the parallel region.

• it can be used for arithmetic reductions: +,*,-,max,min
• and also with logical operator reductions in C: & && | || ˆ
Reduction
#pragma omp parallel
#pragma omp for reduction(+:sum)
for(int i = 0; i < N; i++)
{
sum +=a[i];
}

// Or

#pragma omp parallel for reduction(+:sum)
for(int i = 0; i < N; i++)
{
sum += a[i];
}
!$omp parallel !$omp do reduction(+:sum)
do i = 1, n
sum = sum + a(i)
end do
!$omp end do !$omp end parallel

!! Or

!$omp parallel do reduction(+:sum) do i = 1, n sum = sum + a(i) end do !$omp end parallel do
Examples and Question: Reduction
#include <iostream>
#include <omp.h>

using namespace std;

int main()
{
int sum,N = 10;
float *a = (float*)malloc(sizeof(float) * N);

#pragma omp parallel for reduction(+:sum)
for(int i = 0; i < N; i++)
{
a[i] = i;
sum += a[i];
}
cout << "Sum is "<< sum << endl;

return 0;
}
program main
use omp_lib
implicit none

! Input vectors
real(8), dimension(:), allocatable :: a

integer :: n, i, sum
n=10

! Allocate memory for vector
allocate(a(n))

!$omp parallel do reduction(+:sum) do i = 1, n a(i) = i sum = sum + a(i) end do !$omp end parallel do

print *, 'Sum is ', sum

end program main
• What happens if you do not use the reduction clause? Do we still get the correct answer?

#### Matrix Multiplication¶

In this example, we consider a square matrix; M=N is equal for both A and B matrices. Even though we deal here with a 2D matrix, we create a 1D array to represent a 2D matrix. In this example, we must use collapse clause since matrix multiplication deals with 3 loops. The first 2 outer loops will take rows of the A matrix and columns of the B matrix. Therefore, these two loops can be easily parallelised. But then we need to sum the value of those two outer loops value finally; this is where we should use the reduction clause.

matrix multiplication function call
for(int row = 0; row < width ; ++row)
{
for(int col = 0; col < width ; ++col)
{
sum=0;
for(int i = 0; i < width ; ++i)
{
sum += a[row*width+i] * b[i*width+col];
}
c[row*width+col] = sum;
}
}
do row = 0, width-1
do col = 0, width-1
sum=0
do i = 0, width-1
sum = sum + (a((row*width)+i+1) * b((i*width)+col+1))
enddo
c(row*width+col+1) = sum
enddo
enddo

### Questions and Solutions¶

Examples: Matrix Multiplication
#include<stdio.h>
#include<stdlib.h>
#include<omp.h>

void Matrix_Multiplication(float *a, float *b, float *c, int width)
{
float sum = 0;
for(int row = 0; row < width ; ++row)
{
for(int col = 0; col < width ; ++col)
{
sum=0;
for(int i = 0; i < width ; ++i)
{
sum += a[row*width+i] * b[i*width+col];
}
c[row*width+col] = sum;
}
}
}

int main()
{
printf("Programme assumes that matrix size is N*N \n");
printf("Please enter the N size number \n");
int N =0;
scanf("%d", &N);

// Initialize the memory
float *a, *b, *c;

// Allocate memory
a = (float*)malloc(sizeof(float) * (N*N));
b = (float*)malloc(sizeof(float) * (N*N));
c = (float*)malloc(sizeof(float) * (N*N));

// Initialize arrays
for(int i = 0; i < (N*N); i++)
{
a[i] = 1.0f;
b[i] = 2.0f;
}

// Fuction call
Matrix_Multiplication(a, b, c, N);

// Verification
for(int i = 0; i < N; i++)
{
for(int j = 0; j < N; j++)
{
printf("%f ", c[j]);

}
printf("\n");
}

// Deallocate memory
free(a);
free(b);
free(c);

return 0;
}
module Matrix_Multiplication_Mod
implicit none
contains
subroutine Matrix_Multiplication(a, b, c, width)
use omp_lib
! Input vectors
real(8), intent(in), dimension(:) :: a
real(8), intent(in), dimension(:) :: b
real(8), intent(out), dimension(:) :: c
real(8) :: sum = 0
integer :: i, row, col, width

do row = 0, width-1
do col = 0, width-1
sum=0
do i = 0, width-1
sum = sum + (a((row*width)+i+1) * b((i*width)+col+1))
enddo
c(row*width+col+1) = sum
enddo
enddo

end subroutine Matrix_Multiplication
end module Matrix_Multiplication_Mod

program main
use Matrix_Multiplication_Mod
use omp_lib
implicit none

! Input vectors
real(8), dimension(:), allocatable :: a
real(8), dimension(:), allocatable :: b

! Output vector
real(8), dimension(:), allocatable :: c
! real(8) :: sum = 0

integer :: n, i
print *, "This program does the addition of two vectors "
print *, "Please specify the vector size = "

! Allocate memory for vector
allocate(a(n*n))
allocate(b(n*n))
allocate(c(n*n))

! Initialize content of input vectors,
! vector a[i] = sin(i)^2 vector b[i] = cos(i)^2
do i = 1, n*n
a(i) = sin(i*1D0) * sin(i*1D0)
b(i) = cos(i*1D0) * cos(i*1D0)
enddo

! Call the vector add subroutine
call Matrix_Multiplication(a, b, c, n)

!!Verification
do i=1,n*n
print *, c(i)
enddo

! Delete the memory
deallocate(a)
deallocate(b)
deallocate(c)

end program main
#include<stdio.h>
#include<stdlib.h>
#include<omp.h>

void Matrix_Multiplication(float *a, float *b, float *c, int width)
{
float sum = 0;
for(int row = 0; row < width ; ++row)
{
for(int col = 0; col < width ; ++col)
{
sum=0;
for(int i = 0; i < width ; ++i)
{
sum += a[row*width+i] * b[i*width+col];
}
c[row*width+col] = sum;
}
}
}

int main()
{
printf("Programme assumes that matrix size is N*N \n");
printf("Please enter the N size number \n");
int N =0;
scanf("%d", &N);

// Initialize the memory
float *a, *b, *c;

// Allocate memory
a = (float*)malloc(sizeof(float) * (N*N));
b = (float*)malloc(sizeof(float) * (N*N));
c = (float*)malloc(sizeof(float) * (N*N));

// Initialize arrays
for(int i = 0; i < (N*N); i++)
{
a[i] = 1.0f;
b[i] = 2.0f;
}

// Fuction call
Matrix_Multiplication(a, b, c, N);

// Verification
for(int i = 0; i < N; i++)
{
for(int j = 0; j < N; j++)
{
printf("%f ", c[j]);

}
printf("\n");
}

// Deallocate memory
free(a);
free(b);
free(c);

return 0;
}
module Matrix_Multiplication_Mod
implicit none
contains
subroutine Matrix_Multiplication(a, b, c, width)
use omp_lib
! Input vectors
real(8), intent(in), dimension(:) :: a
real(8), intent(in), dimension(:) :: b
real(8), intent(out), dimension(:) :: c
real(8) :: sum = 0
integer :: i, row, col, width
do row = 0, width-1
do col = 0, width-1
sum=0
do i = 0, width-1
sum = sum + (a((row*width)+i+1) * b((i*width)+col+1))
enddo
c(row*width+col+1) = sum
enddo
enddo

end subroutine Matrix_Multiplication
end module Matrix_Multiplication_Mod

program main
use Matrix_Multiplication_Mod
use omp_lib
implicit none

! Input vectors
real(8), dimension(:), allocatable :: a
real(8), dimension(:), allocatable :: b

! Output vector
real(8), dimension(:), allocatable :: c
! real(8) :: sum = 0

integer :: n, i
print *, "This program does the addition of two vectors "
print *, "Please specify the vector size = "

! Allocate memory for vector
allocate(a(n*n))
allocate(b(n*n))
allocate(c(n*n))

! Initialize content of input vectors,
! vector a[i] = sin(i)^2 vector b[i] = cos(i)^2
do i = 1, n*n
a(i) = sin(i*1D0) * sin(i*1D0)
b(i) = cos(i*1D0) * cos(i*1D0)
enddo

! Call the vector add subroutine
call Matrix_Multiplication(a, b, c, n)

!!Verification
do i=1,n*n
print *, c(i)
enddo

! Delete the memory
deallocate(a)
deallocate(b)
deallocate(c)

end program main
#include<stdio.h>
#include<stdlib.h>
#include<omp.h>

void Matrix_Multiplication(float *a, float *b, float *c, int width)
{
float sum = 0;
#pragma for loop collapse(2) reduction (+:sum)
for(int row = 0; row < width ; ++row)
{
for(int col = 0; col < width ; ++col)
{
sum=0;
for(int i = 0; i < width ; ++i)
{
sum += a[row*width+i] * b[i*width+col];
}
c[row*width+col] = sum;
}
}
}

int main()
{
printf("Programme assumes that matrix size is N*N \n");
printf("Please enter the N size number \n");
int N =0;
scanf("%d", &N);

// Initialize the memory
float *a, *b, *c;

// Allocate memory
a = (float*)malloc(sizeof(float) * (N*N));
b = (float*)malloc(sizeof(float) * (N*N));
c = (float*)malloc(sizeof(float) * (N*N));

// Initialize arrays
for(int i = 0; i < (N*N); i++)
{
a[i] = 1.0f;
b[i] = 2.0f;
}
#pragma omp parallel
// Fuction call
Matrix_Multiplication(a, b, c, N);

// Verification
for(int i = 0; i < N; i++)
{
for(int j = 0; j < N; j++)
{
printf("%f ", c[j]);
}
printf("\n");
}

// Deallocate memory
free(a);
free(b);
free(c);

return 0;
}
module Matrix_Multiplication_Mod
implicit none
contains
subroutine Matrix_Multiplication(a, b, c, width)
use omp_lib
! Input vectors
real(8), intent(in), dimension(:) :: a
real(8), intent(in), dimension(:) :: b
real(8), intent(out), dimension(:) :: c
real(8) :: sum = 0
integer :: i, row, col, width

!$omp do collapse(2) reduction(+:sum) do row = 0, width-1 do col = 0, width-1 sum=0 do i = 0, width-1 sum = sum + (a((row*width)+i+1) * b((i*width)+col+1)) enddo c(row*width+col+1) = sum enddo enddo !$omp end do

end subroutine Matrix_Multiplication
end module Matrix_Multiplication_Mod

program main
use Matrix_Multiplication_Mod
use omp_lib
implicit none

! Input vectors
real(8), dimension(:), allocatable :: a
real(8), dimension(:), allocatable :: b

! Output vector
real(8), dimension(:), allocatable :: c
! real(8) :: sum = 0

integer :: n, i
print *, "This program does the addition of two vectors "
print *, "Please specify the vector size = "

! Allocate memory for vector
allocate(a(n*n))
allocate(b(n*n))
allocate(c(n*n))

! Initialize content of input vectors,
! vector a[i] = sin(i)^2 vector b[i] = cos(i)^2
do i = 1, n*n
a(i) = sin(i*1D0) * sin(i*1D0)
b(i) = cos(i*1D0) * cos(i*1D0)
enddo

!$omp parallel ! Call the vector add subroutine call Matrix_Multiplication(a, b, c, n) !$omp end parallel

!!Verification
do i=1,n*n
print *, c(i)
enddo

! Delete the memory
deallocate(a)
deallocate(b)
deallocate(c)

end program main
Compilation and Output
// compilation
$gcc Matrix-multiplication.c -o Matrix-Multiplication-Serial // execution$ ./Matrix-Multiplication-Serial

Programme assumes that matrix (square matrix) size is N*N
Please enter the N size number
4
8 8 8 8
8 8 8 8
8 8 8 8
8 8 8 8
// compilation
$gfortran Matrix-multiplication.f90 -o Matrix-Multiplication-Serial // execution$ ./Matrix-Multiplication-Serial

Programme assumes that matrix (square matrix) size is N*N
Please enter the N size number
4
8 8 8 8
8 8 8 8
8 8 8 8
8 8 8 8
// compilation
$gcc -fopenmp Matrix-multiplication-Solution.c -o Matrix-Multiplication-Solution // execution$ ./Matrix-Multiplication-Solution
Programme assumes that matrix (square matrix) size is N*N
Please enter the N size number
4
8 8 8 8
8 8 8 8
8 8 8 8
8 8 8 8
// compilation
$gfortran -fopenmp Matrix-multiplication-Solution.f90 -o Matrix-Multiplication-Solution // execution$ ./Matrix-Multiplication-Solution
Programme assumes that matrix (square matrix) size is N*N
Please enter the N size number
4
8 8 8 8
8 8 8 8
8 8 8 8
8 8 8 8
Questions
• Right now, we are dealing with square matrices. Could you write a code for a different matrix size while still fulfilling the matrix multiplication condition?

• Could you use any one of the loop scheduling, for example, dynamic or static? Do you see any performance gain?

Last update: January 31, 2024 09:18:25
Created: April 26, 2023 10:45:49