OpenMP is discussed in *Slides from lectures* starting with Lecture 13.

There are a few sample codes in the $CLASSHG/codes/openmp directory. See the README.txt file for instructions on compiling and executing.

Here is a very simple code, that simply evaluates a costly function at many points:

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! $CLASSHG/codes/openmp/yeval.f90
program yeval
use omp_lib
implicit none
integer, parameter :: n = 100000000
integer :: i, nthreads
real(kind=8), dimension(n) :: y
real(kind=8) :: dx, x
! Specify number of threads to use:
!$ print *, "How many threads to use? "
!$ read *, nthreads
!$ call omp_set_num_threads(nthreads)
!$ print "('Using OpenMP with ',i3,' threads')", nthreads
dx = 1.d0 / (n+1.d0)
!$omp parallel do private(x)
do i=1,n
x = i*dx
y(i) = exp(x)*cos(x)*sin(x)*sqrt(5*x+6.d0)
enddo
print *, "Filled vector y of length", n
end program yeval
``` |

Note the following:

- Lines starting with !$ are only executed if the code is compiled and run with the flag -fopenmp, otherwise they are comments.
- x must be declared a private variable in the omp parallel do loop, so that each thread has its own version. Otherwise another thread might reset x between the time its assigned a value and the time this value is used to set y(i).
- The loop iterator i is private by default, but all other varaibles are shared by default.

Consider the problem of normalizing a vector by dividing each element by the 1-norm of the vector, defined by \|x\|_1 = \sum_{i=1}^n |x_i|.

We must first loop over all points to compute the norm. Then we must loop over all points and set y_i = x_i / \|x\|_1. Note that we cannot combine these two loops into a single loop!

Here is an example with *fine-grain paralellism*, where we use the OpenMP
omp parallel do directive or the omp do directive within a omp
parallel block.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 | ```
! $CLASSHG/codes/openmp/normalize1.f90
! Example of normalizing a vector using fine-grain parallelism.
program main
use omp_lib
implicit none
integer :: i, thread_num
integer, parameter :: n = 1000
real(kind=8), dimension(n) :: x, y
real(kind=8) :: norm,ynorm
integer :: nthreads
! Specify number of threads to use:
nthreads = 1 ! need this value in serial mode
!$ nthreads = 4
!$ call omp_set_num_threads(nthreads)
!$ print "('Using OpenMP with ',i3,' threads')", nthreads
! Specify number of threads to use:
!$ call omp_set_num_threads(4)
! initialize x:
!$omp parallel do
do i=1,n
x(i) = dble(i) ! convert to double float
enddo
norm = 0.d0
ynorm = 0.d0
!$omp parallel private(i)
!$omp do reduction(+ : norm)
do i=1,n
norm = norm + abs(x(i))
enddo
!$omp barrier ! not needed (implicit)
!$omp do reduction(+ : ynorm)
do i=1,n
y(i) = x(i) / norm
ynorm = ynorm + abs(y(i))
enddo
!$omp end parallel
print *, "norm of x = ",norm, " n(n+1)/2 = ",n*(n+1)/2
print *, 'ynorm should be 1.0: ynorm = ', ynorm
end program main
``` |

Note the following:

- We initialize x_i=i as a test, so \|x\|_1 = n(n+1)/2.
- The compiler decides how to split the loop between threads. The loop starting on line 38 might be split differently than the loop starting on line 45.
- Because of this, all threads must have access to all of memory.

Next is a version with *coarse-grain parallelism*, were we decide how to
split up the array between threads and then execute the same code on each
thread, but each thread will compute its own version of istart and iend
for its portion of the array. With this code we are guaranteed that
thread 0 always handles x(1), for example, so in principle the data could
be distributed. When using OpenMP on a shared memory computer this doesn’t
matter, but this version is more easily generalized to MPI.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 | ```
! $CLASSHG/codes/openmp/normalize2.f90
! Example of normalizing a vector using coarse-grain parallelism.
program main
use omp_lib
implicit none
integer, parameter :: n = 1000
real(kind=8), dimension(n) :: x,y
real(kind=8) :: norm,norm_thread,ynorm,ynorm_thread
integer :: nthreads, points_per_thread,thread_num
integer :: i,istart,iend
! Specify number of threads to use:
nthreads = 1 ! need this value in serial mode
!$ nthreads = 4
!$ call omp_set_num_threads(nthreads)
!$ print "('Using OpenMP with ',i3,' threads')", nthreads
! Determine how many points to handle with each thread.
! Note that dividing two integers and assigning to an integer will
! round down if the result is not an integer.
! This, together with the min(...) in the definition of iend below,
! insures that all points will get distributed to some thread.
points_per_thread = (n + nthreads - 1) / nthreads
print *, "points_per_thread = ",points_per_thread
! initialize x:
do i=1,n
x(i) = dble(i) ! convert to double float
enddo
norm = 0.d0
ynorm = 0.d0
!$omp parallel private(i,norm_thread, &
!$omp istart,iend,thread_num,ynorm_thread)
thread_num = 0 ! needed in serial mode
!$ thread_num = omp_get_thread_num() ! unique for each thread
! Determine start and end index for the set of points to be
! handled by this thread:
istart = thread_num * points_per_thread + 1
iend = min((thread_num+1) * points_per_thread, n)
!$omp critical
print 201, thread_num, istart, iend
!$omp end critical
201 format("Thread ",i2," will take i = ",i6," through i = ",i6)
norm_thread = 0.d0
do i=istart,iend
norm_thread = norm_thread + abs(x(i))
enddo
! update global norm with value from each thread:
!$omp critical
norm = norm + norm_thread
print *, "norm updated to: ",norm
!$omp end critical
! make sure all have updated norm before proceeding:
!$omp barrier
ynorm_thread = 0.d0
do i=istart,iend
y(i) = x(i) / norm
ynorm_thread = ynorm_thread + abs(y(i))
enddo
! update global ynorm with value from each thread:
!$omp critical
ynorm = ynorm + ynorm_thread
print *, "ynorm updated to: ",ynorm
!$omp end critical
!$omp barrier
!$omp end parallel
print *, "norm of x = ",norm, " n(n+1)/2 = ",n*(n+1)/2
print *, 'ynorm should be 1.0: ynorm = ', ynorm
end program main
``` |

Note the following:

- istart and iend, the starting and ending values of i taken by each thread, are explicitly computed in terms of the thread number. We must be careful to handle the case when the number of threads does not evenly divide n.
- Various variables must be declared private in lines 37-38.
- norm must be initialized to 0 before the omp parallel block. Otherwise some thread might set it to 0 after another thread has already updated it by its norm_thread.
- The update to norm on line 60 must be in a omp critical block, so two threads don’t try to update it simultaneously (data race).
- There must be an omp barrier on line 65 between updating norm by each thread and using norm to compute each y(i). We must make sure all threads have updated norm or it won’t have the correct value when we use it.

For comparison of fine-grain and coarse-grain parallelism on Jacobi iteration, see

*OpenMP:*in bibliography- http://openmp.org/wp/
- Livermore tutorial
- NERSC tutorial