Introduction to Programming with OpenMP
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Practical Exercise 3 (More Syntax and SIMD)
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Use similar commands to compile and run the program as in practical
exercise 2.  You should specify static scheduling explicitly, and
continue to declare all variables inside OpenMP directive blocks.


Question 1
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In doing this question, declare every variable and array that is
used in any of the loops inside the DO/for directive as either shared
or private.  Declare all loop indices and temporary variables as
private, and the main arrays as shared.  More details are given on
this in the next lecture.


1.1 Starting with Programs/Stats.f90 or Programs/Stats.c, add directives
to parallelise both loops in procedure Stats, using a combined parallel
and DO/for directive and reductions.  Use exactly the same arguments and
files as in practical exercise 2.

Note that the example output is for Fortran, and includes times using
the intrinsic functions as well as your code; the C does not.  Fortran
users may like to experiment with the tuned libraries and see whether
they improve the times for the intrinsics.

Also note that the data are not normally distributed (Gaussian), so do
not expect the skewness and kurtosis to be exactly 0 and 3.


1.2 Change the program to split the directives into separate parallel
and DO/for ones, putting the former around both DO/for loops.  Note that
doing this correctly is a lot trickier than in practical exercise 2.

You should notice no difference in the values or the times.


Question 2
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2.1 Starting with Programs/Cholesky.f90 or Programs/Cholesky.c, add
directives to parallelise the innermost loops of both loops in procedure
Cholesky and both in procedure Solve, using a combined parallel and
DO/for directive and reductions.  You may need to define extra temporary
variables.  Use exactly the same arguments and files as in practical
exercise 2.

Note that the CPU time goes up but the wall-clock time down for
procedure Cholesky; this is common when things are going well.  Note
that the wall-clock time is a lot less than the CPU time for procedure
Solve, but both times are ridiculously high; this is common when things
are going badly.  In some implementations, the time will be so high that
the program appears to hang - if that happens, just break in.  We need
to try a different approach for this.


2.2 Change the program to parallelise the outermost loops that are
independent in procedure Solve; that is the middle loop for the first
set of loops and the outermost loop for the second.  Study the code to
see why, and why parallelising the middle loop in the second will not
work.

Note that we now have both Cholesky and Solver wall-clock times much
less than the serial code, even though their CPU times are larger.

Make a safe copy of this program and call it Britomart.