• #### About ParallelFor() and the grainsize..

From Wisdom90@21:1/5 to All on Tue Dec 31 17:31:39 2019
Hello,

I have just read the following web page:

Parallelization: Harder than it looks

https://www.jayconrod.com/posts/29/parallelization--harder-than-it-looks

Notice that MIT's Cilk is using a divide and conquer approach to
calculate the grainsize for the Parallel For, here it is:

-------
void run_loop(first, last) {
if (last - first < grainsize) {
for (int i = first; i < last; ++i) LOOP_BODY;
} else {
int mid = (last-first)/2;
cilk_spawn run_loop(first, mid);
run_loop(mid, last);
}
}
-------

But as you are noticing if i do a simulation of it by
running my following Delphi program:

----------------------

program test;

var c,d:uint64;

begin

c:=high(uint64);

d:=0;

repeat

c:=c div 2;
d:=d+1;

until c<=1000;

writeln(c);
writeln(d);

end.

-------

So as you are noticing for a grainsize of 1000 the above Delphi program
gives 511, that means that the Cilk's divide and conquer approach to
calculate the grainsize for the Parallel For is "not" good.

This is why you have to take a look at my Threadpool engine with
priorities that scales very well that is really powerful because it
scales very well on multicore and NUMA systems, also it comes with a ParallelFor() that scales very well on multicores and NUMA systems, and
take a look at its source code to notice i am calculating much more
precisely and correctly the grainsize for ParallelFor() than the Cilk's
divide and conquer to calculate the grainsize that is "not" good.

Today i will talk about data dependency and parallel loops..

For a loop to be parallelized, every iteration must be independent of
the others, one way to be sure of it is to execute the loop
in the direction of the incremented index of the loop and in the
direction of the decremented index of the loop and verify if the results
are the same. A data dependency happens if memory is modified: a loop
has a data dependency if an iteration writes a variable that is read or
write in another iteration of the loop. There is no data dependency if
only one iteration reads or writes a variable or if many iterations read
the same variable without modifying it. So this is the "general" "rules".

Now there remains to know that you have for example to know how to
construct the parallel for loop if there is an induction variable or if
there is a reduction operation, i will give an example of them:

If we have the following (the code looks like Algol or modern Object
Pascal):

IND:=0

For I:=1 to N
Do
Begin
IND := IND + 1;
A[I]:=B[IND];
End;

So as you are noticing since IND is an induction variable , so
to parallelize the loop you have to do the following:

For I:=1 to N
Do
Begin
IND:=(I*(I+1))/2;
A[I]:=B[IND];
End;

Now for the reduction operation example, you will notice that my
invention that is my Threadpool with priorities that scales very well (
read about it below) supports a Parallel For that scales very well that supports "grainsize", and you will notice that the grainsize can be used
in the ParallelFor() with a reduction operation and you will notice that
my following powerful scalable Adder is also used in this scenario, here
it is:

So here is the example with a reduction operation in modern Object Pascal:

TOTAL:=0.0
For I := 1 to N
Do
Begin
TOTAL:=TOTAL+A[I]
End;

So with my powerful scalable Adder and with my powerful invention that
is my ParallelFor() that scales very well, you will parallelize the
above like this:

procedure test1(j:integer;ptr:pointer);
begin

end;

// Let's suppose that N is 100000
// In the following, 10000 is the grainsize

obj.ParallelFor(1,N,test1,10000,pointer(0));

TOTAL:=T.get();

And read the following to understand how to use grainsize of my Parallel
for that scales well:

About my ParallelFor() that scales very well that uses my efficient

With ParallelFor() you have to:

1- Ensure Sufficient Work

Each iteration of a loop involves a certain amount of work,
so you have to ensure a sufficient amount of the work,

2- In OpenMP we have that:

Static and Dynamic Scheduling

One basic characteristic of a loop schedule is whether it is static or
dynamic:

• In a static schedule, the choice of which thread performs a particular iteration is purely a function of the iteration number and number of
threads. Each thread performs only the iterations assigned to it at the beginning of the loop.

• In a dynamic schedule, the assignment of iterations to threads can
vary at runtime from one execution to another. Not all iterations are
requests more iterations after it has completed the work already
assigned to it.

But with my ParallelFor() that scales very well, since it is using my
efficient Threadpool that scales very well, so it is using Round-robin scheduling and it uses also work stealing, so i think that this is
sufficient.

My Threadpool engine with priorities that scales very well is really
powerful because it scales very well on multicore and NUMA systems, also
it comes with a ParallelFor() that scales very well on multicores and
NUMA systems.

Here is the explanation of my ParallelFor() that scales very well:

I have also implemented a ParallelFor() that scales very well, here is
the method:

procedure ParallelFor(nMin, nMax:integer;aProc: TParallelProc;GrainSize:integer=1;Ptr:pointer=nil;pmode:TParallelMode=pmBlocking;Priority:TPriorities=NORMAL_PRIORITY);

nMin and nMax parameters of the ParallelFor() are the minimum and
maximum integer values of the variable of the ParallelFor() loop, aProc parameter of ParallelFor() is the procedure to call, and GrainSize
integer parameter of ParallelFor() is the following:

The grainsize sets a minimum threshold for parallelization.

A rule of thumb is that grainsize iterations should take at least
100,000 clock cycles to execute.

For example, if a single iteration takes 100 clocks, then the grainsize
needs to be at least 1000 iterations. When in doubt, do the following experiment:

1- Set the grainsize parameter higher than necessary. The grainsize is specified in units of loop iterations.

If you have no idea of how many clock cycles an iteration might take,

The rationale is that each iteration normally requires at least one
clock per iteration. In most cases, step 3 will guide you to a much
smaller value.

3- Iteratively halve the grainsize parameter and see how much the
algorithm slows down or speeds up as the value decreases.

A drawback of setting a grainsize too high is that it can reduce
parallelism. For example, if the grainsize is 1000 and the loop has 2000 iterations, the ParallelFor() method distributes the loop across only
two processors, even if more are available.

And you can pass a parameter in Ptr as pointer to ParallelFor(), and you
can set pmode parameter of to pmBlocking so that ParallelFor() is
blocking or to pmNonBlocking so that ParallelFor() is non-blocking, and
the Priority parameter is the priority of ParallelFor(). Look inside the test.pas example to see how to use it.

Thank you,
Amine Moulay Ramdane.

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