Lesson on basic parallelism¶

Parallelism in ABINIT, generalities and environments.¶

There are many situations where a sequential code is not enough, often because it would take too much time to get a result. There are also cases where you just want things to go as fast as your computational resources allow it. By using more than one processor, you might also have access to more memory than with only one processor. To this end, it is possible to use ABINIT in parallel, with dozens, hundreds or even thousands processors.

This tutorial offers you a little reconnaissance tour inside the complex world that emerges as soon as you want to use more than one processor. From now on, we will suppose that you are already familiar with ABINIT and that you have gone through all four basic tutorials. If this is not the case, we strongly advise you to do so, in order to truly benefit from this tutorial.

We strongly recommend you to acquaint yourself with some basic concepts of parallel computing too. In particular Almdalh’s law, that rationalizes the fact that, beyond some number of processors, the inherently sequential parts will dominate parallel parts, and give a limitation to the maximal speed-up that can be achieved.

Generalities¶

With the broad availability of multi-core processors, everybody now has a parallel machine at hand. ABINIT will be able to take advantage of the availability of several cores for most of its capabilities, be it ground-state calculations, molecular dynamics, linear-response, many-body perturbation theory, …

Such tightly integrated multi-core processors (or so-called SMP machines, meaning Symmetric Multi-Processing) can be interlinked within networks, based on Ethernet or other types of connections (Quadrics, Myrinet, etc …). The number of cores in such composite machines can easily exceed one hundred, and go up to a fraction of a million these days. Most ABINIT capabilities can use efficiently several hundred computing cores. In some cases, even more than ten thousand computing cores can be used efficiently.

Before actually starting this tutorial and the associated ones, we strongly advise you to get familiar with your own parallel environment. It might be relatively simple for a SMP machine, but more difficult for very powerful machines. You will need at least to have MPI (see next section) installed on your machine. Take some time to determine how you can launch a job in parallel with MPI (typically the qsub or sbatch command and an associated shell script), what are the resources available and the limitations as well, and do not hesitate to discuss with your system administrator if you feel that something is not clear to you.

We will suppose in the following that you know how to run a parallel program and that you are familiar with the peculiarities of your system. Please remember that, as there is no standard way of setting up a parallel environment, we are not able to provide you with support beyond ABINIT itself.

2 Characteristics of parallel environments¶

Different software solutions can be used to benefit from parallelism. Most of ABINIT parallelism is based on MPI, but some additional speed-up (or a better distribution of data, allowing to run bigger calculations) is based on OpenMP. As of writing, efforts also focus on Graphical Processing Units (GPUs), with CUDA and MAGMA. The latter will not be described in the present tutorial.

MPI¶

MPI stands for Message Passing Interface. The goal of MPI, simply stated, is to develop a widely used standard for writing message- passing programs. As such the interface attempts to establish a practical, portable, efficient, and flexible standard for message passing.

The main advantages of establishing a message-passing standard are portability and ease-of-use. In a distributed memory communication environment in which the higher level routines and/or abstractions are build upon lower-level message-passing routines, the benefits of standardization are particularly obvious. Furthermore, the definition of a message-passing standard provides vendors with a clearly defined base set of routines that they can implement efficiently, or in some cases provide hardware support for, thereby enhancing scalability (see http://mpi-forum.org).

At some point in its history MPI has reach a critical popularity level, and a bunch of projects have popped-up like daisies in the grass. Now the tendency is back to gathering and merging. For instance, Open MPI is a project combining technologies and resources from several other projects (FT-MPI, LA-MPI, LAM/MPI, and PACX-MPI) in order to build the best MPI library available. Open MPI is a completely new MPI2-compliant implementation, offering advantages for system and software vendors, application developers and computer science researchers (see https://www.open-mpi.org)

OpenMP¶

The OpenMP Application Program Interface (API) supports multi-platform shared-memory parallel programming in C/C++ and Fortran on all architectures, including Unix platforms and Windows NT platforms. Jointly defined by a group of major computer hardware and software vendors, OpenMP is a portable, scalable model that gives shared-memory parallel programmers a simple and flexible interface for developing parallel applications for platforms ranging from the desktop to the supercomputer (http://www.openmp.org).

OpenMP is rarely used within ABINIT, and only for specific purposes. In any case, the first level of parallelism for these parts is based on MPI. Thus, the use of OpenMP in ABINIT will not be described in this tutorial.

Scalapack¶

Scalapack is the parallel version of the popular LAPACK library (for linear algebra). It can play some role in the parallelism of several parts of ABINIT, especially the Band-FFT parallelism, and the parallelism for the Bethe- Salpether equation. ScaLAPACK being itself based on MPI, we will not discuss its use in ABINIT in this tutorial.

Fast/slow communications¶

Characterizing the data-transfer efficiency between two computing cores (or the whole set of cores) is a complex task. At a quite basic level, one has to recognize that not only the quantity of data that can be transferred per unit of time is important, but also the time that is needed to initialize such a transfer (so called “latency”).

Broadly speaking, one can categorize computers following the speed of communications. In the fast communication machines, the latency is very low and the transfer time, once initialized, is very low too. For the parallelised part of ABINIT, SMP machines and machines with fast interconnect (Quadrics, Myrinet …) will usually not be limited by their network characteristics, but by the existence of residual sequential parts. The tutorials that have been developed for ABINIT have been based on fast communication machines.

If the set of computing cores that you plan to use is not entirely linked using a fast network, but includes some connections based e.g. on Ethernet, then, you might not be able to benefit from the speed-up announced in the tutorials. You have to perform some tests on your actual machine to gain knowledge of it.

3 What parts of ABINIT are parallel?¶

Parallelizing a code is a very delicate and complicated task, thus do not expect that things will systematically go faster just because you are using a parallel version of ABINIT. Please keep also in mind that in some situations, parallelization is simply impossible. At the present time, the parts of ABINIT that have been parallelized, and for which a tutorial is available, include:

Note that the tutorial on ground state with plane waves presents a complete overview of this parallelism, including up to four levels of parallelisation and, as such, is rather complex. Of course, it is also quite powerful, and allows to use several hundreds of processors.

Actually, the two levels based on

• the treatment of k-points in reciprocal space;
• the treatment of spins, for spin-polarized collinear situations nsppol=2);

are, on the contrary, quite easy to use. An example of such parallelism will be given in the next section.

4 A simple example of parallelism in ABINIT¶

Running a job¶

Before starting, you might consider working in a different subdirectory as for the other lessons. Why not “Work_paral”?

Copy the files file and the input file from the ~abinit/tests/tutorial directory to your work directory. They are named tbasepar_1.files and tbasepar_1.in. You can start immediately a sequential run, to have a reference CPU time. On a 2.8GHz PC, it runs in about one minute.

Contrary to the sequential case, it is worth to have a look at the “files” file, and to modify it for the parallel execution, as one should avoid unnecessary network communications. If every node has its own temporary or scratch directory, you can achieve this by providing a path to a local disk for the temporary files in abinit.files. Supposing each processor has access to a local temporary disk space named /scratch/user , then you might modify the 5th line of the files file so that it becomes:

tbasepar_1.in
tbasepar_1.out
tbasepar_1i
tbasepar_1o
/scratch/user/tbasepar_1
../../Psps_for_tests/HGH/82pb.4.hgh


Note that determining ahead of time the precise resources you will need for your run will save you a lot of time if you are using a batch queue system.

Parallelism over the k-points¶

The most favorable case for a parallel run is to treat the k-points concurrently, since the calculations can be done independently for each one of them.

Actually, tbasepar_1.in corresponds to the investigation of a fcc crystal of lead, which requires a large number of k-points if one wants to get an accurate description of the ground state. Examine this file. Note that the cut-off is realistic, as well as the grid of k-points (giving 60 k points in the irreducible Brillouin zone). However, the number of SCF steps, nstep, has been set to 3 only. This is to keep the CPU time reasonable for this tutorial, without affecting the way parallelism on the k points will be able to increase the speed. Once done, your output files have likely been produced. Examine the timing in the output file (the last line gives the overall CPU and Wall time), and keep note of it.

Now you should run the parallel version of ABINIT. On a multi-core PC, you might succeed to use two compute cores by issuing the run command for your MPI implementation, and mention the number of processors you want to use, as well as the abinit command:

mpirun -np 2 ../../src/main/abinit < tbasepar_1.files >& tbasepar_1.log &


Depending on your particular machine, “mpirun” might have to be replaced by “mpiexec”, and “-np” by some other option.

On a cluster, with the MPICH implementation of MPI, you have to set up a file with the addresses of the different CPUs. Let’s suppose you call it cluster. For a PC bi-processor machine, this file could have only one line, like the following:

sleepy.pcpm.ucl.ac.be:2


For a cluster of four machines, you might have something like:

tux0
tux1
tux2
tux3


More possibilities are mentioned in the file ~abinit/doc/users/paral_use.

Then, you have to issue the run command for your MPI implementation, and mention the number of processors you want to use, as well as the abinit command and the file containing the CPU addresses.

On a PC bi-processor machine, this gives the following:

mpirun -np 2 -machinefile cluster ../../src/main/abinit < tbasepar_1.files >& tbasepar_1.log &


Now, examine the corresponding output file. If you have kept the output from the sequential job, you can make a diff between the two files. You will notice that the numerical results are quite identical. You will also see that 60 k-points have been kept in the memory in the sequential case, while 30 k-points have been kept in the memory (per processor !) in the parallel case.

The timing can be found at the end of the file. Here is an example:

- Proc.   0 individual time (sec): cpu=         28.3  wall=         28.3

================================================================================

Calculation completed.
Delivered    1 WARNINGs and   1 COMMENTs to log file.
+Overall time at end (sec) : cpu=         56.6  wall=         56.6


This corresponds effectively to a speed-up of the job by a factor of two. Let’s examine it. The line beginning with Proc. 0 corresponds to the CPU and Wall clock timing seen by the processor number 0 (processor indexing always starts at 0: here the other is number 1): 28.3 sec of CPU time, and the same amount of Wall clock time. The line that starts with +Overall time corresponds to the sum of CPU times and Wall clock timing for all processors. The summation is quite meaningful for the CPU time, but not so for the wall clock time: the job was finished after 28.3 sec, and not 56.6 sec.

Now, you might try to increase the number of processors, and see whether the CPU time is shared equally amongst the different processors, so that the Wall clock time seen by each processor decreases. At some point (depending on your machine, and the sequential part of ABINIT), you will not be able to decrease further the Wall clock time seen by one processor. It is not worth to try to use more processors. You should get a curve similar to this one:

The red curve materializes the speed-up achieved, while the green one is the “y = x” line. The shape of the red curve will vary depending on your hardware configuration. The definition of the speed-up is the time taken in a sequential calculation divided by the time for your parallel calculation (hopefully > 1) .

One last remark: the number of k-points need not be a multiple of the number of processors. As an example, you might try to run the above case with 16 processors: most of the processors will treat 4 k points, but four of them will only treat 3 k points. The maximal speed-up will only be 15 (=60/4), instead of 16.

Try to avoid leaving an empty processor as this can make abinit fail with certain compilers. An empty processor happens, for example, if you use 14 processors: you obtain ceiling(60/14) = 5 k points per processor. In this case 12 processors are filled with 5 k points each (giving 60), and the last 2 processors are completely empty. Obviously there is no point in not reducing the number of processors to 12. The extra processors do no useful work, but have to run anyway, just to confirm to abinit once in a while that all 14 processors are alive.

Parallelism over the spins¶

The parallelization over the spins (up, down) is done along with the one over the k-points, so it works exactly the same way. The files ~abinit/tests/tutorial/tbasepar_2.in and ~abinit/tests/tutorial/tbasepar_2.files treat a spin-polarized system (distorted FCC Iron) with only one k-point in the Irreducible Brillouin Zone. This is quite unphysical, and has the sole purpose to show the spin parallelism with as few as two processors: the k-point parallelism has precedence over the spin parallelism, so that with 2 processors, one needs only one k-point to see the spin parallelism.
If needed, modify the files file, to provide a local temporary disk space. Run this test case, in sequential, then in parallel.

While the jobs are running, read the input and files file. Then look closely at the output and log files. They are quite similar. With a diff, you will see the only obvious manifestation of the parallelism in the following:

< P newkpt: treating     40 bands with npw=    2698 for ikpt=   1
< P newkpt: treating     40 bands with npw=    2698 for ikpt=   1
---
> P newkpt: treating     40 bands with npw=    2698 for ikpt=   1 by node    0
> P newkpt: treating     40 bands with npw=    2698 for ikpt=   1 by node    1


In the second case (parallelism), node 0 is taking care of the up state for k-point 1, while node 1 is taking care of the down state for k-point 1. The timing analysis is very similar to the k-point parallelism case.

If you have more than 2 processors at hand, you might increase the value of ngkpt, so that more than one k-point is available, and see that the k-point and spin parallelism indeed work concurrently.

Number of computing cores to accomplish a task¶

Balancing efficiently the load on the processors is not always straightforward. When using k-point- and spin-parallelism, the ideal numbers of processors to use are those that divide the product of nsppol by nkpt (e.g. for nsppol*nkpt, it is quite efficient to use 2, 3, 4, 6 or 12 processors). ABINIT will nevertheless handle correctly other numbers of processors, albeit slightly less efficiently, as the final time will be determined by the processor that will have the biggest share of the work to do.

Beyond a certain number of processors, the efficiency of parallelism saturates, and may even decrease. This is due to the inevitable overhead resulting from the increasing amount of communication between the processors. The loss of efficiency is highly dependent on the implementation and linked to the decreasing charge on each processor too.

5 Details of the implementation¶

The MPI toolbox in ABINIT¶

The ABINIT-specific MPI routines are located in different subdirectories of ~abinit/src : 12_hide_mpi/, 51_manage_mpi/, 56_io_mpi/, 79_seqpar_mpi/. They include:

• low-level communication handlers (xfuncmpi, initmpi_*,xdef_comm);
• header I/O helpers (hdr_io, hdr_io_netcdf);
• wavefunction I/O helpers (Wff*);
• a multiprocess-aware output routine (wrtout);
• a clean exit routine (leave_new).

They are used by a wide range of routines.

You might want to have a look at the routine headers for more detailed descriptions.

How to parallelize a routine: some hints¶

Here we will give you some advice on how to parallelize a subroutine of ABINIT. Do not expect too much, and remember that you remain mostly on your own for most decisions. Furthermore, we will suppose that you are familiar with ABINIT internals and source code. Anyway, you can skip this section without hesitation, as it is primarily intended for advanced developers.

First, every call to a MPI routine and every purely parallel section of your subroutine must be surrounded by the following preprocessing directives:

#if defined MPI
...
#endif


The first block of this type will likely appear in the “local variables” section, where you will declare all MPI-specific variables. Please note that some of them will be used in sequential mode as well, and thus will be declared outside this block (typically am_master , master, me_loc, etc.).

The MPI communications should be initialized at the very beginning of your subroutine. To do this, we suggest the following piece of code:

! Init mpi_comm
call xcomm_world(spaceComm)
am_master=.true.
master = 0

! Init ntot proc max
call xproc_max(nproc_loc,ierr)

! Define who i am
call xme_whoiam(me_loc)

#if defined HAVE_MPI
if (me_loc/=0) then
am_master=.FALSE.
endif

write(message, '(a,i3,a)' ) ' <ROUTINE NAME> ',nproc_loc,' CPU synchronized'
call wrtout(std_out,message,'COLL')
...
#endif


Note that the first calls to x* are outside the preprocessing - they must be called in all cases, and have their own pre-processed sections. The cleaning and closing of MPI stuff is done in a central part of abinit at the end of the run.