The following post is based on a paper generously contributed by Jerome Huck, a senior aerospace/defence engineer, scientist, and author. A link to figures and the code can be found at the bottom of this post.
So you want to run some heavy-duty algorithms on your Android device, and you’re wondering what is the best environment to use, and whether your Nexus 7 tablet would be up to the job. In this post, based upon a paper generously contributed by Jerome Huck, a senior aerospace engineer & scientist, we’ll take a look at a test involving some heavy-duty computational fluid dynamics equations, and we’ll compare the execution times on a PC and a Nexus 7 tablet.
Implementation languages
Which language & development environment is the best fit? The Eclipse SDK is one obvious choice to go, with development usually done in Java. Unlocking additional performance through native C & C++ code can also be done via the Native Development Kit (NDK), though this adds complexity due to the mixing of Java, C/C++, and JNI glue code.
What if you want to develop directly on your device? Thanks to the openness of Google Play, there are many options available. The Java AIDE will allow you to write, compile and run programs directly on your Android tablet.
For native performance, C/C++ are available through C4DROID and CCTOOLS, an implementation of the GNU GCC 4.8.1 compiler. Fortran is also available for download from CCTOOLS’s menu.
Python development is available via QPython or Kivy. QPython implements the Python language but is still in beta stage; the Kivy Launcher enables you to run Kivy applications, an open source Python library for rapid development. Kivy applications can also make use of innovative user interfaces, including multi-touch apps.
So, just how powerful is your Nexus 7? Java, Basic, C/C++, Python and Fortran all seem like good candidates to evaluate the power of a Nexus 7 with a test case.
The Test Case
The test developed by Jerome involves some heavy-duty math, of the type often employed by scientists and engineers. Here are the details, as specified by Jerome and edited for formatting within this post:
For evaluating the performance, let’s use a test case using computational fluid dynamics algorithms, including Navier-Stokes fluid equations, the Maxwell electromagnetism equations, forming the magnetohydrodynamics (MHD) set of equations. The original Fortran code was published in An Introduction to Computational Fluid Mechanics
by Chuen-Yen-Chow, in 1983. The MHD stationary flow calculation is no longer included in the 2011 update by Biringen and Chow, but the details pertaining to the equations discretization, stability analysis, and so on can still be found in their Benard and Taylor instabilities example of the instationary solution of Navier-Stokes equations coupled with the temperature equation.
For simplicity, a stream-vorticity formulation is used. Standard boundary conditions, or even simplified ones, are used, with a value or derivative given. Discretization of the nonlinear terms in the Navier-Stokes, the one involving the velocity components, was, historically, a source of problems. The numerical scheme has to properly capture the flow direction.
Upwind differencing form solves this problem. The spatial difference is on the upwind side of the point indexed (i,j). This numerical scheme is only first order by reference to a Taylor series expansion. The second order upwind schemes introduces non physical behaviour, such as oscillations. Total Variation Diminishing (TVD) schemes are a cure to this problem. They introduce stable, non-oscillatory, high order schemes, preserving monotonicity, with no overshot or undershoot for the solution. They are the result of more than 30 years of research in CFD.
Only the upwind scheme was present in the original Fortran code. It was rewritten using a general TVD formulation. Corner Transport Upwind (CTU) was also added as an experiment, and not fully tested. Details can be in good CFD books such as An Introduction to Computational Fluid Dynamics: The Finite Volume Method (2nd Edition)
by Versteeg and Malalasekera, or Finite Volume Methods for Hyperbolic Problems
by Leveque.
The solution procedure is straightforward. The current flow, RH variable, is solved via the Laplace equation solver. Then the electromagnetic force, EM variable, is computed. Time stepping is used to find the solution of the flow until the convergence criteria are matched, error or maximum step. A Poisson solver is used.
Comments are given in the Fortran source code.
The results are presented for a Reynolds number of 50, a magnetic pressure number C of 0.3, using the upwind scheme.
Execution times on a PC
Before looking at the Nexus 7 results, let’s first compare the results on the PC. Here are the results that Jerome obtained on a i3 2.1 GHz laptop, running Windows 7 64-bit:
| GNU Fortran | 62ms |
| GNU GCC | 78ms |
| Oracle Java JDK 7u45 | 150ms |
| PyPy 2.0 | 1020ms |
| Python 3.3.2 | 6780ms |
For this particular run, Fortran is the best, with C a close second; the Java JDK also put in a good showing here. The interpreted languages are very disappointing, as expected.
Even with the slower execution times, some scientists are still moving some their code to Python; they want to benefit from the scripting capabilities of interpreted languages. Users don’t need to edit the source code to change the boundary equations or add a subroutine to solve a particular equation. FiPy, a finite volume code from NIST, uses this approach. However, most of the critical parts are still written in C or in Fortran.
Another approach is to use a dedicated language such the one implemented in FreeFem++, a partial differential equation solver. With this tool, a problem with one billion unknowns was solved in 2 minutes on the Curie Thin Node, a CEA machine. The CEA is the French Atomic Energy and Alternative Energies Commission.
What does the Nexus 7 has to offer?
Let’s now take a look at the results on a 1.2 GHz 2012 Nexus 7; the 2013 model, with its Qualcomm Snapdragon S4 Pro at 1.5 GHz, may boost these results a step further.
| Fortran CCTOOLS with -march=armv7-a -mfloat-abi=softfp -mfpu=vfpv3 -03 | 70ms |
| Fortran CCTOOLS with -march=armv7-a -mfloat-abi=softfp -mfpu=vfpv3 -02 | 79ms |
| C99 C4DROID with -march=armv7-a -mfloat-abi=softfp -mfpu=vfpv3 -02 (64-bit floats) | 120ms |
| C99 C4DROID with -march=armv7-a -mfloat-abi=softfp -mfpu=vfpv3 (32-bit floats) | 380ms |
| C99 C4DROID with mfloat-abi=softfp (32-bit floats) | 394ms |
| C99 C4DROID with -march=armv7-a -mfloat-abi=softfp -mfpu=vfpv3 (32-bit floats) | 420ms |
| C99 C4DROID with mfloat-abi=softfp (64-bit floats) | 450ms |
| C4DROID with -msoft-float (32-bit floats) | 1163ms |
| C4DROID with -msoft-float (64-bit floats) | 1500ms |
| Java compiled with Eclipse | 1563ms |
| Java AIDE with dex optimizations | 2100ms |
| Java AIDE | 3030ms |
| QPython | 24702ms |
These are the best execution times. Some variance was seen with C4DROID, while CCTOOLS was more stable overall. As before, we can see the same ranking, with Fortran emerging as the leader, and C, Java, and Python following behind. With the proper compiler flags, CCTOOLS Fortran is even competitive against the PC, which is a very good result.
The Java results, on the other hand, are quite bad. Is it a fault of the Dalvik virtual machine? Results may improve with the ART runtime, but they’d have to improve dramatically to come close to the performance of optimized FORTRAN and C.
Python, with an execution time of over 24 seconds, can definitely be forgotten for serious scientific computations.
Verdict
The Nexus 7 2012 is very powerful on this particular test, when running Fortran or C code compiled to native machine code. Can these good results be extrapolated to more demanding programs, and software that needs more time to run?
The Nexus 7 tablets are very high-quality products, and Android is a smart and fun operating system to use. The 2012 model is already quite powerful, and the 2013 should see even better results; all that’s needed is a dedicated approach to unleash the power sleeping within those processors.
This blog post is based on work generously contributed by Jerome Huck, a senior aerospace/defence engineer, scientist, and author. Jerome graduated from the École nationale supérieure de l’aéronautique et de l’espace in Toulouse, and has worked on various projects including the Hermes space shuttle, Rafale fighter, and is the author of “The Fire of the Magicians“.