Mathematica 8 Gets Performance Boost, Integration with Wolfram Alpha

By Michael Feldman

December 14, 2010

The eighth version of Mathematica was released last month, the latest in Wolfram Research’s 22-year-old computational software platform. Although the tool is a relative newcomer to the high performance computing world, a raft of new capabilities have been added over the last several years that are aimed directly at the performance crowd. Mathematica 8 builds on those capabilities and adds some new ones that make it a serious contender for HPC applications.

Focus on performance started in earnest with Mathematica 4 back in 1999. Beginning with that release, Wolfram Research started to incorporate a variety of features and capabilities that improved runtime execution, including optimizing algorithms, supporting linkage of external C and Fortran libraries, and adding the ability to compile code. In 2008, with Mathematica 7, built-in support for multicore parallelism and compute clusters was added.

Mathematics 8 adds a number of new features that should boost performance even further. Perhaps the most important is the ability to generate, compile and link C code. The new feature allows Mathematica code to be automatically translated into C source code. The source can then be driven through a standard compiler (requiring a native Windows or Mac C compiler) and linked into a Mathematica executable for production.

The idea here is to take advantage of the speed of C-compiled code to boost performance of critical pieces of the Mathematic program. Previously Mathematica only supported compilation to a Java-like virtual machine byte-code, which although faster than interpreted execution, tended to be a good deal slower than compiled C code. In one example, a rendering application using vanilla Mathematica delivered just one frame every 10 to 15 seconds, while C compiled code was able to achieve two to four frames per second. Comparable speedups are to be expected from similar compute-intensive codes. All of this can be accomplished without the programmer ever having to write a single line of C.

Better yet, a parallelization option can be applied to a compiled function, which Mathematica will use to create a multi-threaded implementation. This can speed execution even further, assuming of course that the target CPU is multicore.

Compiled C code can be collected in dynamic link libraries (DLLs), which can be sucked back into the application or shared with other Mathematica programs. The ability to link DLLs also means externally developed C and C++ libraries can be incorporated into Mathematica, opening the door to many more performance optimized packages. Prior to this, talking with external C code involved the MathLink interface, which was burdened with the overhead of inter-program communication. Being able to access DLL routines directly makes calling external code much more efficient and straightforward.

For the GPGPU enthusiast, Mathematica 8 brings in support for CUDA and OpenCL. Unfortunately, this feature doesn’t have the seamless automation offered by the C code generation capability. Rather, the targeted algorithm has to be developed in CUDA or OpenCL first and then folded into the program later. Basically, Mathematica automates some of the housekeeping functions, such as downloading code and data to the GPU card, and uploading the results back to the host. GPGPU support can be scaled to utilize all the GPUs on a system, or, using the gridMathematica add-on, across a cluster.

Although you can’t automagically transform an arbitrary function into a GPU version, Mathematica 8 does include a couple dozen built-in functions that are already optimized for CUDA-enabled GPUs (in other words, those from NVIDIA). The functions are spread out across linear algebra, financial simulation, and image processing. The folks at Wolfram Research will undoubtedly be adding more built-in GPU routines in future versions, while also promising a more streamlined approach for GPU support.

Another category of performance improvements is enabled by speedups to a number of core algorithms. These include optimized solvers for integer linear algebra, highly oscillatory functions, transcendental and high-degree polynomial methods, and a number of new special functions. In some cases, the optimizations can boost performance by an order of magnitude or more, depending upon the size of the problem.

Besides the additional performance-boosting capabilities, Mathematica 8 also includes about 500 new built-in functions — an increase that represent nearly the entire function count in the original Mathematica 1 of 1988. The new capabilities in version 8 encapsulate high-level symbolic functions for probability and statistics; permutations and group theory algorithms; financial engineering routines of general utility; control system functions; wavelet analysis functions; graph and network algorithms; and image processing routine.

The last category encompasses some very useful routine for processing visual data. One of the new capabilities is feature detection, such as facial and character recognition. Also included are geometric transformations and image alignment. For video, Mathematica can now import and export individual frames as well as do real-time capture of webcam streams. All of these capabilities can be combined to deliver some rather sophisticated image processing applications on top of an already full-featured computational engine.

Perhaps the most visible addition to version 8 — at least from a user interface point of view — is the integration with Wolfram Alpha, the company’s Web-based computational knowledge engine. There are a number of advantages to marrying Mathematica to its Web spinoff, which, by the way, is itself a Mathematica application at its core.

First is the ability to tap the store of curated data in Wolfram Alpha, which encompasses a large and growing database that spans many technical and non-technical disciplines. It remains to be seen whether giving Mathematica users access to Wolfram Alpha data spurs new applications or will just be used as a sandbox for more customized data-centric applications.

For the application designer, one of the most potentially interesting uses of Wolfram Alpha is the ability to use its free-form linguistic capabilities. So instead of having to define a problem within the strict confines of the Mathematic language, you can use (more or less) natural language. So, for example, summing all the integers from 1 to 1000 would have to be specified as Sum[i, {i, 1, 1000}] in Mathematica, but could be simply stated as “sum integers 1 to 1000′” using the free-form mode.

The English version is automatically converted to Mathematica syntax on the fly, which can then be tweaked and developed separately. Extending the capability a bit further, users can pass Mathematica variables into Wolfram Alpha calculations.

The nice thing about the Mathematica architecture is nearly all its features, including the new ones described here, are included in the core technology. The Wolfram Alpha team has shied away from toolboxes, libraries, and standalone product add-ons (with the exception of gridMathematica). As a result, the new version 8 features can immediately leverage the large foundation of accumulated Mathematica componentry.

In the kickoff for Mathematica 8 at the Wolfram Technology Conference in November, company CEO Stephen Wolfram reiterated his commitment to maintain the platform as a unified, consistent software tool. Keeping the architecture monolithic means they are free to evolve the product through refinement of the individual pieces and the addition of new ones. With this kind of model, the whole is always guaranteed to be greater than the sum of the parts. “We’ve had a very simple strategic methodology,” explained Wolfram. “Just implement everything.”

Subscribe to HPCwire's Weekly Update!

Be the most informed person in the room! Stay ahead of the tech trends with industy updates delivered to you every week!

Cray+Azure: Can Cloud Propel Supercomputing?

October 23, 2017

Cray and Microsoft today announced they will offer dedicated Cray supercomputers (the XC and CS-Storm lines) inside the Azure platform allowing customers to run their HPC and AI applications alongside their other cloud w Read more…

By Tiffany Trader

2017 Gordon Bell Prize Finalists Named

October 23, 2017

The three finalists for this year’s Gordon Bell Prize in High Performance Computing have been announced. They include two papers on projects run on China’s Sunway TaihuLight system and a third paper on 3D image recon Read more…

By John Russell

Data Vortex Users Contemplate the Future of Supercomputing

October 19, 2017

Last month (Sept. 11-12), HPC networking company Data Vortex held its inaugural users group at Pacific Northwest National Laboratory (PNNL) bringing together about 30 participants from industry, government and academia t Read more…

By Tiffany Trader

HPE Extreme Performance Solutions

Transforming Genomic Analytics with HPC-Accelerated Insights

Advancements in the field of genomics are revolutionizing our understanding of human biology, rapidly accelerating the discovery and treatment of genetic diseases, and dramatically improving human health. Read more…

AI Self-Training Goes Forward at Google DeepMind

October 19, 2017

DeepMind, Google’s AI research organization, announced today in a blog that AlphaGo Zero, the latest evolution of AlphaGo (the first computer program to defeat a Go world champion) trained itself within three days to play Go at a superhuman level (i.e., better than any human) – and to beat the old version of AlphaGo – without leveraging human expertise, data or training. Read more…

By Doug Black

Cray+Azure: Can Cloud Propel Supercomputing?

October 23, 2017

Cray and Microsoft today announced they will offer dedicated Cray supercomputers (the XC and CS-Storm lines) inside the Azure platform allowing customers to run Read more…

By Tiffany Trader

Data Vortex Users Contemplate the Future of Supercomputing

October 19, 2017

Last month (Sept. 11-12), HPC networking company Data Vortex held its inaugural users group at Pacific Northwest National Laboratory (PNNL) bringing together ab Read more…

By Tiffany Trader

AI Self-Training Goes Forward at Google DeepMind

October 19, 2017

DeepMind, Google’s AI research organization, announced today in a blog that AlphaGo Zero, the latest evolution of AlphaGo (the first computer program to defeat a Go world champion) trained itself within three days to play Go at a superhuman level (i.e., better than any human) – and to beat the old version of AlphaGo – without leveraging human expertise, data or training. Read more…

By Doug Black

Student Cluster Competition Coverage New Home

October 16, 2017

Hello computer sports fans! This is the first of many (many!) articles covering the world-wide phenomenon of Student Cluster Competitions. Finally, the Student Read more…

By Dan Olds

Intel Delivers 17-Qubit Quantum Chip to European Research Partner

October 10, 2017

On Tuesday, Intel delivered a 17-qubit superconducting test chip to research partner QuTech, the quantum research institute of Delft University of Technology (TU Delft) in the Netherlands. The announcement marks a major milestone in the 10-year, $50-million collaborative relationship with TU Delft and TNO, the Dutch Organization for Applied Research, to accelerate advancements in quantum computing. Read more…

By Tiffany Trader

Fujitsu Tapped to Build 37-Petaflops ABCI System for AIST

October 10, 2017

Fujitsu announced today it will build the long-planned AI Bridging Cloud Infrastructure (ABCI) which is set to become the fastest supercomputer system in Japan Read more…

By John Russell

HPC Chips – A Veritable Smorgasbord?

October 10, 2017

For the first time since AMD's ill-fated launch of Bulldozer the answer to the question, 'Which CPU will be in my next HPC system?' doesn't have to be 'Whichever variety of Intel Xeon E5 they are selling when we procure'. Read more…

By Dairsie Latimer

Delays, Smoke, Records & Markets – A Candid Conversation with Cray CEO Peter Ungaro

October 5, 2017

Earlier this month, Tom Tabor, publisher of HPCwire and I had a very personal conversation with Cray CEO Peter Ungaro. Cray has been on something of a Cinderell Read more…

By Tiffany Trader & Tom Tabor

Reinders: “AVX-512 May Be a Hidden Gem” in Intel Xeon Scalable Processors

June 29, 2017

Imagine if we could use vector processing on something other than just floating point problems.  Today, GPUs and CPUs work tirelessly to accelerate algorithms Read more…

By James Reinders

NERSC Scales Scientific Deep Learning to 15 Petaflops

August 28, 2017

A collaborative effort between Intel, NERSC and Stanford has delivered the first 15-petaflops deep learning software running on HPC platforms and is, according Read more…

By Rob Farber

Oracle Layoffs Reportedly Hit SPARC and Solaris Hard

September 7, 2017

Oracle’s latest layoffs have many wondering if this is the end of the line for the SPARC processor and Solaris OS development. As reported by multiple sources Read more…

By John Russell

US Coalesces Plans for First Exascale Supercomputer: Aurora in 2021

September 27, 2017

At the Advanced Scientific Computing Advisory Committee (ASCAC) meeting, in Arlington, Va., yesterday (Sept. 26), it was revealed that the "Aurora" supercompute Read more…

By Tiffany Trader

How ‘Knights Mill’ Gets Its Deep Learning Flops

June 22, 2017

Intel, the subject of much speculation regarding the delayed, rewritten or potentially canceled “Aurora” contract (the Argonne Lab part of the CORAL “ Read more…

By Tiffany Trader

GlobalFoundries Puts Wind in AMD’s Sails with 12nm FinFET

September 24, 2017

From its annual tech conference last week (Sept. 20), where GlobalFoundries welcomed more than 600 semiconductor professionals (reaching the Santa Clara venue Read more…

By Tiffany Trader

Google Releases Deeplearn.js to Further Democratize Machine Learning

August 17, 2017

Spreading the use of machine learning tools is one of the goals of Google’s PAIR (People + AI Research) initiative, which was introduced in early July. Last w Read more…

By John Russell

Nvidia Responds to Google TPU Benchmarking

April 10, 2017

Nvidia highlights strengths of its newest GPU silicon in response to Google's report on the performance and energy advantages of its custom tensor processor. Read more…

By Tiffany Trader

Leading Solution Providers

Graphcore Readies Launch of 16nm Colossus-IPU Chip

July 20, 2017

A second $30 million funding round for U.K. AI chip developer Graphcore sets up the company to go to market with its “intelligent processing unit” (IPU) in Read more…

By Tiffany Trader

Amazon Debuts New AMD-based GPU Instances for Graphics Acceleration

September 12, 2017

Last week Amazon Web Services (AWS) streaming service, AppStream 2.0, introduced a new GPU instance called Graphics Design intended to accelerate graphics. The Read more…

By John Russell

EU Funds 20 Million Euro ARM+FPGA Exascale Project

September 7, 2017

At the Barcelona Supercomputer Centre on Wednesday (Sept. 6), 16 partners gathered to launch the EuroEXA project, which invests €20 million over three-and-a-half years into exascale-focused research and development. Led by the Horizon 2020 program, EuroEXA picks up the banner of a triad of partner projects — ExaNeSt, EcoScale and ExaNoDe — building on their work... Read more…

By Tiffany Trader

Delays, Smoke, Records & Markets – A Candid Conversation with Cray CEO Peter Ungaro

October 5, 2017

Earlier this month, Tom Tabor, publisher of HPCwire and I had a very personal conversation with Cray CEO Peter Ungaro. Cray has been on something of a Cinderell Read more…

By Tiffany Trader & Tom Tabor

Cray Moves to Acquire the Seagate ClusterStor Line

July 28, 2017

This week Cray announced that it is picking up Seagate's ClusterStor HPC storage array business for an undisclosed sum. "In short we're effectively transitioning the bulk of the ClusterStor product line to Cray," said CEO Peter Ungaro. Read more…

By Tiffany Trader

Intel Launches Software Tools to Ease FPGA Programming

September 5, 2017

Field Programmable Gate Arrays (FPGAs) have a reputation for being difficult to program, requiring expertise in specialty languages, like Verilog or VHDL. Easin Read more…

By Tiffany Trader

IBM Advances Web-based Quantum Programming

September 5, 2017

IBM Research is pairing its Jupyter-based Data Science Experience notebook environment with its cloud-based quantum computer, IBM Q, in hopes of encouraging a new class of entrepreneurial user to solve intractable problems that even exceed the capabilities of the best AI systems. Read more…

By Alex Woodie

HPC Chips – A Veritable Smorgasbord?

October 10, 2017

For the first time since AMD's ill-fated launch of Bulldozer the answer to the question, 'Which CPU will be in my next HPC system?' doesn't have to be 'Whichever variety of Intel Xeon E5 they are selling when we procure'. Read more…

By Dairsie Latimer

  • arrow
  • Click Here for More Headlines
  • arrow
Share This