Does the Fused Multiply-Add (FMA) instruction make a difference?

I discussed this originally in my Cortex-A7 FFTW benchmarks, but I am repeating it in it's own blog post for clarity as I believe it's an important thing to understand.

I noticed that when enabling the FMA capabilities of FFTW, the performance actually decreased. I thought to myself "but the ARM VFPv4 supports FMA so this should be faster that doing separate multiply and add operations..." so I did a little bit of research as to why this is the case.

In the computation of an FFT, two of the common operations are:

t0 = a + b * c
t1 = a - b * c

The way that the NEON FMA instruction works, however, is not conducive solving this. This is what happens when you use the NEON FMA instruction:

t0 = a
t0 += b * c
t1 = a
t1 -= b * c

Since ARM is a RISC architecture, the instructions are less flexible and generally take a fixed number of operands. For mathematical operations, it makes sense most of the time to use two operands. Because of this limitation, the FMA can still only take 2 operands and so it is used as shown above. Notice that we have to use up two move instructions for initially setting t0 and t1. It turns out that in this specific case it's faster to just use Multiplies and Adds:

t = b * c
t0 = a + t
t1 = a - t

All in all, the FMA version does 2 Moves, 2 FMA's. The optimal version does 1 Multiply and 2 Adds. It's a small difference, one which the compiler may or may not take note of and optimise, but when done a significant number of times it makes a difference which is what we see in the FFTW benchmarks, for example. There will be cases when this instruction does indeed make a difference, but it's important to bear in mind what's going on behind the scenes.

High Speed PCB Routing

I have been quite busy designing high-speed PCB's for my PCI-Express research. I found this video on YouTube from Texas Instruments which provides an excellent overview on high speed routing and I recommend it to anyone interested.

To reiterate the issues one usually faces when designing high speed circuit boards (from the video above):

• Timing: the lengths of the tracks must be similar enough for the electrical signals to arrive at the receiver at the same time. ~0.6 times the speed of light is too slow!
• Signal Integrity: The shape of the signal needs to be right when it arrives at the receiver.
• Noise: There can be a lot of crosstalk and noise on a high speed PCB and this noise can adversely affect signals.

To 'solve' these concerns:

• Maintain the correct impedance from the transmitter to the receiver. This is not always trivial and so this is usually the biggest problem!
• Matched lengths minimise signal skew.
• Leave space around the traces to minimise noise. More space makes an exponential difference.

Nice article on the importance of the SA-CERN program

Nicola Mawson, from ITWeb has written a nice appraisal of the importance of the role of the South Africa - CERN program and its benefits to the country.

http://www.itweb.co.za/index.php?option=com_content&view=article&id=70626:SA-reaps-CERN-rewards

SA's involvement with the Large Hadron Collider (LHC), in Switzerland, is paying dividends as the country embarks on new electronics and physics projects, and benefits from knowledge gained at the European Organisation for Nuclear Research (CERN).

Thanks to collaboration on the project – the £2.6 billion "Big Bang" particle accelerator and the globe's largest experiment – South African universities are developing technology in fast electronics, supercomputing and plastics.

The LHC at CERN led to the discovery, in 2012, of what has become accepted as the elusive Higgs boson. This discovery is anticipated to catapult physics into a new era, as it will be able to probe previously untouched areas, such as dark matter and dark energy.

The Higgs particle – or boson – is named after Peter Higgs, who was one of six authors who theorised about the existence of the particle in the 1960s. It is commonly called the "God Particle", after the title of Nobel physicist Leon Lederman's "The God Particle: If the Universe Is the Answer, What Is the Question?", according to Wikipedia.

Local wins

Locally, about 70 South Africans are involved in the global project and, while the team is small in comparison to those from other countries, there are substantial benefits coming out of its involvement.

  See also

• Two-decade journey for collider
• CERN to go warp speed
• Large Hadron Collider
• European Organisation for Nuclear Research

Four universities are participating in the programme: the University of the Witwatersrand (Wits), University of Cape Town (UCT), the University of Johannesburg, and the University of KwaZulu-Natal.

Tom Dietel, a lecturer at UCT, says CERN is a flagship project and is expected to spark interest in science and physics.

Bruce Mellado, an associate professor at Wits' school of physics, says the tertiary institution is involved with projects to develop fast electronics, a new form of plastic, and create a cheap alternative for high-throughput supercomputing.

Mellado explains South Africans have been given the opportunity to tap into CERN's infrastructure at very little cost to the country. He says the country has been "given the benefit of a huge facility without having to pay hundreds of billions for it".

Professor Jean Cleymans, from the UCT's physics department, explains SA's involvement – mostly with the Atlas experiment – is a national project and is not specifically linked to any university. SA is also making contributions to the Alice and Isolde projects, he says. "It's important to have a first step in there."

Cleymans says SA's involvement gives young physicists access to technology, software being developed and knowledge.

Cleymans says "far from being limited to Europe", the project is a worldwide project to contribute to advances at CERN. SA's first step happened in 1992, when it signed its first agreement of interest, he notes.

Faster technology 

Mellado explains one of the university's initiatives – named sRod – is a faster electronics board, which will be able to process much more data at faster rates. The board, being developed through collaboration in Europe and SA, is being made in conjunction with SA's Square Kilometre Array (SKA) team.

The multibillion-rand telescope project, hosted by SA, Australia and New Zealand, will collect a staggering amount of data as it probes the universe: the data collected by the SKA in a single day would take nearly two million years to play back on an iPod.

Mellado says the prototype board should be in production locally before winter, which will be a "major milestone for SA". He explains there are increasingly large amounts of data to be analysed, but the price for the hardware is currently a "showstopper".

Being able to get university-made technology commercialised will drop the cost and allow SA's technology industry to develop further, says Mellado. "That's the key to further development."

Wits is also developing a supercomputer under its Mass Affordable Computing project, which Mellado says takes the technology from smartphones and uses it for generic applications such as telecoms and computing. This programme will also be used to aid the SKA's data processing needs. "We can proudly say that we are doing it here."

Such projects are critical to SA's science, says Mellado. "Everything now depends on data processing."

The university is also developing – in collaboration with Sasol – plastic scintillators, with a prototype due in a year or two. Mellado says this material will allow the absorption of light.

Break time

The South African consortium launched in 2008 and a few ministerial delegations have visited CERN, says Cleymans. SA's contribution is hosted by iThemba Laboratories, which is a national open laboratory, he adds.

The Department of Science and Technology is funding SA's contribution, says Cleymans, adding that CERN is the first project that has seen South African physics departments team up to collaborate.

CERN is currently temporarily offline in a bid to increase its capacity and explore unknown aspects of physics. In the meantime, South African scientists are helping analyse the data it has collected and are aiding with maintenance.

The experiment will run until 2030 and will be upgraded to 10 times its initial design specification, with the ability to collect 100 times more data.

Wits Honored to be remembered in Madiba's will

Below is a statement from the Vice-Chancellor and Principal of the University of the Witwatersrand:

Dear Colleagues

The University of the Witwatersrand is honoured and deeply appreciative to learn that it is a beneficiary of former president Nelson Mandela’s legacy, and we are indeed humbled that he chose to remember the University in his will.

Wits accepts this generous bequest from one of our most illustrious alumni and commits to using it to address the development of higher education in South Africa, for the benefit of the University and its students, but more importantly to advance and perpetuate the values that our inaugural President has bequeathed to our nation and the world.     

Madiba emphasised the need to address inequality – one of the greatest threats to our young democracy, and Wits is determined to utilise this endowment to tackle this societal peril without delay, through the provision of additional scholarships for our students.  

We understand that this endowment brings with it a tremendous responsibility, given the character and legacy of our great leader and his commitment to the transformative power of education.

Thank you, Tata, for remembering us in your will – you live on in our memory and in our lives. 

Professor Adam Habib

Vice-Chancellor and Principal

University of the Witwatersrand

3 February 2014

Release from Wits press office: SA readies for big data storm

Erna van Wyk has written a nice report of the opening day of the workshop:

http://www.wits.ac.za/newsroom/newsitems/201401/22739/news_item_22739.html

Photo of Peter Jenni with the Wits High Energy Physics group

Below is a picture of Peter Jenni with member of the Wits High Energy Physics group. Prof. John Carter, the Head of the School of Physics, is also in the photo. Missing in the picture are Oana, Itumeleng, Pablo, Rudolph, Trevor, Kieran and Reto.

The High-performance Signal and Data Processing workshop took off on Monday January 27th. The workshop puts together astronomy, astro- and particle physics to address common issues pertaining to the Big Data problem. Attendance has been very nice with over 135 people registered, out of which 60 are students from different parts of the country. Below is the workshop picture:

Tomorrow start the hands-on sessions with FPGA-based electronics.

Herwig Schopper, former CERN Director General, addresses the LHeC workshop. Impressive!

Herwig chairs the LHeC International Advisory Committee.

The LHeC workshop has started. This is the fourth edition and the best attended so far. In the photo one can see Sergio Bertolucci, the Director of Research and Scientific Computing at CERN, addressing the workshop.

LHeC workshop to take place January 20-21st in Chavannes-de-Bogis, Switzerland

The 2014 LHeC workshop follows the publication of its conceptual design report (CDR) and the discovery of the Higgs boson in 2012. Recent LHeC progress concerns the study of the increase of its luminosity to 10^34cm-2s-1, the choice of the frequency of 802 MHz as well as the design towards an energy recovery test facility with up to 1 GeV of electron beam energy. The workshop will discuss progress on the LHeC physics (Higgs, top, heavy ions etc) in conjunction with the evolution and simulation of the detector design. It will consider maximising the ep luminosity in synchronous ep and pp operation at the LHC, including a heavy ion programme, and progress in the design of the ERL test facility at CERN. Very recent developments towards a future multi-TeV proton accelerator at CERN open prospects for ep/eA experimentation at yet enlarged energy. The workshop is open for contributions on the various aspects of the LHeC development and its relation to the LHC. It is prepared by an organising committee in collaboration with the working group convenors and an international advisory committee.

http://indico.cern.ch/conferenceDisplay.py?confId=278903