FLOPS

For other uses, see Flop.

Computer performance

Name	Abbr.	FLOPS
kiloFLOPS	kFLOPS	103
megaFLOPS	MFLOPS	106
gigaFLOPS	GFLOPS	109
teraFLOPS	TFLOPS	1012
petaFLOPS	PFLOPS	1015
exaFLOPS	EFLOPS	1018
zettaFLOPS	ZFLOPS	1021
yottaFLOPS	YFLOPS	1024

In computing, FLOPS or flops (an acronym for floating-point operations per second) is a measure of computer performance, useful in fields of scientific calculations that make heavy use of floating-point calculations. For such cases it is a more accurate measure than the generic instructions per second.

Although the final S stands for "second", singular "flop" is often used, either as a back formation or an abbreviation for "floating-point operation"; e.g. a flop count is a count of these operations carried out by a given algorithm or computer program.

Computing

FLOPS can be calculated using this equation:

$\text{FLOPS} = \text{sockets} \times \frac{\text{cores}}{\text{socket}} \times \text{clock} \times \frac{\text{FLOPs}}{\text{cycle}}$

Most microprocessors today can carry out 4 FLOPs per clock cycle; thus a single-core 2.5 GHz processor has a theoretical performance of 10 billion FLOPS = 10 GFLOPS.

Note: In this context, sockets is referring to processor chip sockets on a motherboard, in other words, how many processor chips are in use, with each chip having one or more cores on it. This equation only applies to one very specific (but common) hardware architecture and it ignores limits imposed by memory bandwidth and other constraints. In general, gigaFLOPS are not determined by theoretical calculations such as this one; instead, they are measured by benchmarks of actual performance/throughput. Because this equation ignores all sources of overhead, in the real world, one will never get actual performance that is anywhere near to what this equation predicts.

Records

Single computer records

In late 1996, Intel's ASCI Red was the world's first computer to achieve one TFLOPS and beyond. Sandia director Bill Camp said that ASCI Red had the best reliability of any supercomputer ever built, and “was supercomputing’s high-water mark in longevity, price, and performance.”

NEC's SX-9 supercomputer was the world's first vector processor to exceed 100 gigaFLOPS per single core.

For comparison, a handheld calculator performs relatively few FLOPS. A computer response time below 0.1 second in a calculation context is usually perceived as instantaneous by a human operator, so a simple calculator needs only about 10 FLOPS to be considered functional.

In June 2006, a new computer was announced by Japanese research institute RIKEN, the MDGRAPE-3. The computer's performance tops out at one petaFLOPS, almost two times faster than the Blue Gene/L, but MDGRAPE-3 is not a general purpose computer, which is why it does not appear in the Top500.org list. It has special-purpose pipelines for simulating molecular dynamics.

By 2007, Intel Corporation unveiled the experimental multi-core POLARIS chip, which achieves 1 TFLOPS at 3.13 GHz. The 80-core chip can raise this result to 2 TFLOPS at 6.26 GHz, although the thermal dissipation at this frequency exceeds 190 watts.

On June 26, 2007, IBM announced the second generation of its top supercomputer, dubbed Blue Gene/P and designed to continuously operate at speeds exceeding one petaFLOPS. When configured to do so, it can reach speeds in excess of three petaFLOPS.

In June 2007, Top500.org reported the fastest computer in the world to be the IBM Blue Gene/L supercomputer, measuring a peak of 596 teraFLOPS. The Cray XT4 hit second place with 101.7 teraFLOPS.

On October 25, 2007, NEC Corporation of Japan issued a press release announcing its SX series model SX-9, claiming it to be the world's fastest vector supercomputer. The SX-9 features the first CPU capable of a peak vector performance of 102.4 gigaFLOPS per single core.

On February 4, 2008, the NSF and the University of Texas at Austin opened full scale research runs on an AMD, Sun supercomputer named Ranger, the most powerful supercomputing system in the world for open science research, which operates at sustained speed of 0.5 petaFLOPS.

On May 25, 2008, an American supercomputer built by IBM, named 'Roadrunner', reached the computing milestone of one petaflops by processing more than 1.026 quadrillion calculations per second. It headed the June 2008 and November 2008 TOP500 list of the most powerful supercomputers (excluding grid computers). The computer is located at Los Alamos National Laboratory in New Mexico, and the computer's name refers to the New Mexico state bird, the Greater Roadrunner.

In June 2008, AMD released ATI Radeon HD4800 series, which are reported to be the first GPUs to achieve one teraFLOPS scale. On August 12, 2008, AMD released the ATI Radeon HD 4870X2 graphics card with two Radeon R770 GPUs totaling 2.4 teraFLOPS.

In November 2008, an upgrade to the Cray XT Jaguar supercomputer at the Department of Energy’s (DOE’s) Oak Ridge National Laboratory (ORNL) raised the system's computing power to a peak 1.64 “petaflops,” or a quadrillion mathematical calculations per second, making Jaguar the world’s first petaflops system dedicated to open research. In early 2009 the supercomputer was named after a mythical creature, Kraken. Kraken was declared the world's fastest university-managed supercomputer and sixth fastest overall in the 2009 TOP500 list, which is the global standard for ranking supercomputers. In 2010 Kraken was upgraded and can operate faster and is more powerful.

In 2009, the Cray Jaguar performed at 1.75 petaFLOPS, beating the IBM Roadrunner for the number one spot on the TOP500 list.

In October 2010, China unveiled the Tianhe-I, a supercomputer that operates at a peak computing rate of 2.5 petaflops.

As of 2010, the fastest six-core PC processor reaches 109 gigaFLOPS (Intel Core i7 980 XE) in double precision calculations. GPUs are considerably more powerful. For example, Nvidia Tesla C2050 GPU computing processors perform around 515 gigaFLOPS in double precision calculations, and the AMD FireStream 9270 peaks at 240 gigaFLOPS. In single precision performance, Nvidia Tesla C2050 computing processors perform around 1.03 teraFLOPS and the AMD FireStream 9270 cards peak at 1.2 teraFLOPS. Both Nvidia and AMD's consumer gaming GPUs may reach higher FLOPS. For example, AMD’s HemlockXT 5970 reaches 928 gigaFLOPS in double precision calculations with two GPUs on board and the Nvidia GTX 480 reaches 672 gigaFLOPS with one GPU on board.

On December 2, 2010, the US Air Force unveiled a defense supercomputer made up of 1,760 PlayStation 3 consoles that can run 500 trillion floating-point operations per second. (500 teraFLOPS)

In November 2011, it was announced that Japan had achieved 10.51 petaflops with its K computer. It is still under development and software performance tuning is currently underway. It has 88,128 SPARC64 VIIIfx processors in 864 racks, with theoretical performance of 11.28 petaflops. It is named after the Japanese word "kei", which stands for 10 quadrillion, corresponding to the target speed of 10 petaFLOPS.

On November 15, 2011, Intel demonstrated a single x86-based processor, code-named "Knights Corner", sustaining more than a TeraFlop on a wide range of DGEMM operations. Intel emphasized during the demonstration that this was a sustained TeraFlop (not "raw TeraFlop" used by others to get higher but less meaningful numbers), and that it was the first general purpose processor to ever cross a TeraFlop.

On June 18, 2012, IBM's Sequoia supercomputer system, based at the U.S. Lawrence Livermore National Laboratory (LLNL), reached 16 petaFLOPS, setting the world record and claiming first place in the latest TOP500 list.

On November 12, 2012, the TOP500 list certified Titan as the world's fastest supercomputer per the LINPACK benchmark, at 17.59 petaFLOPS. It was developed by Cray Inc. at the Oak Ridge National Laboratory and combines AMD Opteron processors with “Kepler” NVIDIA Tesla graphic processing unit (GPU) technologies.

On June 10, 2013, China's Tianhe-2 was ranked the world's fastest with a record of 33.86 petaFLOPS.

Distributed computing records

Distributed computing uses the Internet to link personal computers to achieve more FLOPS:

• Folding@home is sustaining over 25.2 native petaFLOPS as of September 2015 or 43.1 x86 petaFLOPS (x86 FLOPS are an approximate measurement of the speed of a calculation on an x86-based processor, different from native FLOPS). It is the first computing project of any kind to cross the 1, 2, 3, 4, and 5 native petaFLOPS milestone. This level of performance is primarily enabled by the cumulative effort of a vast array of powerful GPU and CPU units.

• As of July 2014, The entire BOINC network averages about 5.6 petaFLOPS.
• As of July 2014, SETI@Home, employing the BOINC software platform, averages 681 teraFLOPS.
• As of July 2014, Einstein@Home, a project using the BOINC network, is crunching at 492 teraFLOPS.
• As of July 2014, MilkyWay@Home, using the BOINC infrastructure, computes at 471 teraFLOPS.
• As of July 2014, GIMPS, is searching for Mersenne primes and sustaining 173 teraFLOPS.

Future developments

Further information: Exascale computing

In 2008, James Bamford's book The Shadow Factory reported that NSA told the Pentagon it would need an exaflop computer by 2018.

Given the current speed of progress, supercomputers are projected to reach 1 exaFLOPS (EFLOPS) in 2018. Cray, Inc. announced in December 2009 a plan to build a 1 EFLOPS supercomputer before 2020. Erik P. DeBenedictis of Sandia National Laboratories theorizes that a zettaFLOPS (ZFLOPS) computer is required to accomplish full weather modeling of two week time span. Such systems might be built around 2030.

Cost of computing

Hardware costs

Date	Approximate cost per GFLOPS	Approximate cost per GFLOPS inflation adjusted to 2013 US dollars	Platform providing the lowest cost per GFLOPS	Comments
1961	US$1,100,000,000,000 ($1.1 trillion)	US$8.3 trillion	About 17 million IBM 1620 units costing $64,000 each	The 1620's multiplication operation takes 17.7 ms.
1984	$18,750,000	$42,780,000	Cray X-MP/48	$15,000,000 / 0.8 GFLOPS
1997	$30,000	$42,000	Two 16-processor Beowulf clusters with Pentium Pro microprocessors
April 2000	$1,000	$1,300	Bunyip Beowulf cluster	Bunyip was the first sub-US$1/MFLOPS computing technology. It won the Gordon Bell Prize in 2000.
May 2000	$640	$836	KLAT2	KLAT2 was the first computing technology which scaled to large applications while staying under US-$1/MFLOPS.
August 2003	$82	$100	KASY0	KASY0 was the first sub-US$100/GFLOPS computing technology.
August 2007	$48	$52	Microwulf	As of August 2007, this 26.25 GFLOPS "personal" Beowulf cluster can be built for $1256.
March 2011	$1.80	$1.80	HPU4Science	This $30,000 cluster was built using only commercially available "gamer" grade hardware.
August 2012	$0.75	$0.73	Quad AMD Radeon 7970 GHz System	A quad AMD Radeon 7970 desktop computer reaching 16 TFlops of single-precision, 4 TFlops of double-precision computing performance. Total system cost was $3000; Built using only commercially available hardware.
June 2013	$0.22	$0.22	Sony PlayStation 4	The Sony PlayStation 4 is listed as having a peak performance of 1.84 TFLOPS, at a price of $400
November 2013	$0.16	$0.16	AMD Sempron 145 & GeForce GTX 760 System	Built using commercially available parts, a system using one AMD Sempron 145 and three Nvidia GeForce GTX 760 reaches a total of 6.771 TFLOPS for a total cost of $1090.66.
December 2013	$0.12	$0.12	Pentium G550 & Radeon R9 290 System	Built using commercially available parts. Intel Pentium G550 and AMD Radeon R9 290 tops out at 4.848 TFLOPS grand total of US$681.84.
January 2015	$0.08	$0.08	Celeron G1830 & Radeon R9 295X2 System	Built using commercially available parts. Intel Celeron G1830 and AMD Radeon R9 295X2 tops out at over 11.5 TFLOPS at a grand total of US$902.57.

Floating-point operation and integer operation

FLOPS measures the computing ability of a computer. An example of a floating-point operation is the calculation of mathematical equations; as such, FLOPS is a useful measure of supercomputer performance. MIPS is used to measure the integer performance of a computer. Examples of integer operation include data movement (A to B) or value testing (If A = B, then C). MIPS as a performance benchmark is adequate for the computer when it is used in database query, word processing, spreadsheets, or to run multiple virtual operating systems. Frank H. McMahon, of the Lawrence Livermore National Laboratory, invented the terms FLOPS and MFLOPS (megaFLOPS) so that he could compare the so-called supercomputers of the day by the number of floating-point calculations they performed per second. This was much better than using the prevalent MIPS to compare computers as this statistic usually had little bearing on the arithmetic capability of the machine.

Fixed-point (integers)

These designations refer to the format used to store and manipulate numeric representations of data without using a decimal point (it is 'fixed' at the end of the number). Fixed-point are designed to represent and manipulate integers – positive and negative whole numbers; for example, 16 bits, yielding up to 65,536 (2¹⁶) possible bit patterns that typically represent the whole numbers from −32768 to +32767.

Floating-point (real numbers)

This is needed for very large or very small real numbers, or numbers requiring the use of a decimal point (such as pi and other irrational values). The encoding scheme used by the processor for floating-point numbers is more complicated than for fixed-point. Floating-point representation is similar to scientific notation, except everything is carried out in base two, rather than base ten. The encoding scheme stores the sign, the exponent (in base two for Cray and IEEE floating point formats, or base 16 for IBM Floating Point Architecture) and the mantissa (number after the decimal point). While several similar formats are in use, the most common is ANSI/IEEE Std. 754-1985. This standard defines the format for 32-bit numbers called single precision, as well as 64-bit numbers called double precision and longer numbers called extended precision (used for intermediate results). Floating-point representations can support a much wider range of values than fixed-point, with the ability to represent very small numbers and very large numbers.

Dynamic range and precision

The exponentiation inherent in floating-point computation assures a much larger dynamic range – the largest and smallest numbers that can be represented – which is especially important when processing data sets which are extremely large or where the range may be unpredictable. As such, floating-point processors are ideally suited for computationally intensive applications.

See also

• Gordon Bell Prize
• Orders of magnitude (computing)
• SPECint
• SPECfp
• Multiply–accumulate operation
• SUPS