FLOPS

# FLOPS

Discussion

Encyclopedia
Computer performance
Name FLOPS
yottaFLOPS 1024
zettaFLOPS 1021
exaFLOPS 1018
petaFLOPS 1015
teraFLOPS 1012
gigaFLOPS 109
megaFLOPS 106
kiloFLOPS 103

In computing
Computing
Computing is usually defined as the activity of using and improving computer hardware and software. It is the computer-specific part of information technology...

, FLOPS (or flops or flop/s, for floating-point operations per second) is a measure of a computer
Computer
A computer is a programmable machine designed to sequentially and automatically carry out a sequence of arithmetic or logical operations. The particular sequence of operations can be changed readily, allowing the computer to solve more than one kind of problem...

's performance
Computer performance
Computer performance is characterized by the amount of useful work accomplished by a computer system compared to the time and resources used.Depending on the context, good computer performance may involve one or more of the following:...

, especially in fields of scientific calculations that make heavy use of floating-point calculation
Calculation
A calculation is a deliberate process for transforming one or more inputs into one or more results, with variable change.The term is used in a variety of senses, from the very definite arithmetical calculation of using an algorithm to the vague heuristics of calculating a strategy in a competition...

s, similar to the older, simpler, instructions per second
Instructions per second
Instructions per second is a measure of a computer's processor speed. Many reported IPS values have represented "peak" execution rates on artificial instruction sequences with few branches, whereas realistic workloads typically lead to significantly lower IPS values...

. Since the final S stands for "second", conservative speakers consider "FLOPS" as both the singular and plural of the term, although the singular "FLOP" is frequently encountered. Alternatively, the singular FLOP (or flop) is used as an abbreviation for "FLoating-point OPeration", and a flop count is a count of these operations (e.g., required by a given algorithm or computer program). In this context, "flops" is simply the plural rather than a rate.

Although it is in common use, FLOPS is not an SI
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

unit. The expression 1 flops is actually interpreted as .

## Measuring performance

In order for FLOPS to be useful as a measure of floating-point performance, a standard benchmark
Benchmark (computing)
In computing, a benchmark is the act of running a computer program, a set of programs, or other operations, in order to assess the relative performance of an object, normally by running a number of standard tests and trials against it...

must be available on all computers of interest. One example is the LINPACK
LINPACK
LINPACK is a software library for performing numerical linear algebra on digital computers. It was written in Fortran by Jack Dongarra, Jim Bunch, Cleve Moler, and Gilbert Stewart, and was intended for use on supercomputers in the 1970s and early 1980s...

benchmark.

There are many factors in computer performance other than raw floating-point computing speed, such as I/O performance, interprocessor communication, cache coherence
Cache coherence
In computing, cache coherence refers to the consistency of data stored in local caches of a shared resource.When clients in a system maintain caches of a common memory resource, problems may arise with inconsistent data. This is particularly true of CPUs in a multiprocessing system...

, and the memory hierarchy
Memory hierarchy
The term memory hierarchy is used in the theory of computation when discussing performance issues in computer architectural design, algorithm predictions, and the lower level programming constructs such as involving locality of reference. A 'memory hierarchy' in computer storage distinguishes each...

. This means that supercomputers are in general only capable of a fraction of their "theoretical peak" FLOPS throughput (obtained by adding together the theoretical peak FLOPS performance of every element of the system). Even when operating on large highly parallel problems, their performance will be bursty, mostly due to the residual effects of Amdahl's law
Amdahl's law
Amdahl's law, also known as Amdahl's argument, is named after computer architect Gene Amdahl, and is used to find the maximum expected improvement to an overall system when only part of the system is improved...

. Real benchmarks therefore measure both peak actual FLOPS performance as well as sustained FLOPS performance.

Supercomputer ratings, like TOP500
TOP500
The TOP500 project ranks and details the 500 most powerful known computer systems in the world. The project was started in 1993 and publishes an updated list of the supercomputers twice a year...

, usually derive theoretical peak FLOPS as a product of number of cores, cycles per second each core runs at, and number of double-precision (64 bit) FLOPS each core can ideally perform, thanks to SIMD
SIMD
Single instruction, multiple data , is a class of parallel computers in Flynn's taxonomy. It describes computers with multiple processing elements that perform the same operation on multiple data simultaneously...

or otherwise. Despite different processor architectures can achieve different parallelism on single core, most mainstream ones, like recent Xeon
Xeon
The Xeon is a brand of multiprocessing- or multi-socket-capable x86 microprocessors from Intel Corporation targeted at the non-consumer server, workstation and embedded system markets.-Overview:...

and Itanium
Itanium
Itanium is a family of 64-bit Intel microprocessors that implement the Intel Itanium architecture . Intel markets the processors for enterprise servers and high-performance computing systems...

models, claim a factor of four. Some ratings adopted the factor as a given constant, and use it to compute peak values for all architectures, often leading to huge difference from sustained performance.

For ordinary (non-scientific) applications, integer
Integer
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...

operations (measured in MIPS) are far more common. Measuring floating-point operation speed, therefore, does not predict accurately how the processor will perform on just any problem. However, for many scientific jobs such as data analysis, a FLOPS rating is effective.

Historically, the earliest reliably documented serious use of the floating-point operation as a metric appears to be AEC
United States Atomic Energy Commission
The United States Atomic Energy Commission was an agency of the United States government established after World War II by Congress to foster and control the peace time development of atomic science and technology. President Harry S...

justification to Congress for purchasing a Control Data CDC 6600
CDC 6600
The CDC 6600 was a mainframe computer from Control Data Corporation, first delivered in 1964. It is generally considered to be the first successful supercomputer, outperforming its fastest predecessor, IBM 7030 Stretch, by about three times...

in the mid-1960s.

The terminology is currently so confusing that until April 24, 2006, U.S. export control was based upon measurement of "Composite Theoretical Performance" (CTP) in millions of "Theoretical Operations Per Second" or MTOPS. On that date, however, the U.S. Department of Commerce's Bureau of Industry and Security
Bureau of Industry and Security
The Bureau of Industry and Security is an agency of the United States Department of Commerce which deals with issues involving national security and high technology. A principal goal for the bureau is helping stop proliferation of weapons of mass destruction, while furthering the growth of United...

amended the Export Administration Regulations to base controls on Adjusted Peak Performance
Adjusted Peak Performance is a metric introduced by the U.S. Department of Commerce's Bureau of Industry and Security to more accurately predict the suitability of a computing system to complex computational problems, specifically those used in simulating nuclear weapons...

(APP) in Weighted TeraFLOPS (WT).

## Records

NEC
NEC
, a Japanese multinational IT company, has its headquarters in Minato, Tokyo, Japan. NEC, part of the Sumitomo Group, provides information technology and network solutions to business enterprises, communications services providers and government....

's SX-9
NEC SX-9
The SX-9 is a supercomputer built by NEC Corporation. The SX-9 Series implements an SMP system in a compact node module and uses an enhanced version of the single chip vector processor that was introduced with the SX-6...

supercomputer was the world's first vector processor
Vector processor
A vector processor, or array processor, is a central processing unit that implements an instruction set containing instructions that operate on one-dimensional arrays of data called vectors. This is in contrast to a scalar processor, whose instructions operate on single data items...

to exceed 100 gigaFLOPS per single core. IBM
IBM
International Business Machines Corporation or IBM is an American multinational technology and consulting corporation headquartered in Armonk, New York, United States. IBM manufactures and sells computer hardware and software, and it offers infrastructure, hosting and consulting services in areas...

's supercomputer
Supercomputer
A supercomputer is a computer at the frontline of current processing capacity, particularly speed of calculation.Supercomputers are used for highly calculation-intensive tasks such as problems including quantum physics, weather forecasting, climate research, molecular modeling A supercomputer is a...

dubbed Roadrunner was the first to reach a sustained performance of 1 petaFLOPS measured by the Linpack
LINPACK
LINPACK is a software library for performing numerical linear algebra on digital computers. It was written in Fortran by Jack Dongarra, Jim Bunch, Cleve Moler, and Gilbert Stewart, and was intended for use on supercomputers in the 1970s and early 1980s...

benchmark. , the 500 fastest supercomputers
TOP500
The TOP500 project ranks and details the 500 most powerful known computer systems in the world. The project was started in 1993 and publishes an updated list of the supercomputers twice a year...

in the world combine for 58.9 petaFLOPS of computing power.

For comparison, a hand-held calculator performs relatively few FLOPS. Each calculation request, such as to add or subtract two numbers, requires only a single operation, so there is rarely any need for its response time
Response time
In technology, response time is the time a system or functional unit takes to react to a given input.- Data processing :In data processing, the response time perceived by the end user is the interval between the instant at which an operator at a terminal enters a request for a response from a...

to exceed what the operator can physically use. 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
RIKEN
is a large natural sciences research institute in Japan. Founded in 1917, it now has approximately 3000 scientists on seven campuses across Japan, the main one in Wako, just outside Tokyo...

, 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
Intel Corporation
Intel Corporation is an American multinational semiconductor chip maker corporation headquartered in Santa Clara, California, United States and the world's largest semiconductor chip maker, based on revenue. It is the inventor of the x86 series of microprocessors, the processors found in most...

unveiled the experimental multi-core POLARIS
Teraflops Research Chip
The Teraflops Research Chip is a research processor containing 80 cores developed by Intel Corporation's Tera-Scale Computing Research Program. The processor was officially announced February 11, 2007 and shown working at the 2007 International Solid-State Circuits Conference...

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
IBM
International Business Machines Corporation or IBM is an American multinational technology and consulting corporation headquartered in Armonk, New York, United States. IBM manufactures and sells computer hardware and software, and it offers infrastructure, hosting and consulting services in areas...

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
Blue Gene
Blue Gene is a computer architecture project to produce several supercomputers, designed to reach operating speeds in the PFLOPS range, and currently reaching sustained speeds of nearly 500 TFLOPS . It is a cooperative project among IBM Blue Gene is a computer architecture project to produce...

supercomputer, measuring a peak of 596 TFLOPS. The Cray XT4
Cray XT4
The Cray XT4 is an updated version of the Cray XT3 supercomputer. It was released on November 18, 2006. It includes an updated version of the SeaStar interconnect router called SeaStar2, processor sockets for Socket AM2 Opteron processors, and 240-pin unbuffered DDR2 memory...

hit second place with 101.7 TFLOPS.

On October 25, 2007, NEC
NEC
, a Japanese multinational IT company, has its headquarters in Minato, Tokyo, Japan. NEC, part of the Sumitomo Group, provides information technology and network solutions to business enterprises, communications services providers and government....

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
National Science Foundation
The National Science Foundation is a United States government agency that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National Institutes of Health...

and the University of Texas opened full scale research runs on an AMD, Sun
Sun Microsystems
Sun Microsystems, Inc. was a company that sold :computers, computer components, :computer software, and :information technology services. Sun was founded on February 24, 1982...

supercomputer named Ranger,
the most powerful supercomputing system in the world for open science research, which operates at sustained speed of half a petaflop.

On May 25, 2008, an American military supercomputer built by IBM
IBM
International Business Machines Corporation or IBM is an American multinational technology and consulting corporation headquartered in Armonk, New York, United States. IBM manufactures and sells computer hardware and software, and it offers infrastructure, hosting and consulting services in areas...

, named 'Roadrunner', reached the computing milestone of one petaflop by processing more than 1.026 quadrillion
Quadrillion may mean either of the two numbers :* 1,000,000,000,000,000 – for all short scale countries; increasingly common meaning in English language usage* 1,000,000,000,000,000,000,000,000 – for all...

calculations per second. It headed the June 2008 and November 2008 TOP500
TOP500
The TOP500 project ranks and details the 500 most powerful known computer systems in the world. The project was started in 1993 and publishes an updated list of the supercomputers twice a year...

list of the most powerful supercomputers (excluding grid computers
Grid computing
Grid computing is a term referring to the combination of computer resources from multiple administrative domains to reach a common goal. The grid can be thought of as a distributed system with non-interactive workloads that involve a large number of files...

). 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
The Greater Roadrunner, taxonomically classified as Geococcyx californianus, meaning "Californian Earth-cuckoo," is a long-legged bird in the cuckoo family, Cuculidae. Along with the Lesser Roadrunner, it is one of two species in the roadrunner genus Geococcyx...

.

In June 2008, AMD released ATI Radeon HD4800 series, which are reported to be the first GPUs to achieve one teraFLOP 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 petaflop system dedicated to open research. In early 2009 the supercomputer was named after a mythical creature, Kraken
Kraken
Kraken are legendary sea monsters of giant proportions said to have dwelt off the coasts of Norway and Iceland.In modern German, Krake means octopus but can also refer to the legendary Kraken...

. Kraken was declared the world's fastest university-managed supercomputer and sixth fastest overall in the 2009 TOP500
TOP500
The TOP500 project ranks and details the 500 most powerful known computer systems in the world. The project was started in 1993 and publishes an updated list of the supercomputers twice a year...

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
Cray
Cray Inc. is an American supercomputer manufacturer based in Seattle, Washington. The company's predecessor, Cray Research, Inc. , was founded in 1972 by computer designer Seymour Cray. Seymour Cray went on to form the spin-off Cray Computer Corporation , in 1989, which went bankrupt in 1995,...

Jaguar performed at 1.75 petaFLOPS, beating the IBM
IBM
International Business Machines Corporation or IBM is an American multinational technology and consulting corporation headquartered in Armonk, New York, United States. IBM manufactures and sells computer hardware and software, and it offers infrastructure, hosting and consulting services in areas...

Roadrunner for the number one spot on the TOP500
TOP500
The TOP500 project ranks and details the 500 most powerful known computer systems in the world. The project was started in 1993 and publishes an updated list of the supercomputers twice a year...

list.

In October 2010, China unveiled the Tianhe-I
Tianhe-I
Tianhe-I, Tianhe-1, or TH-1 , in English, "Milky Way Number One", is a supercomputer capable of an Rmax of 2.566 petaFLOPS...

, a supercomputer that operates at a peak computing rate of 2.5 petaflops.

, the fastest six-core PC processor
Microprocessor
A microprocessor incorporates the functions of a computer's central processing unit on a single integrated circuit, or at most a few integrated circuits. It is a multipurpose, programmable device that accepts digital data as input, processes it according to instructions stored in its memory, and...

reaches 109 GFLOPS (Intel Core i7 980 XE
Gulftown (microprocessor)
Gulftown or Westmere-EP is the codename of a six-core hyperthreaded Intel processor able to run up to 12 threads in parallel. It is based on Westmere microarchitecture, the 32 nm shrink of Nehalem. Originally rumored to be called the Intel Core i9, it is sold as an Intel Core i7...

) in double precision calculations. GPU
Graphics processing unit
A graphics processing unit or GPU is a specialized circuit designed to rapidly manipulate and alter memory in such a way so as to accelerate the building of images in a frame buffer intended for output to a display...

s are considerably more powerful. For example, Nvidia Tesla
Nvidia Tesla
The Tesla graphics processing unit is nVidia's third brand of GPUs. It is based on high-end GPUs from the G80 , as well as the Quadro lineup. Tesla is nVidia's first dedicated General Purpose GPU...

C2050 GPU computing processors perform around 515 GFLOPS in double precision calculations, and the AMD FireStream 9270 peaks at 240 GFLOPS. In single precision performance, Nvidia Tesla C2050 computing processors perform around 1.03 TFLOPS and the AMD FireStream 9270 cards peak at 1.2 TFLOPS. Both Nvidia and AMD's consumer gaming GPUs may reach higher FLOPS. For example, AMD’s HemlockXT 5970 reaches 928 GFLOPS in double precision calculations with two GPUs on board and the Nvidia GTX 480 reaches 672 GFLOPS with one GPU on board.

In November 2011, it was announced that Japan had achieved 10.51 petaflops with its K computer
K computer
The K computer – named for the Japanese word , which stands for 10 quadrillion – is a supercomputer being produced by Fujitsu at the RIKEN Advanced Institute for Computational Science campus in Kobe, Japan. In June 2011, TOP500 ranked K the world's fastest supercomputer, with a rating...

. It is still under development and software performance tuning is currently underway. It has 88,128 SPARC64 VIIIfx processor
Central processing unit
The central processing unit is the portion of a computer system that carries out the instructions of a computer program, to perform the basic arithmetical, logical, and input/output operations of the system. The CPU plays a role somewhat analogous to the brain in the computer. The term has been in...

s in 864 racks, with theoretical performance of 11.28 petaflops. It is named after the Japanese word "kei", which stands for 10 quadrillion
Quadrillion may mean either of the two numbers :* 1,000,000,000,000,000 – for all short scale countries; increasingly common meaning in English language usage* 1,000,000,000,000,000,000,000,000 – for all...

, 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 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.

Distributed computing
Distributed computing
Distributed computing is a field of computer science that studies distributed systems. A distributed system consists of multiple autonomous computers that communicate through a computer network. The computers interact with each other in order to achieve a common goal...

uses the Internet
Internet
The Internet is a global system of interconnected computer networks that use the standard Internet protocol suite to serve billions of users worldwide...

Personal computer
A personal computer is any general-purpose computer whose size, capabilities, and original sales price make it useful for individuals, and which is intended to be operated directly by an end-user with no intervening computer operator...

s to achieve more FLOPS:
• Folding@Home
Folding@home
Folding@home is a distributed computing project designed to use spare processing power on personal computers to perform simulations of disease-relevant protein folding and other molecular dynamics, and to improve on the methods of doing so...

is sustaining over 4.1 native petaFLOPS as of July 2011 or 6.6 x86 PFLOPS (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
Graphics processing unit
A graphics processing unit or GPU is a specialized circuit designed to rapidly manipulate and alter memory in such a way so as to accelerate the building of images in a frame buffer intended for output to a display...

, PlayStation 3
PlayStation 3
The is the third home video game console produced by Sony Computer Entertainment and the successor to the PlayStation 2 as part of the PlayStation series. The PlayStation 3 competes with Microsoft's Xbox 360 and Nintendo's Wii as part of the seventh generation of video game consoles...

and CPU
Central processing unit
The central processing unit is the portion of a computer system that carries out the instructions of a computer program, to perform the basic arithmetical, logical, and input/output operations of the system. The CPU plays a role somewhat analogous to the brain in the computer. The term has been in...

units.

• The entire BOINC network averages about 5.3 PFLOPS ., MilkyWay@Home
MilkyWay@Home
MilkyWay@home is a volunteer distributed computing project in astrophysics running on the Berkeley Open Infrastructure for Network Computing platform...

computes at over 460 TFLOPS, with a large amount of this work coming from GPUs., SETI@Home
SETI@home
SETI@home is an Internet-based public volunteer computing project employing the BOINC software platform, hosted by the Space Sciences Laboratory, at the University of California, Berkeley, in the United States. SETI is an acronym for the Search for Extra-Terrestrial Intelligence...

, which began in 1999, computes data averages more than 500 TFLOPS., Einstein@Home
Einstein@Home
Einstein@Home is a volunteer distributed computing project hosted by the University of Wisconsin–Milwaukee and the Max Planck Institute for Gravitational Physics . The project is directed by Bruce Allen...

is crunching more than 190 TFLOPS., GIMPS
Great Internet Mersenne Prime Search
The Great Internet Mersenne Prime Search is a collaborative project of volunteers who use freely available computer software to search for Mersenne prime numbers. The project was founded by George Woltman, who also wrote the software Prime95 and MPrime for the project...

, which began in 1996, is sustaining 59 TFLOPS.

### Future developments

In 2008, James Bamford
James Bamford
V. James Bamford is an American bestselling author and journalist who writes about United States intelligence agencies, most notably the National Security Agency.-Biography:...

The Shadow Factory: The Ultra-Secret NSA from 9/11 to the Eavesdropping on America is a book on the National Security Agency by bestselling author James Bamford.- Fort Gordon, Georgia :...

reported that NSA told the Pentagon
The Pentagon
The Pentagon is the headquarters of the United States Department of Defense, located in Arlington County, Virginia. As a symbol of the U.S. military, "the Pentagon" is often used metonymically to refer to the Department of Defense rather than the building itself.Designed by the American architect...

it would need an exaflop computer by 2018.

In May 2008, a collaboration was announced between NASA
NASA
The National Aeronautics and Space Administration is the agency of the United States government that is responsible for the nation's civilian space program and for aeronautics and aerospace research...

, SGI
Silicon Graphics
Silicon Graphics, Inc. was a manufacturer of high-performance computing solutions, including computer hardware and software, founded in 1981 by Jim Clark...

, and Intel
Intel Corporation
Intel Corporation is an American multinational semiconductor chip maker corporation headquartered in Santa Clara, California, United States and the world's largest semiconductor chip maker, based on revenue. It is the inventor of the x86 series of microprocessors, the processors found in most...

to build a 1 PFLOPS computer, Pleiades
Pleiades is a petascale supercomputer built by SGI at NASA Ames Research Center in Mountain View, California. , it was the world's seventh fastest computer with a peak performance of more than 970 teraflops. After further extensions, Pleiades is scheduled to reach 10 petaflops in 2012.-See...

, in 2009, scaling up to 10 PFLOPS by 2012. At the same time, IBM
IBM
International Business Machines Corporation or IBM is an American multinational technology and consulting corporation headquartered in Armonk, New York, United States. IBM manufactures and sells computer hardware and software, and it offers infrastructure, hosting and consulting services in areas...

intended to build a 20 PFLOPS supercomputer, Sequoia
IBM Sequoia
Sequoia is a petascale Blue Gene/Q supercomputer being constructed by IBM for the National Nuclear Security Administration as part of the Advanced Simulation and Computing Program...

, at Lawrence Livermore National Laboratory
Lawrence Livermore National Laboratory
The Lawrence Livermore National Laboratory , just outside Livermore, California, is a Federally Funded Research and Development Center founded by the University of California in 1952...

until 2011.

On December 2, 2010, the US Air Force unveiled a defense supercomputer made up of 1,760 Playstation 3
PlayStation 3
The is the third home video game console produced by Sony Computer Entertainment and the successor to the PlayStation 2 as part of the PlayStation series. The PlayStation 3 competes with Microsoft's Xbox 360 and Nintendo's Wii as part of the seventh generation of video game consoles...

consoles that can run 500 trillion floating-point operations per second.

On October 11, 2011, the Oak Ridge National Laboratory
Oak Ridge National Laboratory
Oak Ridge National Laboratory is a multiprogram science and technology national laboratory managed for the United States Department of Energy by UT-Battelle. ORNL is the DOE's largest science and energy laboratory. ORNL is located in Oak Ridge, Tennessee, near Knoxville...

announced they were building a 20 petaflop supercomputer, named Titan, which will become operational in 2012, the hybrid Titan system will combine AMD Opteron processors with “Kepler” NVIDIA Tesla graphic processing unit (GPU) technologies.

Given the current speed of progress, supercomputer
Supercomputer
A supercomputer is a computer at the frontline of current processing capacity, particularly speed of calculation.Supercomputers are used for highly calculation-intensive tasks such as problems including quantum physics, weather forecasting, climate research, molecular modeling A supercomputer is a...

s are projected to reach 1 exaFLOPS (EFLOPS) in 2019. Cray, Inc. announced in December 2009 a plan to build a 1 EFLOPS supercomputer before 2020. Erik P. DeBenedictis of Sandia National Laboratories
Sandia National Laboratories
The Sandia National Laboratories, managed and operated by the Sandia Corporation , are two major United States Department of Energy research and development national laboratories....

theorizes that a zettaFLOPS (ZFLOPS) computer is required to accomplish full weather modeling, which could cover a two week time span accurately. Such systems might be built around 2030.

### Hardware costs

The following is a list of examples of computers that demonstrates how drastically performance has increased and price has decreased. The "cost per GFLOPS" is the cost for a set of hardware that would theoretically operate at one billion floating-point operations per second. During the era when no single computing platform was able to achieve one GFLOPS, this table lists the total cost for multiple instances of a fast computing platform which speed sums to one GFLOPS. Otherwise, the least expensive computing platform able to achieve one GFLOPS is listed.
Date Approximate cost per GFLOPS Technology Comments
1961 US \$1,100,000,000,000 (\$1.1 trillion) About 17 million IBM 1620
IBM 1620
The IBM 1620 was announced by IBM on October 21, 1959, and marketed as an inexpensive "scientific computer". After a total production of about two thousand machines, it was withdrawn on November 19, 1970...

units costing \$64,000 each
The multiplication operation takes 17.7 ms.
1984 \$15,000,000 Cray X-MP
Cray X-MP
The Cray X-MP was a supercomputer designed, built and sold by Cray Research. It was announced in 1982 as the "cleaned up" successor to the 1975 Cray-1, and was the world's fastest computer from 1983 to 1985...

1997 \$30,000 Two 16-processor Beowulf
Beowulf (computing)
A Beowulf cluster is a computer cluster of what are normally identical, commodity-grade computers networked into a small local area network with libraries and programs installed which allow processing to be shared among them...

clusters with Pentium Pro
Pentium Pro
The Pentium Pro is a sixth-generation x86 microprocessor developed and manufactured by Intel introduced in November 1, 1995 . It introduced the P6 microarchitecture and was originally intended to replace the original Pentium in a full range of applications...

microprocessors
\$1,000 Bunyip Beowulf cluster Bunyip was the first sub-US\$1/MFLOPS computing technology. It won the Gordon Bell Prize in 2000.
\$640 KLAT2 KLAT2 was the first computing technology which scaled to large applications while staying under US\$1/MFLOPS.
\$82 KASY0 KASY0 was the first sub-US\$100/GFLOPS computing technology.
\$48 Microwulf As of August 2007, this 26.25 GFLOPS "personal" Beowulf cluster can be built for \$1256.
\$1.80 HPU4Science This \$30,000 cluster was built using only commercially available "gamer" grade hardware.

The trend toward placing ever more transistors inexpensively on an integrated circuit follows Moore's law
Moore's Law
Moore's law describes a long-term trend in the history of computing hardware: the number of transistors that can be placed inexpensively on an integrated circuit doubles approximately every two years....

. This trend explains the rising speed and falling cost of computer processing.

### Operation costs

In energy cost, according to the Green500 list, the most efficient TOP500
TOP500
The TOP500 project ranks and details the 500 most powerful known computer systems in the world. The project was started in 1993 and publishes an updated list of the supercomputers twice a year...

supercomputer runs at 2097.19 MFLOPS per watt. This translates to an energy requirement of 0.477 watt
Watt
The watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:...

s per GFLOPS, however this energy requirement will be much greater for less efficient supercomputers.

Hardware costs for low cost supercomputers may be less significant than energy costs when running continuously for several years.

## Floating-point operation and integer operation

Floating-point operation per second or FLOPS, measures the computing ability of a computer. An example of a floating-point operation is the calculation of mathematical equations. FLOPS is a good indicator to measure performance on DSP
DSP
- Computing :* Digital signal processing, the study and implementation of signals in digital computing and their processing methods* Digital signal processor, a specialized microprocessor designed specifically for digital signal processing...

, supercomputers, robotic motion control, and scientific simulations. MIPS is used to measure the integer performance of a computer. Examples of integer operation is 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 (LLNL), invented the term FLOPS and MFLOPS (MegaFLOPS) so that he could compare the so-called Supercomputers of the day by the number of floating-point calculations they did per second. This was much better than using the prevalent MIPS (Millions of Instructions Per Second) to compare computers as this statistic usually had little bearing on the arithmetic capability of the machine.

Fixed-point (integer
Integer
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...

s). These designations refer to the format used to store and manipulate numeric representations of data. Fixed-point are designed to represent and manipulate integers – positive and negative whole numbers – for example 16 bits, yielding up to 65,536 possible bit patterns (216).

Floating-point (real number
Real number
In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...

s). The encoding scheme for floating-point numbers is more complicated than for fixed-point. The basic idea is the same as used in scientific notation, where a mantissa is multiplied by ten raised to some exponent. For instance, 5.4321 × 106, where 5.4321 is the mantissa and 6 is the exponent. Scientific notation is exceptional at representing very large and very small numbers. For example: 1.2 × 1050, the number of atoms in the earth, or 2.6 × 10−23, the distance a turtle crawls in one second compared to the diameter of our galaxy. Notice that numbers represented in scientific notation are normalized so that there is only a single nonzero digit left of the decimal point. This is achieved by adjusting the exponent as needed. Floating-point representation is similar to scientific notation, except everything is carried out in base two, rather than base ten. 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.

With fixed-point notation, the gaps between adjacent numbers always equal a value of one, whereas in floating-point notation, gaps between adjacent numbers are not uniformly spaced—the gap between any two numbers is approximately ten million times smaller than the value of the numbers (ANSI/IEEE Std. 754 standard format), with large gaps between large numbers and small gaps between small 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. It is also important to consider fixed and floating-point formats in the context of precision – the size of the gaps between numbers. Every time a processor generates a new number via a mathematical calculation, that number must be rounded to the nearest value that can be stored via the format in use. Rounding and/or truncating numbers during processing naturally yields quantization error or ‘noise’ - the deviation between actual values and quantized values. Since the gaps between adjacent numbers can be much larger with fixed-point processing when compared to floating-point processing, round-off error can be much more pronounced. As such, floating-point processing yields much greater precision than fixed-point processing, distinguishing floating-point processors as the ideal CPU when computing accuracy is a critical requirement.