# FLOPS

(Redirected from MFLOPS)
Computer performance
Name FLOPS
yottaFLOPS 1024
zettaFLOPS 1021
exaFLOPS 1018
petaFLOPS 1015
teraFLOPS 1012
gigaFLOPS 109
megaFLOPS 106
kiloFLOPS 103

In computing, FLOPS (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.

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, which would then be "flop/s". The expression 1 flops is actually interpreted as $f_{\text{flop}} = 1\,\mathrm{s}^{-1}\,\Leftrightarrow\, n_{\text{flops}} = 1$.

## Computing

One can calculate FLOPS using this equation:[1]

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

Most microprocessors today can do 4 FLOPs per clock cycle.[1] Therefore, 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 chip sockets on a motherboard, in other words, how many computer 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 actual 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.” [2]

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,[3] 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.[4]

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.[5]

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.[6] The Cray XT4 hit second place with 101.7 teraFLOPS.

On October 25, 2007, NEC Corporation of Japan issued a press release[7] 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 opened full scale research runs on an AMD, Sun supercomputer named Ranger,[8] the most powerful supercomputing system in the world for open science research, which operates at sustained speed of half a 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[9] and November 2008[10] 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.[11]

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.[12]

In October 2010, China unveiled the Tianhe-I, a supercomputer that operates at a peak computing rate of 2.5 petaflops.[13][14]

As of 2010, the fastest six-core PC processor reaches 109 gigaFLOPS (Intel Core i7 980 XE)[15] in double precision calculations. GPUs are considerably more powerful. For example, Nvidia Tesla C2050 GPU computing processors perform around 515 gigaFLOPS[16] in double precision calculations, and the AMD FireStream 9270 peaks at 240 gigaFLOPS.[17] 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[18] reaches 928 gigaFLOPS in double precision calculations with two GPUs on board and the Nvidia GTX 480 reaches 672 gigaFLOPS[19] 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.[20] (500 teraFLOPS)

In November 2011, it was announced that Japan had achieved 10.51 petaflops with its K computer.[21] 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,[22] 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.[23][24]

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.[25]

On November 12, 2012, the TOP500 list certified Titan as the world's fastest supercomputer per the LINPACK benchmark, at 17.59 petaFLOPS.[26][27] 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.[28][29]

On June 10, 2013, China's Tianhe-2 was ranked the world's fastest with a record of 33.86 petaflops.[30]

### Distributed computing records

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

• As of November 2012, GIMPS, which began in 1996, is sustaining 95 teraFLOPS.[31]
• As of November 2012, SETI@Home, which began in 1999, computes data averages more than 597 teraFLOPS.[33]
• As of November 2012, MilkyWay@Home computes at over 490 teraFLOPS, with a large amount of this work coming from GPUs.[34]
• Folding@home is sustaining over 9.6 native petaFLOPS as of October 2013[35] or 19.1 x86 petaFLOPS (x86 FLOPS are an approximate measurement of the speed of a calculation on an x86-based processor, different from native FLOPS[36]). 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, PlayStation 3 and CPU units.[37]
• The entire BOINC network averages about 9.5 petaFLOPS as of March 19, 2013.[38]

### Future developments

In 2008, James Bamford's book The Shadow Factory reported that NSA told the Pentagon it would need an exaflop computer by 2018.[39]

Given the current speed of progress, supercomputers are projected to reach 1 exaFLOPS (EFLOPS) in 2019.[40] Cray, Inc. announced in December 2009 a plan to build a 1 EFLOPS supercomputer before 2020.[41] 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.[42] Such systems might be built around 2030.[43]

In India, ISRO and Indian Institute of Science have stated that they have planned to make a 132.8 EFLOPS supercomputer by 2017, 100 times faster than any supercomputer ever planned. They have estimated that the project would cost US $2 billion, which the state has budgeted.[44] ## Cost of computing ### 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 Approximate cost per GFLOPS inflation adjusted to 2013 US dollars[45] 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.[46] 1984$15,000,000 $33,000,000 Cray X-MP 1997$30,000 $42,000 Two 16-processor Beowulf clusters with Pentium Pro microprocessors[47] 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.[48] August 2003$82 $100 KASY0 KASY0 was the first sub-US-$100/GFLOPS computing technology.[49]
August 2007 $48$52 Microwulf As of August 2007, this 26.25 GFLOPS "personal" Beowulf cluster can be built for $1256.[50] March 2011$1.80 $1.80 HPU4Science This$30,000 cluster was built using only commercially available "gamer" grade hardware.[51]
August 2012 $0.75$0.73 Quad AMD7970 GHz System A quad AMD 7970 desktop computer reaching 16 TFlops of single-precision, 4 TFlops of single-precision computing performance. Total system cost was $3000; it was also built using only commercially available "gamer" grade hardware.[citation needed] 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[52]
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 GeForce GTX 760 reaches a total of 6.771 TFLOPS for a total cost of $1090.66.[53] December 2013$0.12 $0.12 Pentium G550 R9 290 System Built using commercially available parts. Pentium G550 & AMD R9 290 tops out at 4.848 TFLOPS grand total of$681.84 USD. [54]

The trend toward placing ever more transistors inexpensively on an integrated circuit follows Moore's law. This trend explains the rising speed and falling cost of computer processing.

### Operation costs

In energy cost, according to the Green500 list, as of June 2011 the most efficient TOP500 supercomputer runs at 2097.19 MFLOPS per watt. This translates to an energy requirement of 0.477 watts 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

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.[55][56] 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.[57]

### 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.[58]

### 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.[59]

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