Floating point operations per second

 ( Benchmarks ) 

Floating point operations per second ( FLOPS, flops or flop/s) is a measure of computer performance in computing, useful in fields of scientific computations that require floating-point calculations.

For such cases, it is a more accurate measure than measuring instructions per second.

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Floating-point arithmetic

+ Multipliers for flops ! Name ! Unit ! Value
Kilo-	kFLOPS	103
Mega-	MFLOPS	106
Giga-	GFLOPS	109
Tera-	TFLOPS	1012
Peta-	PFLOPS	1015
Exa-	EFLOPS	1018
Zetta-	ZFLOPS	1021
Yotta-	YFLOPS	1024
Ronna-	RFLOPS	1027
Quetta-	QFLOPS	1030

Floating-point arithmetic is needed for very large or very small , or computations that require a large dynamic range. Floating-point representation is similar to scientific notation, except computers use Binary number (with rare exceptions), rather than Decimal. The encoding scheme stores the sign, the exponent (in base two for Cray and VAX, base two or ten for IEEE floating point formats, and base 16 for IBM Floating Point Architecture) and the significand (number after the radix 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. Floating Point Retrieved on December 25, 2009.

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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 where some of the data may have extremely large range of numerical values or where the range may be unpredictable. As such, floating-point processors are ideally suited for computationally intensive applications. Summary: Fixed-point (integer) vs floating-point Retrieved on December 25, 2009.

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Computational performance FLOPS and MIPS are units of measure for the numerical computing performance of a computer. Floating-point operations are typically used in fields such as scientific computational research, as well as in machine learning. However, before the late 1980s floating-point hardware (it's possible to implement FP arithmetic in software over any integer hardware) was typically an optional feature, and computers that had it were said to be "scientific computers", or to have "scientific computation" capability. Thus the unit MIPS was useful to measure integer performance of any computer, including those without such a capability, and to account for architecture differences, similar MOPS (million operations per second) was used as early as 1970 as well. Note that besides integer (or fixed-point) arithmetics, examples of integer operation include data movement (A to B) or value testing (If A = B, then C). That's why MIPS as a performance benchmark is adequate when a computer is used in database queries, word processing, spreadsheets, or to run multiple virtual operating systems. Fixed versus floating point. Retrieved on December 25, 2009. Data manipulation and math calculation. Retrieved on December 25, 2009. In 1974 David Kuck coined the terms flops and megaflops for the description of supercomputer performance 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 on scientific tasks.

FLOPS on an HPC-system can be calculated using this equation:

$\backslash text\{FLOPS\}\; =\; \backslash text\{racks\}\; \backslash times\; \backslash frac\{\backslash text\{nodes\}\}\{\backslash text\{rack\}\}\; \backslash times\; \backslash frac\{\backslash text\{sockets\}\}\{\backslash text\{node\}\}\; \backslash times\; \backslash frac\{\backslash text\{cores\}\}\{\backslash text\{socket\}\}\; \backslash times\; \backslash frac\{\backslash text\{cycles\}\}\{\; \backslash text\{second\}\}\; \backslash times\; \backslash frac\{\backslash text\{FLOPs\}\}\{\backslash text\{cycle\}\}.$

This can be simplified to the most common case: a computer that has exactly 1 CPU:

$\backslash text\{FLOPS\}\; =\; \backslash text\{cores\}\; \backslash times\; \backslash frac\{\backslash text\{cycles\}\}\{\; \backslash text\{second\}\}\; \backslash times\; \backslash frac\{\backslash text\{FLOPs\}\}\{\backslash text\{cycle\}\}.$

FLOPS can be recorded in different measures of precision, for example, the TOP500 supercomputer list ranks computers by 64-bit (double-precision floating-point format) operations per second, abbreviated to FP64. Similar measures are available for 32-bit ( FP32) and 16-bit ( FP16) operations.

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Floating-point operations per clock cycle for various processors

+ Floating-point operations per clock cycle per core ! scope="col"	Microarchitecture ! scope="col"	Instruction set architecture ! scope="col"	FP64 ! scope="col"	FP32 ! scope="col"	FP16
Intel 80486	x87 (32-bit)		0.128
	x87 (32-bit)		0.5
	MMX (64-bit)		1
Intel P6 Pentium III	SSE (64-bit)		2
Intel NetBurst Pentium 4 (Willamette, Northwood)	SSE2 (64-bit)	2	4
Intel P6 Pentium M	SSE2 (64-bit)	1	2
	SSE3 (64-bit)	2	4
SSE3 (128-bit)
AVX (256-bit)	0
	AVX2 & FMA (256-bit)	0
IMCI (512-bit)	0
	AVX-512 & FMA (512-bit)	0
0
	AVX (128-bit)	0
AMD K10	0
AMD Bulldozer (Piledriver, Steamroller, Excavator)		0
	AVX2 & FMA (128-bit, 256-bit decoding)	0
	AVX2 & FMA (256-bit)	0
	AVX-512 & FMA (256-bit)	0
	AVX-512 & FMA (512-bit)	0
ARM architecture	0
ARM architecture	0
ARM architecture	0
ARM architecture	0
ARM architecture
ARM architecture	0
ARM architecture	0
ARM architecture	0
ARM architecture	0
ARM architecture	0
	0
SH-4	0
Nvidia Curie (GeForce 6 series and GeForce 7 series)
Nvidia Tesla 2.0 (GeForce GTX 260–295)
Nvidia Fermi (only GeForce GTX 465–480, 560 Ti, 570–590)	PTX	0
Nvidia Fermi (only Quadro 600–2000)	PTX	0
Nvidia Fermi (only Quadro 4000–7000, Tesla)	PTX	0
Nvidia Kepler (GeForce (except Titan and Titan Black), Quadro (except K6000), Tesla K10)	PTX	0
Nvidia Kepler (GeForce GTX Titan and Titan Black, Quadro K6000, Tesla (except K10))	PTX	0
4
PTX	16
PTX	4
PTX	16
PTX	32
	8
32
AMD TeraScale 1 (Radeon HD 4000 series)
AMD TeraScale 2 (Radeon HD 5000 series)
AMD TeraScale 3 (Radeon HD 6000 series)
AMD GCN (only Radeon Pro W 8100–9100)
AMD GCN (all except Radeon Pro W 8100–9100, Vega 10–20)	4
4
GCN	4
AMD GCN Vega 20 (only Radeon Instinct MI50 / MI60 and Radeon Pro VII)	GCN	4
	RDNA	4
RDNA	8?
CDNA	16
CDNA 2	16
Xe	4
16
32
16
Qualcomm Adreno 5x0	4
Qualcomm Adreno 6x0	4
Graphcore Colossus GC2Archived at Ghostarchive and the target="_blank" rel="nofollow"> Wayback Machine:	64
	128
ENIAC @ 100 kHz in 1945		0.004ENIAC @ 100 kHz with 385 Flops (~)
48-bit processor @ 208 Kilohertz in CDC 1604 in 1960
60-bit processor @ 10 MHz in CDC 6600 in 1964		0.3 (FP60)
60-bit processor @ 10 MHz in CDC 7600 in 1967		1.0 (FP60)
Cray-1 @ 80 MHz in 1976		2 (700 FLOPS/W)
CDC Cyber 205 @ 50 MHz in 1981 Fortran compiler (ANSI 77 with vector extensions)		8	16
Transputer IMS T800-20 @ 20 MHz in 1987		0.08
Parallella E16 @ 1000 MHz in 2012		2 Epiphany-III 16-core 65nm Microprocessor (E16G301) // admin (August 19, 2012) (5.0 GFLOPS/W)
Parallella E64 @ 800 MHz in 2012		2 Epiphany-IV 64-core 28nm Microprocessor (E64G401) // admin (August 19, 2012) (50.0 GFLOPS/W)

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Performance records

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Single computer records In June 1997, Intel's ASCI Red was the world's first computer to achieve one teraFLOPS 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.

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

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

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, faster than the Blue Gene/L. When configured to do so, it can reach speeds in excess of three petaFLOPS.

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 Microsystems 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 'IBM Roadrunner', reached the computing milestone of one petaFLOPS. It headed the June 2008 and November 2008 TOP500 list of the most powerful supercomputers (excluding grid computing). The computer is located at Los Alamos National Laboratory in New Mexico. The computer's name refers to the New Mexico state bird, the greater roadrunner ( Geococcyx californianus).

In June 2008, AMD released ATI Radeon HD 4800 series, which are reported to be the first GPUs to achieve one teraFLOPS. 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 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, 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. 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-1, a supercomputer that operates at a peak computing rate of 2.5 petaFLOPS.

the fastest PC [[processor|microprocessor]] reached 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 November 2011, it was announced that Japan had achieved 10.51 petaFLOPS with its K computer. It has 88,128 SPARC64 VIIIfx processors in 864 racks, with theoretical performance of 11.28 petaFLOPS. It is named after the Japanese word "", which stands for 10 quadrillion,See Japanese numbers 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 teraFLOPS on a wide range of DGEMM operations. Intel emphasized during the demonstration that this was a sustained teraFLOPS (not "raw teraFLOPS" used by others to get higher but less meaningful numbers), and that it was the first general purpose processor to ever cross a teraFLOPS.

On June 18, 2012, IBM Sequoia, 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 graphics processing unit (GPU) technologies.

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

On June 20, 2016, China's Sunway TaihuLight was ranked the world's fastest with 93 petaFLOPS on the LINPACK benchmark (out of 125 peak petaFLOPS). The system was installed at the National Supercomputing Center in Wuxi, and represented more performance than the next five most powerful systems on the TOP500 list did at the time combined.

In June 2019, Summit, an IBM-built supercomputer now running at the Department of Energy's (DOE) Oak Ridge National Laboratory (ORNL), captured the number one spot with a performance of 148.6 petaFLOPS on High Performance Linpack (HPL), the benchmark used to rank the TOP500 list. Summit has 4,356 nodes, each one equipped with two 22-core Power9 CPUs, and six NVIDIA Tesla V100 GPUs.

In June 2022, the United States' Frontier was the most powerful supercomputer on TOP500, reaching 1102 petaFlops (1.102 exaFlops) on the LINPACK benchmarks.

In November 2024, the United States’ El Capitan exascale supercomputer, hosted at the Lawrence Livermore National Laboratory in Livermore, displaced Frontier as the world's fastest supercomputer in the 64th edition of the Top500 (Nov 2024).

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

• , the Folding@home network has over 2.3 exaFLOPS of total computing power. It is the most powerful distributed computer network, being the first ever to break 1 exaFLOPS of total computing power. This level of performance is primarily enabled by the cumulative effort of a vast array of powerful GPU and CPU units.

• , the entire BOINC network averages about 31 petaFLOPS.
• , SETI@home, employing the BOINC software platform, averages 896 teraFLOPS.
• , Einstein@Home, a project using the BOINC network, is crunching at 3 petaFLOPS.
• , MilkyWay@home, using the BOINC infrastructure, computes at 847 teraFLOPS.
• , GIMPS, searching for , is sustaining 1,354 teraFLOPS.

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Cost of computing

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Hardware costs

1945	$1.265trillion	$T	ENIAC: in 1945 and $ in 2023.	/ . First-generation (vacuum tube-based) electronic digital computer.
1961	$18.672billion	$B	A basic installation of IBM 7030 Stretch had a cost at the time of each.	The IBM 7030 Stretch performs one floating-point multiply every . Second-generation (discrete transistor-based) computer.
1964	$2.3B	$B	Base model CDC 6600 price: $6,891,300.	The CDC 6600 is considered to be the first commercially-successful supercomputer.
1984	$18,750,000	$	Cray X-MP/48	$15,000,000 / 0.8 GFLOPS. Third-generation (integrated circuit-based) computer.
1997	$30,000	$	Two 16-processor Beowulf clusters with Pentium Pro microprocessors
	$1,000	$	Beowulf cluster	Bunyip was the first sub- 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 .
	$83.86	$	KASY0	KASY0 was the first sub- computing technology. KASY0 achieved 471 GFLOPS on 32-bit HPL. At a cost of less than $39,500, that makes it the first supercomputer to break $100/GFLOPS.
	$48.31	$	Microwulf	As of August 2007, this "personal" Beowulf cluster can be built for $1256.
	$1.80	$	HPU4Science	This $30,000 cluster was built using only commercially available "gamer" grade hardware.Adam Stevenson, Yann Le Du, and Mariem El Afrit. " High-performance computing on gamer PCs." Ars Technica. March 31, 2011.
	75¢	$	Quad AMD Radeon 7970 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.
	21.68¢	¢	Sony PlayStation 4	The Sony PlayStation 4 is listed as having a peak performance of , at a price of $399" Sony Sparks Price War With PS4 Priced at $399." CNBC. June 11, 2013.
	16.11¢	¢	Sempron & 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 for a total cost of .
	12.41¢	¢	Sandy Bridge & Radeon R9 290 system	Built using commercially available parts. Intel Sandy Bridge and AMD Radeon R9 290 tops out at grand total of .
	7.85¢	¢	Celeron G1830 & Radeon R9 295X2 system	Built using commercially available parts. Intel Celeron G1830 and AMD Radeon R9 295X2 tops out at over at a grand total of .
	6¢	¢	AMD Ryzen 7 1700 & Radeon Pro system	Built using commercially available parts. AMD Ryzen 7 1700 CPU combined with AMD Radeon Vega FE cards in CrossFire tops out at over at just under for the complete system.
October 2017	2.73¢	¢	Kaby Lake & AMD RX Vega 64 system	Built using commercially available parts. Three AMD RX Vega 64 graphics cards provide just over 75 TFLOPS half precision (38 TFLOPS SP or 2.6 TFLOPS DP when combined with the CPU) at ~$2,050 for the complete system.
November 2020	3.14¢	¢	AMD Ryzen 3600 & 3× NVIDIA RTX 3080 system	AMD Ryzen 3600 @ 484 GFLOPS & $199.99 3× NVIDIA RTX 3080 @ 29,770 GFLOPS each & $699.99 Total system GFLOPS = 89,794 / TFLOPS = 89.794 Total system cost incl. realistic but low cost parts; matched with other example = $2839 /GFLOP = $0.0314
November 2020	3.88¢	¢	PlayStation 5	The Sony PlayStation 5 Digital Edition is listed as having a peak performance of 10.28 TFLOPS (20.56 TFLOPS at half precision) at a retail price of $399.
November 2020	4.11¢	¢	Xbox Series X	Microsoft's Xbox Series X is listed as having a peak performance of 12.15 TFLOPS (24.30 TFLOPS at half precision) at a retail price of $499.
September 2022	1.94¢	¢	RTX 4090	Nvidia's RTX 4090 is listed as having a peak performance of 82.6 TFLOPS (1.32 PFLOPS at 8-bit precision) at a retail price of $1599.
May 2023	1.25¢	¢	Radeon RX 7600	AMD's RX 7600 is listed as having a peak performance of 21.5 TFLOPS at a retail price of $269.

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See also

• Computer performance by orders of magnitude
• Exascale computing
• Gordon Bell Prize
• LINPACK benchmarks
• Moore's law
• Multiply–accumulate operation
• Performance per watt#FLOPS per watt
• SPECfp
• SPECint
• SUPS
• TOP500

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