Floating point operations per second

Floating-point arithmetic

multipliers

Floating-point arithmetic is needed for very large or very small real numbers, or computations that require a large dynamic range. Floating-point representation is similar to scientific notation, except computers use base two (with rare exceptions), rather than base ten. 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.

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.

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. 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:

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

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

: \text{FLOPS} = \text{cores} \times \frac{\text{cycles}}{ \text{second}} \times \frac{\text{FLOPs}}{\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.

FLOPSforProcessors

Floating-point operations per clock cycle for various processors

Performance records

Single computer records

The NEC SX-2, a supercomputer developed by NEC in 1983, achieved gigaFLOPS (GFLOPS) performance with 1.3 billion FLOPS.

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 Corporation 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 IBM Blue Gene/L 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 supercomputer named Ranger,{{cite web |access-date = September 13, 2010 |archive-url = https://web.archive.org/web/20090801102108/http://www.tacc.utexas.edu/resources/hpcsystems/ |archive-date = August 1, 2009 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. 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. 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 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 "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 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'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 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) and kept its place in the June 2025 list.

Distributed computing records

Distributed computing uses the Internet to link personal computers, and sometimes supercomputers to achieve more FLOPS:

• , a group of computer scientists and astronomers have performed a star-forming simulations on a heterogeneous grid of 5 workstations distributed across the Netherlands, several including GPU. The calculation was performed by combining AMUSE with Ibis.

• , the CosmoGrid simulation, a cosmological 8589934592-particle dark-matter simulation, was run concurrently across 3 supercomputers to address the question of the Galactic missing satellite problem. Using supercomputers in Espoo (Finland), Edinburgh (UK), and Amsterdam (the Netherlands), with 19644 compute cores they achieved 80% of the hardware's peak efficiency.

• , 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.{{cite press release |access-date = December 11, 2008 |url-status = dead |archive-url = https://web.archive.org/web/20090131082202/http://www.scei.co.jp/corporate/release/081106de.html |archive-date = January 31, 2009

• , 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 Mersenne primes, is sustaining 1,354 teraFLOPS.

Cost of computing

Hardware costs

START OF A BUNCH OF DELETED STUFF

|- |Q4 2018 |$0.02 |$ |$20 |Nvidia Jetson AGX Xavier

| | $0.42 | Ambric AM2045 | |- | | $0.13 (single precision) | ATI Radeon R800

| | $0.13 | AMD Radeon HD 6990 Overclocked |Floating-point performance (peak): 5.40 TFLOPS. Price: $699.

| | $0.12 | $0.12 | AMD Radeon HD 7990 | The AMD Radeon HD 7990 is a GPU with single precision computing performance reaching 8.2 TFLOPS. It was released on April 24, 2013 with a price point of $1000.

END OF A BUNCH OF DELETED STUFF

References

References

1. "Understand measures of supercomputer performance and storage system capacity".
2. "GPU GFLOPS Statistics 2007-2025: NVIDIA AMD Intel". Axiom Gaming.
3. [http://www.dspguide.com/ch4/3.htm Floating Point] Retrieved on December 25, 2009.
4. [http://www.analog.com/en/embedded-processing-dsp/content/Fixed-Point_vs_Floating-Point_DSP/fca.html Summary: Fixed-point (integer) vs floating-point] {{Webarchive. link. (December 31, 2009 Retrieved on December 25, 2009.)
5. (1970). "NASA Technical Note". National Aeronautics and Space Administration..
6. [http://www.dspguide.com/ch28/4.htm Fixed versus floating point.] Retrieved on December 25, 2009.
7. [http://www.dspguide.com/ch28/1.htm Data manipulation and math calculation.] Retrieved on December 25, 2009.
8. Kuck, D. J.. (1974). "Computer System Capacity Fundamentals". U.S. Department of Commerce, National Bureau of Standards.
9. ""Nodes, Sockets, Cores and FLOPS, Oh, My" by Dr. Mark R. Fernandez, Ph.D.".
10. "FREQUENTLY ASKED QUESTIONS".
11. "Floating-Point Operations Per Second (FLOPS)".
12. "home.iae.nl".
13. "Computing Power throughout History".
14. (2017). "Theoretical Peak FLOPS per instruction set: a tutorial". Journal of Supercomputing.
15. "New instructions support for Bulldozer (FMA3) and Piledriver (FMA3+4 and CVT, BMI, TB M)".
16. "Agner's CPU blog - Test results for AMD Ryzen".
17. https://arstechnica.com/gadgets/2017/03/amds-moment-of-zen-finally-an-architecture-that-can-compete/2/ "each core now has a pair of 128-bit FMA units of its own"
18. Mike Clark. (August 23, 2016). "A New x86 Core Architecture for the Next Generation of Computing". AMD.
19. "The microarchitecture of Intel and AMD CPUs".
20. (May 27, 2019). "AMD CEO Lisa Su's COMPUTEX 2019 Keynote".
21. "Leadership HPC Performance with 5th Generation AMD EPYC Processors".
22. (1999). "Entertainment Systems and High-Performance Processor SH-4". [[Hitachi]].
23. (2000). "SH-4 Next-Generation DSP Architecture for VoIP". [[Hitachi]].
24. (May 10, 2017). "Inside Volta: The World's Most Advanced Data Center GPU".
25. (May 14, 2020). "NVIDIA Ampere Architecture In-Depth".
26. "NVIDIA A100 GPUs Power the Modern Data Center".
27. Schilling, Andreas. (June 10, 2019). "Die RDNA-Architektur - Seite 2".
28. "AMD Radeon RX 5700 XT Specs".
29. "AMD Instinct MI100 Accelerator".
30. "Introduction to the Xe-HPG Architecture".
31. (November 9, 2022). "Intel Data Center GPU Max".
32. (October 26, 2018). "250 TFLOPs/s for two chips with FP16 mixed precision".
33. (October 25, 2017). "Estimation via power consumption that FP32 is 1/4 of FP16 and that clock frequency is below 1.5GHz".
34. (July 15, 2020). "Introducing Graphcore's Mk2 IPU systems".
35. "Bow-2000 IPU-Machine".
36. "Computers of Yore".
37. "National Museum of the United States Army".
38. "IMS T800 Architecture".
39. [http://www.adapteva.com/products/silicon-devices/e16g301/ Epiphany-III 16-core 65nm Microprocessor (E16G301)] // [http://www.adapteva.com/author/admin/ admin] (August 19, 2012)
40. [http://www.adapteva.com/products/silicon-devices/e64g401/ Epiphany-IV 64-core 28nm Microprocessor (E64G401)] // [http://www.adapteva.com/author/admin/ admin] (August 19, 2012)
41. Feldman, Michael. (August 22, 2012). "Adapteva Unveils 64-Core Chip". HPCWire.
42. "【NEC】 SX-1, SX-2". [[Information Processing Society of Japan]].
43. "Sandia's ASCI Red, world's first teraflop supercomputer, is decommissioned".
44. Richard Swinburne. (April 30, 2007). "The Arrival of TeraFLOP Computing". bit-tech.net.
45. (June 23, 2007). "29th TOP500 List of World's Fastest Supercomputers Released".
46. "June 2008". TOP500.
47. (October 25, 2007). "NEC Launches World's Fastest Vector Supercomputer, SX-9". NEC.
48. Sharon Gaudin. (June 9, 2008). "IBM's Roadrunner smashes 4-minute mile of supercomputing". Computerworld.
49. (November 14, 2008). "Austin ISC08". Top500.org.
50. Fildes, Jonathan. (June 9, 2008). "Supercomputer sets petaflop pace". BBC News.
51. Greenberg, Andy. (November 16, 2009). "Cray Dethrones IBM in Supercomputing". Forbes.
52. (October 28, 2010). "China claims supercomputer crown". BBC News.
53. Dillow, Clay. (October 28, 2010). "China Unveils 2507 Petaflop Supercomputer, the World's Fastest".
54. (March 10, 2010). "Intel's Core i7-980X Extreme Edition – Ready for Sick Scores?: Mathematics: Sandra Arithmetic, Crypto, Microsoft Excel".
55. "NVIDIA Tesla Personal Supercomputer". Nvidia.com.
56. "AMD FireStream 9270 GPU Compute Accelerator". Amd.com.
57. "'K computer' Achieves Goal of 10 Petaflops". Fujitsu.com.
58. See [[Japanese numerals#Large numbers. Japanese numbers]]
59. (November 16, 2011). "Intel's Knights Corner: 50+ Core 22nm Co-processor".
60. "Intel unveils 1 TFLOP/s Knight's Corner".
61. Clark, Don. (June 18, 2012). "IBM Computer Sets Speed Record". The Wall Street Journal.
62. (November 12, 2012). "US Titan supercomputer clocked as world's fastest". BBC.
63. (November 12, 2012). "Oak Ridge Claims No. 1 Position on Latest TOP500 List with Titan | TOP500 Supercomputer Sites". Top500.org.
64. Montalbano, Elizabeth. (October 11, 2011). "Oak Ridge Labs Builds Fastest Supercomputer".
65. Tibken, Shara. (October 29, 2012). "Titan supercomputer debuts for open scientific research | Cutting Edge".
66. (June 17, 2013). "Chinese Supercomputer Is Now The World's Fastest – By A Lot".
67. Feldman, Michael. "China Races Ahead in TOP500 Supercomputer List, Ending US Supremacy".
68. "June 2018".
69. "TOP500".
70. "June 2025 - TOP500".
71. "Distributed Multi-Model / Multi-Kernel Simulations: A Case Study in Jungle Computing using eScience Infrastructure and High Speed Networks".
72. "amusecode.org".
73. "Ibis".
74. "CosmoGrid".
75. "Folding@Home Active CPUs & GPUs by OS".
76. Folding@home. (March 25, 2020). "Thanks to our AMAZING community, we've crossed the exaFLOP barrier! That's over a 1,000,000,000,000,000,000 operations per second, making us ~10x faster than the IBM Summit!pic.twitter.com/mPMnb4xdH3".
77. "Folding@Home Crushes Exascale Barrier, Now Faster Than Dozens of Supercomputers - ExtremeTech".
78. (March 26, 2020). "Folding@Home exceeds 1.5 ExaFLOPS in the battle against Covid-19".
79. "BOINC Computing Power". BOINC.
80. "SETI@Home Credit overview". BOINC.
81. "Einstein@Home Credit overview". BOINC.
82. "MilkyWay@Home Credit overview". BOINC.
83. "Internet PrimeNet Server Distributed Computing Technology for the Great Internet Mersenne Prime Search". GIMPS.
84. "The IBM 7030 (STRETCH)". Norman Hardy.
85. (July 13, 1997). "Loki and Hyglac". Loki-www.lanl.gov.
86. "Kentucky Linux Athlon Testbed 2 (KLAT2)".
87. (August 23, 2003). "Haveland-Robinson Associates - Home Page".
88. "Microwulf: A Personal, Portable Beowulf Cluster".
89. Adam Stevenson, Yann Le Du, and Mariem El Afrit. "[https://arstechnica.com/science/news/2011/03/high-performance-computing-on-gamer-pcs-part-1-hardware.ars High-performance computing on gamer PCs]." ''Ars Technica''. March 31, 2011.
90. Tom Logan. (January 9, 2012). "HD7970 Quadfire Eyefinity Review".
91. "[https://www.cnbc.com/id/100805004 Sony Sparks Price War With PS4 Priced at $399]." ''CNBC''. June 11, 2013.
92. "FreezePage".
93. "FreezePage".
94. "FreezePage".
95. (April 8, 2014). "Radeon R9 295X2 8 GB Review: Project Hydra Gets Liquid Cooling".
96. Perez, Carol E.. (July 13, 2017). "Building a 50 Teraflops AMD Vega Deep Learning Box for Under $3K". Intuition Machine.
97. "lowest_$/fp16 - mattebaughman's Saved Part List - Celeron G3930 2.9GHz Dual-Core, Radeon RX VEGA 64 8GB (3-Way CrossFire), XON-350_BK ATX Mid Tower".
98. "System Builder".
99. "AMD Playstation 5 GPU Specs".
100. "Xbox Series X | Xbox".
101. (September 20, 2022). "Nvidia Announces RTX 4090 Coming October 12, RTX 4080 Later".
102. "Jetson FAQ". NVIDIA Corporation.
103. [https://developer.nvidia.com/embedded/buy/jetson-xavier-devkit NVIDIA Jetson Xavier Developer Kit]
104. "NVIDIA Jetson AGX Xavier Benchmarks - Incredible Performance On The Edge". Phoronix Media 2018.
105. Halfill, Tom R.. (October 10, 2006). "Ambric's New Parallel Processor". Reed Electronics Group.
106. Valich, Theo. (September 29, 2009). "The fastest ATI 5870 card achieves 3TFLOPS!". Bright Side of News.
107. http://www.hardocp.com/images/articles/1299536835FpEmksdSXb_1_3_l.gif {{Dead link. (February 2022)
108. Hermida, Alfred. (May 17, 2005). "Sony shows off new PlayStation 3". BBC News.