Floating point operations per second (FLOPS,flops orflop/s) is a measure ofcomputer performance incomputing, useful in fields of scientific computations that requirefloating-point calculations.[1]
For such cases, it is a more accurate measure than measuringinstructions per second.[citation needed]
| Name | Unit | Value |
|---|---|---|
| kiloFLOPS | kFLOPS | 103 |
| megaFLOPS | MFLOPS | 106 |
| gigaFLOPS | GFLOPS | 109 |
| teraFLOPS | TFLOPS | 1012 |
| petaFLOPS | PFLOPS | 1015 |
| exaFLOPS | EFLOPS | 1018 |
| zettaFLOPS | ZFLOPS | 1021 |
| yottaFLOPS | YFLOPS | 1024 |
| ronnaFLOPS | RFLOPS | 1027 |
| quettaFLOPS | QFLOPS | 1030 |
Floating-point arithmetic is needed for very large or very smallreal numbers, or computations that require a large dynamic range. Floating-point representation is similar to scientific notation, except computers usebase two (with rare exceptions), rather thanbase ten. The encoding scheme stores the sign, theexponent (in base two for Cray andVAX, base two or ten forIEEE floating point formats, and base 16 forIBM Floating Point Architecture) and thesignificand (number after theradix point). While several similar formats are in use, the most common isANSI/IEEE Std. 754-1985. This standard defines the format for 32-bit numbers calledsingle precision, as well as 64-bit numbers calleddouble precision and longer numbers calledextended 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.[2]
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.[3]
FLOPS andMIPS 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 inmachine 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[4] 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.[5][6] In 1974David 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.[7] 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.
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FLOPS on an HPC-system can be calculated using this equation:[8]
This can be simplified to the most common case: a computer that has exactly 1 CPU:
FLOPS can be recorded in different measures of precision, for example, theTOP500 supercomputer list ranks computers by 64 bit (double-precision floating-point format) operations per second, abbreviated toFP64.[9] Similar measures are available for32-bit (FP32) and16-bit (FP16) operations.
| Microarchitecture | Instruction set architecture | FP64 | FP32 | FP16 |
|---|---|---|---|---|
| Intel CPU | ||||
| Intel 80486 | x87 (32-bit) | ? | 0.128[11] | ? |
| x87 (32-bit) | ? | 0.5[11] | ? |
| MMX (64-bit) | ? | 1[12] | ? |
| IntelP6Pentium III | SSE (64-bit) | ? | 2[12] | ? |
| IntelNetBurstPentium 4 (Willamette, Northwood) | SSE2 (64-bit) | 2 | 4 | ? |
| IntelP6Pentium M | SSE2 (64-bit) | 1 | 2 | ? |
| SSE3 (64-bit) | 2 | 4 | ? | |
| 4 | 8 | ? | ||
| IntelAtom (Bonnell,Saltwell,Silvermont andGoldmont) | SSE3 (128-bit) | 2 | 4 | ? |
| IntelSandy Bridge (Sandy Bridge,Ivy Bridge) | AVX (256-bit) | 8 | 16 | 0 |
| AVX2 &FMA (256-bit) | 16 | 32 | 0 | |
| IntelXeon Phi (Knights Corner) | IMCI (512-bit) | 16 | 32 | 0 |
| AVX-512 &FMA (512-bit) | 32 | 64 | 0 |
| AMD CPU | ||||
| AMDBobcat | AMD64 (64-bit) | 2 | 4 | 0 |
| AVX (128-bit) | 4 | 8 | 0 | |
| AMDK10 | SSE4/4a (128-bit) | 4 | 8 | 0 |
| AMDBulldozer[13] (Piledriver,Steamroller,Excavator) | 4 | 8 | 0 | |
| AVX2 &FMA (128-bit, 256-bit decoding)[18] | 8 | 16 | 0 | |
| AVX2 &FMA (256-bit) | 16 | 32 | 0 | |
| ARM CPU | ||||
| ARM Cortex-A7, A9, A15 | ARMv7 | 1 | 8 | 0 |
| ARM Cortex-A32, A35 | ARMv8 | 2 | 8 | 0 |
| ARM Cortex-A53,A55,A57,[13]A72,A73,A75 | ARMv8 | 4 | 8 | 0 |
| ARM Cortex-A76,A77,A78 | ARMv8 | 8 | 16 | 0 |
| ARM Cortex-X1 | ARMv8 | 16 | 32 | ? |
| QualcommKrait | ARMv8 | 1 | 8 | 0 |
| QualcommKryo (1xx - 3xx) | ARMv8 | 2 | 8 | 0 |
| QualcommKryo (4xx - 5xx) | ARMv8 | 8 | 16 | 0 |
| SamsungExynos M1 and M2 | ARMv8 | 2 | 8 | 0 |
| SamsungExynos M3 and M4 | ARMv8 | 3 | 12 | 0 |
| IBM PowerPCA2 (Blue Gene/Q) | ? | 8 | 8 (as FP64) | 0 |
| Hitachi SH-4[20][21] | SH-4 | 1 | 7 | 0 |
| Nvidia GPU | ||||
| NvidiaCurie (GeForce 6 series andGeForce 7 series) | PTX | ? | 8 | ? |
| NvidiaTesla 2.0 (GeForce GTX 260–295) | PTX | ? | 2 | ? |
| NvidiaFermi (only GeForce GTX 465–480, 560 Ti, 570–590) | PTX | 1⁄4 (locked by driver, 1 in hardware) | 2 | 0 |
| NvidiaFermi (only Quadro 600–2000) | PTX | 1⁄8 | 2 | 0 |
| NvidiaFermi (only Quadro 4000–7000, Tesla) | PTX | 1 | 2 | 0 |
| NvidiaKepler (GeForce (except Titan and Titan Black), Quadro (except K6000), Tesla K10) | PTX | 1⁄12 (forGK110: locked by driver, 2⁄3 in hardware) | 2 | 0 |
| NvidiaKepler (GeForce GTX Titan and Titan Black, Quadro K6000, Tesla (except K10)) | PTX | 2⁄3 | 2 | 0 |
| PTX | 1⁄16 | 2 | 1⁄32 | |
| NvidiaPascal (only Quadro GP100 and Tesla P100) | PTX | 1 | 2 | 4 |
| NvidiaVolta[22] | PTX | 1 | 2 (FP32) + 2 (INT32) | 16 |
| NvidiaTuring (only GeForce16XX) | PTX | 1⁄16 | 2 (FP32) + 2 (INT32) | 4 |
| NvidiaTuring (all except GeForce16XX) | PTX | 1⁄16 | 2 (FP32) + 2 (INT32) | 16 |
| NvidiaAmpere[23][24] (only Tesla A100/A30) | PTX | 2 | 2 (FP32) + 2 (INT32) | 32 |
| PTX | 1⁄32 | 2 (FP32) + 0 (INT32) or 1 (FP32) + 1 (INT32) | 8 |
| NvidiaHopper | PTX | 2 | 2 (FP32) + 1 (INT32) | 32 |
| AMD GPU | ||||
| AMDTeraScale 1 (Radeon HD 4000 series) | TeraScale 1 | 0.4 | 2 | ? |
| AMDTeraScale 2 (Radeon HD 5000 series) | TeraScale 2 | 1 | 2 | ? |
| AMDTeraScale 3 (Radeon HD 6000 series) | TeraScale 3 | 1 | 4 | ? |
| AMDGCN (only Radeon Pro W 8100–9100) | GCN | 1 | 2 | ? |
| AMDGCN (all except Radeon Pro W 8100–9100, Vega 10–20) | GCN | 1⁄8 | 2 | 4 |
| AMDGCN Vega 10 | GCN | 1⁄8 | 2 | 4 |
| AMDGCN Vega 20 (only Radeon VII) | GCN | 1⁄2 (locked by driver, 1 in hardware) | 2 | 4 |
| AMDGCN Vega 20 (only Radeon Instinct MI50 / MI60 and Radeon Pro VII) | GCN | 1 | 2 | 4 |
| RDNA | 1⁄8 | 2 | 4 | |
| AMD RDNA3 | RDNA | 1⁄8? | 4 | 8? |
| AMDCDNA | CDNA | 1 | 4 (Tensor)[27] | 16 |
| AMDCDNA 2 | CDNA 2 | 4 (Tensor) | 4 (Tensor) | 16 |
| Intel GPU | ||||
| Intel Xe-LP (Iris Xe MAX)[28] | Xe | 1⁄2? | 2 | 4 |
| Intel Xe-HPG (Arc Alchemist)[28] | Xe | 0 | 2 | 16 |
| Intel Xe-HPC (Ponte Vecchio)[29] | Xe | 2 | 2 | 32 |
| Intel Xe2 (Arc Battlemage) | Xe2 | 1⁄8 | 2 | 16 |
| Qualcomm GPU | ||||
| QualcommAdreno 5x0 | Adreno 5xx | 1 | 2 | 4 |
| QualcommAdreno 6x0 | Adreno 6xx | 1 | 2 | 4 |
| Graphcore | ||||
| Graphcore Colossus GC2[30][31] | ? | 0 | 16 | 64 |
| ? | 0 | 32 | 128 | |
| Supercomputer | ||||
| ENIAC @ 100 kHz in 1945 | 0.004[34] (~3×10−8 FLOPS/W) | |||
| 48-bit processor @ 208kHz inCDC 1604 in 1960 | ||||
| 60-bit processor @ 10 MHz inCDC 6600 in 1964 | 0.3 (FP60) | |||
| 60-bit processor @ 10 MHz inCDC 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[35] | |||
| Parallella E16 @ 1000 MHz in 2012 | 2[36] (5.0 GFLOPS/W)[37] | |||
| Parallella E64 @ 800 MHz in 2012 | 2[38] (50.0 GFLOPS/W)[37] | |||
| Microarchitecture | Instruction set architecture | FP64 | FP32 | FP16 |
In June 1997,Intel'sASCI 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".[39]
NEC'sSX-9 supercomputer was the world's firstvector processor to exceed 100 gigaFLOPS per single core.
In June 2006, a new computer was announced by Japanese research instituteRIKEN, theMDGRAPE-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 theTop500.org list. It has special-purposepipelines for simulating molecular dynamics.
By 2007,Intel Corporation unveiled the experimentalmulti-corePOLARIS 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.[40]
In June 2007, Top500.org reported the fastest computer in the world to be theIBM Blue Gene/L supercomputer, measuring a peak of 596 teraFLOPS.[41] TheCray 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.[42]
On October 25, 2007,NEC Corporation of Japan issued a press release announcing its SX series modelSX-9,[43] claiming it to be the world's fastest vector supercomputer. TheSX-9 features the first CPU capable of a peak vector performance of 102.4 gigaFLOPS per single core.
On February 4, 2008, theNSF and theUniversity of Texas at Austin opened full scale research runs on anAMD,Sun supercomputer named Ranger,[44]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 byIBM, named 'Roadrunner', reached the computing milestone of one petaFLOPS. It headed the June 2008 and November 2008TOP500 list of the most powerful supercomputers (excludinggrid computers).[45][46] The computer is located at Los Alamos National Laboratory in New Mexico. The computer's name refers to the New Mexicostate bird, thegreater roadrunner (Geococcyx californianus).[47]
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 twoRadeon R770 GPUs totaling 2.4 teraFLOPS.
In November 2008, an upgrade to the CrayJaguar 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 toopen 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, theCray Jaguar performed at 1.75 petaFLOPS, beating the IBM Roadrunner for the number one spot on theTOP500 list.[48]
In October 2010, China unveiled theTianhe-1, a supercomputer that operates at a peak computing rate of 2.5 petaFLOPS.[49][50]
As of 2010[update] the fastest PCprocessor reached 109 gigaFLOPS (Intel Core i7980 XE)[51] in double precision calculations.GPUs are considerably more powerful. For example,Nvidia Tesla C2050 GPU computing processors perform around 515 gigaFLOPS[52] in double precision calculations, and the AMD FireStream 9270 peaks at 240 gigaFLOPS.[53]
In November 2011, it was announced that Japan had achieved 10.51 petaFLOPS with itsK computer.[54] It has 88,128SPARC64 VIIIfxprocessors in 864 racks, with theoretical performance of 11.28 petaFLOPS. It is named after the Japanese word "kei", which stands for 10quadrillion,[55] 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 ofDGEMM 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.[56][57]
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.[58]
On November 12, 2012, the TOP500 list certifiedTitan as the world's fastest supercomputer per the LINPACK benchmark, at 17.59 petaFLOPS.[59][60] It was developed by Cray Inc. at theOak Ridge National Laboratory and combines AMD Opteron processors with "Kepler" NVIDIA Tesla graphics processing unit (GPU) technologies.[61][62]
On June 10, 2013, China'sTianhe-2 was ranked the world's fastest with 33.86 petaFLOPS.[63]
On June 20, 2016, China'sSunway 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.[64]
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.[65]
In June 2022, the United States'Frontier was the most powerful supercomputer on TOP500, reaching 1102 petaFlops (1.102 exaFlops) on the LINPACK benchmarks.[66][circular reference]
In November 2024, the United States’El Capitanexascalesupercomputer, hosted at theLawrence Livermore National Laboratory inLivermore, displaced Frontier as theworld's fastest supercomputer in the 64th edition of theTop500 (Nov 2024).
Distributed computing uses the Internet to link personal computers to achieve more FLOPS:
| Date | Approximate USD per GFLOPS | Platform providing the lowest cost per GFLOPS | Comments | |
|---|---|---|---|---|
| Unadjusted | 2024[77] | |||
| 1945 | $1.265T | $22.094T | ENIAC:$487,000 in 1945 and $8,506,000 in 2023. | $487,000 /0.000000385 GFLOPS.First-generation (vacuum tube-based) electronic digital computer. |
| 1961 | $18.672B | $196.472B | A basic installation ofIBM 7030 Stretch had a cost at the time ofUS$7.78 million each. | TheIBM 7030 Stretch performs one floating-point multiply every2.4 microseconds.[78]Second-generation (discretetransistor-based) computer. |
| 1964 | $2.3B | $23.318B | Base modelCDC 6600 price: $6,891,300. | The CDC 6600 is considered to be the first commercially-successfulsupercomputer. |
| 1984 | $18,750,000 | $56,748,479 | Cray X-MP/48 | $15,000,000 / 0.8 GFLOPS. Third-generation (integrated circuit-based) computer. |
| 1997 | $30,000 | $58,762 | Two 16-processorBeowulf clusters withPentium Pro microprocessors[79] | |
| April 2000 | $1,000 | $1,855 | Bunyip Beowulf cluster | Bunyip was the first sub-US$1/MFLOPS computing technology. It won the Gordon Bell Prize in 2000. |
| May 2000 | $640 | $1,169 | KLAT2 | KLAT2 was the first computing technology which scaled to large applications while staying underUS$1/MFLOPS.[80] |
| August 2003 | $83.86 | $143.34 | KASY0 | KASY0 was the first sub-US$100/GFLOPS 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.[81] |
| August 2007 | $48.31 | $73.26 | Microwulf | As of August 2007, this26 GFLOPS "personal" Beowulf cluster can be built for $1256.[82] |
| March 2011 | $1.80 | $2.52 | HPU4Science | This $30,000 cluster was built using only commercially available "gamer" grade hardware.[83] |
| August 2012 | 75.00¢ | 102.72¢ | QuadAMD Radeon 7970 System | A quadAMDRadeon 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.[84] |
| June 2013 | 21.68¢ | 29.26¢ | Sony PlayStation 4 | The SonyPlayStation 4 is listed as having a peak performance of1.84 TFLOPS, at a price of $399[85] |
| November 2013 | 16.11¢ | 21.75¢ | AMD Sempron 145 &GeForce GTX 760 system | Built using commercially available parts, a system using one AMDSempron 145 and threeNvidiaGeForce GTX 760 reaches a total of6.771 TFLOPS for a total cost ofUS$1,090.66.[86] |
| December 2013 | 12.41¢ | 16.75¢ | Pentium G550 &Radeon R9 290 system | Built using commercially available parts.IntelPentium G550 and AMDRadeon R9 290 tops out at4.848 TFLOPS grand total ofUS$681.84.[87] |
| January 2015 | 7.85¢ | 10.41¢ | Celeron G1830 &Radeon R9 295X2 system | Built using commercially available parts. IntelCeleron G1830 and AMDRadeon R9 295X2 tops out at over11.5 TFLOPS at a grand total ofUS$902.57.[88][89] |
| June 2017 | 6.00¢ | 7.7¢ | AMD Ryzen 7 1700 &AMD Radeon Vega Frontier Edition system | Built using commercially available parts. AMD Ryzen 7 1700 CPU combined with AMD Radeon Vega FE cards in CrossFire tops out at over50 TFLOPS at just underUS$3,000 for the complete system.[90] |
| October 2017 | 2.73¢ | 3.5¢ | Intel Celeron G3930 &AMD RX Vega 64 system | Built using commercially available parts. ThreeAMD 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.[91] |
| November 2020 | 3.14¢ | 3.82¢ | 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 = $2839[92] US$/GFLOP = $0.0314 |
| November 2020 | 3.88¢ | 4.71¢ | PlayStation 5 | The SonyPlayStation 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.[93] |
| November 2020 | 4.11¢ | 4.99¢ | Xbox Series X | Microsoft'sXbox 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.[94] |
| September 2022 | 1.94¢ | 2.08¢ | RTX 4090 | Nvidia'sRTX 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.[95] |
| May 2023 | 1.25¢ | 1.29¢ | Radeon RX 7600 | AMD'sRX 7600 is listed as having a peak performance of 21.5 TFLOPS at a retail price of $269.[96] |
Any researcher at a U.S. institution can submit a proposal to request an allocation of cycles on the system.
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