# FLOPS

(Redirected from GFLOPS)

In computing, floating point operations per second (FLOPS, flops or flop/s) is a measure of computer performance, 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.

Computer performance
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
FLOPS by the largest supercomputer over time

## Floating-point arithmetic

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 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 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.[1]

### 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.[2]

### 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. The unit MIPS measures 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 when a computer is used in database queries, word processing, spreadsheets, or to run multiple virtual operating systems.[3][4] Frank H. McMahon, of the Lawrence Livermore National Laboratory, invented the terms FLOPS and MFLOPS (megaFLOPS) so that he could compare the 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.

FLOPS on an HPC-system can be calculated using this equation:[5]

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

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

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

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.[6] Similar measures are available for 32-bit (FP32) and 16-bit] (FP16) operations.

## FLOPS per cycle for various processors

Microarchitecture ISA FP64 FP32 FP16
Intel Atom (Bonnell, Saltwell, Silvermont and Goldmont) SSE3 (64-bit) 2 4 0
Intel Core (Merom, Penryn)
Intel Nehalem[7] (Nehalem, Westmere)
SSE4 (128-bit) 4 8 0
Intel Sandy Bridge (Sandy Bridge, Ivy Bridge) AVX (256-bit) 8 16 0
Intel Haswell[7] (Haswell, Devil's Canyon, Broadwell)
Intel Skylake (Skylake, Kaby Lake, Coffee Lake, Whiskey lake, Amber lake)
AVX2 & FMA (256-bit) 16 32 0
Intel Xeon Phi (Knights Corner) SSE & FMA (256-bit) 16 32 0
Intel Skylake-X
Intel Xeon Phi (Knights Landing, Knights Mill)
AVX-512 & FMA (512-bit) 32 64 0
AMD Bobcat AMD64 (64-bit) 2 4 0
AMD Jaguar
AMD Puma
AVX (128-bit) 4 8 0
AMD K10 SSE4/4a (128-bit) 4 8 0
AMD Bulldozer[7] (Piledriver, Steamroller, Excavator) AVX (128-bit) Bulldozer-Steamroller

AVX2 (128-bit) Excavator

FMA3 (Bulldozer)[8]

FMA3/4 (Piledriver-Excavator)

4 8 0
AMD Zen (Ryzen 1000 series, Threadripper 1000 series, Epyc Naples)
AMD Zen+[7][9][10][11] (Ryzen 2000 series, Threadripper 2000 series)
AVX2 & FMA (128-bit, 256-bit decoding)[12] 8 16 0
AMD Zen 2[13] (Ryzen 3000 series, Threadripper 3000 series, Epyc Rome))
AMD Zen 3 (Ryzen 5000 series)
AVX2 & FMA (256-bit) 16 32 0
ARM Cortex-A7, A9, A15 ARMv7 1 8 0
ARM Cortex-A32, A35, A53, A55, A72, A73, A75 ARMv8 2 8 0
ARM Cortex-A57[7] ARMv8 4 8 0
ARM Cortex-A76, A77 ARMv8 8 16 0
Qualcomm Krait ARMv8 1 8 0
Qualcomm Kryo (1xx - 3xx) ARMv8 2 8 0
Qualcomm Kryo (4xx - 5xx) ARMv8 8 16 0
Samsung Exynos M1 and M2 ARMv8 2 8 0
Samsung Exynos M3 and M4 ARMv8 3 12 0
IBM PowerPC A2 (Blue Gene/Q) ? 8 8 (as FP64) 0
Hitachi SH-4[14][15] SH-4 1 7 0
Nvidia Fermi (only GeForce GTX 465–480, 560 Ti, 570-590) PTX 1/4 (locked by driver, 1 in hardware) 2 0
Nvidia Fermi (only Quadro 600-2000) PTX 1/8 2 0
Nvidia Fermi (only Quadro 4000–7000, Tesla) PTX 1 2 0
Nvidia Kepler (GeForce (except Titan and Titan Black), Quadro (except K6000), Tesla K10) PTX 1/12 (for GK110: locked by driver, 2/3 in hardware) 2 0
Nvidia Kepler (GeForce GTX Titan and Titan Black, Quadro K6000, Tesla (except K10)) PTX 2/3 2 0
Nvidia Maxwell
Nvidia Pascal (all except Quadro GP100 and Tesla P100)
PTX 1/16 2 1/32
Nvidia Pascal (only Quadro GP100 and Tesla P100) PTX 1 2 4
Nvidia Volta[16] PTX 1 2 (FP32) + 2 (INT32) 16
Nvidia Turing (only GeForce 16XX) PTX 1/16 2 (FP32) + 2 (INT32) 4
Nvidia Turing (all except GeForce 16XX) PTX 1/16 2 (FP32) + 2 (INT32) 16
Nvidia Ampere[17][18] (only A100) PTX 2 2 (FP32) + 2 (INT32) 32
Nvidia Ampere (only GeForce) PTX 1/32 2 (FP32) + 0 (INT32) or 1 (FP32) + 1 (INT32) 16
AMD GCN (only Radeon Pro WX 2100-7100) GCN 1/8 2 2
AMD GCN (all except Radeon VII, Instinct MI50 and MI60, Radeon Pro WX 2100-7100) GCN 1/8 2 4
AMD GCN Vega 20 (only Radeon VII) GCN 1/2 (locked by driver, 1 in hardware) 2 4
AMD GCN Vega 20 (only Radeon Instinct MI50 / MI60 and Radeon Pro VII) GCN 1 2 4
AMD RDNA[19][20] RDNA 1/8 2 4
Graphcore Colossus GC2[21][22][23] (values estimated) ? 0 18 72
Graphcore Colossus GC200 Mk2[24] (values estimated) ? 0 18 144

[25]

## Performance records

### 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".[26]

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.[27]

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.[28] 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.[29]

On October 25, 2007, NEC Corporation of Japan issued a press release announcing its SX series model SX-9,[30] 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,[31] 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).[32][33] 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).[34]

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.[35]

In October 2010, China unveiled the Tianhe-1, a supercomputer that operates at a peak computing rate of 2.5 petaFLOPS.[36][37]

As of 2010 the fastest PC processor reached 109 gigaFLOPS (Intel Core i7 980 XE)[38] in double precision calculations. GPUs are considerably more powerful. For example, Nvidia Tesla C2050 GPU computing processors perform around 515 gigaFLOPS[39] in double precision calculations, and the AMD FireStream 9270 peaks at 240 gigaFLOPS.[40]

In November 2011, it was announced that Japan had achieved 10.51 petaFLOPS with its K computer.[41] 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,[42] 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.[43][44]

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.[45]

On November 12, 2012, the TOP500 list certified Titan as the world's fastest supercomputer per the LINPACK benchmark, at 17.59 petaFLOPS.[46][47] 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.[48][49]

On June 10, 2013, China's Tianhe-2 was ranked the world's fastest with 33.86 petaFLOPS.[50]

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, which is almost exclusively based on technology developed in China, is installed at the National Supercomputing Center in Wuxi, and represents more performance than the next five most powerful systems on the TOP500 list combined.[51]

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.[52]

In June 2020, Fugaku turned in a High Performance Linpack (HPL) result of 415.5 petaFLOPS, besting the now second-place Summit system by a factor of 2.8x.  Fugaku is powered by Fujitsu’s 48-core A64FX SoC, becoming the first number one system on the list to be powered by ARM processors. In single or further reduced precision, used in machine learning and AI applications, Fugaku’s peak performance is over 1,000 petaflops (1 exaflops). The new system is installed at RIKEN Center for Computational Science (R-CCS) in Kobe, Japan.[citation needed]

### Distributed computing records

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

• As of April 2020, the Folding@home network has over 2.3 exaFLOPS of total computing power.[53][54][55][56] 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.[57]

## Cost of computing

### Hardware costs

Date Approximate USD per GFLOPS Platform providing the lowest cost per GFLOPS Comments
1961 $18.7 billion$160 billion A basic installation of IBM 7030 Stretch had a cost at the time of US$7.78 million each. The IBM 7030 Stretch performs one floating-point multiply every 2.4 microseconds.[64] 1984$18,750,000 $46,140,000 Cray X-MP/48$15,000,000 / 0.8 GFLOPS
1997 $30,000$48,000 Two 16-processor Beowulf clusters with Pentium Pro microprocessors[65]
April 2000 $1,000$1,510 Bunyip Beowulf cluster Bunyip was the first sub-US$1/MFLOPS computing technology. It won the Gordon Bell Prize in 2000. May 2000$640 $964 KLAT2 KLAT2 was the first computing technology which scaled to large applications while staying under US-$1/MFLOPS.[66]
August 2003 $82$114 KASY0 KASY0 was the first sub-US$100/GFLOPS computing technology.[67] August 2007$48 $59 Microwulf As of August 2007, this 26.25 GFLOPS "personal" Beowulf cluster can be built for$1256.[68]
March 2011 $1.80$2.07 HPU4Science This $30,000 cluster was built using only commercially available "gamer" grade hardware.[69] August 2012$0.75 $0.84 Quad AMD Radeon 7970 GHz 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.[70]
June 2013 $0.22$0.24 Sony PlayStation 4 The Sony PlayStation 4 is listed as having a peak performance of 1.84 TFLOPS, at a price of $400[71] November 2013$0.16 $0.18 AMD Sempron 145 & 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 6.771 TFLOPS for a total cost of$1090.66.[72]
December 2013 $0.12$0.13 Pentium G550 & Radeon R9 290 System Built using commercially available parts. Intel Pentium G550 and AMD Radeon R9 290 tops out at 4.848 TFLOPS grand total of US$681.84.[73] January 2015$0.08 $0.09 Celeron G1830 & Radeon R9 295X2 System Built using commercially available parts. Intel Celeron G1830 and AMD Radeon R9 295X2 tops out at over 11.5 TFLOPS at a grand total of US$902.57.[74][75]
June 2017 $0.06$0.06 AMD Ryzen 7 1700 & AMD Radeon Vega Frontier Edition Built using commercially available parts. AMD Ryzen 7 1700 CPU combined with AMD Radeon Vega FE cards in CrossFire tops out at over 50 TFLOPS at just under US$3,000 for the complete system.[76] October 2017$0.03 $0.03 Intel Celeron G3930 & AMD RX Vega 64 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.[77]

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