# FLOPS

Last updated

Computer performance
NameUnitValue
kiloFLOPSkFLOPS103
megaFLOPSMFLOPS106
gigaFLOPSGFLOPS109
teraFLOPSTFLOPS1012
petaFLOPSPFLOPS1015
exaFLOPSEFLOPS1018
zettaFLOPSZFLOPS1021
yottaFLOPSYFLOPS1024

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.

## Contents

The similar term FLOP is often used for floating-point operation, for example as a unit of counting floating-point operations carried out by an algorithm or computer hardware.

## 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 per cycle for various processors

MicroarchitectureISAFP64FP32FP16
Intel Atom (Bonnell, Saltwell, Silvermont and Goldmont) SSE3 (64-bit)240
Intel Core (Merom, Penryn)
Intel Nehalem [6] (Nehalem, Westmere)
SSE4 (128-bit)480
Intel Sandy Bridge (Sandy Bridge, Ivy Bridge) AVX (256-bit)8160
Intel Haswell [6] (Haswell, Devil's Canyon, Broadwell)
Intel Skylake (Skylake, Kaby Lake, Coffee Lake, Whiskey lake, Amber lake)
AVX2 & FMA (256-bit)16320
Intel Xeon Phi (Knights Corner) SSE & FMA (256-bit)16320
Intel Skylake-X
Intel Xeon Phi (Knights Landing, Knights Mill)
AVX-512 & FMA (512-bit)32640
AMD Bobcat AMD64 (64-bit)240
AMD Jaguar
AMD Puma
AVX (128-bit)480
AMD K10 SSE4/4a (128-bit)480
AMD Bulldozer [6] (Piledriver, Steamroller, Excavator) AVX (128-bit) Bulldozer-Steamroller

AVX2 (128-bit) Excavator

FMA3 (Bulldozer) [7]

FMA3/4 (Piledriver-Excavator)

480
AMD Zen (Ryzen 1000 series, Threadripper 1000 series, Epyc Naples)
AMD Zen+ [6] [8] [9] [10] (Ryzen 2000 series, Threadripper 2000 series)
AVX2 & FMA (128-bit, 256-bit decoding) [11] 8160
AMD Zen 2 [12] (Ryzen 3000 series, Threadripper 3000 series, Epyc Rome) AVX2 & FMA (256-bit)16320
ARM Cortex-A7, A9, A15 ARMv7 180
ARM Cortex-A32, A35, A53, A55, A72, A73, A75 ARMv8 280
ARM Cortex-A57 [6] ARMv8 480
ARM Cortex-A76, A77 ARMv8 8160
Qualcomm Krait ARMv8 180
Qualcomm Kryo (1xx - 3xx) ARMv8 280
Qualcomm Kryo (4xx) ARMv8 8160
Samsung Exynos M1 and M2 ARMv8 280
Samsung Exynos M3 and M4 ARMv8 3120
IBM PowerPC A2 (Blue Gene/Q)?88 (as FP64)0
Hitachi SH-4 [13] [14] SH-4 170
Nvidia Fermi (only GeForce GTX 465-480, 560 Ti, 570-590) PTX 1/4 (locked by driver, 1 in hardware)20
Nvidia Fermi (only Quadro 600-2000) PTX 1/820
Nvidia Fermi (only Quadro 4000-7000, Tesla) PTX 120
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)20
Nvidia Kepler (GeForce GTX Titan and Titan Black, Quadro K6000, Tesla (except K10)) PTX 2/320
Nvidia Maxwell
Nvidia Pascal (all except Quadro GP100 and Tesla P100)
PTX 1/1621/32
Nvidia Pascal (only Quadro GP100 and Tesla P100) PTX 124
Nvidia Volta [15] PTX 12 (FP32) + 2 (INT32)16
Nvidia Turing (only GeForce 16XX) PTX 1/162 (FP32) + 2 (INT32)4
Nvidia Turing (all except GeForce 16XX) PTX 1/162 (FP32) + 2 (INT32)16
Nvidia Ampere [16] [17] PTX 22 (FP32) + 2 (INT32)32
AMD GCN (only Radeon Pro WX 2100-7100) GCN 1/822
AMD GCN (all except Radeon VII, Instinct MI50 and MI60, Radeon Pro WX 2100-7100) GCN 1/824
AMD GCN Vega 20 (only Radeon VII) GCN 1/2 (locked by driver, 1 in hardware)24
AMD GCN Vega 20 (only Radeon Instinct MI50 / MI60 and Radeon Pro VII) GCN 124
AMD RDNA [18] [19] RDNA 1/824
Graphcore Colossus GC2 [20] [21] [22] (values estimated)?01872

[23]

## 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". [24]

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, [25] 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 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. [26]

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. [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 October 25, 2007, NEC Corporation of Japan issued a press release announcing its SX series model SX-9, [29] 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, [30] 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). [31] [32] 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). [33]

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. [34]

In October 2010, China unveiled the Tianhe-1, a supercomputer that operates at a peak computing rate of 2.5 petaFLOPS. [35] [36]

As of 2010 the fastest PC processor reached 109 gigaFLOPS (Intel Core i7 980 XE) [37] in double precision calculations. GPUs are considerably more powerful. For example, Nvidia Tesla C2050 GPU computing processors perform around 515 gigaFLOPS [38] in double precision calculations, and the AMD FireStream 9270 peaks at 240 gigaFLOPS. [39]

In November 2011, it was announced that Japan had achieved 10.51 petaFLOPS with its K computer. [40] 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, [41] 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. [42] [43]

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. [44]

On November 12, 2012, the TOP500 list certified Titan as the world's fastest supercomputer per the LINPACK benchmark, at 17.59 petaFLOPS. [45] [46] 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. [47] [48]

On June 10, 2013, China's Tianhe-2 was ranked the world's fastest with 33.86 petaFLOPS. [49]

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. [50]

In June 2018, 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 122.3 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. [51]

### 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. [52] [53] [54] [55] 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. [56]

## Cost of computing

### Hardware costs

DateApproximate cost per GFLOPSApproximate cost per GFLOPS (2019 US dollars) [62] Approximate cost per TFLOPS (2017 US dollars)Platform providing the lowest cost per GFLOPSComments
1961$18.7 billion$160 billion$160 trillionA 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. [63]
1984$18,750,000$46,140,000$44.2 billion Cray X-MP/48$15,000,000 / 0.8 GFLOPS
1997$30,000$48,000$46,000,000Two 16-processor Beowulf clusters with Pentium Pro microprocessors [64] April 2000$1,000$1,510$1,440,000 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$922,000 KLAT2 KLAT2 was the first computing technology which scaled to large applications while staying under US-$1/MFLOPS. [65] August 2003$82$114$109,000KASY0KASY0 was the first sub-US$100/GFLOPS computing technology. [66] August 2007$48$59$57,000MicrowulfAs of August 2007, this 26.25 GFLOPS "personal" Beowulf cluster can be built for $1256. [67] March 2011$1.80$2.07$1,980HPU4ScienceThis $30,000 cluster was built using only commercially available "gamer" grade hardware. [68] August 2012$0.75$0.84$800Quad AMD Radeon 7970 GHz SystemA 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. [69] June 2013$0.22$0.24$230Sony PlayStation 4The Sony PlayStation 4 is listed as having a peak performance of 1.84 TFLOPS, at a price of $400 [70] November 2013$0.16$0.18$170AMD Sempron 145 & GeForce GTX 760 SystemBuilt 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. [71] December 2013$0.12$0.13$130Pentium G550 & Radeon R9 290 SystemBuilt using commercially available parts. Intel Pentium G550 and AMD Radeon R9 290 tops out at 4.848 TFLOPS grand total of US$681.84. [72] January 2015$0.08$0.09$80Celeron G1830 & Radeon R9 295X2 SystemBuilt 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. [73] [74] June 2017$0.06$0.06$60AMD Ryzen 7 1700 & AMD Radeon Vega Frontier EditionBuilt 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. [75] October 2017$0.03$0.03$30Intel Celeron G3930 & AMD RX Vega 64Built 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. [76] ## See also ## Related Research Articles A supercomputer is a computer with a high level of performance as compared to a general-purpose computer. The performance of a supercomputer is commonly measured in floating-point operations per second (FLOPS) instead of million instructions per second (MIPS). Since 2017, there are supercomputers which can perform over a hundred quadrillion FLOPS (petaFLOPS). Since November 2017, all of the world's fastest 500 supercomputers run Linux-based operating systems. Additional research is being conducted in China, the United States, the European Union, Taiwan and Japan to build faster, more powerful and technologically superior exascale supercomputers. Cray Inc., a subsidiary of Hewlett Packard Enterprise, is an American supercomputer manufacturer headquartered in Seattle, Washington. It also manufactures systems for data storage and analytics. Several Cray supercomputer systems are listed in the TOP500, which ranks the most powerful supercomputers in the world. MareNostrum is the main supercomputer in the Barcelona Supercomputing Center. It is the most powerful supercomputer in Spain, one of thirteen supercomputers in the Spanish Supercomputing Network and one of the seven supercomputers of the European infrastructure PRACE. MDGRAPE-3 is an ultra-high performance petascale supercomputer system developed by the Riken research institute in Japan. It is a special purpose system built for molecular dynamics simulations, especially protein structure prediction. The TOP500 project ranks and details the 500 most powerful non-distributed computer systems in the world. The project was started in 1993 and publishes an updated list of the supercomputers twice a year. The first of these updates always coincides with the International Supercomputing Conference in June, and the second is presented at the ACM/IEEE Supercomputing Conference in November. The project aims to provide a reliable basis for tracking and detecting trends in high-performance computing and bases rankings on HPL, a portable implementation of the high-performance LINPACK benchmark written in Fortran for distributed-memory computers. In computing, performance per watt is a measure of the energy efficiency of a particular computer architecture or computer hardware. Literally, it measures the rate of computation that can be delivered by a computer for every watt of power consumed. This rate is typically measured by performance on the LINPACK benchmark when trying to compare between computing systems. In computing, petascale refers to a computer system capable of reaching performance in excess of one petaflops, i.e. one quadrillion floating point operations per second. The standard benchmark tool is LINPACK and Top500.org is the organization which tracks the fastest supercomputers. Some uniquely specialized petascale computers do not rank on the Top500 list since they cannot run LINPACK. This makes comparisons to ordinary supercomputers hard. The petaFLOP barrier was first broken in September 16, 2007 by the Folding@home project, used to fold proteins for medical research. Petascale supercomputers are planned to be succeeded by Exascale computers. The National Center for Computational Sciences (NCCS) is a United States Department of Energy (DOE) Leadership Computing Facility that houses the Oak Ridge Leadership Computing Facility (OLCF), a DOE Office of Science User Facility charged with helping researchers solve challenging scientific problems of global interest with a combination of leading high-performance computing (HPC) resources and international expertise in scientific computing. Jaguar or OLCF-2 was a petascale supercomputer built by Cray at Oak Ridge National Laboratory (ORNL) in Oak Ridge, Tennessee. The massively parallel Jaguar had a peak performance of just over 1,750 teraFLOPS. It had 224,256 x86-based AMD Opteron processor cores, and operated with a version of Linux called the Cray Linux Environment. Jaguar was a Cray XT5 system, a development from the Cray XT4 supercomputer. Tianhe-I, Tianhe-1, or TH-1 is a supercomputer capable of an Rmax of 2.5 petaFLOPS. Located at the National Supercomputing Center of Tianjin, China, it was the fastest computer in the world from October 2010 to June 2011 and is one of the few petascale supercomputers in the world. The National Computational Infrastructure is a high-performance computing and data services facility, located at the Australian National University in Canberra, Australian Capital Territory. The NCI is supported by the Australian Government's National Collaborative Research Infrastructure Strategy (NCRIS), with operational funding provided through a formal collaboration incorporating CSIRO, the Bureau of Meteorology, The Australian National University, Geoscience Australia, the Australian Research Council, and a number of research intensive universities and medical research institutes. Exascale computing refers to computing systems capable of at least one exaFLOPS, or a billion billion (i.e. a quintillion) calculations per second. Such capacity represents a thousandfold increase over the first petascale computer that came into operation in 2008. (One exaflop is a thousand petaflops or a quintillion, 1018, double precision floating point operations per second.) At a supercomputing conference in 2009, Computerworld projected exascale implementation by 2018. Although the exascale wall for FLOPS was not broken in 2019, the Oak Ridge National Laboratory performed a 1.8×1018 operation calculation per second (which is not the same as 1.8×1018 flops) on the Summit OLCF-4 Supercomputer while analyzing genomic information in 2018. They were Gordon Bell Award winners at Supercomputing 2018. The exaFLOP barrier was first broken in March of 2020 by the Folding@home project, used to fold proteins for medical research. This list compares various amounts of computing power in instructions per second organized by order of magnitude in FLOPS. Several centers for supercomputing exist across Europe, and distributed access to them is coordinated by European initiatives to facilitate high-performance computing. One such initiative, the HPC Europa project, fits within the Distributed European Infrastructure for Supercomputing Applications (DEISA), which was formed in 2002 as a consortium of eleven supercomputing centers from seven European countries. Operating within the CORDIS framework, HPC Europa aims to provide access to supercomputers across Europe. Xeon Phi is a series of x86 manycore processors designed and made by Intel. It is intended for use in supercomputers, servers, and high-end workstations. Its architecture allows use of standard programming languages and application programming interfaces (APIs) such as OpenMP. Titan or OLCF-3 was a supercomputer built by Cray at Oak Ridge National Laboratory for use in a variety of science projects. Titan was an upgrade of Jaguar, a previous supercomputer at Oak Ridge, that uses graphics processing units (GPUs) in addition to conventional central processing units (CPUs). Titan was the first such hybrid to perform over 10 petaFLOPS. The upgrade began in October 2011, commenced stability testing in October 2012 and it became available to researchers in early 2013. The initial cost of the upgrade was US$60 million, funded primarily by the United States Department of Energy.

ScREC is a supercomputer developed by the Research Centre for Modeling and Simulation (RCMS) at the National University of Sciences and Technology, Pakistan (NUST) in Islamabad, Pakistan. With a 132 teraflops performance, it is currently the fastest supercomputer in Pakistan.

XK7 is a supercomputing platform, produced by Cray, launched on October 29, 2012. XK7 is the second platform from Cray to use a combination of central processing units ("CPUs") and graphical processing units ("GPUs") for computing; the hybrid architecture requires a different approach to programming to that of CPU-only supercomputers. Laboratories that host XK7 machines host workshops to train researchers in the new programming languages needed for XK7 machines. The platform is used in Titan, the world's second fastest supercomputer in the November 2013 list as ranked by the TOP500 organization. Other customers include the Swiss National Supercomputing Centre which has a 272 node machine and Blue Waters has a machine that has Cray XE6 and XK7 nodes that performs at approximately 1 petaFLOPS (1015 floating-point operations per second).

The Cray XC40 is a massively parallel multiprocessor supercomputer manufactured by Cray. It consists of Intel Haswell Xeon processors, with optional Nvidia Tesla or Intel Xeon Phi accelerators, connected together by Cray's proprietary "Aries" interconnect, stored in air-cooled or liquid-cooled cabinets. The XC series supercomputers are available with the Cray DataWarp applications I/O accelerator technology.

Summit or OLCF-4 is a supercomputer developed by IBM for use at Oak Ridge National Laboratory, which as of November 2019 is the fastest supercomputer in the world, capable of 200 petaFLOPS. Its current LINPACK benchmark is clocked at 148.6 petaFLOPS. As of November 2019, the supercomputer is also the 5th most energy efficient in the world with a measured power efficiency of 14.668 gigaFLOPS/watt. Summit is the first supercomputer to reach exaflop speed, achieving 1.88 exaflops during a genomic analysis and is expected to reach 3.3 exaflops using mixed precision calculations.

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