# FLOPS

(Redirected from Exaflops)
For other uses, see Flop.
Computer performance
Name Abbr. FLOPS
kiloFLOPS kFLOPS 103
megaFLOPS MFLOPS 106
gigaFLOPS GFLOPS 109
teraFLOPS TFLOPS 1012
petaFLOPS PFLOPS 1015
exaFLOPS EFLOPS 1018
zettaFLOPS ZFLOPS 1021
yottaFLOPS YFLOPS 1024

In computing, FLOPS or flops (an acronym for floating-point operations per second) is a measure of computer performance, useful in fields of scientific calculations that make heavy use of floating-point calculations. For such cases it is a more accurate measure than the generic instructions per second.

Although the final S stands for "second", singular "flop" is often used, either as a back formation or an abbreviation for "floating-point operation"; e.g. a flop count is a count of these operations carried out by a given algorithm or computer program.

## Computing

FLOPS can be calculated using this equation:[1]

${\displaystyle {\text{FLOPS}}={\text{sockets}}\times {\frac {\text{cores}}{\text{socket}}}\times {\text{clock}}\times {\frac {\text{FLOPs}}{\text{cycle}}}}$

### FLOPs per cycle

CPU Family Dual precision Single precision
Intel Core and Intel Nehalem 4 DP FLOPs/cycle: 2-wide SSE2 addition + 2-wide SSE2 multiplication 8 SP FLOPs/cycle: 4-wide SSE addition + 4-wide SSE multiplication
Intel Sandy Bridge and Intel Ivy Bridge 8 DP FLOPs/cycle: 4-wide AVX addition + 4-wide AVX multiplication 16 SP FLOPs/cycle: 8-wide AVX addition + 8-wide AVX multiplication
Intel Haswell, Intel Broadwell and Intel Skylake 16 DP FLOPs/cycle: two 4-wide FMA instructions 32 SP FLOPs/cycle: two 8-wide FMA instructions
AMD K10 4 DP FLOPs/cycle: 2-wide SSE2 addition + 2-wide SSE2 multiplication 8 SP FLOPs/cycle: 4-wide SSE addition + 4-wide SSE multiplication
AMD Bulldozer, AMD Piledriver and AMD Steamroller, per module (two cores) 8 DP FLOPs/cycle: 4-wide FMA 16 SP FLOPs/cycle: 8-wide FMA
Intel Atom (Bonnell, Saltwell and Silvermont) 1.5 DP FLOPs/cycle: scalar SSE2 addition + scalar SSE2 multiplication every other cycle

6 SP FLOPs/cycle: 4-wide SSE addition + 4-wide SSE multiplication every other cycle

AMD Bobcat 1.5 DP FLOPs/cycle: scalar SSE2 addition + scalar SSE2 multiplication every other cycle 4 SP FLOPs/cycle: 4-wide SSE addition every other cycle + 4-wide SSE multiplication every other cycle
AMD Jaguar 3 DP FLOPs/cycle: 4-wide AVX addition every other cycle + 4-wide AVX multiplication in four cycles 8 SP FLOPs/cycle: 8-wide AVX addition every other cycle + 8-wide AVX multiplication every other cycle
ARM Cortex-A7 1 DP FLOPs/cycle: one VADD.F64 (VFP) every cycle 2 SP FLOPs/cycle: one VMLA.F32 (VFP) every cycle
ARM Cortex-A9 1.5 DP FLOPs/cycle: scalar addition + scalar multiplication every other cycle 4 SP FLOPs/cycle: 4-wide NEON addition every other cycle + 4-wide NEON multiplication every other cycle
ARM Cortex-A15 2 DP FLOPs/cycle: scalar FMA or scalar multiply-add 8 SP FLOPs/cycle: 4-wide NEONv2 FMA or 4-wide NEON multiply-add
Qualcomm Krait 2 DP FLOPs/cycle: scalar FMA or scalar multiply-add 8 SP FLOPs/cycle: 4-wide NEONv2 FMA or 4-wide NEON multiply-add
IBM PowerPC A2 (Blue Gene/Q), per core 8 DP FLOPs/cycle: 4-wide QPX FMA every cycle (SP elements are extended to DP and processed on the same units)
IBM PowerPC A2 (Blue Gene/Q), per thread 4 DP FLOPs/cycle: 4-wide QPX FMA every other cycle (SP elements are extended to DP and processed on the same units)
Intel Xeon Phi (Knights Corner), per core 16 DP FLOPs/cycle: 8-wide FMA every cycle 32 SP FLOPs/cycle: 16-wide FMA every cycle
Intel Xeon Phi (Knights Corner), per thread (two per core) 8 DP FLOPs/cycle: 8-wide FMA every other cycle 16 SP FLOPs/cycle: 16-wide FMA every other cycle

Processors, which have FMA, they also have AVX and processors, which have AVX they also have SSE. If you want to check FLOPs per cycle for AVX, see "Intel Sandy Bridge and Intel Ivy Bridge" and if you want to check FLOPs per cycle for SSE, see "Intel Core and Intel Nehalem". If you want to check FLOPs per cycle at higher numbers than 64 bit, you must check the microarchitecture's registers. Wide of registers shows, how big number core of processor can count one time. Remember, that two or more registers can connect together.[clarification needed]

## Records

### Single computer records

In late 1996 Intel's ASCI Red was the world's first computer to achieve one TFLOPS 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.” [2]

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,[3] 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 TFLOPS at 3.13 GHz. The 80-core chip can raise this result to 2 TFLOPS at 6.26 GHz, although the thermal dissipation at this frequency exceeds 190 watts.[4]

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.[5]

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.[6] 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,[7] 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,[8] 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 by processing more than 1.026 quadrillion calculations per second. It headed the June 2008 and November 2008 TOP500 list of the most powerful supercomputers (excluding grid computers).[9][10] The computer is located at Los Alamos National Laboratory in New Mexico, and the computer's name refers to the New Mexico state bird, the Greater Roadrunner.[11]

In June 2008 AMD released ATI Radeon HD4800 series, which are reported to be the first GPUs to achieve one teraFLOPS scale. 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 XT 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,” or a quadrillion mathematical calculations per second, 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, which is the global standard for ranking supercomputers. 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.[12]

In October 2010 China unveiled the Tianhe-I, a supercomputer that operates at a peak computing rate of 2.5 petaflops.[13][14]

As of 2010 the fastest six-core PC processor reaches 109 gigaFLOPS (Intel Core i7 980 XE)[15] in double precision calculations. GPUs are considerably more powerful. For example, Nvidia Tesla C2050 GPU computing processors perform around 515 gigaFLOPS[16] in double precision calculations, and the AMD FireStream 9270 peaks at 240 gigaFLOPS.[17] In single precision performance, Nvidia Tesla C2050 computing processors perform around 1.03 teraFLOPS and the AMD FireStream 9270 cards peak at 1.2 teraFLOPS. Both Nvidia and AMD's consumer gaming GPUs may reach higher FLOPS. For example, AMD’s HemlockXT 5970[18] reaches 928 gigaFLOPS in double precision calculations with two GPUs on board and the Nvidia GTX 480 reaches 672 gigaFLOPS[19] with one GPU on board.

On December 2, 2010, the US Air Force unveiled a defense supercomputer made up of 1,760 PlayStation 3 consoles that can run 500 trillion floating-point operations per second.[20] (500 teraFLOPS)

In November 2011 it was announced that Japan had achieved 10.51 petaflops with its K computer.[21] It is still under development and software performance tuning is currently underway. 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,[22] 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 TeraFlop on a wide range of DGEMM operations. Intel emphasized during the demonstration that this was a sustained TeraFlop (not "raw TeraFlop" used by others to get higher but less meaningful numbers), and that it was the first general purpose processor to ever cross a TeraFlop.[23][24]

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.[25]

On November 12, 2012, the TOP500 list certified Titan as the world's fastest supercomputer per the LINPACK benchmark, at 17.59 petaFLOPS.[26][27] 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.[28][29]

On June 10, 2013, China's Tianhe-2 was ranked the world's fastest with 33.86 petaFLOPS.[30] Holding this position for three years, another Chinese computer, TaihuLight, took the top place with 93 petaFLOPS,[31]

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 list combined.[32]

### Distributed computing records

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

• As of May 2016,Folding@home is nearing 100 petaFLOPS.[33] It was the first computing project of any kind to cross the 1, 2, 3, 4, and 5 native petaFLOPS milestones. This level of performance is primarily enabled by the cumulative effort of a vast array of powerful GPU and CPU units.[34]

### Future developments

Further information: Exascale computing

In 2008, James Bamford's book The Shadow Factory reported that NSA told the Pentagon it would need an exaflop computer by 2018.[40]

Given the current speed of progress, supercomputers are projected to reach 1 exaFLOPS (EFLOPS) in 2018.[41] Cray, Inc. announced in December 2009 a plan to build a 1 EFLOPS supercomputer before 2020.[42] Erik P. DeBenedictis of Sandia National Laboratories theorizes that a zettaFLOPS (ZFLOPS) computer is required to accomplish full weather modeling of two week time span.[43] Such systems might be built around 2030.[44]

## Cost of computing

### Hardware costs

Date Approximate cost per GFLOPS Approximate cost per GFLOPS inflation adjusted to 2013 US dollars[45] Platform providing the lowest cost per GFLOPS Comments
1961 US$1,100,000,000,000 ($1.1 trillion) US$8.3 trillion About 17 million IBM 1620 units costing$64,000 each The 1620's multiplication operation takes 17.7 ms.[46]
1984 $18,750,000$42,780,000 Cray X-MP/48 $15,000,000 / 0.8 GFLOPS 1997$30,000 $42,000 Two 16-processor Beowulf clusters with Pentium Pro microprocessors[47] April 2000$1,000 $1,300 Bunyip Beowulf cluster Bunyip was the first sub-US$1/MFLOPS computing technology. It won the Gordon Bell Prize in 2000.
May 2000 $640$836 KLAT2 KLAT2 was the first computing technology which scaled to large applications while staying under US-$1/MFLOPS.[48] August 2003$82 $100 KASY0 KASY0 was the first sub-US$100/GFLOPS computing technology.[49]
August 2007 $48$52 Microwulf As of August 2007, this 26.25 GFLOPS "personal" Beowulf cluster can be built for $1256.[50] March 2011$1.80 $1.80 HPU4Science This$30,000 cluster was built using only commercially available "gamer" grade hardware.[51]
August 2012 $0.75$0.73 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. [52] June 2013$0.22 $0.22 Sony PlayStation 4 The Sony PlayStation 4 is listed as having a peak performance of 1.84 TFLOPS, at a price of$400[53]
November 2013 $0.16$0.16 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.[54] December 2013$0.12 $0.12 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.[55]
January 2015 $0.08$0.06 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.[56][57] ## Floating-point operation and integer operation FLOPS measures the computing ability of a computer. An example of a floating-point operation is the calculation of mathematical equations; as such, FLOPS is a useful measure of supercomputer performance. MIPS is used to measure the 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 for the computer when it is used in database query, word processing, spreadsheets, or to run multiple virtual operating systems.[58][59] Frank H. McMahon, of the Lawrence Livermore National Laboratory, invented the terms FLOPS and MFLOPS (megaFLOPS) so that he could compare the so-called 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. ### Fixed-point (integers) These designations refer to the format used to store and manipulate numeric representations of data without using a decimal point (it is 'fixed' at the end of the number). Fixed-point are designed to represent and manipulate integers – positive and negative whole numbers; for example, 16 bits, yielding up to 65,536 (216) possible bit patterns that typically represent the whole numbers from −32768 to +32767.[60] ### Floating-point (real numbers) This is needed for very large or very small real numbers, or numbers requiring the use of a decimal point (such as pi and other irrational values). The encoding scheme used by the processor for floating-point numbers is more complicated than for fixed-point. 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 IEEE floating point formats, or base 16 for IBM Floating Point Architecture) and the mantissa (number after the decimal 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.[61] ### 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 which are extremely large or where the range may be unpredictable. As such, floating-point processors are ideally suited for computationally intensive applications.[62] ## See also ## References 1. ^ "Nodes, Sockets, Cores and FLOPS, Oh, My" by Dr. Mark R. Fernandez, Ph.D. 2. ^ "Sandia’s ASCI Red, world’s first teraflop supercomputer, is decommissioned" (PDF). Archived from the original (PDF) on November 5, 2010. Retrieved November 17, 2011. 3. ^ "Response Times: The Three Important Limits". Jakob Nielsen. Retrieved June 11, 2008. 4. ^ Richard Swinburne (April 30, 2007). "The Arrival of TeraFLOP Computing". bit-tech.net. Retrieved February 9, 2012 5. ^ "June 2008". TOP500. Retrieved July 8, 2008. 6. ^ "29th TOP500 List of World's Fastest Supercomputers Released". Top500.org. June 23, 2007. Retrieved July 8, 2008. 7. ^ "NEC Launches World's Fastest Vector Supercomputer, SX-9". NEC. October 25, 2007. Retrieved July 8, 2008. 8. ^ "University of Texas at Austin, Texas Advanced Computing Center". Retrieved September 13, 2010. Any researcher at a U.S. institution can submit a proposal to request an allocation of cycles on the system. 9. ^ Sharon Gaudin (June 9, 2008). "IBM's Roadrunner smashes 4-minute mile of supercomputing". Computerworld. Retrieved June 10, 2008. 10. ^ "Austin ISC08". Top500.org. November 14, 2008. Retrieved February 9, 2012. 11. ^ Fildes, Jonathan (June 9, 2008). "Supercomputer sets petaflop pace". BBC News. Retrieved July 8, 2008. 12. ^ Greenberg, Andy (November 16, 2009). "Cray Dethrones IBM In Supercomputing". Forbes. 13. ^ "China claims supercomputer crown". BBC News. October 28, 2010. 14. ^ Dillow, Clay (October 28, 2010). "China Unveils 2507 Petaflop Supercomputer, the World's Fastest". Popsci.com. Retrieved February 9, 2012 15. ^ "Intel's Core i7-980X Extreme Edition – Ready for Sick Scores?: Mathematics: Sandra Arithmetic, Crypto, Microsoft Excel". Techgage. March 10, 2010. Retrieved February 9, 2012 16. ^ "NVIDIA Tesla Personal Supercomputer". Nvidia.com. Retrieved February 9, 2012 17. ^ "AMD FireStream 9270 GPU Compute Accelerator". Amd.com. Retrieved February 9, 2012 18. ^ http://www.amd.com/us/products/desktop/graphics/ati-radeon-hd-5000/hd-5970/Pages/ati-radeon-hd-5970-specifications.aspx 19. ^ "GeForce GTX 480". Nvidia.com. July 20, 2010. Retrieved February 9, 2012 20. ^ Dillow, Clay. "Air Force Unveils Fastest Defense Supercomputer, Made of 1760 PlayStation 3". Popsci.com. Retrieved February 9, 2012 21. ^ "'K computer' Achieves Goal of 10 Petaflops". Fujitsu.com. Retrieved February 9, 2012. 22. ^ 23. ^ "Intel's Knights Corner: 50+ Core 22nm Co-processor". Retrieved November 16, 2011. 24. ^ "Intel unveils 1 TFLOP/s Knight's Corner". Retrieved November 16, 2011. 25. ^ Clark, Don (June 18, 2012). "IBM Computer Sets Speed Record". The Wall Street Journal. Retrieved June 18, 2012. 26. ^ "BBC News – US Titan supercomputer clocked as world's fastest". Bbc.co.uk. November 12, 2012. Retrieved February 28, 2013. 27. ^ "Oak Ridge Claims No. 1 Position on Latest TOP500 List with Titan | TOP500 Supercomputer Sites". Top500.org. November 12, 2012. Retrieved February 28, 2013. 28. ^ Montalbano, Elizabeth (October 11, 2011). "Oak Ridge Labs Builds Fastest Supercomputer". Informationweek. Retrieved February 9, 2012 29. ^ Tibken, Shara (October 29, 2012). "Titan supercomputer debuts for open scientific research | Cutting Edge – CNET News". News.cnet.com. Retrieved February 28, 2013. 30. ^ "Chinese Supercomputer Is Now The World's Fastest - By A Lot". Forbes Magazine. June 17, 2013. Retrieved June 17, 2013. 31. ^ "China Tops Supercomputer Rankings with New 93-Petaflop Machine". Top500.org. June 20, 2016. Retrieved June 20, 2016. 32. ^ http://www.top500.org/news/china-races-ahead-in-top500-supercomputer-list-ending-us-supremacy/. Missing or empty |title= (help) 33. ^ "Closing in on 100 Petaflops". Folding@Home. May 11, 2016. Retrieved July 17, 2016. 34. ^ Staff (November 6, 2008). "Sony Computer Entertainment's Support for Folding@home Project on PlayStation3 Receives This Year's "Good Design Gold Award"". Sony Computer Entertainment Inc. (Sony Computer Entertainment Inc.). Sony Computer Entertainment Inc. Retrieved December 11, 2008. 35. ^ "Computering Power". BOINC. Retrieved July 31, 2014. 36. ^ "SETI@Home Credit overview". BOINC. Retrieved July 31, 2014. 37. ^ "Einstein@Home Credit overview". BOINC. Retrieved July 31, 2014. 38. ^ "MilkyWay@Home Credit overview". BOINC. Retrieved July 31, 2014. 39. ^ "Internet PrimeNet Server Distributed Computing Technology for the Great Internet Mersenne Prime Search". GIMPS. Retrieved July 31, 2014. 40. ^ p339, Shadow Factory, Bamford 41. ^ http://singularityhub.com/2012/11/01/the-race-to-a-billion-billion-operations-per-second-an-exaflop-by-2018/ 42. ^ "Cray studies exascale computing in Europe". Eetimes.com. Retrieved February 9, 2012 43. ^ DeBenedictis, Erik P. (2005). "Reversible logic for supercomputing". Proceedings of the 2nd conference on Computing frontiers. New York, NY: ACM Press. pp. 391–402. ISBN 1-59593-019-1. 44. ^ "IDF: Intel says Moore's Law holds until 2029". Heise Online. April 4, 2008. 45. ^ 46. ^ "IBM 1961 BRL Report". Ed-thelen.org. Retrieved February 9, 2012 47. ^ "Loki and Hyglac". Loki-www.lanl.gov. July 13, 1997. Retrieved February 9, 2012 48. ^ "Kentucky Linux Athlon Testbed 2 (KLAT2)". The Aggregate. Retrieved February 9, 2012 49. ^ "KASY0". The Aggregate. August 22, 2003. Retrieved February 9, 2012 50. ^ "Microwulf: A Personal, Portable Beowulf Cluster". Replay.waybackmachine.org. September 12, 2007. Archived from the original on September 12, 2007. Retrieved February 9, 2012 51. ^ Adam Stevenson, Yann Le Du, and Mariem El Afrit. "High-performance computing on gamer PCs." Ars Technica. March 31, 2011. 52. ^ http://www.overclock3d.net/reviews/gpu_displays/hd7970_quadfire_eyefinity_review/12 53. ^ "Sony Sparks Price War With PS4 Priced at$399." CNBC. June 11, 2013.
54. ^ http://www.freezepage.com/1384601420XCIGYKCBKJ
55. ^ http://www.freezepage.com/1387480124PSLSILVCMJ
56. ^ http://www.freezepage.com/1420850340WGSMHXRBLE
58. ^ Fixed versus floating point. Retrieved on December 25, 2009.
59. ^ Data manipulation and math calculation. Retrieved on December 25, 2009.
60. ^ Integer Retrieved on December 25, 2009.
61. ^ Floating Point Retrieved on December 25, 2009.
62. ^ Summary: Fixed-point (integer) vs floating-point Retrieved on December 25, 2009.