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Journal articles on the topic 'Floating point'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Jorgensen, Alan A., Las Vegas, Connie R. Masters, Ratan K. Guha, and Andrew C. Masters. "Bounded Floating Point: Identifying and Revealing Floating-Point Error." Advances in Science, Technology and Engineering Systems Journal 6, no. 1 (2021): 519–31. http://dx.doi.org/10.25046/aj060157.

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2

M. Somasekhar, M. Somasekhar. "Floating Point Operations in PipeRench CGRA." International Journal of Scientific Research 1, no. 6 (2012): 67–68. http://dx.doi.org/10.15373/22778179/nov2012/24.

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3

Boldo, Sylvie, Claude-Pierre Jeannerod, Guillaume Melquiond, and Jean-Michel Muller. "Floating-point arithmetic." Acta Numerica 32 (May 2023): 203–90. http://dx.doi.org/10.1017/s0962492922000101.

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Floating-point numbers have an intuitive meaning when it comes to physics-based numerical computations, and they have thus become the most common way of approximating real numbers in computers. The IEEE-754 Standard has played a large part in making floating-point arithmetic ubiquitous today, by specifying its semantics in a strict yet useful way as early as 1985. In particular, floating-point operations should be performed as if their results were first computed with an infinite precision and then rounded to the target format. A consequence is that floating-point arithmetic satisfies the ‘sta

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4

Boldo, Sylvie, Claude-Pierre Jeannerod, Guillaume Melquiond, and Jean-Michel Muller. "Floating-point arithmetic." Acta Numerica 32 (May 1, 2023): 203–90. https://doi.org/10.1017/s0962492922000101.

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Floating-point numbers have an intuitive meaning when it comes to physics-based numerical computations, and they have thus become the most common way of approximating real numbers in computers. The IEEE-754 Standard has played a large part in making floating-point arithmetic ubiquitous today, by specifying its semantics in a strict yet useful way as early as 1985. In particular, floating-point operations should be performed as if their results were first computed with an infinite precision and then rounded to the target format. A consequence is that floating-point arithmetic satisfies the 'sta

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5

Blinn, J. F. "Floating-point tricks." IEEE Computer Graphics and Applications 17, no. 4 (1997): 80–84. http://dx.doi.org/10.1109/38.595279.

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6

Ghosh, Aniruddha, Satrughna Singha, and Amitabha Sinha. ""Floating point RNS"." ACM SIGARCH Computer Architecture News 40, no. 2 (2012): 39–43. http://dx.doi.org/10.1145/2234336.2234343.

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7

Harrison, John. "Floating-Point Verification." JUCS - Journal of Universal Computer Science 13, no. (5) (2007): 629–38. https://doi.org/10.3217/jucs-013-05-0629.

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This paper overviews the application of formal verification techniques to hardware ingeneral, and to floating-point hardware in particular. A specific challenge is to connect the usual mathematical view of continuous arithmetic operations with the discrete world, in a credible andverifiable way.

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8

Kavya, Nagireddy. "Design and Implementation of Floating-Point Addition and Floating-Point Multiplication." International Journal for Research in Applied Science and Engineering Technology 10, no. 1 (2022): 98–101. http://dx.doi.org/10.22214/ijraset.2022.39742.

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Abstract: In this paper, we present the design and implementation of Floating point addition and Floating point Multiplication. There are many multipliers in existence in which Floating point Multiplication and Floating point addition offers a high precision and more accuracy for the data representation of the image. This project is designed and simulated on Xilinx ISE 14.7 version software using verilog. Simulation results show area reduction and delay reduction as compared to the conventional method. Keywords: FIR Filter, Floating point Addition, Floating point Multiplication, Carry Look Ahe

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9

Ms., Anuja A. Bhat* &. Prof. Rutuja Warbhe. "DESIGN OF FLOATING POINT MULTIPLIER BASED ON BOOTH ALGORITHM USING VHDL." INTERNATIONAL JOURNAL OF RESEARCH SCIENCE & MANAGEMENT 4, no. 5 (2017): 123–30. https://doi.org/10.5281/zenodo.580862.

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In this paper, high Speed, low power and less delay 32-bit IEEE 754 Floating PointSubtractor andMultiplierispresented using Booth Multiplier. Multiplication is an important fundamental function in many Digital Signal Processing (DSP) applications such as Fast Fourier Transform (FFT). Since multiplication dominates the execution time of most DSP algorithms, so there is a need of high speed multiplier. The main objective of this researchis to reduce delay, power and to increase the speed.The coding is done in VHDL, synthesis and simulationhas been done using Xilinx ISE simulator. The modules des

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10

Mishra, Raj Gaurav, and Amit Kumar Shrivastava. "Implementation of Custom Precision Floating Point Arithmetic on FPGAs." HCTL Open International Journal of Technology Innovations and Research (IJTIR) 1, January 2013 (2013): 10–26. https://doi.org/10.5281/zenodo.160887.

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Floating point arithmetic is a common requirement in signal processing, image processing and real time data acquisition & processing algorithms. Implementation of such algorithms on FPGA requires an efficient implementation of floating point arithmetic core as an initial process. We have presented an empirical result of the implementation of custom-precision floating point numbers on an FPGA processor using the rules of IEEE standards defined for single and double precision floating point numbers. Floating point operations are difficult to implement on FPGAs because of their complexity in

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11

Ms., Anuja A. Bhat* &. Prof. Mangesh N. Thakare. "DESIGN OF FLOATING POINT MULTIPLIER BASED ON BOOTH ALGORITHM USING VHDL." INTERNATIONAL JOURNAL OF RESEARCH SCIENCE & MANAGEMENT 4, no. 5 (2017): 55–62. https://doi.org/10.5281/zenodo.572573.

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In this paper, we have presented of High Speed, low power and less delay 32-bit IEEE 754 Floating Point Subtractor and Multiplier using Booth Multiplier. Multiplication is an important fundamental function in many Digital Signal Processing (DSP) applications such as Fast Fourier Transform (FFT). Since multiplication dominates the execution time of most DSP algorithms, so there is a need of high speed multiplier. The main objective of this research is to reduce delay, power and to increase the speed. The coding is done in VHDL, synthesis and simulation has been done using Xilinx ISE simulator.

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12

Singamsetti, Mrudula, Sadulla Shaik, and T. Pitchaiah. "Merged Floating Point Multipliers." International Journal of Engineering and Advanced Technology 9, no. 1s5 (2019): 178–82. http://dx.doi.org/10.35940/ijeat.a1042.1291s519.

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Floating point multipliers are extensively used in many scientific and signal processing computations, due to high speed and memory requirements of IEEE-754 floating point multipliers which prevents its implementation in many systems because of fast computations. Hence floating point multipliers became one of the research criteria. This research aims to design a new floating point multiplier that occupies less area, low power dissipation and reduces computational time (more speed) when compared to the conventional architectures. After an extensive literature survey, new architecture was recogn

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13

Baidas, Z., A. D. Brown, and A. C. Williams. "Floating-point behavioral synthesis." IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 20, no. 7 (2001): 828–39. http://dx.doi.org/10.1109/43.931000.

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14

Sayers, David, and du Croz Jeremy. "Validating floating-point systems." Physics World 2, no. 6 (1989): 59–62. http://dx.doi.org/10.1088/2058-7058/2/6/33.

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15

Erle, Mark A., Brian J. Hickmann, and Michael J. Schulte. "Decimal Floating-Point Multiplication." IEEE Transactions on Computers 58, no. 7 (2009): 902–16. http://dx.doi.org/10.1109/tc.2008.218.

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16

Nannarelli, Alberto. "Tunable Floating-Point Adder." IEEE Transactions on Computers 68, no. 10 (2019): 1553–60. http://dx.doi.org/10.1109/tc.2019.2906907.

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17

Shirayanagi, Kiyoshi. "Floating point Gröbner bases." Mathematics and Computers in Simulation 42, no. 4-6 (1996): 509–28. http://dx.doi.org/10.1016/s0378-4754(96)00027-4.

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18

Wichmann, Brian. "Improving floating-point programming." Science of Computer Programming 15, no. 2-3 (1990): 255–56. http://dx.doi.org/10.1016/0167-6423(90)90092-r.

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19

Weiss, S., and A. Goldstein. "Floating point micropipeline performance." Journal of Systems Architecture 45, no. 1 (1998): 15–29. http://dx.doi.org/10.1016/s1383-7621(97)00070-2.

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20

Advanced Micro Devices. "IEEE floating-point format." Microprocessors and Microsystems 12, no. 1 (1988): 13–23. http://dx.doi.org/10.1016/0141-9331(88)90031-2.

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21

Espelid, T. O. "On Floating-Point Summation." SIAM Review 37, no. 4 (1995): 603–7. http://dx.doi.org/10.1137/1037130.

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22

Umemura, Kyoji. "Floating-point number LISP." Software: Practice and Experience 21, no. 10 (1991): 1015–26. http://dx.doi.org/10.1002/spe.4380211003.

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23

Hockert, Neil, and Katherine Compton. "Improving Floating-Point Performance in Less Area: Fractured Floating Point Units (FFPUs)." Journal of Signal Processing Systems 67, no. 1 (2011): 31–46. http://dx.doi.org/10.1007/s11265-010-0561-y.

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24

Ramya Rani, N. "Implementation of Embedded Floating Point Arithmetic Units on FPGA." Applied Mechanics and Materials 550 (May 2014): 126–36. http://dx.doi.org/10.4028/www.scientific.net/amm.550.126.

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:Floating point arithmetic plays a major role in scientific and embedded computing applications. But the performance of field programmable gate arrays (FPGAs) used for floating point applications is poor due to the complexity of floating point arithmetic. The implementation of floating point units on FPGAs consumes a large amount of resources and that leads to the development of embedded floating point units in FPGAs. Embedded applications like multimedia, communication and DSP algorithms use floating point arithmetic in processing graphics, Fourier transformation, coding, etc. In this paper,

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25

Albert, Anitha Juliette, and Seshasayanan Ramachandran. "NULL Convention Floating Point Multiplier." Scientific World Journal 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/749569.

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Floating point multiplication is a critical part in high dynamic range and computational intensive digital signal processing applications which require high precision and low power. This paper presents the design of an IEEE 754 single precision floating point multiplier using asynchronous NULL convention logic paradigm. Rounding has not been implemented to suit high precision applications. The novelty of the research is that it is the first ever NULL convention logic multiplier, designed to perform floating point multiplication. The proposed multiplier offers substantial decrease in power cons

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26

T.Govinda, Rao, Pradeep P.Devi, and P.Kalyanchakravarthi. "DESIGN OF DOUBLE PRECISION FLOATING POINT MULTIPLICATION ALGORITHM WITH VECTOR SUPPORT." International Journal Of Microwave Engineering (JMICRO) 1, no. 2 (2022): 9. https://doi.org/10.5281/zenodo.7353323.

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This paper presents floating point multiplier capable of supporting wide range of application domains like scientific computing and multimedia applications and also describes an implementation of a floating point multiplier that supports the IEEE 754-2008 binary interchange format with methodology for estimating the power and speed has been developed. This Pipelined vectorized floating point multiplier supporting FP16, FP32, FP64 input data and reduces the area, power, latency and increases throughput. Precision can be implemented by taking the 128 bit input operands.The floating point units c

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27

Luсkij, Georgi, and Oleksandr Dolholenko. "Development of floating point operating devices." Technology audit and production reserves 5, no. 2(73) (2023): 11–17. http://dx.doi.org/10.15587/2706-5448.2023.290127.

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The paper shows a well-known approach to the construction of cores in multi-core microprocessors, which is based on the application of a data flow graph-driven calculation model. The architecture of such kernels is based on the application of the reduced instruction set level data flow model proposed by Yale Patt. The object of research is a model of calculations based on data flow management in a multi-core microprocessor. The results of the floating-point multiplier development that can be dynamically reconfigured to handle five different formats of floating-point operands and an approach to

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28

Yang, Hongru, Jinchen Xu, Jiangwei Hao, Zuoyan Zhang, and Bei Zhou. "Detecting Floating-Point Expression Errors Based Improved PSO Algorithm." IET Software 2023 (October 23, 2023): 1–16. http://dx.doi.org/10.1049/2023/6681267.

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The use of floating-point numbers inevitably leads to inaccurate results and, in certain cases, significant program failures. Detecting floating-point errors is critical to ensuring that floating-point programs outputs are proper. However, due to the sparsity of floating-point errors, only a limited number of inputs can cause significant floating-point errors, and determining how to detect these inputs and to selecting the appropriate search technique is critical to detecting significant errors. This paper proposes characteristic particle swarm optimization (CPSO) algorithm based on particle s

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29

Sravani, Chinta, Dr Prasad Janga, and Mrs S. SriBindu. "Floating Point Operations Compatible Streaming Elements for FPGA Accelerators." International Journal of Trend in Scientific Research and Development Volume-2, Issue-5 (2018): 302–9. http://dx.doi.org/10.31142/ijtsrd15853.

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30

Aruna Mastani, S., and Riyaz Ahamed Shaik. "Inexact Floating Point Adders Analysis." International Journal of Applied Engineering Research 15, no. 11 (2020): 1075–80. http://dx.doi.org/10.37622/ijaer/15.11.2020.1075-1080.

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31

Meyer, Quirin, Jochen Süßmuth, Gerd Sußner, Marc Stamminger, and Günther Greiner. "On Floating-Point Normal Vectors." Computer Graphics Forum 29, no. 4 (2010): 1405–9. http://dx.doi.org/10.1111/j.1467-8659.2010.01737.x.

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32

Ghatte, Najib, Shilpa Patil, and Deepak Bhoir. "Floating Point Engine using VHDL." International Journal of Engineering Trends and Technology 8, no. 4 (2014): 198–203. http://dx.doi.org/10.14445/22315381/ijett-v8p236.

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33

Lange, Marko, and Siegfried M. Rump. "Faithfully Rounded Floating-point Computations." ACM Transactions on Mathematical Software 46, no. 3 (2020): 1–20. http://dx.doi.org/10.1145/3290955.

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34

Winter, Dik T. "Floating point attributes in Ada." ACM SIGAda Ada Letters XI, no. 7 (1991): 244–73. http://dx.doi.org/10.1145/123533.123577.

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35

Toronto, Neil, and Jay McCarthy. "Practically Accurate Floating-Point Math." Computing in Science & Engineering 16, no. 4 (2014): 80–95. http://dx.doi.org/10.1109/mcse.2014.90.

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36

Kadric, Edin, Paul Gurniak, and Andre DeHon. "Accurate Parallel Floating-Point Accumulation." IEEE Transactions on Computers 65, no. 11 (2016): 3224–38. http://dx.doi.org/10.1109/tc.2016.2532874.

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37

Lam, Michael O., Jeffrey K. Hollingsworth, and G. W. Stewart. "Dynamic floating-point cancellation detection." Parallel Computing 39, no. 3 (2013): 146–55. http://dx.doi.org/10.1016/j.parco.2012.08.002.

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38

Scheidt, J. K., and C. W. Schelin. "Distributions of floating point numbers." Computing 38, no. 4 (1987): 315–24. http://dx.doi.org/10.1007/bf02278709.

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39

Oavrielov, Moshe, and Lev Epstein. "The NS32081 Floating-point Unit." IEEE Micro 6, no. 2 (1986): 6–12. http://dx.doi.org/10.1109/mm.1986.304737.

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40

Groza, V. Z. "High-resolution floating-point ADC." IEEE Transactions on Instrumentation and Measurement 50, no. 6 (2001): 1822–29. http://dx.doi.org/10.1109/19.982987.

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41

Nikmehr, H., B. Phillips, and Cheng-Chew Lim. "Fast Decimal Floating-Point Division." IEEE Transactions on Very Large Scale Integration (VLSI) Systems 14, no. 9 (2006): 951–61. http://dx.doi.org/10.1109/tvlsi.2006.884047.

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42

Serebrenik, Alexander, and Danny De Schreye. "Termination of Floating-Point Computations." Journal of Automated Reasoning 34, no. 2 (2005): 141–77. http://dx.doi.org/10.1007/s10817-005-6546-z.

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43

Rivera, Joao, Franz Franchetti, and Markus Püschel. "Floating-Point TVPI Abstract Domain." Proceedings of the ACM on Programming Languages 8, PLDI (2024): 442–66. http://dx.doi.org/10.1145/3656395.

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Floating-point arithmetic is natively supported in hardware and the preferred choice when implementing numerical software in scientific or engineering applications. However, such programs are notoriously hard to analyze due to round-off errors and the frequent use of elementary functions such as log, arctan, or sqrt. In this work, we present the Two Variables per Inequality Floating-Point (TVPI-FP) domain, a numerical and constraint-based abstract domain designed for the analysis of floating-point programs. TVPI-FP supports all features of real-world floating-point programs including condition

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44

Hammadi Jassim, Manal. "Floating Point Optimization Using VHDL." Engineering and Technology Journal 27, no. 16 (2009): 3023–49. http://dx.doi.org/10.30684/etj.27.16.11.

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45

Yang, Fengyuan. "Research and Analysis of Floating-Point Adder Principle." Applied and Computational Engineering 8, no. 1 (2023): 113–17. http://dx.doi.org/10.54254/2755-2721/8/20230092.

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With the development of the times, computers are used more and more widely, and the research and development of adder, as the most basic operation unit, determine the development of the computer field. This paper analyzes the principle of one-bit adder and floating-point adder by literature analysis. One-bit adder is the most basic type of traditional adder, besides bit-by-bit adder, overrun adder and so on. The purpose of this paper is to understand the basic principle of adder, among them, IEEE-754 binary floating point operation is very important. So that the traditional fixed-point adder i

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46

Mohammed, Falih Hassan, Farhood Hussein Karime, and Al-Musawi Bahaa. "Design and implementation of fast floating point units for FPGAs." Indonesian Journal of Electrical Engineering and Computer Science 19, no. 3 (2022): 1480–89. https://doi.org/10.11591/ijeecs.v19.i3.pp1480-1489.

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Due to growth in demand for high-performance applications that require high numerical stability and accuracy, the need for floating-point FPGA has been increased. In this work, an open-source and efficient floating-point unit is implemented on a standard Xilinx Sparton-6 FPGA platform. The proposed design is described in a hierarchal way starting from functional block descriptions toward modules level design. Our implementation used minimal resources available on the targeting FPGA board, tested on the Sparton-6 FPGA platform and verified on ModelSim. The open-source framework can be embedded

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47

Kurniawan, Wakhid, Hafizd Ardiansyah, Annisa Dwi Oktavianita, and Mr Fitree Tahe. "Integer Representation of Floating-Point Manipulation with Float Twice." IJID (International Journal on Informatics for Development) 9, no. 1 (2020): 15. http://dx.doi.org/10.14421/ijid.2020.09103.

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In the programming world, understanding floating point is not easy, especially if there are floating point and bit-level interactions. Although there are currently many libraries to simplify the computation process, still many programmers today who do not really understand how the floating point manipulation process. Therefore, this paper aims to provide insight into how to manipulate IEEE-754 32-bit floating point with different representation of results, which are integers and code rules of float twice. The method used is a literature review, adopting a float-twice prototype using C programm

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48

Blanton, Marina, Michael T. Goodrich, and Chen Yuan. "Secure and Accurate Summation of Many Floating-Point Numbers." Proceedings on Privacy Enhancing Technologies 2023, no. 3 (2023): 432–45. http://dx.doi.org/10.56553/popets-2023-0090.

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Motivated by the importance of floating-point computations, we study the problem of securely and accurately summing many floating-point numbers. Prior work has focused on security absent accuracy or accuracy absent security, whereas our approach achieves both of them. Specifically, we show how to implement floating-point superaccumulators using secure multi-party computation techniques, so that a number of participants holding secret shares of floating-point numbers can accurately compute their sum while keeping the individual values private.

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49

R., Bhuvanapriya, and T. Menakadevi. "Design and Implementation of FPU for Optimised Speed." International Journal of Engineering and Advanced Technology (IJEAT) 9, no. 3 (2020): 3922–33. https://doi.org/10.35940/ijeat.C6444.029320.

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Currently, each CPU has one or additional Floating Point Units (FPUs) integrated inside it. It is usually utilized in math wide-ranging applications, such as digital signal processing. It is found in places be established in engineering, medical and military fields in adding along to in different fields requiring audio, image or video handling. A high-speed and energy-efficient floating point unit is naturally needed in the electronics diligence as an arithmetic unit in microprocessors. The most operations accounting 95% of conformist FPU are multiplication and addition. Many applications need

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50

Yang, Xu, Zhenbang Chen, Wei Dong, and Ji Wang. "QSF: Multi-objective Optimization Based Efficient Solving for Floating-Point Constraints." Proceedings of the ACM on Software Engineering 2, FSE (2025): 511–32. https://doi.org/10.1145/3715739.

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Floating-point constraint solving is challenging due to the complex representation and non-linear computations. Search-based constraint solving provides an effective method for solving floating-point constraints. In this paper, we propose QSF to improve the efficiency of search-based solving for floating-point constraints. The key idea of QSF is to model the floating-point constraint solving problem as a multi-objective optimization problem. Specifically, QSF considers both the number of unsatisfied constraints and the sum of the violation degrees of unsatisfied constraints as the objectives f

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