- published: 07 Nov 2020
- views: 98
Significant figures
The significant figures of a number are digits that carry meaning contributing to its measurement resolution. This includes all digits except:
Significance arithmetic are approximate rules for roughly maintaining significance throughout a computation. The more sophisticated scientific rules are known as propagation of uncertainty.
Numbers are often rounded to avoid reporting insignificant figures. For example, it would create false precision to express a measurement as 12,345.00 kg (which has seven significant figures) if the scales only measured to the nearest gram and gave a reading of 12,345 kg (which has five significant figures) . Numbers can also be rounded merely for simplicity rather than to indicate a given precision of measurement, for example to make them faster to pronounce in news broadcasts.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Significant_figures
Precision
- Arbitrary-precision arithmetic, methods for computing with big numbers
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Precision
Precision (march)
Precision is the authorized march of Royal Military College of Canada. The RMC band performs Precision on parades for march pasts, on Ex Cadet Weekends for the parade to the Memorial Arch, and on the return, the Cadet Wing sings Tom Gelley’s words to welcome the Ex Cadets to the Parade Square.
History
Precision was composed in 1932 by Denise Chabot, wife of Major C. A. Chabot, a Royal Canadian Artillery officer on staff as professor of French at the College at the time. She earned the degree of Associate of the Royal Conservatory of Music and was the president of the Kingston Music Club.
Precision was inspired by "Madelon", one of the popular marching songs sung and whistled by the cadets marching on their way to the Riding School, and the favourite song of the Class of 1932. Mme Chabot improvised a variation on the song, to represent the cadence of the cadets on the march. The composition starts, “We are the gentlemen cadets of RMC We have sworn to love and serve Her Majesty…”
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Precision_(march)
Precision (statistics)
In statistics, the dual term variability is preferred to the use of precision. Variability is the amount of imprecision.
There can be differences in usage of the term for particular statistical models but, in common statistical usage, the precision is defined to be the reciprocal of the variance, while the precision matrix is the matrix inverse of the covariance matrix.
One particular use of the precision matrix is in the context of Bayesian analysis of the multivariate normal distribution: for example, Bernardo & Smith prefer to parameterise the multivariate normal distribution in terms of the precision matrix rather than the covariance matrix because of certain simplifications that then arise.
History
The term precision in this sense (“mensura praecisionis observationum”) first appeared in the works of Gauss (1809) “Theoria motus corporum coelestium in sectionibus conicis solem ambientium” (page 212). Gauss’s definition differs from the modern one by a factor of 
. He writes, for the density function of a normal random variable with precision h,
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Precision_(statistics)
Arithmetic
Arithmetic or arithmetics (from the Greek ἀριθμός arithmos, "number") is the oldest and most elementary branch of mathematics. It consists of the study of numbers, especially the properties of the traditional operations between them—addition, subtraction, multiplication and division. Arithmetic is an elementary part of number theory, and number theory is considered to be one of the top-level divisions of modern mathematics, along with algebra, geometry, and analysis. The terms arithmetic and higher arithmetic were used until the beginning of the 20th century as synonyms for number theory and are sometimes still used to refer to a wider part of number theory.
History
The prehistory of arithmetic is limited to a small number of artifacts which may indicate the conception of addition and subtraction, the best-known being the Ishango bone from central Africa, dating from somewhere between 20,000 and 18,000 BC, although its interpretation is disputed.
The earliest written records indicate the Egyptians and Babylonians used all the elementary arithmetic operations as early as 2000 BC. These artifacts do not always reveal the specific process used for solving problems, but the characteristics of the particular numeral system strongly influence the complexity of the methods. The hieroglyphic system for Egyptian numerals, like the later Roman numerals, descended from tally marks used for counting. In both cases, this origin resulted in values that used a decimal base but did not include positional notation. Complex calculations with Roman numerals required the assistance of a counting board or the Roman abacus to obtain the results.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Arithmetic
Arithmetic (song)
"Arithmetic" is a single by Brooke Fraser released in 2004. The song is the first track Fraser's debut album What To Do With Daylight, which takes its name from this song in the line "Wondering what to do with daylight until I can make you mine." The song was later included on the Sony BMG compilation More Nature, a collection of songs from the New Zealand Sony BMG catalogue (in particular, those who promote nature and conservation).
The song debuted on the New Zealand Singles Chart at number thirty eight on 26 July 2004 and peaked at number eight. It spent nineteen weeks on the chart.
Music clip
The film clip for "Arithmetic" features Fraser in a dimly lit studio surrounded by fairy lights and with fairy lights all over her piano. As the song only features piano and a string quartet, the quartet is also visible in another part of the studio with their music stands also lit by fairy lights. For this abundance of fairy lights, "Arithmetic" was awarded the satirical award for "Most used fairy lights in a video clip" in the 2004 Studio 2 Awards.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Arithmetic_(song)
Podcasts:
-
Group 6 - High Precision Arithmetic
High Precision Arithmetic is the process of doing arithmetic on large-valued integers or 'long integers'. In this video, we will show how to store long integers using a doubly-linked list and how to perform addition using two long integers.
published: 07 Nov 2020 -
CppCon 2018: “Multi-Precision Arithmetic for Cryptology in C++, at Run-Time and at Compile-Time”
http://CppCon.org Niek J. Bouman “Multi-Precision Arithmetic for Cryptology in C++, at Run-Time and at Compile-Time” — Presentation Slides, PDFs, Source Code and other presenter materials are available at: https://github.com/CppCon/CppCon2018 — In the talk, I will present a new C++17 library for multi-precision arithmetic for integers in the order of 100--500 bits. Many cryptographic schemes and applications, like elliptic-curve encryption schemes and secure multiparty computation frameworks require multiprecision arithmetic with integers whose bit-lengths lie in that range. The library is written in “optimizing-compiler-friendly” C++, with an emphasis on the use of fixed-size arrays and particular function-argument-passing styles (including the avoidance of naked pointers) to allow the ...
published: 24 Oct 2018 -
Arbitrary-Precision Arithmetics on the GPU
by Bernhard Langer (TU Wien, Austria) Abstract: The majority of computer applications employ numerical data types with a fixed amount of precision for their computations. Their limited numerical range and precision are sufficient for most use cases. However, for some purposes, such as cryptography or geometrical computations, the required range and precision can become arbitrarily large. Numerical types that can handle such demands have higher memory requirements and are not natively supported by common hardware, which leads to increased computational complexity. In this paper, we examine how basic arithmetic operations on arbitrary-precision integers can be adapted to many-core architectures in the form of graphics processing units, which are widely available as commodity hardware. Apart...
published: 01 May 2015 -
Mixed precision arithmetic: hardware, algorithms and analysis, Theo Mary
========== The London Mathematical Society has, since 1865, been the UK's learned society for the advancement, dissemination and promotion of mathematical knowledge. Our mission is to advance mathematics through our members and the broader scientific community worldwide. For further information: ► Website: https://www.lms.ac.uk ► Events: https://www.lms.ac.uk/events ► Grants and Prizes: https://www.lms.ac.uk/grants-prizes ► Publications: https://www.lms.ac.uk/publications ► Membership: https://www.lms.ac.uk/membership Follow us: ► Twitter: https://twitter.com/LondMathSoc ► Facebook: https://www.facebook.com/londonmathematicalsociety ► LinkedIn: https://www.linkedin.com/company/the-london-mathematical-society/ ► Youtube: @LondonMathematicalSociety
published: 24 Nov 2020 -
Why Is This Happening?! Floating Point Approximation
⭐ Join my Patreon: https://www.patreon.com/b001io 💬 Discord: https://discord.gg/jA8SShU8zJ 🐦 Follow me on Twitter: https://twitter.com/b001io 🔗 More links: https://linktr.ee/b001io Background Music: Gentle Lo-Fi Vlog Background Music | Cookies by Alex-Productions | https://onsound.eu/ Music promoted by https://www.free-stock-music.com Creative Commons Attribution 3.0 Unported License https://creativecommons.org/licenses/by/3.0/deed.en_US
published: 23 Nov 2022 -
Arbitrary-precision arithmetic Top # 5 Facts
Arbitrary-precision arithmetic Top # 5 Facts
published: 29 Oct 2015 -
Arbitrary-precision arithmetic
In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are limited only by the available memory of the host system. This contrasts with the faster fixed-precision arithmetic found in most arithmetic logic unit hardware, which typically offers between 8 and 64 bits of precision. Several modern programming languages have built-in support for bignums, and others have libraries available for arbitrary-precision integer and floating-point math. Rather than store values as a fixed number of binary bits related to the size of the processor register, these implementations typically use variable-length arrays of digits...
published: 30 Dec 2015 -
Simple Algorithm for Arbitrary-Precision Integer Division
Writing a set of steps to divide two very large numbers isn't as easy as it sounds! For more information, go to http://justinparrtech.com and search for INTEGER DIVISION.
published: 23 Oct 2015 -
Computing in arbitrary precision
In certain areas, computational results in high precision are desired. For example, one may need to examine eigenvalues, 60 digits after decimal point, to confirm if a pair of two are not identical. In this seminar, we will talk about a few packages that physicists and chemists might want to use with examples. We will also mention packages that are available for general purposes. _________________________________________________ This webinar was presented by Ge Baolai (SHARCNET) on February 3, 2021, as a part of a series of regular biweekly General Interest webinars ran by SHARCNET. The webinars cover different high performance computing (HPC) topics, are approximately 45 minutes in length, and are delivered by experts in the relevant fields. Further details can be found on this web pag...
published: 08 Feb 2021 -
Arbitrary-precision arithmetic Explanation
Welcome to Mixible, your go-to source for comprehensive and informative content covering a broad range of topics from Stack Exchange websites. Our channel is committed to providing you with valuable insights and discussions on various subjects, ensuring that you stay informed about the latest trends and developments in your area of interest. We offer an extensive library of videos that cover a wide range of topics, including programming, computer science, mathematics, physics, and much more. Our videos are designed to cater to diverse audiences, ranging from beginners to advanced learners, and are presented in an engaging and easy-to-understand format. At Mixible, we are dedicated to being a trusted source of information. We base our videos on questions and answers posted on various St...
published: 06 Jun 2024
developed with YouTube
5:02
Group 6 - High Precision Arithmetic
- Order: Reorder
- Duration: 5:02
- Uploaded Date: 07 Nov 2020
- views: 98
High Precision Arithmetic is the process of doing arithmetic on large-valued integers or 'long integers'. In this video, we will show how to store long integers...
High Precision Arithmetic is the process of doing arithmetic on large-valued integers or 'long integers'. In this video, we will show how to store long integers using a doubly-linked list and how to perform addition using two long integers.
https://wn.com/Group_6_High_Precision_Arithmetic
High Precision Arithmetic is the process of doing arithmetic on large-valued integers or 'long integers'. In this video, we will show how to store long integers using a doubly-linked list and how to perform addition using two long integers.
31:29
CppCon 2018: “Multi-Precision Arithmetic for Cryptology in C++, at Run-Time and at Compile-Time”
- Order: Reorder
- Duration: 31:29
- Uploaded Date: 24 Oct 2018
- views: 4602
http://CppCon.org
Niek J. Bouman “Multi-Precision Arithmetic for Cryptology in C++, at Run-Time and at Compile-Time”
—
Presentation Slides, PDFs, Source Code an...
http://CppCon.org
Niek J. Bouman “Multi-Precision Arithmetic for Cryptology in C++, at Run-Time and at Compile-Time”
—
Presentation Slides, PDFs, Source Code and other presenter materials are available at: https://github.com/CppCon/CppCon2018
—
In the talk, I will present a new C++17 library for multi-precision arithmetic for integers in the order of 100--500 bits. Many cryptographic schemes and applications, like elliptic-curve encryption schemes and secure multiparty computation frameworks require multiprecision arithmetic with integers whose bit-lengths lie in that range.
The library is written in “optimizing-compiler-friendly” C++, with an emphasis on the use of fixed-size arrays and particular function-argument-passing styles (including the avoidance of naked pointers) to allow the limbs to be allocated on the stack or even in registers. Depending on the particular functionality, we get close to, or significantly beat the performance of existing libraries for multiprecision arithmetic that employ hand-optimized assembly code.
Beyond the favorable runtime performance, our library is, to the best of the author’s knowledge, the first library that offers big-integer computations during compile-time. For example, when implementing finite-field arithmetic with a fixed modulus, this feature enables the automatic precomputation (at compile time) of the special modulus- dependent constants required for Barrett and Montgomery reduction. Another application is to parse (at compile-time) a base-10-encoded big-integer literal.
In this talk, I will focus on some Modern C++ language features that I've used to write the library and design its API (e.g., std::array, variadic templates, std::integer_sequence, constexpr, user-defined literals, using-declarations and decltype, and combinations thereof). Also, I will show some benchmarks, and will argue that the integer types offered by the library compose well with STL containers or other libraries (like Eigen for matrix/linear algebra operations).
I will also present some results on formal verification of correctness and the "constant-time" property:
- Correctness is verified using a tool named SAW (Software Analysis Workbench), which tries to prove equivalence between the compiled C++ code (represented as LLVM bitcode) and a behavioral specification given in a high-level functional language;
- "Constant-timeness" is a property that is crucial for implementations of cryptographic protocols to prevent timing attacks. In particular, I succeeded to verify my C++ code with "ct-verif", a tool for verifying the constant-time property for C programs (which was, in its original form, incompatible with C++ due to usage of non-ANSI C in one of its header files)
The library is on Github (Apache 2 licensed)
https://github.com/niekbouman/ctbignum
—
Niek J. Bouman, Eindhoven University of Technology
Researcher Secure Multiparty Computation
2017 - now Postdoc TU/e SODA (Scalable Oblivious Data Mining) project, Eindhoven University of Technology, the Netherlands 2016-2017 Senior Researcher Fraud Detection @ ABN AMRO Bank, Amsterdam, the Netherlands 2014-2016 Postdoc at Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland PhD (2012) Quantum Cryptography/Quantum Information Theory from CWI/Universiteit Leiden, the Netherlands BS'05 MS’07 Electrical Engineering from Universiteit Twente, Enschede, the Netherlands
—
Videos Filmed & Edited by Bash Films: http://www.BashFilms.com
*-----*
Register Now For CppCon 2022: https://cppcon.org/registration/
*-----*
https://wn.com/Cppcon_2018_“Multi_Precision_Arithmetic_For_Cryptology_In_C_,_At_Run_Time_And_At_Compile_Time”
http://CppCon.org
Niek J. Bouman “Multi-Precision Arithmetic for Cryptology in C++, at Run-Time and at Compile-Time”
—
Presentation Slides, PDFs, Source Code and other presenter materials are available at: https://github.com/CppCon/CppCon2018
—
In the talk, I will present a new C++17 library for multi-precision arithmetic for integers in the order of 100--500 bits. Many cryptographic schemes and applications, like elliptic-curve encryption schemes and secure multiparty computation frameworks require multiprecision arithmetic with integers whose bit-lengths lie in that range.
The library is written in “optimizing-compiler-friendly” C++, with an emphasis on the use of fixed-size arrays and particular function-argument-passing styles (including the avoidance of naked pointers) to allow the limbs to be allocated on the stack or even in registers. Depending on the particular functionality, we get close to, or significantly beat the performance of existing libraries for multiprecision arithmetic that employ hand-optimized assembly code.
Beyond the favorable runtime performance, our library is, to the best of the author’s knowledge, the first library that offers big-integer computations during compile-time. For example, when implementing finite-field arithmetic with a fixed modulus, this feature enables the automatic precomputation (at compile time) of the special modulus- dependent constants required for Barrett and Montgomery reduction. Another application is to parse (at compile-time) a base-10-encoded big-integer literal.
In this talk, I will focus on some Modern C++ language features that I've used to write the library and design its API (e.g., std::array, variadic templates, std::integer_sequence, constexpr, user-defined literals, using-declarations and decltype, and combinations thereof). Also, I will show some benchmarks, and will argue that the integer types offered by the library compose well with STL containers or other libraries (like Eigen for matrix/linear algebra operations).
I will also present some results on formal verification of correctness and the "constant-time" property:
- Correctness is verified using a tool named SAW (Software Analysis Workbench), which tries to prove equivalence between the compiled C++ code (represented as LLVM bitcode) and a behavioral specification given in a high-level functional language;
- "Constant-timeness" is a property that is crucial for implementations of cryptographic protocols to prevent timing attacks. In particular, I succeeded to verify my C++ code with "ct-verif", a tool for verifying the constant-time property for C programs (which was, in its original form, incompatible with C++ due to usage of non-ANSI C in one of its header files)
The library is on Github (Apache 2 licensed)
https://github.com/niekbouman/ctbignum
—
Niek J. Bouman, Eindhoven University of Technology
Researcher Secure Multiparty Computation
2017 - now Postdoc TU/e SODA (Scalable Oblivious Data Mining) project, Eindhoven University of Technology, the Netherlands 2016-2017 Senior Researcher Fraud Detection @ ABN AMRO Bank, Amsterdam, the Netherlands 2014-2016 Postdoc at Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland PhD (2012) Quantum Cryptography/Quantum Information Theory from CWI/Universiteit Leiden, the Netherlands BS'05 MS’07 Electrical Engineering from Universiteit Twente, Enschede, the Netherlands
—
Videos Filmed & Edited by Bash Films: http://www.BashFilms.com
*-----*
Register Now For CppCon 2022: https://cppcon.org/registration/
*-----*
- published: 24 Oct 2018
- views: 4602
0:25
Arbitrary-Precision Arithmetics on the GPU
- Order: Reorder
- Duration: 0:25
- Uploaded Date: 01 May 2015
- views: 918
by Bernhard Langer (TU Wien, Austria)
Abstract: The majority of computer applications employ numerical data types with a fixed amount of precision for their co...
by Bernhard Langer (TU Wien, Austria)
Abstract: The majority of computer applications employ numerical data types with a fixed amount of precision for their computations. Their limited numerical range and precision are sufficient for most use cases. However, for some purposes, such as cryptography or geometrical computations, the required range and precision can become arbitrarily large. Numerical types that can handle such demands have higher memory requirements and are not natively supported by common hardware, which leads to increased computational complexity. In this paper, we examine how basic arithmetic operations on arbitrary-precision integers can be adapted to many-core architectures in the form of graphics processing units, which are widely available as commodity hardware. Apart from a detailed description of our method, we show superior performance characteristics of our implementation in comparison to state-of-the-art CPU libraries for high computational loads.
Full paper: http://cescg.org/CESCG-2015/papers/Langer-Arbitrary-Precision_Arithmetics_on_the_GPU.pdf
https://wn.com/Arbitrary_Precision_Arithmetics_On_The_Gpu
by Bernhard Langer (TU Wien, Austria)
Abstract: The majority of computer applications employ numerical data types with a fixed amount of precision for their computations. Their limited numerical range and precision are sufficient for most use cases. However, for some purposes, such as cryptography or geometrical computations, the required range and precision can become arbitrarily large. Numerical types that can handle such demands have higher memory requirements and are not natively supported by common hardware, which leads to increased computational complexity. In this paper, we examine how basic arithmetic operations on arbitrary-precision integers can be adapted to many-core architectures in the form of graphics processing units, which are widely available as commodity hardware. Apart from a detailed description of our method, we show superior performance characteristics of our implementation in comparison to state-of-the-art CPU libraries for high computational loads.
Full paper: http://cescg.org/CESCG-2015/papers/Langer-Arbitrary-Precision_Arithmetics_on_the_GPU.pdf
- published: 01 May 2015
- views: 918
43:11
Mixed precision arithmetic: hardware, algorithms and analysis, Theo Mary
- Order: Reorder
- Duration: 43:11
- Uploaded Date: 24 Nov 2020
- views: 871
==========
The London Mathematical Society has, since 1865, been the UK's learned society for the advancement, dissemination and promotion of mathematical know...
==========
The London Mathematical Society has, since 1865, been the UK's learned society for the advancement, dissemination and promotion of mathematical knowledge. Our mission is to advance mathematics through our members and the broader scientific community worldwide.
For further information:
► Website: https://www.lms.ac.uk
► Events: https://www.lms.ac.uk/events
► Grants and Prizes: https://www.lms.ac.uk/grants-prizes
► Publications: https://www.lms.ac.uk/publications
► Membership: https://www.lms.ac.uk/membership
Follow us:
► Twitter: https://twitter.com/LondMathSoc
► Facebook: https://www.facebook.com/londonmathematicalsociety
► LinkedIn: https://www.linkedin.com/company/the-london-mathematical-society/
► Youtube: @LondonMathematicalSociety
https://wn.com/Mixed_Precision_Arithmetic_Hardware,_Algorithms_And_Analysis,_Theo_Mary
==========
The London Mathematical Society has, since 1865, been the UK's learned society for the advancement, dissemination and promotion of mathematical knowledge. Our mission is to advance mathematics through our members and the broader scientific community worldwide.
For further information:
► Website: https://www.lms.ac.uk
► Events: https://www.lms.ac.uk/events
► Grants and Prizes: https://www.lms.ac.uk/grants-prizes
► Publications: https://www.lms.ac.uk/publications
► Membership: https://www.lms.ac.uk/membership
Follow us:
► Twitter: https://twitter.com/LondMathSoc
► Facebook: https://www.facebook.com/londonmathematicalsociety
► LinkedIn: https://www.linkedin.com/company/the-london-mathematical-society/
► Youtube: @LondonMathematicalSociety
- published: 24 Nov 2020
- views: 871
5:46
Why Is This Happening?! Floating Point Approximation
- Order: Reorder
- Duration: 5:46
- Uploaded Date: 23 Nov 2022
- views: 135233
⭐ Join my Patreon: https://www.patreon.com/b001io
💬 Discord: https://discord.gg/jA8SShU8zJ
🐦 Follow me on Twitter: https://twitter.com/b001io
🔗 More links: http...
⭐ Join my Patreon: https://www.patreon.com/b001io
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Music promoted by https://www.free-stock-music.com
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https://wn.com/Why_Is_This_Happening_Floating_Point_Approximation
⭐ Join my Patreon: https://www.patreon.com/b001io
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Background Music:
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Music promoted by https://www.free-stock-music.com
Creative Commons Attribution 3.0 Unported License
https://creativecommons.org/licenses/by/3.0/deed.en_US
- published: 23 Nov 2022
- views: 135233
0:41
Arbitrary-precision arithmetic Top # 5 Facts
- Order: Reorder
- Duration: 0:41
- Uploaded Date: 29 Oct 2015
- views: 206
Arbitrary-precision arithmetic Top # 5 Facts
Arbitrary-precision arithmetic Top # 5 Facts
https://wn.com/Arbitrary_Precision_Arithmetic_Top_5_Facts
Arbitrary-precision arithmetic Top # 5 Facts
- published: 29 Oct 2015
- views: 206
18:15
Arbitrary-precision arithmetic
- Order: Reorder
- Duration: 18:15
- Uploaded Date: 30 Dec 2015
- views: 3009
In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple precision arithmetic, or sometimes infinite-precision arithmetic, i...
In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are limited only by the available memory of the host system. This contrasts with the faster fixed-precision arithmetic found in most arithmetic logic unit hardware, which typically offers between 8 and 64 bits of precision.
Several modern programming languages have built-in support for bignums, and others have libraries available for arbitrary-precision integer and floating-point math. Rather than store values as a fixed number of binary bits related to the size of the processor register, these implementations typically use variable-length arrays of digits.
This video is targeted to blind users.
Attribution:
Article text available under CC-BY-SA
Creative Commons image source in video
https://wn.com/Arbitrary_Precision_Arithmetic
In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are limited only by the available memory of the host system. This contrasts with the faster fixed-precision arithmetic found in most arithmetic logic unit hardware, which typically offers between 8 and 64 bits of precision.
Several modern programming languages have built-in support for bignums, and others have libraries available for arbitrary-precision integer and floating-point math. Rather than store values as a fixed number of binary bits related to the size of the processor register, these implementations typically use variable-length arrays of digits.
This video is targeted to blind users.
Attribution:
Article text available under CC-BY-SA
Creative Commons image source in video
- published: 30 Dec 2015
- views: 3009
18:36
Simple Algorithm for Arbitrary-Precision Integer Division
- Order: Reorder
- Duration: 18:36
- Uploaded Date: 23 Oct 2015
- views: 5753
Writing a set of steps to divide two very large numbers isn't as easy as it sounds!
For more information, go to http://justinparrtech.com and search for INTEGER...
Writing a set of steps to divide two very large numbers isn't as easy as it sounds!
For more information, go to http://justinparrtech.com and search for INTEGER DIVISION.
https://wn.com/Simple_Algorithm_For_Arbitrary_Precision_Integer_Division
Writing a set of steps to divide two very large numbers isn't as easy as it sounds!
For more information, go to http://justinparrtech.com and search for INTEGER DIVISION.
- published: 23 Oct 2015
- views: 5753
51:44
Computing in arbitrary precision
- Order: Reorder
- Duration: 51:44
- Uploaded Date: 08 Feb 2021
- views: 2205
In certain areas, computational results in high precision are desired. For example, one may need to examine eigenvalues, 60 digits after decimal point, to confi...
In certain areas, computational results in high precision are desired. For example, one may need to examine eigenvalues, 60 digits after decimal point, to confirm if a pair of two are not identical. In this seminar, we will talk about a few packages that physicists and chemists might want to use with examples. We will also mention packages that are available for general purposes.
_________________________________________________
This webinar was presented by Ge Baolai (SHARCNET) on February 3, 2021, as a part of a series of regular biweekly General Interest webinars ran by SHARCNET. The webinars cover different high performance computing (HPC) topics, are approximately 45 minutes in length, and are delivered by experts in the relevant fields. Further details can be found on this web page: https://www.sharcnet.ca/help/index.php/Online_Seminars . Subscribe to our twitter account (@SHARCNET) to stay updated about our upcoming webinars.
SHARCNET is a consortium of 19 Canadian academic institutions who share a network of high performance computers (http://www.sharcnet.ca). SHARCNET is a part of Compute Ontario (http://computeontario.ca/) and Compute Canada (https://computecanada.ca).
https://wn.com/Computing_In_Arbitrary_Precision
In certain areas, computational results in high precision are desired. For example, one may need to examine eigenvalues, 60 digits after decimal point, to confirm if a pair of two are not identical. In this seminar, we will talk about a few packages that physicists and chemists might want to use with examples. We will also mention packages that are available for general purposes.
_________________________________________________
This webinar was presented by Ge Baolai (SHARCNET) on February 3, 2021, as a part of a series of regular biweekly General Interest webinars ran by SHARCNET. The webinars cover different high performance computing (HPC) topics, are approximately 45 minutes in length, and are delivered by experts in the relevant fields. Further details can be found on this web page: https://www.sharcnet.ca/help/index.php/Online_Seminars . Subscribe to our twitter account (@SHARCNET) to stay updated about our upcoming webinars.
SHARCNET is a consortium of 19 Canadian academic institutions who share a network of high performance computers (http://www.sharcnet.ca). SHARCNET is a part of Compute Ontario (http://computeontario.ca/) and Compute Canada (https://computecanada.ca).
- published: 08 Feb 2021
- views: 2205
2:21
Arbitrary-precision arithmetic Explanation
- Order: Reorder
- Duration: 2:21
- Uploaded Date: 06 Jun 2024
- views: 0
Welcome to Mixible, your go-to source for comprehensive and informative content covering a broad range of topics from Stack Exchange websites.
Our channel is c...
Welcome to Mixible, your go-to source for comprehensive and informative content covering a broad range of topics from Stack Exchange websites.
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https://wn.com/Arbitrary_Precision_Arithmetic_Explanation
Welcome to Mixible, your go-to source for comprehensive and informative content covering a broad range of topics from Stack Exchange websites.
Our channel is committed to providing you with valuable insights and discussions on various subjects, ensuring that you stay informed about the latest trends and developments in your area of interest.
We offer an extensive library of videos that cover a wide range of topics, including programming, computer science, mathematics, physics, and much more.
Our videos are designed to cater to diverse audiences, ranging from beginners to advanced learners, and are presented in an engaging and easy-to-understand format.
At Mixible, we are dedicated to being a trusted source of information. We base our videos on questions and answers posted on various Stack Exchange sites, including:
- Stack Overflow for programming-related questions
- Super User for computer software and hardware-related questions
- Mathematics for mathematical questions
- Physics for physics-related questions
- Cross Validated for statistics and data analysis-related questions
- Server Fault for server and network-related questions
and many more!
We give credit to the specific threads that inspire our content at the end of each video.
Additionally, you can visit the Stack Exchange website (https://stackexchange.com/) for more information on the topics we cover.
So, if you're looking to expand your knowledge and stay up-to-date with the latest trends and developments, subscribe to Mixible today, and join our community of curious minds.
Thank you for watching!
Link to Stack Overflow: https://stackoverflow.com/
- published: 06 Jun 2024
- views: 0
5:02
Group 6 - High Precision Arithmetic
High Precision Arithmetic is the process of doing arithmetic on large-valued integers or '...
published: 07 Nov 2020
Group 6 - High Precision Arithmetic
Group 6 - High Precision Arithmetic
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- published: 07 Nov 2020
- views: 98
High Precision Arithmetic is the process of doing arithmetic on large-valued integers or 'long integers'. In this video, we will show how to store long integers using a doubly-linked list and how to perform addition using two long integers.
31:29
CppCon 2018: “Multi-Precision Arithmetic for Cryptology in C++, at Run-Time and at Compile-Time”
http://CppCon.org
Niek J. Bouman “Multi-Precision Arithmetic for Cryptology in C++, at Run...
published: 24 Oct 2018
CppCon 2018: “Multi-Precision Arithmetic for Cryptology in C++, at Run-Time and at Compile-Time”
CppCon 2018: “Multi-Precision Arithmetic for Cryptology in C++, at Run-Time and at Compile-Time”
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- published: 24 Oct 2018
- views: 4602
http://CppCon.org
Niek J. Bouman “Multi-Precision Arithmetic for Cryptology in C++, at Run-Time and at Compile-Time”
—
Presentation Slides, PDFs, Source Code and other presenter materials are available at: https://github.com/CppCon/CppCon2018
—
In the talk, I will present a new C++17 library for multi-precision arithmetic for integers in the order of 100--500 bits. Many cryptographic schemes and applications, like elliptic-curve encryption schemes and secure multiparty computation frameworks require multiprecision arithmetic with integers whose bit-lengths lie in that range.
The library is written in “optimizing-compiler-friendly” C++, with an emphasis on the use of fixed-size arrays and particular function-argument-passing styles (including the avoidance of naked pointers) to allow the limbs to be allocated on the stack or even in registers. Depending on the particular functionality, we get close to, or significantly beat the performance of existing libraries for multiprecision arithmetic that employ hand-optimized assembly code.
Beyond the favorable runtime performance, our library is, to the best of the author’s knowledge, the first library that offers big-integer computations during compile-time. For example, when implementing finite-field arithmetic with a fixed modulus, this feature enables the automatic precomputation (at compile time) of the special modulus- dependent constants required for Barrett and Montgomery reduction. Another application is to parse (at compile-time) a base-10-encoded big-integer literal.
In this talk, I will focus on some Modern C++ language features that I've used to write the library and design its API (e.g., std::array, variadic templates, std::integer_sequence, constexpr, user-defined literals, using-declarations and decltype, and combinations thereof). Also, I will show some benchmarks, and will argue that the integer types offered by the library compose well with STL containers or other libraries (like Eigen for matrix/linear algebra operations).
I will also present some results on formal verification of correctness and the "constant-time" property:
- Correctness is verified using a tool named SAW (Software Analysis Workbench), which tries to prove equivalence between the compiled C++ code (represented as LLVM bitcode) and a behavioral specification given in a high-level functional language;
- "Constant-timeness" is a property that is crucial for implementations of cryptographic protocols to prevent timing attacks. In particular, I succeeded to verify my C++ code with "ct-verif", a tool for verifying the constant-time property for C programs (which was, in its original form, incompatible with C++ due to usage of non-ANSI C in one of its header files)
The library is on Github (Apache 2 licensed)
https://github.com/niekbouman/ctbignum
—
Niek J. Bouman, Eindhoven University of Technology
Researcher Secure Multiparty Computation
2017 - now Postdoc TU/e SODA (Scalable Oblivious Data Mining) project, Eindhoven University of Technology, the Netherlands 2016-2017 Senior Researcher Fraud Detection @ ABN AMRO Bank, Amsterdam, the Netherlands 2014-2016 Postdoc at Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland PhD (2012) Quantum Cryptography/Quantum Information Theory from CWI/Universiteit Leiden, the Netherlands BS'05 MS’07 Electrical Engineering from Universiteit Twente, Enschede, the Netherlands
—
Videos Filmed & Edited by Bash Films: http://www.BashFilms.com
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Register Now For CppCon 2022: https://cppcon.org/registration/
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0:25
Arbitrary-Precision Arithmetics on the GPU
by Bernhard Langer (TU Wien, Austria)
Abstract: The majority of computer applications emp...
published: 01 May 2015
Arbitrary-Precision Arithmetics on the GPU
Arbitrary-Precision Arithmetics on the GPU
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- published: 01 May 2015
- views: 918
by Bernhard Langer (TU Wien, Austria)
Abstract: The majority of computer applications employ numerical data types with a fixed amount of precision for their computations. Their limited numerical range and precision are sufficient for most use cases. However, for some purposes, such as cryptography or geometrical computations, the required range and precision can become arbitrarily large. Numerical types that can handle such demands have higher memory requirements and are not natively supported by common hardware, which leads to increased computational complexity. In this paper, we examine how basic arithmetic operations on arbitrary-precision integers can be adapted to many-core architectures in the form of graphics processing units, which are widely available as commodity hardware. Apart from a detailed description of our method, we show superior performance characteristics of our implementation in comparison to state-of-the-art CPU libraries for high computational loads.
Full paper: http://cescg.org/CESCG-2015/papers/Langer-Arbitrary-Precision_Arithmetics_on_the_GPU.pdf
43:11
Mixed precision arithmetic: hardware, algorithms and analysis, Theo Mary
==========
The London Mathematical Society has, since 1865, been the UK's learned society...
published: 24 Nov 2020
Mixed precision arithmetic: hardware, algorithms and analysis, Theo Mary
Mixed precision arithmetic: hardware, algorithms and analysis, Theo Mary
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- published: 24 Nov 2020
- views: 871
==========
The London Mathematical Society has, since 1865, been the UK's learned society for the advancement, dissemination and promotion of mathematical knowledge. Our mission is to advance mathematics through our members and the broader scientific community worldwide.
For further information:
► Website: https://www.lms.ac.uk
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5:46
Why Is This Happening?! Floating Point Approximation
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published: 23 Nov 2022
Why Is This Happening?! Floating Point Approximation
Why Is This Happening?! Floating Point Approximation
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- published: 23 Nov 2022
- views: 135233
⭐ Join my Patreon: https://www.patreon.com/b001io
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0:41
Arbitrary-precision arithmetic Top # 5 Facts
Arbitrary-precision arithmetic Top # 5 Facts
published: 29 Oct 2015
Arbitrary-precision arithmetic Top # 5 Facts
Arbitrary-precision arithmetic Top # 5 Facts
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- published: 29 Oct 2015
- views: 206
Arbitrary-precision arithmetic Top # 5 Facts
18:15
Arbitrary-precision arithmetic
In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multip...
published: 30 Dec 2015
Arbitrary-precision arithmetic
Arbitrary-precision arithmetic
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- published: 30 Dec 2015
- views: 3009
In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are limited only by the available memory of the host system. This contrasts with the faster fixed-precision arithmetic found in most arithmetic logic unit hardware, which typically offers between 8 and 64 bits of precision.
Several modern programming languages have built-in support for bignums, and others have libraries available for arbitrary-precision integer and floating-point math. Rather than store values as a fixed number of binary bits related to the size of the processor register, these implementations typically use variable-length arrays of digits.
This video is targeted to blind users.
Attribution:
Article text available under CC-BY-SA
Creative Commons image source in video
18:36
Simple Algorithm for Arbitrary-Precision Integer Division
Writing a set of steps to divide two very large numbers isn't as easy as it sounds!
For mo...
published: 23 Oct 2015
Simple Algorithm for Arbitrary-Precision Integer Division
Simple Algorithm for Arbitrary-Precision Integer Division
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- published: 23 Oct 2015
- views: 5753
Writing a set of steps to divide two very large numbers isn't as easy as it sounds!
For more information, go to http://justinparrtech.com and search for INTEGER DIVISION.
51:44
Computing in arbitrary precision
In certain areas, computational results in high precision are desired. For example, one ma...
published: 08 Feb 2021
Computing in arbitrary precision
Computing in arbitrary precision
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- published: 08 Feb 2021
- views: 2205
In certain areas, computational results in high precision are desired. For example, one may need to examine eigenvalues, 60 digits after decimal point, to confirm if a pair of two are not identical. In this seminar, we will talk about a few packages that physicists and chemists might want to use with examples. We will also mention packages that are available for general purposes.
_________________________________________________
This webinar was presented by Ge Baolai (SHARCNET) on February 3, 2021, as a part of a series of regular biweekly General Interest webinars ran by SHARCNET. The webinars cover different high performance computing (HPC) topics, are approximately 45 minutes in length, and are delivered by experts in the relevant fields. Further details can be found on this web page: https://www.sharcnet.ca/help/index.php/Online_Seminars . Subscribe to our twitter account (@SHARCNET) to stay updated about our upcoming webinars.
SHARCNET is a consortium of 19 Canadian academic institutions who share a network of high performance computers (http://www.sharcnet.ca). SHARCNET is a part of Compute Ontario (http://computeontario.ca/) and Compute Canada (https://computecanada.ca).
2:21
Arbitrary-precision arithmetic Explanation
Welcome to Mixible, your go-to source for comprehensive and informative content covering a...
published: 06 Jun 2024
Arbitrary-precision arithmetic Explanation
Arbitrary-precision arithmetic Explanation
- Report rights infringement
- published: 06 Jun 2024
- views: 0
Welcome to Mixible, your go-to source for comprehensive and informative content covering a broad range of topics from Stack Exchange websites.
Our channel is committed to providing you with valuable insights and discussions on various subjects, ensuring that you stay informed about the latest trends and developments in your area of interest.
We offer an extensive library of videos that cover a wide range of topics, including programming, computer science, mathematics, physics, and much more.
Our videos are designed to cater to diverse audiences, ranging from beginners to advanced learners, and are presented in an engaging and easy-to-understand format.
At Mixible, we are dedicated to being a trusted source of information. We base our videos on questions and answers posted on various Stack Exchange sites, including:
- Stack Overflow for programming-related questions
- Super User for computer software and hardware-related questions
- Mathematics for mathematical questions
- Physics for physics-related questions
- Cross Validated for statistics and data analysis-related questions
- Server Fault for server and network-related questions
and many more!
We give credit to the specific threads that inspire our content at the end of each video.
Additionally, you can visit the Stack Exchange website (https://stackexchange.com/) for more information on the topics we cover.
So, if you're looking to expand your knowledge and stay up-to-date with the latest trends and developments, subscribe to Mixible today, and join our community of curious minds.
Thank you for watching!
Link to Stack Overflow: https://stackoverflow.com/
Significant figures
The significant figures of a number are digits that carry meaning contributing to its measurement resolution. This includes all digits except:
Significance arithmetic are approximate rules for roughly maintaining significance throughout a computation. The more sophisticated scientific rules are known as propagation of uncertainty.
Numbers are often rounded to avoid reporting insignificant figures. For example, it would create false precision to express a measurement as 12,345.00 kg (which has seven significant figures) if the scales only measured to the nearest gram and gave a reading of 12,345 kg (which has five significant figures) . Numbers can also be rounded merely for simplicity rather than to indicate a given precision of measurement, for example to make them faster to pronounce in news broadcasts.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Significant_figures
Group 6 - High Precision Arithmetic...
CppCon 2018: “Multi-Precision Arithmetic for Crypt...
Arbitrary-Precision Arithmetics on the GPU...
Mixed precision arithmetic: hardware, algorithms a...
Why Is This Happening?! Floating Point Approximati...
Arbitrary-precision arithmetic Top # 5 Facts...
Arbitrary-precision arithmetic...
Simple Algorithm for Arbitrary-Precision Integer D...
Computing in arbitrary precision...
Arbitrary-precision arithmetic Explanation...
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On The Road: Falkirk ascent is driven by hopes and fears... but the glass of ...
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Low-energy ion implantation enables 2D lateral p-n junction construction
The basic idea of atomic level manufacturing is to process and manipulate matters with atomic level precision, which will greatly reduce the power consumption of the chip and achieve a huge increase in the chip's arithmetic power.
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Consequently, extreme care should be taken with thetrigonometric functions to avoid subtraction cancellations, which would lead to a serious loss of precision and produce catastrophic results, particularly with a poor arithmetic precision.
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Crunching Numbers: Accessing The Calculator On IPhone 12
The Calculator app on the iPhone 12 is a versatile tool that goes beyond basic arithmetic operations ... Basic Arithmetic Operations. The Calculator app on the iPhone 12 offers a seamless platform for performing basic arithmetic operations.
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RSA and other crypto systems vulnerable to side-channel attack
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