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Multi-modular Arithmetic
A residue number system or residue numeral system (RNS) is a numeral system representing integers by their values modular arithmetic, modulo several pairwise coprime integers called the moduli. This representation is allowed by the Chinese remainder theorem, which asserts that, if is the product of the moduli, there is, in an interval of length , exactly one integer having any given set of modular values. Using a residue numeral system for arithmetic operations is also called multi-modular arithmetic. Multi-modular arithmetic is widely used for computation with large integers, typically in linear algebra, because it provides faster computation than with the usual numeral systems, even when the time for converting between numeral systems is taken into account. Other applications of multi-modular arithmetic include polynomial greatest common divisor#Modular GCD algorithm, polynomial greatest common divisor, Gröbner basis computation and cryptography. Definition A residue numeral ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer Overflow
In computer programming, an integer overflow occurs when an arithmetic operation on integers attempts to create a numeric value that is outside of the range that can be represented with a given number of digits – either higher than the maximum or lower than the minimum representable value. The most common result of an overflow is that the least significant representable digits of the result are stored; the result is said to ''wrap'' around the maximum (i.e. modulo a power of the radix, usually two in modern computers, but sometimes ten or other number). On some processors like graphics processing units (GPUs) and digital signal processors (DSPs) which support saturation arithmetic, overflowed results would be ''clamped'', i.e. set to the minimum value in the representable range if the result is below the minimum and set to the maximum value in the representable range if the result is above the maximum, rather than wrapped around. An overflow condition may give results lead ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Journal Of Computer Mathematics
The ''International Journal of Computer Mathematics'' is a monthly peer-reviewed scientific journal covering numerical analysis and scientific computing. It was established in 1964 and is published by Taylor & Francis. The editors-in-chief are Choi-Hong Lai (University of Greenwich), Abdul Khaliq (Middle Tennessee State University), and Qin (Tim) Sheng (Baylor University). The collaborative sister journal ''International Journal of Computer Mathematics: Computer Systems Theory'', covering the theory of computing and computer systems was established in 2016. Abstracting and indexing The journal is abstracted and indexed in the Science Citation Index Expanded, MathSciNet, and Scopus. According to the ''Journal Citation Reports'', the journal has a 2018 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a type of journal ranking. Journals with higher impact factor values are considered more prestigious or important within their field. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IEEE Press
The Institute of Electrical and Electronics Engineers (IEEE) is an American 501(c)(3) public charity professional organization for electrical engineering, electronics engineering, and other related disciplines. The IEEE has a corporate office in New York City and an operations center in Piscataway, New Jersey. The IEEE was formed in 1963 as an amalgamation of the American Institute of Electrical Engineers and the Institute of Radio Engineers. History The IEEE traces its founding to 1884 and the American Institute of Electrical Engineers. In 1912, the rival Institute of Radio Engineers was formed. Although the AIEE was initially larger, the IRE attracted more students and was larger by the mid-1950s. The AIEE and IRE merged in 1963. The IEEE is headquartered in New York City, but most business is done at the IEEE Operations Center in Piscataway, New Jersey, opened in 1975. The Australian Section of the IEEE existed between 1972 and 1985, after which it split into state- and te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
McGraw-Hill
McGraw Hill is an American education science company that provides educational content, software, and services for students and educators across various levels—from K-12 to higher education and professional settings. They produce textbooks, digital learning tools, and adaptive technology to enhance learning experiences and outcomes. It is one of the "big three" educational publishers along with Houghton Mifflin Harcourt and Pearson Education. McGraw Hill also publishes reference and trade publications for the medical, business, and engineering professions. Formerly a division of The McGraw Hill Companies (later renamed McGraw Hill Financial, now S&P Global), McGraw Hill Education was divested and acquired by Apollo Global Management in March 2013 for $2.4 billion in cash. McGraw Hill was sold in 2021 to Platinum Equity for $4.5 billion. History McGraw Hill was founded in 1888, when James H. McGraw, co-founder of McGraw Hill, purchased the ''American Journal of Railway ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IEEE Access
IEEE Access is a peer-reviewed open-access scientific journal published by the Institute of Electrical and Electronics Engineers (IEEE). It was established in 2013 and covers all IEEE fields of interest. The founding editor-in-chief was Michael Pecht (University of Maryland) and the current editor-in-chief is Derek Abbott ( University of Adelaide). The journal won a PROSE Award in 2015 for the best new journal in science, technology, engineering, and mathematics. Special sections The journal hosts special sections that highlight a specific topic of general IEEE interest. Associate editors propose a concentration area that emphasizes applications-oriented and interdisciplinary topics. Together with the editorial staff a "Call for Papers" is then sent to academic and industrial researchers soliciting the submissions of manuscripts that identify and discuss technical challenges and recent results on the topic of that section. Abstracting and indexing The journal is abstracted and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oxford University Press
Oxford University Press (OUP) is the publishing house of the University of Oxford. It is the largest university press in the world. Its first book was printed in Oxford in 1478, with the Press officially granted the legal right to print books by decree in 1586. It is the second-oldest university press after Cambridge University Press, which was founded in 1534. It is a department of the University of Oxford. It is governed by a group of 15 academics, the Delegates of the Press, appointed by the Vice Chancellor, vice-chancellor of the University of Oxford. The Delegates of the Press are led by the Secretary to the Delegates, who serves as OUP's chief executive and as its major representative on other university bodies. Oxford University Press has had a similar governance structure since the 17th century. The press is located on Walton Street, Oxford, Walton Street, Oxford, opposite Somerville College, Oxford, Somerville College, in the inner suburb of Jericho, Oxford, Jericho. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reduced Residue System
In mathematics, a subset ''R'' of the integers is called a reduced residue system modulo ''n'' if: #gcd(''r'', ''n'') = 1 for each ''r'' in ''R'', #''R'' contains φ(''n'') elements, #no two elements of ''R'' are congruent modulo ''n''. Here φ denotes Euler's totient function. A reduced residue system modulo ''n'' can be formed from a complete residue system modulo ''n'' by removing all integers not relatively prime to ''n''. For example, a complete residue system modulo 12 is . The so-called totatives 1, 5, 7 and 11 are the only integers in this set which are relatively prime to 12, and so the corresponding reduced residue system modulo 12 is . The cardinality of this set can be calculated with the totient function: φ(12) = 4. Some other reduced residue systems modulo 12 are: * * * * Facts *Every number in a reduced residue system modulo ''n'' is a generator for the additive group of integers modulo ''n''. *A reduced residue system modulo ''n'' is a group under multipli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Covering System
In mathematics, a covering system (also called a complete residue system) is a collection :\ of finitely many residue classes : a_i\pmod = \, whose union contains every integer. Examples and definitions The notion of covering system was introduced by Paul Erdős in the early 1930s. The following are examples of covering systems: # \, # \, # \. A covering system is called ''disjoint'' (or ''exact'') if no two members overlap. A covering system is called ''distinct'' (or ''incongruent'') if all the moduli n_i are different (and bigger than 1). Hough and Nielsen (2019) proved that any distinct covering system has a modulus that is divisible by either 2 or 3. A covering system is called ''irredundant'' (or ''minimal'') if all the residue classes are required to cover the integers. The first two examples are disjoint. The third example is distinct. A system (i.e., an unordered multi-set) :\ of finitely many residue classes is called an m-cover if it covers every integer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Arithmetic
Computer arithmetic is the scientific field that deals with representation of numbers on computers and corresponding implementations of the arithmetic operations. It includes: *Fixed-point arithmetic *Floating-point arithmetic *Interval arithmetic *Arbitrary-precision arithmetic *Modular arithmetic ** Multi-modular arithmetic ** ''p''-adic arithmetic, consisting of computing modulo a single prime number and retrieving the integer or rational result by using Hensel lifting **Finite field arithmetic * Matrix arithmetic In the cases where the size of the representation of a number is fixed (fixed-point, floating-point and interval arithmetic), the main concern is to control the computational error, as far as possible; see, for example IEEE 754. In the other cases, where an exact result should be provided, the main concern is the practical efficiency, which is optimized by combining improvements of computational complexity In computer science, the computational complexity or si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
