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Class Library For Numbers
Class Library for Numbers (CLN) is a free library for arbitrary precision arithmetic. It operates on signed integers, rational numbers, floating point numbers, complex numbers, modular numbers, and univariate polynomials. Its implementation programming language is C++. Details CLN uses object oriented techniques and operator overloading to achieve a natural algebraic syntax: The sum ''x'' of two variables ''a'' and ''b'' is written as ''x'' = ''a'' + ''b'', as opposed to the function sum(&''x'', ''a'', ''b''). CLN uses class inheritance to model the natural subsets of the available number types: E.g. the integer class is a subtype of the rational class, just as the integer numbers are a subset of the rational numbers. The complex numbers and all its subtypes behave exactly like the types of numbers known to the Common Lisp language, giving CLN another meaning: it becomes an abbreviation of ''Common Lisp Numbers''. Due to this, CLN can be and is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
C++11
C++11 is a version of a joint technical standard, ISO/IEC 14882, by the International Organization for Standardization (ISO) and International Electrotechnical Commission (IEC), for the C++ programming language. C++11 replaced the prior version of the C++ standard, named C++03, and was later replaced by C++14. The name follows the tradition of naming language versions by the publication year of the specification, though it was formerly named ''C++0x'' because it was expected to be published before 2010. Although one of the design goals was to prefer changes to the libraries over changes to the core language, C++11 does make several additions to the core language. Areas of the core language that were significantly improved include multithreading support, generic programming support, uniform initialization, and performance. Significant changes were also made to the C++ Standard Library, incorporating most of the C++ Technical Report 1 (TR1) libraries, except the library ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inheritance (object-oriented Programming)
In object-oriented programming, inheritance is the mechanism of basing an Object (computer science), object or Class (computer programming), class upon another object (Prototype-based programming, prototype-based inheritance) or class (Class-based programming, class-based inheritance), retaining similar implementation. Also defined as deriving new classes (#Subclasses and superclasses, sub classes) from existing ones such as super class or Fragile base class, base class and then forming them into a hierarchy of classes. In most class-based object-oriented languages like C++, an object created through inheritance, a "child object", acquires all the properties and behaviors of the "parent object", with the exception of: Constructor (object-oriented programming), constructors, destructors, operator overloading, overloaded operators and friend functions of the base class. Inheritance allows programmers to create classes that are built upon existing classes, to specify a new implementat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
C++ Numerical Libraries
C, or c, is the third letter of the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''cee'' (pronounced ), plural ''cees''. History "C" comes from the same letter as "G". The Semites named it gimel. The sign is possibly adapted from an Egyptian hieroglyph for a staff sling, which may have been the meaning of the name ''gimel''. Another possibility is that it depicted a camel, the Semitic name for which was ''gamal''. Barry B. Powell, a specialist in the history of writing, states "It is hard to imagine how gimel = "camel" can be derived from the picture of a camel (it may show his hump, or his head and neck!)". In the Etruscan language, plosive consonants had no contrastive voicing, so the Greek ' Γ' (Gamma) was adopted into the Etruscan alphabet to represent . Already in the Western Greek alphabet, Gamma first took a '' form in Early Etruscan, then '' in Classical E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Software Programmed In C++
Free may refer to: Concept * Freedom, the ability to act or change without constraint or restriction * Emancipate, attaining civil and political rights or equality * Free (''gratis''), free of charge * Gratis versus libre, the difference between the two common meanings of the adjective "free". Computing * Free (programming), a function that releases dynamically allocated memory for reuse * Free software, software usable and distributable with few restrictions and no payment *, an emoji in the Enclosed Alphanumeric Supplement block. Mathematics * Free object ** Free abelian group ** Free algebra ** Free group ** Free module ** Free semigroup * Free variable People * Free (surname) * Free (rapper) (born 1968), or Free Marie, American rapper and media personality * Free, a pseudonym for the activist and writer Abbie Hoffman * Free (active 2003–), American musician in the band FreeSol Arts and media Film and television * ''Free'' (film), a 2001 American dramedy * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GiNaC
GiNaC is a free computer algebra system released under the GNU General Public License. The name is a recursive acronym for "GiNaC is Not a CAS" (Computer Algebra System). This is similar to the GNU acronym "GNU's not Unix". What distinguishes GiNaC from most other computer algebra systems is that it does not provide a high-level interface for user interaction. Rather, it encourages its users to write symbolic algorithms directly in C++, which is GiNaC's implementation programming language. The algebraic syntax is achieved in C++ through the use of operator overloading. The name GiNaC is also explained by its developers' perception that most "computer algebra systems" put too much emphasis on a high-level interface and too little on interoperability. GiNaC uses the CLN library for implementing arbitrary-precision arithmetic. Symbolically, it can do multivariate polynomial arithmetic, factor polynomials, compute GCDs, expand series, and compute with matrices. It is equipped t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Garbage Collection (computer Science)
In computer science, garbage collection (GC) is a form of automatic memory management. The ''garbage collector'' attempts to reclaim memory that was allocated by the program, but is no longer referenced; such memory is called ''garbage (computer science), garbage''. Garbage collection was invented by American computer scientist John McCarthy (computer scientist), John McCarthy around 1959 to simplify manual memory management in Lisp (programming language), Lisp. Garbage collection relieves the programmer from doing manual memory management, where the programmer specifies what objects to de-allocate and return to the memory system and when to do so. Other, similar techniques include stack-based memory allocation, stack allocation, region inference, and memory ownership, and combinations thereof. Garbage collection may take a significant proportion of a program's total processing time, and affect computer performance, performance as a result. Resources other than memory, such a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reference Counting
In computer science, reference counting is a programming technique of storing the number of references, pointers, or handles to a resource, such as an object, a block of memory, disk space, and others. In garbage collection algorithms, reference counts may be used to deallocate objects that are no longer needed. Advantages and disadvantages The main advantage of the reference counting over tracing garbage collection is that objects are reclaimed ''as soon as'' they can no longer be referenced, and in an incremental fashion, without long pauses for collection cycles and with clearly defined lifetime of every object. In real-time applications or systems with limited memory, this is important to maintain responsiveness. Reference counting is also among the simplest forms of memory management to implement. It also allows for effective management of non-memory resources such as operating system objects, which are often much scarcer than memory (tracing garbage collection systems ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Constants
A mathematical constant is a number whose value is fixed by an unambiguous definition, often referred to by a special symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. Constants arise in many areas of mathematics, with constants such as and occurring in such diverse contexts as geometry, number theory, statistics, and calculus. Some constants arise naturally by a fundamental principle or intrinsic property, such as the ratio between the circumference and diameter of a circle (). Other constants are notable more for historical reasons than for their mathematical properties. The more popular constants have been studied throughout the ages and computed to many decimal places. All named mathematical constants are definable numbers, and usually are also computable numbers ( Chaitin's constant being a significant exception). Basic mathematical constants These are constants which one is likely to enco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Splitting
In mathematics, binary splitting is a technique for speeding up numerical evaluation of many types of series with rational terms. In particular, it can be used to evaluate hypergeometric series at rational points. Method Given a series :S(a,b) = \sum_^b \frac where ''pn'' and ''qn'' are integers, the goal of binary splitting is to compute integers ''P''(''a'', ''b'') and ''Q''(''a'', ''b'') such that :S(a,b) = \frac{Q(a,b)}. The splitting consists of setting ''m'' = ''a'' + ''b'')/2and recursively computing ''P''(''a'', ''b'') and ''Q''(''a'', ''b'') from ''P''(''a'', ''m''), ''P''(''m'', ''b''), ''Q''(''a'', ''m''), and ''Q''(''m'', ''b''). When ''a'' and ''b'' are sufficiently close, ''P''(''a'', ''b'') and ''Q''(''a'', ''b'') can be computed directly from ''pa...pb'' and ''qa...qb''. Comparison with other methods Binary splitting requires more memory than direct term-by-term summation, but is asymptotically faster since the sizes of all occurring subproducts are re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schönhage–Strassen Algorithm
The Schönhage–Strassen algorithm is an asymptotically fast multiplication algorithm for large integers, published by Arnold Schönhage and Volker Strassen in 1971. It works by recursively applying fast Fourier transform (FFT) over the integers modulo 2^n + 1. The run-time bit complexity to multiply two -digit numbers using the algorithm is O(n \cdot \log n \cdot \log \log n) in big notation. The Schönhage–Strassen algorithm was the asymptotically fastest multiplication method known from 1971 until 2007. It is asymptotically faster than older methods such as Karatsuba and Toom–Cook multiplication, and starts to outperform them in practice for numbers beyond about 10,000 to 100,000 decimal digits. In 2007, Martin Fürer published an algorithm with faster asymptotic complexity. In 2019, David Harvey and Joris van der Hoeven demonstrated that multi-digit multiplication has theoretical O(n\log n) complexity; however, their algorithm has constant factors which make it im ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inner Loop
In computer programs, an important form of control flow is the Loop (computing), loop which causes a block of code to be executed more than once. A common idiom is to have a loop Nested loop, nested inside another loop, with the contained loop being commonly referred to as the inner loop. Program optimization Because the entire inner loop is performed for each iteration of the outer loop, loop optimization, optimizations of the inner loop will have much greater effect than optimizations of the outer loop. In many languages there are at least two types of loops – for loop, for loops and while loop, while loops – and they can be nested within each other. Tosin P. Adewumi has shown that performance of a while loop with an inner for loop is better than of a while loop without the inner for loop. It was observed that more computations are performed per unit time when an inner for loop is involved than otherwise. This implies, given the same number of computations to perform, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GNU Multi-Precision Library
GNU ( ) is an extensive collection of free software (394 packages ), which can be used as an operating system or can be used in parts with other operating systems. The use of the completed GNU tools led to the family of operating systems popularly known as Linux. Most of GNU is licensed under the GNU Project's own General Public License ( GPL). GNU is also the project within which the free software concept originated. Richard Stallman, the founder of the project, views GNU as a "technical means to a social end". Relatedly, Lawrence Lessig states in his introduction to the second edition of Stallman's book '' Free Software, Free Society'' that in it Stallman has written about "the social aspects of software and how Free Software can create community and social justice". Name ''GNU'' is a recursive acronym for "GNU's Not Unix!", chosen because GNU's design is Unix-like, but differs from Unix by being free software and containing no Unix code. Stallman chose the name by usin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
