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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 used ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
C++11
C++11 is a version of the ISO/IEC 14882 standard for the C++ programming language. C++11 replaced the prior version of the C++ standard, called 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 of mathematical special functions. C++11 was published as ''ISO/IEC 14882:2011'' in September 2011 and is available for a fee. The worki ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operator Overloading
In computer programming, operator overloading, sometimes termed ''operator ad hoc polymorphism'', is a specific case of polymorphism, where different operators have different implementations depending on their arguments. Operator overloading is generally defined by a programming language, a programmer, or both. Rationale Operator overloading is syntactic sugar, and is used because it allows programming using notation nearer to the target domain and allows user-defined types a similar level of syntactic support as types built into a language. It is common, for example, in scientific computing, where it allows computing representations of mathematical objects to be manipulated with the same syntax as on paper. Operator overloading does not change the expressive power of a language (with functions), as it can be emulated using function calls. For example, consider variables , and of some user-defined type, such as matrices: In a language that supports operator overloading, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Software Programmed In C++
Free may refer to: Concept * Freedom, having the ability to do something, without having to obey anyone/anything * Freethought, a position that beliefs should be formed only on the basis of logic, reason, and empiricism * Emancipate, to procure political rights, as for a disenfranchised group * Free will, control exercised by rational agents over their actions and decisions * Free of charge, also known as gratis. See Gratis vs libre. Computing * Free (programming), a function that releases dynamically allocated memory for reuse * Free format, a file format which can be used without restrictions * Free software, software usable and distributable with few restrictions and no payment * Freeware, a broader class of software available at no cost 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 personal ... [...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 which was allocated by the program, but is no longer referenced; such memory is called '' garbage''. Garbage collection was invented by American computer scientist John McCarthy around 1959 to simplify manual memory management in 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 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 performance as a result. Resources other than memory, such as network sockets, database handles, windows, file descriptors, and device descriptors, are not typically handled by garbage collection, but ... [...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 us ... [...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. It was developed by Arnold Schönhage and Volker Strassen in 1971.A. Schönhage and V. Strassen,Schnelle Multiplikation großer Zahlen, ''Computing'' 7 (1971), pp. 281–292. The run-time bit complexity is, in big O notation, O(n \cdot \log n \cdot \log \log n) for two ''n''-digit numbers. The algorithm uses recursive fast Fourier transforms in rings with 2''n''+1 elements, a specific type of number theoretic transform. The Schönhage–Strassen algorithm was the asymptotically fastest multiplication method known from 1971 until 2007, when a new method, Fürer's algorithm, was announced with lower asymptotic complexity, and is used in the Basic Polynomial Algebra Subprograms (BPAS) open source library. The algorithm does not adapt for polynomials over finite fields though. The current best multiplication algorithm in terms of asymptotic complexity is by David Harvey and Jor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inner Loop , United States
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Inner loop may refer to: *Inner loop in computer programs *Inner Loop (Phoenix), a section of Interstate 10 in downtown Phoenix, Arizona, United States *Inner Loop (Rochester), an expressway around downtown Rochester, New York, United States * Inner Loop (Washington, D.C.), a previously proposed freeway loop in Washington, D.C., United States *Inner–outer directions, where "inner loop" is used to describe the clockwise traveling lanes of a roadway **This usage of "inner loop" is commonly applied to the clockwise roadway of Interstate 495 (Capital Beltway) *Interstate 610 (Texas), the innermost highway loop around the central area of Houston, Texas Houston (; ) is the most populous city in Texas, the most populous city in the Southern United States, the fourth-most populous city in the United States, and the sixth-most populous city in North America, with a population of 2,304,580 in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GNU Multi-Precision Library
GNU Multiple Precision Arithmetic Library (GMP) is a free library for arbitrary-precision arithmetic, operating on signed integers, rational numbers, and floating-point numbers. There are no practical limits to the precision except the ones implied by the available memory (operands may be of up to 232−1 bits on 32-bit machines and 237 bits on 64-bit machines). GMP has a rich set of functions, and the functions have a regular interface. The basic interface is for C, but wrappers exist for other languages, including Ada, C++, C#, Julia, .NET, OCaml, Perl, PHP, Python, R, Ruby, and Rust. Prior to 2008, Kaffe, a Java virtual machine, used GMP to support Java built-in arbitrary precision arithmetic. Shortly after, GMP support was added to GNU Classpath. The main target applications of GMP are cryptography applications and research, Internet security applications, and computer algebra systems. GMP aims to be faster than any other bignum library for all operand sizes. Some impo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Algebra System
A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The development of the computer algebra systems in the second half of the 20th century is part of the discipline of "computer algebra" or "symbolic computation", which has spurred work in algorithms over mathematical objects such as polynomials. Computer algebra systems may be divided into two classes: specialized and general-purpose. The specialized ones are devoted to a specific part of mathematics, such as number theory, group theory, or teaching of elementary mathematics. General-purpose computer algebra systems aim to be useful to a user working in any scientific field that requires manipulation of mathematical expressions. To be useful, a general-purpose computer algebra system must include various features such as: *a user interface allo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Common Lisp
Common Lisp (CL) is a dialect of the Lisp programming language, published in ANSI standard document ''ANSI INCITS 226-1994 (S20018)'' (formerly ''X3.226-1994 (R1999)''). The Common Lisp HyperSpec, a hyperlinked HTML version, has been derived from the ANSI Common Lisp standard. The Common Lisp language was developed as a standardized and improved successor of Maclisp. By the early 1980s several groups were already at work on diverse successors to MacLisp: Lisp Machine Lisp (aka ZetaLisp), Spice Lisp, NIL and S-1 Lisp. Common Lisp sought to unify, standardise, and extend the features of these MacLisp dialects. Common Lisp is not an implementation, but rather a language specification. Several implementations of the Common Lisp standard are available, including free and open-source software and proprietary products. Common Lisp is a general-purpose, multi-paradigm programming language. It supports a combination of procedural, functional, and object-oriented programming paradigms ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subset
In mathematics, Set (mathematics), set ''A'' is a subset of a set ''B'' if all Element (mathematics), elements of ''A'' are also elements of ''B''; ''B'' is then a superset of ''A''. It is possible for ''A'' and ''B'' to be equal; if they are unequal, then ''A'' is a proper subset of ''B''. The relationship of one set being a subset of another is called inclusion (or sometimes containment). ''A'' is a subset of ''B'' may also be expressed as ''B'' includes (or contains) ''A'' or ''A'' is included (or contained) in ''B''. A ''k''-subset is a subset with ''k'' elements. The subset relation defines a partial order on sets. In fact, the subsets of a given set form a Boolean algebra (structure), Boolean algebra under the subset relation, in which the join and meet are given by Intersection (set theory), intersection and Union (set theory), union, and the subset relation itself is the Inclusion (Boolean algebra), Boolean inclusion relation. Definition If ''A'' and ''B'' are sets and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
