|
Linear Congruential Generator
A linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear equation. The method represents one of the oldest and best-known pseudorandom number generator algorithms. The theory behind them is relatively easy to understand, and they are easily implemented and fast, especially on computer hardware which can provide modular arithmetic by storage-bit truncation. The generator is defined by the recurrence relation: :X_ = \left( a X_n + c \right)\bmod m where X is the sequence of pseudo-random values, and : m,\, 0 |
Linear Congruential Generator Visualisation
Linearity is the property of a mathematical relationship (''function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear relationship of voltage and current in an electrical conductor (Ohm's law), and the relationship of mass and weight. By contrast, more complicated relationships are ''nonlinear''. Generalized for functions in more than one dimension, linearity means the property of a function of being compatible with addition and scaling, also known as the superposition principle. The word linear comes from Latin ''linearis'', "pertaining to or resembling a line". In mathematics In mathematics, a linear map or linear function ''f''(''x'') is a function that satisfies the two properties: * Additivity: . * Homogeneity of degree 1: for all α. These properties are known as the superposition principle. In this definition, ''x'' is not necessarily a real nu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mersenne Prime
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. If is a composite number then so is . Therefore, an equivalent definition of the Mersenne primes is that they are the prime numbers of the form for some prime . The exponents which give Mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31, ... and the resulting Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, ... . Numbers of the form without the primality requirement may be called Mersenne numbers. Sometimes, however, Mersenne numbers are defined to have the additional requirement that be prime. The smallest composite Mersenne number with prime exponent ''n'' is . Mersenne primes were studied in antiquity because of their close connection to perfect numbers: the Euclid–Euler theorem as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Glibc
The GNU C Library, commonly known as glibc, is the GNU Project's implementation of the C standard library. Despite its name, it now also directly supports C++ (and, indirectly, other programming languages). It was started in the 1980s by the Free Software Foundation (FSF) for the GNU operating system. Released under the GNU Lesser General Public License, glibc is free software. The GNU C Library project provides the core libraries for the GNU system, as well as many systems that use Linux as the kernel. These libraries provide critical APIs including ISO C11, POSIX.1-2008, BSD, OS-specific APIs and more. These APIs include such foundational facilities as open, read, write, malloc, printf, getaddrinfo, dlopen, pthread_create, crypt, login, exit and more. History The glibc project was initially written mostly by Roland McGrath, working for the Free Software Foundation (FSF) in the 1980s as a teenager. In February 1988, FSF described glibc as having nearly completed the func ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Borland
Borland Software Corporation was a computer technology company founded in 1983 by Niels Jensen, Ole Henriksen, Mogens Glad and Philippe Kahn. Its main business was the development and sale of software development and software deployment products. Borland was first headquartered in Scotts Valley, California, then in Cupertino, California and then in Austin, Texas. In 2009 the company became a full subsidiary of the British firm Micro Focus International plc. History The 1980s: Foundations Borland Ltd. was founded in August 1981 by three Danish citizens, Niels Jensen, Ole Henriksen, and Mogens Glad, to develop products like Word Index for the CP/M operating system using an off-the-shelf company. However, the response to the company's products at the CP/M-82 show in San Francisco showed that a U.S. company would be needed to reach the American market. They met Philippe Kahn, who had just moved to Silicon Valley, and who had been a key developer of the Micral. The three Danes h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Recipes
''Numerical Recipes'' is the generic title of a series of books on algorithms and numerical analysis by William H. Press, Saul A. Teukolsky, William T. Vetterling and Brian P. Flannery. In various editions, the books have been in print since 1986. The most recent edition was published in 2007. Overview The ''Numerical Recipes'' books cover a range of topics that include both classical numerical analysis ( interpolation, integration, linear algebra, differential equations, and so on), signal processing ( Fourier methods, filtering), statistical treatment of data, and a few topics in machine learning (hidden Markov model, support vector machines). The writing style is accessible and has an informal tone. The emphasis is on understanding the underlying basics of techniques, not on the refinements that may, in practice, be needed to achieve optimal performance and reliability. Few results are proved with any degree of rigor, although the ideas behind proofs are often sketched, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ZX81
The ZX81 is a home computer that was produced by Sinclair Research and manufactured in Dundee, Scotland, by Timex Corporation. It was launched in the United Kingdom in March 1981 as the successor to Sinclair's ZX80 and designed to be a low-cost introduction to home computing for the general public. It was hugely successful; more than 1.5 million units were sold. In the United States it was initially sold as the ZX-81 under licence by Timex. Timex later produced its own versions of the ZX81: the Timex Sinclair 1000 and Timex Sinclair 1500. Unauthorized ZX81 clones were produced in several countries. The ZX81 was designed to be small, simple, and above all, inexpensive, with as few components as possible. Video output is to a television set rather than a dedicated monitor. Programs and data are loaded and saved onto compact audio cassettes. It uses only four silicon chips and a mere 1 KB of memory. It has no power switch or moving parts, with the exception of a VHF ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compiler
In computing, a compiler is a computer program that translates computer code written in one programming language (the ''source'' language) into another language (the ''target'' language). The name "compiler" is primarily used for programs that translate source code from a high-level programming language to a low-level programming language (e.g. assembly language, object code, or machine code) to create an executable program. Compilers: Principles, Techniques, and Tools by Alfred V. Aho, Ravi Sethi, Jeffrey D. Ullman - Second Edition, 2007 There are many different types of compilers which produce output in different useful forms. A ''cross-compiler'' produces code for a different CPU or operating system than the one on which the cross-compiler itself runs. A ''bootstrap compiler'' is often a temporary compiler, used for compiling a more permanent or better optimised compiler for a language. Related software include, a program that translates from a low-level language to a h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Runtime Library
In computer programming, a runtime library is a set of low-level routines used by a compiler to invoke some of the behaviors of a runtime environment, by inserting calls to the runtime library into compiled executable binary. The runtime environment implements the execution model, built-in functions, and other fundamental behaviors of a programming language. During execution (run time) of that computer program, execution of those calls to the runtime library cause communication between the executable binary and the runtime environment. A runtime library often includes built-in functions for memory management or exception handling. Therefore, a runtime library is always specific to the platform and compiler. The runtime library may implement a portion of the runtime environment's behavior, but if one reads the code of the calls available, they are typically only thin wrappers that simply package information, and send it to the runtime environment or operating system. However, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spectral Test
The spectral test is a statistical test for the quality of a class of pseudorandom number generators (PRNGs), the linear congruential generators (LCGs). LCGs have a property that when plotted in 2 or more dimensions, lines or hyperplanes will form, on which all possible outputs can be found. The spectral test compares the distance between these planes; the further apart they are, the worse the generator is. As this test is devised to study the lattice structures of LCGs, it can not be applied to other families of PRNGs. According to Donald Knuth, this is by far the most powerful test known, because it can fail LCGs which pass most statistical tests. The IBM subroutine RANDU RANDUCompaq Fortran Language Reference Manual (Order Number: AA-Q66SD-TK) September 1999 (formerly DIGITAL Fortran and DEC Fortran 90) is a linear congruential pseudorandom number generator (LCG) of the Park–Miller type, which was used primar ... LCG fails in this test for 3 dimensions and above. Refe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square-free Integer
In mathematics, a square-free integer (or squarefree integer) is an integer which is divisible by no square number other than 1. That is, its prime factorization has exactly one factor for each prime that appears in it. For example, is square-free, but is not, because 18 is divisible by . The smallest positive square-free numbers are Square-free factorization Every positive integer n can be factored in a unique way as n=\prod_^k q_i^i, where the q_i different from one are square-free integers that are pairwise coprime. This is called the ''square-free factorization'' of . To construct the square-free factorization, let n=\prod_^h p_j^ be the prime factorization of n, where the p_j are distinct prime numbers. Then the factors of the square-free factorization are defined as q_i=\prod_p_j. An integer is square-free if and only if q_i=1 for all i > 1. An integer greater than one is the kth power of another integer if and only if k is a divisor of all i such that q_i\neq 1. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Word Size
In computing, a word is the natural unit of data used by a particular processor design. A word is a fixed-sized datum handled as a unit by the instruction set or the hardware of the processor. The number of bits or digits in a word (the ''word size'', ''word width'', or ''word length'') is an important characteristic of any specific processor design or computer architecture. The size of a word is reflected in many aspects of a computer's structure and operation; the majority of the registers in a processor are usually word-sized and the largest datum that can be transferred to and from the working memory in a single operation is a word in many (not all) architectures. The largest possible address size, used to designate a location in memory, is typically a hardware word (here, "hardware word" means the full-sized natural word of the processor, as opposed to any other definition used). Documentation for older computers with fixed word size commonly states memory sizes in words ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Factor
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, or , involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order. The property of being prime is called primality. A simple but slow method of checking the primality of a given number n, called trial division, tests whether n is a multiple of any integer between 2 and \sqrt. Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which always pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
