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Cyclic Shift
In combinatorial mathematics, a circular shift is the operation of rearranging the entries in a tuple, either by moving the final entry to the first position, while shifting all other entries to the next position, or by performing the inverse operation. A circular shift is a special kind of cyclic permutation, which in turn is a special kind of permutation. Formally, a circular shift is a permutation σ of the ''n'' entries in the tuple such that either :\sigma(i)\equiv (i+1) modulo ''n'', for all entries ''i'' = 1, ..., ''n'' or :\sigma(i)\equiv (i-1) modulo ''n'', for all entries ''i'' = 1, ..., ''n''. The result of repeatedly applying circular shifts to a given tuple are also called the circular shifts of the tuple. For example, repeatedly applying circular shifts to the four-tuple (''a'', ''b'', ''c'', ''d'') successively gives * (''d'', ''a'', ''b'', ''c''), * (''c'', ''d'', ''a'', ''b''), * (''b'', ''c'', ''d'', ''a''), * (''a'', ''b'', ''c'', ''d'') (the original four-tup ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Permutation Matrix
In mathematics, particularly in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column with all other entries 0. An permutation matrix can represent a permutation of elements. Pre- multiplying an -row matrix by a permutation matrix , forming , results in permuting the rows of , while post-multiplying an -column matrix , forming , permutes the columns of . Every permutation matrix ''P'' is orthogonal, with its inverse equal to its transpose: P^=P^\mathsf. Indeed, permutation matrices can be characterized as the orthogonal matrices whose entries are all non-negative. The two permutation/matrix correspondences There are two natural one-to-one correspondences between permutations and permutation matrices, one of which works along the rows of the matrix, the other along its columns. Here is an example, starting with a permutation in two-line form at the upper left: :\begin \pi\colon\begin1&2&3&4\\3&2&4&1\e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Cryptography
Cryptography, or cryptology (from "hidden, secret"; and ''graphein'', "to write", or ''-logy, -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of Adversary (cryptography), adversarial behavior. More generally, cryptography is about constructing and analyzing Communication protocol, protocols that prevent third parties or the public from reading private messages. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, information security, electrical engineering, digital signal processing, physics, and others. Core concepts related to information security (confidentiality, data confidentiality, data integrity, authentication, and non-repudiation) are also central to cryptography. Practical applications of cryptography include electronic commerce, Smart card#EMV, chip-based payment cards, digital currencies, password, computer passwords, and military communications. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
String (computer Science)
In computer programming, a string is traditionally a sequence of character (computing), characters, either as a literal (computer programming), literal constant or as some kind of Variable (computer science), variable. The latter may allow its elements to be Immutable object, mutated and the length changed, or it may be fixed (after creation). A string is often implemented as an array data structure of bytes (or word (computer architecture), words) that stores a sequence of elements, typically characters, using some character encoding. More general, ''string'' may also denote a sequence (or List (abstract data type), list) of data other than just characters. Depending on the programming language and precise data type used, a variable (programming), variable declared to be a string may either cause storage in memory to be statically allocated for a predetermined maximum length or employ dynamic allocation to allow it to hold a variable number of elements. When a string appears lit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Block Code
In coding theory, block codes are a large and important family of Channel coding, error-correcting codes that encode data in blocks. There is a vast number of examples for block codes, many of which have a wide range of practical applications. The abstract definition of block codes is conceptually useful because it allows coding theorists, mathematicians, and computer scientists to study the limitations of ''all'' block codes in a unified way. Such limitations often take the form of ''bounds'' that relate different parameters of the block code to each other, such as its rate and its ability to detect and correct errors. Examples of block codes are Reed–Solomon codes, Hamming codes, Hadamard codes, Expander codes, Golay code (other), Golay codes, Reed–Muller codes and Polar code (coding theory), Polar codes. These examples also belong to the class of linear codes, and hence they are called linear block codes. More particularly, these codes are known as algebraic block ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Cyclic Code
In coding theory, a cyclic code is a block code, where the circular shifts of each codeword gives another word that belongs to the code. They are error-correcting codes that have algebraic properties that are convenient for efficient error detection and correction. Definition Let \mathcal be a linear code over a finite field (also called '' Galois field'') GF(q) of block length n. \mathcal is called a cyclic code if, for every Code word (communication), codeword c=(c_1,\ldots,c_n) from \mathcal, the word (c_n,c_1,\ldots,c_) in GF(q)^n obtained by a circular shift, cyclic right shift of components is again a codeword. Because one cyclic right shift is equal to n-1 cyclic left shifts, a cyclic code may also be defined via cyclic left shifts. Therefore, the linear code \mathcal is cyclic precisely when it is invariant under all cyclic shifts. Cyclic codes have some additional structural constraint on the codes. They are based on Galois fields and because of their structural properti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Rotate Right
Rotation or rotational/rotary motion is the circular movement of an object around a central line, known as an ''axis of rotation''. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersecting anywhere inside or outside the figure at a ''center of rotation''. A solid figure has an infinite number of possible axes and angles of rotation, including chaotic rotation (between arbitrary orientations), in contrast to rotation around a axis. The special case of a rotation with an internal axis passing through the body's own center of mass is known as a spin (or ''autorotation''). In that case, the surface intersection of the internal ''spin axis'' can be called a ''pole''; for example, Earth's rotation defines the geographical poles. A rotation around an axis completely external to the moving body is called a revolution (or ''orbit''), e.g. Earth's orbit around the Sun. The ends of the external ''axis of revolution'' can be ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Undefined Behaviour
In computer programming, a program exhibits undefined behavior (UB) when it contains, or is executing code for which its programming language specification does not mandate any specific requirements. This is different from unspecified behavior, for which the language specification does not prescribe a result, and implementation-defined behavior that defers to the documentation of another component of the platform (such as the ABI or the translator documentation). In the C programming community, undefined behavior may be humorously referred to as "nasal demons", after a comp.std.c post that explained undefined behavior as allowing the compiler to do anything it chooses, even "to make demons fly out of your nose". Overview Some programming languages allow a program to operate differently or even have a different control flow from the source code, as long as it exhibits the same user-visible side effects, ''if undefined behavior never happens during program execution''. Undef ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
John Regehr
John Regehr is a computer scientist specializing in compiler correctness and undefined behavior. , he is a professor at the University of Utah. He is best known for the integer overflow sanitizer which was merged into the Clang C compiler, the C compiler fuzzer Csmith, and his widely read bloEmbedded in Academia He spent the 2015-2016 academic year on sabbatical in Paris, France, working with TrustInSoft on Frama-C Frama-C is a set of interoperable program analyzers for C programs. The name ''Frama-C'' stands for ''Framework for Modular Analysis of C programs''. Frama-C has been developed by the French Commissariat à l'Énergie Atomique et aux Énergi ... and related code analysis tools. References External links John Regehr's home pageJohn Regehr on Mastodon {{DEFAULTSORT:Regehr, John Living people American computer scientists University of Utah faculty Science bloggers 21st-century science writers Year of birth missing (living people) University of Virginia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
ANSI C
ANSI C, ISO C, and Standard C are successive standards for the C programming language published by the American National Standards Institute (ANSI) and ISO/IEC JTC 1/SC 22/WG 14 of the International Organization for Standardization (ISO) and the International Electrotechnical Commission (IEC). Historically, the names referred specifically to the original and best-supported version of the standard (known as C89 or C90). Software developers writing in C are encouraged to conform to the standards, as doing so helps portability between compilers. History and outlook The first standard for C was published by ANSI. Although this document was subsequently adopted by ISO/IEC and subsequent revisions published by ISO/IEC have been adopted by ANSI, "ANSI C" is still used to refer to the standard. While some software developers use the term ISO C, others are standards-body neutral and use Standard C. Informal specification: K&R C (''C78'') Informal specification in 1978 (Brian Kernig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Intrinsic Function
In computer software, in compiler theory, an intrinsic function, also called built-in function or builtin function, is a function ( subroutine) available for use in a given programming language whose implementation is handled specially by the compiler. Typically, it may substitute a sequence of automatically generated instructions for the original function call, similar to an inline function. Unlike an inline function, the compiler has an intimate knowledge of an intrinsic function and can thus better integrate and optimize it for a given situation. Compilers that implement intrinsic functions may enable them only when a program requests optimization, otherwise falling back to a default implementation provided by the language runtime system (environment). Vectorization and parallelization Intrinsic functions are often used to explicitly implement vectorization and parallelization in languages which do not address such constructs. Some application programming interfaces (API ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Intel X86
x86 (also known as 80x86 or the 8086 family) is a family of complex instruction set computer (CISC) instruction set architectures initially developed by Intel, based on the 8086 microprocessor and its 8-bit-external-bus variant, the 8088. The 8086 was introduced in 1978 as a fully 16-bit extension of 8-bit Intel's 8080 microprocessor, with memory segmentation as a solution for addressing more memory than can be covered by a plain 16-bit address. The term "x86" came into being because the names of several successors to Intel's 8086 processor end in "86", including the 80186, 80286, 80386 and 80486. Colloquially, their names were "186", "286", "386" and "486". The term is not synonymous with IBM PC compatibility, as this implies a multitude of other computer hardware. Embedded systems and general-purpose computers used x86 chips before the PC-compatible market started, some of them before the IBM PC (1981) debut. , most desktop and laptop computers sold are based on the x ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
