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Bit-reversal Permutation
In applied mathematics, a bit-reversal permutation is a permutation of a sequence of n items, where n=2^k is a power of two. It is defined by indexing the elements of the sequence by the numbers from 0 to n-1, representing each of these numbers by its binary representation (padded to have length exactly k), and mapping each item to the item whose representation has the same bits in the reversed order. Repeating the same permutation twice returns to the original ordering on the items, so the bit reversal permutation is an involution. This permutation can be applied to any sequence in linear time while performing only simple index calculations. It has applications in the generation of low-discrepancy sequences and in the evaluation of fast Fourier transforms. Example Consider the sequence of eight letters '. Their indexes are the binary numbers 000, 001, 010, 011, 100, 101, 110, and 111, which when reversed become 000, 100, 010, 110, 001, 101, 011, and 111. Thus, the letter ''a'' i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Hammersley Set 2D
Hammersley is a surname. Notable people with the surname include: *Ben Hammersley (born 1976), British photojournalist *Charles E. Hammersley (died 1957), American politician *Frederick Hammersley (born 1824), Frederick Hammersley (1824–1901), Major-General and the first Inspector of Gymnasia in the British Army *Frederick Hammersley (British Army officer), Frederick Hammersley (1858-1924), British Army officer, commanded the Landing at Suvla Bay by his division during the Gallipoli Campaign *Frederick Hammersley (1919–2009), American abstract painter *James Astbury Hammersley (1815–1869), English painter, and teacher of art and design *John Hammersley (1920–2004), British mathematician *Martyn Hammersley (born 1949), British sociologist *Peter Hammersley (1928–2020), British admiral *Rachel Hammersley (born 1974), British historian *Reuben Hammersley (1897–1940), English World War I flying ace *Rodolfo Hammersley (born 1889, date of death unknown), Chilean track and f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Van Der Corput Sequence
A van der Corput sequence is an example of the simplest one-dimensional low-discrepancy sequence over the unit interval; it was first described in 1935 by the Dutch mathematician J. G. van der Corput. It is constructed by reversing the base-''n'' representation of the sequence of natural numbers (1, 2, 3, …). The b-ary representation of the positive integer n \geq 1 is n ~=~ \sum_^ d_k(n) b^k ~=~ d_0(n) b^0 + \cdots + d_(n) b^, where b is the base in which the number n is represented, and 0 \leq d_k(n) , there exists a subsequence of the van der Corput sequence that converges to that number. They are also equidistributed over the unit interval. Python implementation def corput(n, base: int) -> float: """ Returns the n-th element of the van der Corput sequence in a given base """ output = 0.0 output_increment = 1 / base while n > 0: # process the least significant digit of the sequence position n # to get the most significant digit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Permutations
In mathematics, a permutation of a Set (mathematics), set can mean one of two different things: * an arrangement of its members in a sequence or linear order, or * the act or process of changing the linear order of an ordered set. An example of the first meaning is the six permutations (orderings) of the set : written as tuples, they are (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). Anagrams of a word whose letters are all different are also permutations: the letters are already ordered in the original word, and the anagram reorders them. The study of permutations of finite sets is an important topic in combinatorics and group theory. Permutations are used in almost every branch of mathematics and in many other fields of science. In computer science, they are used for analyzing sorting algorithms; in quantum physics, for describing states of particles; and in biology, for describing RNA sequences. The number of permutations of distinct objects is &nbs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Memory Hierarchy
In computer architecture, the memory hierarchy separates computer storage into a hierarchy based on response time. Since response time, complexity, and capacity are related, the levels may also be distinguished by their performance and controlling technologies. Memory hierarchy affects performance in computer architectural design, algorithm predictions, and lower level programming constructs involving locality of reference. Designing for high performance requires considering the restrictions of the memory hierarchy, i.e. the size and capabilities of each component. Each of the various components can be viewed as part of a hierarchy of memories in which each member is typically smaller and faster than the next highest member of the hierarchy. To limit waiting by higher levels, a lower level will respond by filling a buffer and then signaling for activating the transfer. There are four major storage levels. * ''Internal''processor registers and cache. * Mainthe system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Vectored I/O
In computing, vectored I/O, also known as scatter/gather I/O, is a method of input and output by which a single procedure call sequentially reads data from multiple buffers and writes it to a single data stream (gather), or reads data from a data stream and writes it to multiple buffers (scatter), as defined in a vector of buffers. ''Scatter/gather'' refers to the process of gathering data from, or scattering data into, the given set of buffers. Vectored I/O can operate synchronously or asynchronously. The main reasons for using vectored I/O are efficiency and convenience. Vectored I/O has several potential uses: * Atomicity: if the particular vectored I/O implementation supports atomicity, a process can write into or read from a set of buffers to or from a file without risk that another thread or process might perform I/O on the same file between the first process' reads or writes, thereby corrupting the file or compromising the integrity of the input * Concatenating output: a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Random-access Machine
In computer science, random-access machine (RAM or RA-machine) is a model of computation that describes an abstract machine in the general class of register machines. The RA-machine is very similar to the counter machine but with the added capability of 'indirect addressing' of its registers. The 'registers' are intuitively equivalent to Random-access memory, main memory of a common computer, except for the additional ability of registers to store natural numbers of any size. Like the counter machine, the RA-machine contains the execution instructions in the finite-state portion of the machine (the so-called Harvard architecture). The RA-machine's equivalent of the universal Turing machinewith its Computer program, program in the registers as well as its datais called the random-access stored-program machine or RASP-machine. It is an example of the so-called von Neumann architecture and is closest to the common notion of a computer. Together with the Turing machine and counter-m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
In-place Algorithm
In computer science, an in-place algorithm is an algorithm that operates directly on the input data structure without requiring extra space proportional to the input size. In other words, it modifies the input in place, without creating a separate copy of the data structure. An algorithm which is not in-place is sometimes called not-in-place or out-of-place. In-place can have slightly different meanings. In its strictest form, the algorithm can only have a constant amount of extra space, counting everything including function calls and pointers. However, this form is very limited as simply having an index to a length array requires bits. More broadly, in-place means that the algorithm does not use extra space for manipulating the input but may require a small though nonconstant extra space for its operation. Usually, this space is , though sometimes anything in is allowed. Note that space complexity also has varied choices in whether or not to count the index lengths as part ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Splay Trees
A splay tree is a binary search tree with the additional property that recently accessed elements are quick to access again. Like self-balancing binary search trees, a splay tree performs basic operations such as insertion, look-up and removal in big O notation, O(log ''n'') amortized analysis, amortized time. For random access patterns drawn from a non-uniform random distribution, their amortized time can be faster than logarithmic, proportional to the Entropy (information theory), entropy of the access pattern. For many patterns of non-random operations, also, splay trees can take better than logarithmic time, without requiring advance knowledge of the pattern. According to the unproven dynamic optimality conjecture, their performance on all access patterns is within a constant factor of the best possible performance that could be achieved by any other self-adjusting binary search tree, even one selected to fit that pattern. The splay tree was invented by Daniel Sleator and Rob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Binary Search Tree
In computer science, a binary search tree (BST), also called an ordered or sorted binary tree, is a Rooted tree, rooted binary tree data structure with the key of each internal node being greater than all the keys in the respective node's left subtree and less than the ones in its right subtree. The time complexity of operations on the binary search tree is Time complexity#Linear time, linear with respect to the height of the tree. Binary search trees allow Binary search algorithm, binary search for fast lookup, addition, and removal of data items. Since the nodes in a BST are laid out so that each comparison skips about half of the remaining tree, the lookup performance is proportional to that of binary logarithm. BSTs were devised in the 1960s for the problem of efficient storage of labeled data and are attributed to Conway Berners-Lee and David_Wheeler_(computer_scientist), David Wheeler. The performance of a binary search tree is dependent on the order of insertion of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Data Structures
In computer science, a data structure is a data organization and storage format that is usually chosen for efficient access to data. More precisely, a data structure is a collection of data values, the relationships among them, and the functions or operations that can be applied to the data, i.e., it is an algebraic structure about data. Usage Data structures serve as the basis for abstract data types (ADT). The ADT defines the logical form of the data type. The data structure implements the physical form of the data type. Different types of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks. For example, relational databases commonly use B-tree indexes for data retrieval, while compiler implementations usually use hash tables to look up identifiers. Data structures provide a means to manage large amounts of data efficiently for uses such as large databases and internet indexing services. Usually, effici ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Dyadic Rational Number
In mathematics, a dyadic rational or binary rational is a number that can be expressed as a fraction whose denominator is a power of two. For example, 1/2, 3/2, and 3/8 are dyadic rationals, but 1/3 is not. These numbers are important in computer science because they are the only ones with finite binary representations. Dyadic rationals also have applications in weights and measures, musical time signatures, and early mathematics education. They can accurately approximate any real number. The sum, difference, or product of any two dyadic rational numbers is another dyadic rational number, given by a simple formula. However, division of one dyadic rational number by another does not always produce a dyadic rational result. Mathematically, this means that the dyadic rational numbers form a ring, lying between the ring of integers and the field of rational numbers. This ring may be denoted \Z tfrac12/math>. In advanced mathematics, the dyadic rational numbers are central to the cons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Fixed-point Arithmetic
In computing, fixed-point is a method of representing fractional (non-integer) numbers by storing a fixed number of digits of their fractional part. Dollar amounts, for example, are often stored with exactly two fractional digits, representing the cents (1/100 of dollar). More generally, the term may refer to representing fractional values as integer multiples of some fixed small unit, e.g. a fractional amount of hours as an integer multiple of ten-minute intervals. Fixed-point number representation is often contrasted to the more complicated and computationally demanding floating-point representation. In the fixed-point representation, the fraction is often expressed in the same number base as the integer part, but using negative powers of the base ''b''. The most common variants are decimal (base 10) and binary (base 2). The latter is commonly known also as binary scaling. Thus, if ''n'' fraction digits are stored, the value will always be an integer multiple of ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
