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Restoring Division
A division algorithm is an algorithm which, given two integers N and D, computes their quotient and/or remainder, the result of Euclidean division. Some are applied by hand, while others are employed by digital circuit designs and software. Division algorithms fall into two main categories: slow division and fast division. Slow division algorithms produce one digit of the final quotient per iteration. Examples of slow division include restoring, non-performing restoring, non-restoring, and SRT division. Fast division methods start with a close approximation to the final quotient and produce twice as many digits of the final quotient on each iteration. Newton–Raphson and Goldschmidt algorithms fall into this category. Variants of these algorithms allow using fast multiplication algorithms. It results that, for large integers, the computer time needed for a division is the same, up to a constant factor, as the time needed for a multiplication, whichever multiplication algo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a Heuristic (computer science), heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radix
In a positional numeral system, the radix or base is the number of unique digits, including the digit zero, used to represent numbers. For example, for the decimal/denary system (the most common system in use today) the radix (base number) is ten, because it uses the ten digits from 0 through 9. In any standard positional numeral system, a number is conventionally written as with ''x'' as the string of digits and ''y'' as its base, although for base ten the subscript is usually assumed (and omitted, together with the pair of parentheses), as it is the most common way to express value. For example, (the decimal system is implied in the latter) and represents the number one hundred, while (100)2 (in the binary system with base 2) represents the number four. Etymology ''Radix'' is a Latin word for "root". ''Root'' can be considered a synonym for ''base,'' in the arithmetical sense. In numeral systems In the system with radix 13, for example, a string of digits such as 398 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Approximation
An approximation is anything that is intentionally similar but not exactly equality (mathematics), equal to something else. Etymology and usage The word ''approximation'' is derived from Latin ''approximatus'', from ''proximus'' meaning ''very near'' and the prefix ''ad-'' (''ad-'' before ''p'' becomes ap- by assimilation (phonology), assimilation) meaning ''to''. Words like ''approximate'', ''approximately'' and ''approximation'' are used especially in technical or scientific contexts. In everyday English, words such as ''roughly'' or ''around'' are used with a similar meaning. It is often found abbreviated as ''approx.'' The term can be applied to various properties (e.g., value, quantity, image, description) that are nearly, but not exactly correct; similar, but not exactly the same (e.g., the approximate time was 10 o'clock). Although approximation is most often applied to numbers, it is also frequently applied to such things as Function (mathematics), mathematical functio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fused Multiply–add
Fuse or FUSE may refer to: Devices * Fuse (electrical), a device used in electrical systems to protect against excessive current ** Fuse (automotive), a class of fuses for vehicles * Fuse (hydraulic), a device used in hydraulic systems to protect against sudden loss of fluid pressure * Fuse (explosives) or fuze, the part of the device that initiates function * Fuze or fuse, a mechanism for exploding military munitions such as bombs, shells, and mines Computing * Fuse ESB, an open-source integration platform based on Apache Camel * Filesystem in Userspace, a virtual file system interface for Unix-like operating systems * Fuse (emulator), the Free Unix Spectrum Emulator of the ZX Spectrum * Fuse Internet Service, a former Cincinnati Bell Internet service provider based in Cincinnati, Ohio, United States * Fuse Universal, a learning platform Science * Far Ultraviolet Spectroscopic Explorer, a space-based ultraviolet telescope and spectroscope * Intramembranous ossification, the fus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplicative Inverse
In mathematics, a multiplicative inverse or reciprocal for a number ''x'', denoted by 1/''x'' or ''x''−1, is a number which when Multiplication, multiplied by ''x'' yields the multiplicative identity, 1. The multiplicative inverse of a rational number, fraction ''a''/''b'' is ''b''/''a''. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the Function (mathematics), function ''f''(''x'') that maps ''x'' to 1/''x'', is one of the simplest examples of a function which is its own inverse (an Involution (mathematics), involution). Multiplying by a number is the same as Division (mathematics), dividing by its reciprocal and vice versa. For example, multiplication by 4/5 (or 0.8) will give the same result as division by 5/4 (or 1.25). Therefore, multiplication by a number followed by multiplication by its reciprocal yiel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newton's Method
In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version starts with a single-variable function defined for a real variable , the function's derivative , and an initial guess for a root of . If the function satisfies sufficient assumptions and the initial guess is close, then :x_ = x_0 - \frac is a better approximation of the root than . Geometrically, is the intersection of the -axis and the tangent of the graph of at : that is, the improved guess is the unique root of the linear approximation at the initial point. The process is repeated as :x_ = x_n - \frac until a sufficiently precise value is reached. This algorithm is first in the class of Householder's methods, succeeded by Halley's method. The method can also be extended to complex functions an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pentium FDIV Bug
The Pentium FDIV bug is a hardware bug affecting the floating-point unit (FPU) of the early Intel Pentium processors. Because of the bug, the processor would return incorrect binary floating point results when dividing certain pairs of high-precision numbers. The bug was discovered in 1994 by Thomas R. Nicely, a professor of mathematics at Lynchburg College. Missing values in a lookup table used by the FPU's floating-point division algorithm led to calculations acquiring small errors. While these errors would in most use-cases only occur rarely and result in small deviations from the correct output values, in certain circumstances the errors can occur frequently and lead to more significant deviations. The severity of the FDIV bug is debated. Though rarely encountered by most users (''Byte'' magazine estimated that 1 in 9 billion floating point divides with random parameters would produce inaccurate results), both the flaw and Intel's initial handling of the matter were heavily ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Original Intel Pentium (P5 Microarchitecture)
The Pentium (also referred to as P5, its microarchitecture, or i586) is a fifth generation, 32-bit x86 microprocessor that was introduced by Intel on March 22, 1993, as the very first CPU in the Pentium brand. It was instruction set compatible with the 80486 but was a new and very different microarchitecture design from previous iterations. The P5 Pentium was the first superscalar x86 microarchitecture and the world's first superscalar microprocessor to be in mass productionmeaning it generally executes at least 2 instructions per clock mainly because of a design-first dual integer pipeline design previously thought impossible to implement on a CISC microarchitecture. Additional features include a faster floating-point unit, wider data bus, separate code and data caches, and many other techniques and features to enhance performance and support security, encryption, and multiprocessing, for workstations and servers when compared to the next best previous industry standard proce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lookup Table
In computer science, a lookup table (LUT) is an array that replaces runtime computation with a simpler array indexing operation. The process is termed as "direct addressing" and LUTs differ from hash tables in a way that, to retrieve a value v with key k, a hash table would store the value v in the slot h(k) where h is a hash function i.e. k is used to compute the slot, while in the case of LUT, the value v is stored in slot k, thus directly addressable. The savings in processing time can be significant, because retrieving a value from memory is often faster than carrying out an "expensive" computation or input/output operation. The tables may be precalculated and stored in static program storage, calculated (or "pre-fetched") as part of a program's initialization phase ( memoization), or even stored in hardware in application-specific platforms. Lookup tables are also used extensively to validate input values by matching against a list of valid (or invalid) items in an array and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Imperial College London
Imperial College London (legally Imperial College of Science, Technology and Medicine) is a public research university in London, United Kingdom. Its history began with Prince Albert, consort of Queen Victoria, who developed his vision for a cultural area that included the Royal Albert Hall, Victoria & Albert Museum, Natural History Museum and royal colleges. In 1907, Imperial College was established by a royal charter, which unified the Royal College of Science, Royal School of Mines, and City and Guilds of London Institute. In 1988, the Imperial College School of Medicine was formed by merging with St Mary's Hospital Medical School. In 2004, Queen Elizabeth II opened the Imperial College Business School. Imperial focuses exclusively on science, technology, medicine, and business. The main campus is located in South Kensington, and there is an innovation campus in White City. Facilities also include teaching hospitals throughout London, and with Imperial College Healthcare ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Illinois
The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the University of Illinois system and was founded in 1867. Enrolling over 56,000 undergraduate and graduate students, the University of Illinois is one of the largest public universities by enrollment in the country. The University of Illinois Urbana-Champaign is a member of the Association of American Universities and is classified among "R1: Doctoral Universities – Very high research activity". In fiscal year 2019, research expenditures at Illinois totaled $652 million. The campus library system possesses the second-largest university library in the United States by holdings after Harvard University. The university also hosts the National Center for Supercomputing Applications and is home to the fastest supercomputer on a university campus. The u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microprocessor
A microprocessor is a computer processor where the data processing logic and control is included on a single integrated circuit, or a small number of integrated circuits. The microprocessor contains the arithmetic, logic, and control circuitry required to perform the functions of a computer's central processing unit. The integrated circuit is capable of interpreting and executing program instructions and performing arithmetic operations. The microprocessor is a multipurpose, clock-driven, register-based, digital integrated circuit that accepts binary data as input, processes it according to instructions stored in its memory, and provides results (also in binary form) as output. Microprocessors contain both combinational logic and sequential digital logic, and operate on numbers and symbols represented in the binary number system. The integration of a whole CPU onto a single or a few integrated circuits using Very-Large-Scale Integration (VLSI) greatly reduced the cost of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
