|
Wang's Factor-combining Method
CORDIC (for "coordinate rotation digital computer"), also known as Volder's algorithm, or: Digit-by-digit method Circular CORDIC (Jack E. Volder), Linear CORDIC, Hyperbolic CORDIC (John Stephen Walther), and Generalized Hyperbolic CORDIC (GH CORDIC) (Yuanyong Luo et al.), is a simple and efficient algorithm to calculate trigonometric functions, hyperbolic functions, square roots, multiplications, Division (mathematics), divisions, and Exponentiation, exponentials and logarithms with arbitrary base, typically converging with one digit (or bit) per iteration. CORDIC is therefore also an example of digit-by-digit algorithms. CORDIC and closely related methods known as pseudo-multiplication and pseudo-division or factor combining are commonly used when no hardware multiplier is available (e.g. in simple microcontrollers and FPGAs), as the only operations it requires are additions, subtractions, bitshift and lookup tables. As such, they all belong to the class of shift-and-add algor ... [...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] |
Henry Briggs (mathematician)
Henry Briggs (1 February 1561 – 26 January 1630) was an English mathematician notable for changing the original logarithms invented by John Napier into common (base 10) logarithms, which are sometimes known as Briggsian logarithms in his honour. The specific algorithm for long division in modern use was introduced by Briggs 1600 AD. Briggs was a committed Puritan and an influential professor in his time. Personal life Briggs was born at Daisy Bank, Sowerby Bridge, near Halifax, in Yorkshire, England. After studying Latin and Greek at a local grammar school, he entered St John's College, Cambridge, in 1577, and graduated in 1581. In 1588, he was elected a Fellow of St John's. In 1592, he was made reader of the physical lecture founded by Thomas Linacre; he also read some of the mathematical lectures. During this period, he took an interest in navigation and astronomy, collaborating with Edward Wright. In 1596, he became first professor of geometry in the recently fou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplication
Multiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a ''product''. The multiplication of whole numbers may be thought of as repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the ''multiplicand'', as the quantity of the other one, the ''multiplier''. Both numbers can be referred to as ''factors''. :a\times b = \underbrace_ For example, 4 multiplied by 3, often written as 3 \times 4 and spoken as "3 times 4", can be calculated by adding 3 copies of 4 together: :3 \times 4 = 4 + 4 + 4 = 12 Here, 3 (the ''multiplier'') and 4 (the ''multiplicand'') are the ''factors'', and 12 is the ''product''. One of the main properties of multiplication is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Function
The exponential function is a mathematical function denoted by f(x)=\exp(x) or e^x (where the argument is written as an exponent). Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras. The exponential function originated from the notion of exponentiation (repeated multiplication), but modern definitions (there are several equivalent characterizations) allow it to be rigorously extended to all real arguments, including irrational numbers. Its ubiquitous occurrence in pure and applied mathematics led mathematician Walter Rudin to opine that the exponential function is "the most important function in mathematics". The exponential function satisfies the exponentiation identity e^ = e^x e^y \text x,y\in\mathbb, which, along with the definition e = \exp(1), shows that e^n=\underbrace_ for positive i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logarithm
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number to the base is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 of is , or . The logarithm of to ''base'' is denoted as , or without parentheses, , or even without the explicit base, , when no confusion is possible, or when the base does not matter such as in big O notation. The logarithm base is called the decimal or common logarithm and is commonly used in science and engineering. The natural logarithm has the number as its base; its use is widespread in mathematics and physics, because of its very simple derivative. The binary logarithm uses base and is frequently used in computer science. Logarithms were introduced by John Napier in 1614 as a means of simplifying calculations. They were rapidly adopted by navigators, scientists, engineers, surveyors and others to perform high-a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coordinate Rotation
Rotation in mathematics is a concept originating in geometry. Any rotation is a motion of a certain space that preserves at least one point. It can describe, for example, the motion of a rigid body around a fixed point. Rotation can have sign (as in the sign of an angle): a clockwise rotation is a negative magnitude so a counterclockwise turn has a positive magnitude. A rotation is different from other types of motions: translations, which have no fixed points, and (hyperplane) reflections, each of them having an entire -dimensional flat of fixed points in a -dimensional space. Mathematically, a rotation is a map. All rotations about a fixed point form a group under composition called the rotation group (of a particular space). But in mechanics and, more generally, in physics, this concept is frequently understood as a coordinate transformation (importantly, a transformation of an orthonormal basis), because for any motion of a body there is an inverse transformation which i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sine
In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse. For an angle \theta, the sine and cosine functions are denoted simply as \sin \theta and \cos \theta. More generally, the definitions of sine and cosine can be extended to any real value in terms of the lengths of certain line segments in a unit circle. More modern definitions express the sine and cosine as infinite series, or as the solutions of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers. The sine and cosine functions are commonly used to model periodic phenomena such as sound and lig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CRC Handbook Of Chemistry And Physics
The ''CRC Handbook of Chemistry and Physics'' is a comprehensive one-volume reference resource for science research. First published in 1914, it is currently () in its 103rd edition, published in 2022. It is sometimes nicknamed the "Rubber Bible" or the "Rubber Book", as CRC originally stood for "Chemical Rubber Company". As late as the 1962–1963 edition (3604 pages) the ''Handbook'' contained myriad information for every branch of science and engineering. Sections in that edition include: Mathematics, Properties and Physical Constants, Chemical Tables, Properties of Matter, Heat, Hygrometric and Barometric Tables, Sound, Quantities and Units, and Miscellaneous. Earlier editions included sections such as "Antidotes of Poisons", "Rules for Naming Organic Compounds", "Surface Tension of Fused Salts", "Percent Composition of Anti-Freeze Solutions", "Spark-gap Voltages", "Greek Alphabet", "Musical Scales", "Pigments and Dyes", "Comparison of Tons and Pounds", "Twist Drill and St ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Resolver
Digital usually refers to something using discrete digits, often binary digits. Technology and computing Hardware *Digital electronics, electronic circuits which operate using digital signals **Digital camera, which captures and stores digital images ***Digital versus film photography **Digital computer, a computer that handles information represented by discrete values **Digital recording, information recorded using a digital signal Socioeconomic phenomena *Digital culture, the anthropological dimension of the digital social changes * Digital divide, a form of economic and social inequality in access to or use of information and communication technologies * Digital economy, an economy based on computing and telecommunications resources Other uses in technology and computing *Digital data, discrete data, usually represented using binary numbers *Digital marketing, search engine & social media presence booster, usually represented using online visibility. *Digital media, media s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
B-58 Hustler
The Convair B-58 Hustler, designed and produced by American aircraft manufacturer Convair, was the first operational bomber capable of Mach 2 flight. The B-58 was developed during the 1950s for the United States Air Force (USAF) Strategic Air Command (SAC). To achieve the high speeds desired, Convair chose a delta wing design used by contemporary fighters such as the Convair F-102. The bomber was powered by four General Electric J79 engines in underwing pods. It had no bomb bay: it carried a single nuclear weapon plus fuel in a combination bomb/fuel pod underneath the fuselage. Later, four external hardpoints were added, enabling it to carry up to five weapons. The B-58 entered service in March 1960, and flew for a decade with two SAC bomb wings: the 43rd Bombardment Wing and the 305th Bombardment Wing. It was considered difficult to fly, imposing a high workload upon its three-man crews. Designed to replace the subsonic Boeing B-47 Stratojet strategic bomber, the B-58 beca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analog Resolver
A resolver is a type of rotary electrical transformer used for measuring degrees of rotation. It is considered an analog device, and has digital counterparts such as the digital resolver, rotary (or pulse) encoder. Description The most common type of resolver is the brushless transmitter resolver (other types are described at the end). On the outside, this type of resolver may look like a small electrical motor having a stator and rotor. On the inside, the configuration of the wire windings makes it different. The stator portion of the resolver houses three windings: an exciter winding and two two-phase windings (usually labeled "x" and "y") (case of a brushless resolver). The exciter winding is located on the top; it is a coil of a turning (rotary) transformer. This rotary transformer induces current in the rotor without wires or brushes to provide a direct electrical connection. The two other windings are on the bottom, wound on a lamination. They are configured at 90 degree ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
_(1906).jpg "Click for more on -> Henry Briggs (mathematician)")
