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Characteristic (significand)
The significand (also coefficient, sometimes argument, or more ambiguously mantissa, fraction, or characteristic) is the first (left) part of a number in scientific notation or related concepts in floating-point representation, consisting of its significant digits. For negative numbers, it does not include the initial minus sign. Depending on the interpretation of the exponent, the significand may represent an integer or a fractional number, which may cause the term "mantissa" to be misleading, since the ''mantissa'' of a logarithm is always its fractional part. Although the other names mentioned are common, ''significand'' is the word used by IEEE 754, an important technical standard for floating-point arithmetic. In mathematics, the term "argument" may also be ambiguous, since "the argument of a number" sometimes refers to the length of a circular arc from 1 to a number on the unit circle in the complex plane. Example The number 123.45 can be represented as a decimal floatin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientific Notation
Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form, since to do so would require writing out an inconveniently long string of digits. It may be referred to as scientific form or standard index form, or standard form in the United Kingdom. This base ten notation is commonly used by scientists, mathematicians, and engineers, in part because it can simplify certain arithmetic operations. On scientific calculators, it is usually known as "SCI" display mode. In scientific notation, nonzero numbers are written in the form or ''m'' times ten raised to the power of ''n'', where ''n'' is an integer, and the coefficient ''m'' is a nonzero real number (usually between 1 and 10 in absolute value, and nearly always written as a terminating decimal). The integer ''n'' is called the exponent and the real number ''m'' is called the '' significand'' or ''mantissa''. The term "mantissa" can be ambiguous where loga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modula-2
Modula-2 is a structured, procedural programming language developed between 1977 and 1985/8 by Niklaus Wirth at ETH Zurich. It was created as the language for the operating system and application software of the Lilith personal workstation. It was later used for programming outside the context of the Lilith. Wirth viewed Modula-2 as a successor to his earlier programming languages Pascal and Modula. The main concepts are: # The module as a compiling unit for separate compiling # The coroutine as the basic building block for concurrent processes # Types and procedures that allow access to machine-specific data The language design was influenced by the Mesa language and the Xerox Alto, both from Xerox PARC, that Wirth saw during his 1976 sabbatical year there. Page 4. The computer magazine ''Byte'' devoted the August 1984 issue to the language and its surrounding environment. Wirth created the Oberon series of languages as the successor to Modula-2, while others (particularl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fast Inverse Square Root
Fast inverse square root, sometimes referred to as or by the hexadecimal constant , is an algorithm that estimates \frac, the Multiplicative inverse, reciprocal (or multiplicative inverse) of the square root of a 32-bit floating-point number x in Single-precision floating-point format#IEEE 754 standard: binary32, IEEE 754 floating-point format. The algorithm is best known for its implementation in 1999 in ''Quake III Arena'', a first-person shooter video game heavily based on 3D graphics. With subsequent hardware advancements, especially the x86 Streaming SIMD Extensions, SSE instruction rsqrtss, this algorithm is not generally the best choice for modern computers, though it remains an interesting historical example. The algorithm accepts a 32-bit floating-point number as the input and stores a halved value for later use. Then, treating the bits representing the floating-point number as a 32-bit integer, a logical shift right by one bit is performed and the result subtracted from ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Methods Of Computing Square Roots
Square root algorithms compute the non-negative square root \sqrt of a positive real number S. Since all square roots of natural numbers, other than of perfect squares, are irrational, square roots can usually only be computed to some finite precision: these algorithms typically construct a series of increasingly accurate approximations. Most square root computation methods are iterative: after choosing a suitable initial estimate of \sqrt, an iterative refinement is performed until some termination criterion is met. One refinement scheme is Heron's method, a special case of Newton's method. If division is much more costly than multiplication, it may be preferable to compute the inverse square root instead. Other methods are available to compute the square root digit by digit, or using Taylor series. Rational approximations of square roots may be calculated using continued fraction expansions. The method employed depends on the needed accuracy, and the available tools and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cleve Barry Moler
Cleve Barry Moler (born August 17, 1939) is an American mathematician and computer programmer specializing in numerical analysis. In the mid to late 1970s, he was one of the authors of LINPACK and EISPACK, Fortran libraries for numerical computing. He created MATLAB, a numerical computing package, to give his students at the University of New Mexico easy access to these libraries without writing Fortran. In 1984, he co-founded MathWorks with Jack Little to commercialize this program. Biography He received his bachelor's degree from California Institute of Technology in 1961, and a Ph.D. in 1965 from Stanford University, both in mathematics. He worked for Charles Lawson at the Jet Propulsion Laboratory in 1961 and 1962. He was a professor of mathematics and computer science for almost 20 years at the University of Michigan, Stanford University, and the University of New Mexico. Before joining MathWorks full-time in 1989, he also worked for Intel Hypercube, where he coined t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Elmer Forsythe
George Elmer Forsythe (January 8, 1917 – April 9, 1972) was an American computer scientist and numerical analyst who founded and led Stanford University's Computer Science Department. Forsythe came to Stanford in the Mathematics Department in 1959, and served as professor and chairman of the Computer Science department from 1965 until his death. He served as the president of the Association for Computing Machinery (ACM), coauthored four books on computer science and a fifth on meteorology, and edited more than 75 other books on computer science. Early life George Elmer Forsythe was born on January 8, 1917, in State College, Pennsylvania. Forsythe's family moved to Ann Arbor, Michigan when George was a young boy. Forsythe became interested in computing at a young age, experimenting with hand-cranked desk calculators. Forsythe earned a Bachelor of Science in mathematics at Swarthmore College in 1937, where he was awarded a scholarship. He completed a Ph.D. in mathematics at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Scientist
A computer scientist is a scientist who specializes in the academic study of computer science. Computer scientists typically work on the theoretical side of computation. Although computer scientists can also focus their work and research on specific areas (such as algorithm and data structure development and design, software engineering, information theory, database theory, theoretical computer science, numerical analysis, programming language theory, compiler, computer graphics, computer vision, robotics, computer architecture, operating system), their foundation is the theoretical study of computing from which these other fields derive. A primary goal of computer scientists is to develop or validate models, often mathematical, to describe the properties of computational systems (Processor (computing), processors, programs, computers interacting with people, computers interacting with other computers, etc.) with an overall objective of discovering designs that yield useful ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Common Logarithm
In mathematics, the common logarithm (aka "standard logarithm") is the logarithm with base 10. It is also known as the decadic logarithm, the decimal logarithm and the Briggsian logarithm. The name "Briggsian logarithm" is in honor of the British mathematician Henry Briggs who conceived of and developed the values for the "common logarithm". Historically', the "common logarithm" was known by its Latin name ''logarithmus decimalis'' or ''logarithmus decadis''. The mathematical notation for using the common logarithm is , , or sometimes with a capital ; on calculators, it is printed as "log", but mathematicians usually mean natural logarithm (logarithm with base ≈ 2.71828) rather than common logarithm when writing "log". Before the early 1970s, handheld electronic calculators were not available, and mechanical calculators capable of multiplication were bulky, expensive and not widely available. Instead, tables of base-10 logarithms were used in science, engineering and navi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arthur Burks
Arthur Walter Burks (October 13, 1915 – May 14, 2008) was an American mathematician who worked in the 1940s as a senior engineer on the project that contributed to the design of the ENIAC, the first general-purpose electronic digital computer. Decades later, Burks and his wife Alice Burks outlined their case for the subject matter of the ENIAC having been derived from John Vincent Atanasoff. Burks was also for several decades a faculty member at the University of Michigan in Ann Arbor. Early life and education Burks was born in Duluth, Minnesota. He earned his B.A. in mathematics and physics from DePauw University in Greencastle, Indiana, in 1936 and his M.A. and Ph.D. in philosophy from the University of Michigan in Ann Arbor in 1937 and 1941, respectively. The Moore School The summer after obtaining his Ph.D., Burks moved to Philadelphia, Pennsylvania, and enrolled in the national defense electronics course offered by the University of Pennsylvania's Moore School of Elec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Floating-point Arithmetic
In computing, floating-point arithmetic (FP) is arithmetic on subsets of real numbers formed by a ''significand'' (a Sign (mathematics), signed sequence of a fixed number of digits in some Radix, base) multiplied by an integer power of that base. Numbers of this form are called floating-point numbers. For example, the number 2469/200 is a floating-point number in base ten with five digits: 2469/200 = 12.345 = \! \underbrace_\text \! \times \! \underbrace_\text\!\!\!\!\!\!\!\overbrace^ However, 7716/625 = 12.3456 is not a floating-point number in base ten with five digits—it needs six digits. The nearest floating-point number with only five digits is 12.346. And 1/3 = 0.3333… is not a floating-point number in base ten with any finite number of digits. In practice, most floating-point systems use Binary number, base two, though base ten (decimal floating point) is also common. Floating-point arithmetic operations, such as addition and division, approximate the correspond ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leonardo Torres Quevedo
Leonardo Torres Quevedo (; 28 December 1852 – 18 December 1936) was a Spanish civil engineer, mathematician and inventor, known for his numerous engineering innovations, including Aerial tramway, aerial trams, airships, catamarans, and remote control. He was also a pioneer in the field of Computer science, computing and robotics. Torres was a member of several scientific and cultural institutions and held such important positions as the seat ''N'' of the Royal Spanish Academy, Real Academia Española (1920–1936) and the presidency of the Spanish Royal Academy of Sciences (1928–1934). In 1927 he became a foreign associate of the French Academy of Sciences. His first groundbreaking invention was a cable car system patented in 1887 for the safe transportation of people, an activity that culminated in 1916 when the Whirlpool Aero Car was opened in Niagara Falls. In the 1890s, Torres focused his efforts on Analog computer, analog computation. He published ''Sur les machines alg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Double-precision Floating-point Format
Double-precision floating-point format (sometimes called FP64 or float64) is a floating-point number format, usually occupying 64 bits in computer memory; it represents a wide range of numeric values by using a floating radix point. Double precision may be chosen when the range or precision of single precision would be insufficient. In the IEEE 754 standard, the 64-bit base-2 format is officially referred to as binary64; it was called double in IEEE 754-1985. IEEE 754 specifies additional floating-point formats, including 32-bit base-2 ''single precision'' and, more recently, base-10 representations (decimal floating point). One of the first programming languages to provide floating-point data types was Fortran. Before the widespread adoption of IEEE 754-1985, the representation and properties of floating-point data types depended on the computer manufacturer and computer model, and upon decisions made by programming-language implementers. E.g., GW-BASIC's double-precision ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
