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William M. Kahan
William "Velvel" Morton Kahan (born June 5, 1933) is a Canadian mathematician and computer scientist, who received the Turing Award in 1989 for "''his fundamental contributions to numerical analysis''", was named an ACM Fellow in 1994, and inducted into the National Academy of Engineering in 2005. Biography Born to a Canadian Jewish family, he attended the University of Toronto, where he received his bachelor's degree in 1954, his master's degree in 1956, and his Ph.D. in 1958, all in the field of mathematics. Kahan is now emeritus professor of mathematics and of electrical engineering and computer sciences (EECS) at the University of California, Berkeley. Kahan was the primary architect behind the IEEE 754-1985 standard for floating-point computation (and its radix-independent follow-on, IEEE 854). He has been called "The Father of Floating Point", since he was instrumental in creating the original IEEE 754 specification. Kahan continued his contributions to the IEEE 754 revisio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Toronto
Toronto ( ; or ) is the capital city of the Canadian province of Ontario. With a recorded population of 2,794,356 in 2021, it is the most populous city in Canada and the fourth most populous city in North America. The city is the anchor of the Golden Horseshoe, an urban agglomeration of 9,765,188 people (as of 2021) surrounding the western end of Lake Ontario, while the Greater Toronto Area proper had a 2021 population of 6,712,341. Toronto is an international centre of business, finance, arts, sports and culture, and is recognized as one of the most multicultural and cosmopolitan cities in the world. Indigenous peoples have travelled through and inhabited the Toronto area, located on a broad sloping plateau interspersed with rivers, deep ravines, and urban forest, for more than 10,000 years. After the broadly disputed Toronto Purchase, when the Mississauga surrendered the area to the British Crown, the British established the town of York in 1793 and later designat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
History Of The Jews In Canada
Canadian citizens who follow Judaism as their religion and/or are Jewish ethnic divisions, ethnically Jewish are a part of the greater Jewish diaspora and form the third largest Jewish community in the world, exceeded only by those Israeli Jews, in Israel and American Jews, in the United States. As of 2021, Statistics Canada listed 335,295 adherents to the Jewish religion in Canada. This total would account for approximately 1.4% of the Canadian population. The Jewish community in Canada is composed predominantly of Ashkenazi Jews and their descendants. Other Jewish ethnic divisions are also represented and include Sephardi Jews, Mizrahi Jews, and Bene Israel. A number of converts to Judaism make up the Jewish-Canadian community, which manifests a wide range of Jewish cultural traditions and the Jewish religious movements#Modern divisions or denominations, full spectrum of Jewish religious observance. Though they are a small minority, they have had an open presence in the count ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hewlett-Packard Journal
''Hewlett-Packard Journal'' was a magazine published by Hewlett-Packard (HP) between 1949–1998. The first issue appeared in September 1949. Headquartered in Palo Alto, California Palo Alto (; Spanish language, Spanish for "tall stick") is a charter city in the northwestern corner of Santa Clara County, California, United States, in the San Francisco Bay Area, named after a Sequoia sempervirens, coastal redwood tree kno ..., it covered technical and product news from HP. The magazine was started as monthly, but then its frequency switched to bimonthly. It is available as web-pages - or as scanned and available on HPs home page as PDF downloads. References {{Reflist External links leapsecond.com: Time & Frequency Articles from ''Hewlett Packard Journal'' Bimonthly magazines published in the United States Monthly magazines published in the United States Defunct computer magazines published in the United States Hewlett-Packard Magazines disestablished in 1998 Magazines e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
HP-35
The HP-35 was Hewlett-Packard's first pocket calculator and the world's first ''scientific'' pocket calculator: a calculator with trigonometric and exponential functions. It was introduced in 1972. History In about 1970 HP co-founder Bill Hewlett challenged his co-workers to create a "shirt-pocket sized HP-9100". At the time, slide rules were the only practical portable devices for performing trigonometric and exponential functions, as existing pocket calculators could only perform addition, subtraction, multiplication, and division. Introduced at , like HP's first scientific calculator, the desktop 9100A, it used reverse Polish notation (RPN) rather than what came to be called "algebraic" entry. The "35" in the calculator's name came from the number of keys. The original HP-35 was available from 1972 to 1975. In 2007 HP announced the release of the "retro"-look HP 35s to commemorate the 35th anniversary of the launch of the original HP-35. It was priced at . The HP-35 was na ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hewlett-Packard
The Hewlett-Packard Company, commonly shortened to Hewlett-Packard ( ) or HP, was an American multinational information technology company headquartered in Palo Alto, California. HP developed and provided a wide variety of hardware components, as well as software and related services to consumers, small and medium-sized businesses ( SMBs), and large enterprises, including customers in the government, health, and education sectors. The company was founded in a one-car garage in Palo Alto by Bill Hewlett and David Packard in 1939, and initially produced a line of electronic test and measurement equipment. The HP Garage at 367 Addison Avenue is now designated an official California Historical Landmark, and is marked with a plaque calling it the "Birthplace of 'Silicon Valley'". The company won its first big contract in 1938 to provide test and measurement instruments for Walt Disney's production of the animated film ''Fantasia'', which allowed Hewlett and Packard to formally esta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hilbert Space
In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces. Formally, a Hilbert space is a vector space equipped with an inner product that defines a distance function for which the space is a complete metric space. The earliest Hilbert spaces were studied from this point of view in the first decade of the 20th century by David Hilbert, Erhard Schmidt, and Frigyes Riesz. They are indispensable tools in the theories of partial differential equations, quantum mechanics, Fourier analysis (which includes applications to signal processing and heat transfer), and ergodic theory (which forms the mathematical underpinning of thermodynamics). John von Neumann coined the term ''Hilbert space'' for the abstract concept that under ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transcendental Function
In mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation, in contrast to an algebraic function. In other words, a transcendental function "transcends" algebra in that it cannot be expressed algebraically. Examples of transcendental functions include the exponential function, the logarithm, and the trigonometric functions. Definition Formally, an analytic function ''f''(''z'') of one real or complex variable ''z'' is transcendental if it is algebraically independent of that variable. This can be extended to functions of several variables. History The transcendental functions sine and cosine were tabulated from physical measurements in antiquity, as evidenced in Greece (Hipparchus) and India ( jya and koti-jya). In describing Ptolemy's table of chords, an equivalent to a table of sines, Olaf Pedersen wrote: A revolutionary understanding of these circular functions occurred in the 17th century and was explicated by Leonhard ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Table-maker's Dilemma
Rounding means replacing a number with an approximation, approximate value that has a shorter, simpler, or more explicit representation. For example, replacing $ with $, the fraction 312/937 with 1/3, or the expression with . Rounding is often done to obtain a value that is easier to report and communicate than the original. Rounding can also be important to avoid false precision, misleadingly precise reporting of a computed number, measurement, or estimate; for example, a quantity that was computed as but is known to be accuracy and precision, accurate only to within a few hundred units is usually better stated as "about ". On the other hand, rounding of exact numbers will introduce some round-off error in the reported result. Rounding is almost unavoidable when reporting many computations – especially when dividing two numbers in integer or fixed-point arithmetic; when computing mathematical functions such as square roots, logarithms, and sines; or when using a floating- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Floating-point Number
In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can be represented as a base-ten floating-point number: 12.345 = \underbrace_\text \times \underbrace_\text\!\!\!\!\!\!^ In practice, most floating-point systems use base two, though base ten (decimal floating point) is also common. The term ''floating point'' refers to the fact that the number's radix point can "float" anywhere to the left, right, or between the significant digits of the number. This position is indicated by the exponent, so floating point can be considered a form of scientific notation. A floating-point system can be used to represent, with a fixed number of digits, numbers of very different orders of magnitude — such as the number of meters between galaxies or between protons in an atom. For this reason, floating-point ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IEEE 754-2008
The Institute of Electrical and Electronics Engineers (IEEE) is a 501(c)(3) professional association for electronic engineering and electrical engineering (and associated disciplines) with its corporate office in New York City and its operations center in Piscataway, New Jersey. The mission of the IEEE is ''advancing technology for the benefit of humanity''. The IEEE was formed from the amalgamation of the American Institute of Electrical Engineers and the Institute of Radio Engineers in 1963. Due to its expansion of scope into so many related fields, it is simply referred to by the letters I-E-E-E (pronounced I-triple-E), except on legal business documents. , it is the world's largest association of technical professionals with more than 423,000 members in over 160 countries around the world. Its objectives are the educational and technical advancement of electrical and electronic engineering, telecommunications, computer engineering and similar disciplines. History Origins ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IEEE 754 Revision
IEEE 754-2008 (previously known as ''IEEE 754r'') was published in August 2008 and is a significant revision to, and replaces, the IEEE 754-1985 floating-point standard, while in 2019 it was updated with a minor revision IEEE 754-2019. The 2008 revision extended the previous standard where it was necessary, added decimal arithmetic and formats, tightened up certain areas of the original standard which were left undefined, and merged in IEEE 854 (the radix-independent floating-point standard). In a few cases, where stricter definitions of binary floating-point arithmetic might be performance-incompatible with some existing implementation, they were made optional. Revision process The standard had been under revision since 2000, with a target completion date of December 2006. The revision of an IEEE standard broadly follows three phases: # Working group – a committee that creates a draft standard # Ballot – interested parties subscribe to the ''balloting group'' an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
