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	William Kahan - Wikipedia, the free encyclopedia
		William Velvel Kahan (born June 5, 1933, in Toronto, Ontario, Canada) is an eminent mathematician and computer scientist.
		Kahan's main area of contribution has been numerical analysis — the study of accurate and efficient methods of solving numerical problems on a computer with finite precision — a field vitally important in physics and engineering.
		Among his many contributions, Kahan was the primary architect behind the IEEE 754 standard for floating-point computation (and its radix-independent follow-on, IEEE 854) and contributed an important algorithm for minimizing error introduced when adding a sequence of finite precision floating point numbers (see the Kahan Summation Algorithm).
	en.wikipedia.org /wiki/William_Kahan (201 words)

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	Learn more about William Kahan in the online encyclopedia. (Site not responding. Last check: 2007-10-19)
		William Kahan (born June 5, 1933, in Toronto, Alberta, Canada)is an eminent mathematician and computer scientist whose main area of contribution was numerical analysis, the study of accurate and efficient methods of solving numerical problems on a computer with finite precision—a field vitally important in physics and engineering.
		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 1959, all in the field of mathematics.
		Among his many contributions, Kahan was the primary architect behind the ANSI/IEEE standard for floating-point computation and contributed an important algorithm for minimizing error introduced when adding a sequence of finite precision floating point numbers (see the Kahan Summation Algorithm).
	www.onlineencyclopedia.org /w/wi/william_kahan.html (269 words)

	Minutes from 754R meeting 15 November, 2001
		Kahan: Rounding precision control would exist only on certain kinds of hardware, whose natural register destination was wider than the operands.
		After some debate, Kahan suggested that we say there are three basic formats and two families of extended formats, and include text to explain that double is a member of the single-extended family and quad is a member of the double-extended family.
		Kahan suggested we refer to the "widest precision supported by hardware"; several people objected that such language contradicted the statement that the standard could be implemented in any mix of hardware and software.
	grouper.ieee.org /groups/754/meeting-minutes/01-11-15.html (2284 words)

	Basic Floating Point Representation
		William Kahan, Lecture Notes on the Status of IEEE Standard 754 for Binary Floating-Point Arithmetic, EECS, University of California at Berkeley, May 1996.
		Note: Kahan uses "N = p" for the precision of the fraction and "K+1=q" for the precision of the exponent".
		Kahan uses the notation such that "k = exp" for unbiased exponent and "n=(1+frac)*2^(p-1)" for the unsigned significand integer for the fraction.
	www.math.uic.edu /~hanson/mcs471/FloatingPointRep.html (564 words)

	On to Hydro (Site not responding. Last check: 2007-10-19)
		I found some examples of algorithms which benefit by allowing division by zero at http://http.cs.berkeley.edu/~wkahan/ieee754status/ieee754.ps, an article by William Kahan, inventor of the IEEE 754 floating point standard.
		Kahan gives some examples on pages 10-14 where allowing division by zero simplifies calculations.
		If you disable the DBZ trap then it produces positive or negative infinity as the answer, and in some cases this can then be used in a meaningful way as a further operand, in particular as a divisor.
	www.eros-os.org /pipermail/e-lang/2000-August/003705.html (190 words)

	Dan 0411 - Pentium II Math Bug? (Site not responding. Last check: 2007-10-19)
		Professor William Kahan of Berkeley has written a suite of floating point test programs in the FORTRAN programming language.
		Technically, it looks like the original intent of Dr. Kahan's was to use a bit-wise AND instead of a logical AND in his original FORTRAN source code; this is a potential non-portability issue -- as I'm not sure how AND is defined by the FORTRAN standard.
		Dan recognized Dr. Kahan's original intent and used the proper bit-wise AND operator in his C source code.
	www.x86.org /secrets/dan0411.htm (1759 words)

	Java's floating point hurts everyone everywhere - Infomatics (Site not responding. Last check: 2007-10-19)
		Kahan reports that Java is inadequate in its treatment of floating point calculations and complex numbers.
		Kahan and a group of engineers, as part of the Java Grande Forum, spelled out what they consider serious deficiencies in the Java programming language.
		Kahan explained that Borneo's design was constrained to be upwards compatible with Java.
	infomaticsonline.co.uk /vnunet/news/2100657/... (558 words)

	[No title]
		Palmer, now the manager of Intel's floating-point effort, recruited Kahan as a consultant to help design the arithmetic for the i432 (which died later) and for the i8086/8's upcoming i8087 coprocessor.
		After that 1977 meeting Kahan went back to Intel and requested permission to participate in the standard effort.
		Kahan presented the K-C-S draft to the IEEE p754 working group.
	www.cs.berkeley.edu /~wkahan/ieee754status/754story.html (3542 words)

	DDJ>A Conversation with William Kahan (Site not responding. Last check: 2007-10-19)
		Kahan, a noted mathematician and computer scientist who received his doctorate at the University of Toronto, was a consultant on the design of the original 8087 mathematical coprocessor.
		Among Kahan's many awards and lectureships are the John von Neumann Memorial Lecture for the Society for Industrial and Applied Mathematics (1997), the ACM Turing Award (1989), the Prize for Outstanding Paper (with J. Demmel) from the SIAM Activity Group on Linear Algebra (1991), and the ACM G.E. Forsythe Memorial Award (1972).
		Over the years, Kahan has been known for his rigorous analysis of numerical computation techniques in an era of rapid change and challenge for scientific and engineering programming.
	www.ddj.com /documents/s=935/ddj9711a/9711a.htm (693 words)

	Undergraduate Education Colloquium, The College of Letters and Science, UC Berkeley
		The winners of the LandS Award for Distinguished Research Mentoring of Undergraduates were William Berry (Earth and Planetary Sciences), David Cohen (Rhetoric), Stefano DellaVigna (Economics), William Kahan (Mathematics), and Jeremy Thorner (MCB).
		For ten years Professor William Kahan has prepared Berkeley undergraduates to compete in the annual William Lowell Putnam Mathematics Competition, one of the oldest and most prestigious prizes for young students interested in mathematics.
		The chair of Mathematics noted that, "Professor Kahan's dedication and enthusiasm to work with these students year after year is the great fortune of the Berkeley Mathematics department.
	ls.berkeley.edu /undergrad/colloquia/04-09.html (1002 words)

	[No title]
		My source material for this effort is primarily the HP Journal article by William H. Kahan on the implementation of Solve for the HP-34C.
		Of course, as Kahan points out in his Solve article, any algorithm which depends upon function sampling can be led astray by a careful selection of the function.
		Your example, though, is problematic to the HP Solve algorithm due to the mulitples of pi/n that the algorithm tends to generate.
	www.hpmuseum.org /cgi-sys/cgiwrap/hpmuseum/archv013.cgi?read=44479 (2244 words)

	[No title] (Site not responding. Last check: 2007-10-19)
		However at a lecture I gave on the Pentium bug a week ago at Stanford, William Kahan who was in the audience said that the five entries were missing because it had been proved (erroneously) that they were never accessed by the division algorithm, like all the entries above them in the table.
		Obviously one cannot test any of the inaccessible entries by running the algorithm, so if you believe these five are inaccessible then you will of course not provide a test case for them.
		Having heard such conflicting accounts from Intel and Kahan, neither of whom I am competent to contradict, I am now thoroughly mystified as to the real origin of the bug.
	boole.stanford.edu /pub/FDIV/individual.bugs/bug73 (1333 words)

	Triangle - Wikipedia, the free encyclopedia
		It uses the Fermat point to prove Napoleon's theorem without transformations by Antonio Gutierrez from "Geometry Step by Step from the Land of the Incas"
		William Kahan: Miscalculating Area and Angles of a Needle-like Triangle.
		Lists some 1600 interesting points associated with any triangle.
	en.wikipedia.org /wiki/Triangle (2072 words)

	William Kahan -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-19)
		William Kahan -- Facts, Info, and Encyclopedia article
		He received the (Click link for more info and facts about Turing Award) Turing Award in 1989, and was named an ACM Fellow in 1994.
		He is now a professor of mathematics, computer science, and electrical engineering at the (Click link for more info and facts about University of California, Berkeley) University of California, Berkeley, and continues his contributions to the (Click link for more info and facts about ongoing revision of IEEE 754) ongoing revision of IEEE 754.
	www.absoluteastronomy.com /encyclopedia/w/wi/william_kahan.htm (87 words)

	09.01.99 - Awards
		Computer science Professor William Kahan received the Institute of Electrical and Electronics Engineers' Emanuel R. Piore Award for "contributions to numerical analysis and standardization of floating-point arithmetic."
		The Piore Award is one of the prestigious 2000 IEEE Technical Field Awards, whose 15 recipients were announced in June.
		Kahan, a faculty member since 1968, is a past recipient of the A. Turing Award from the Association for Computing Machinery, which is sometimes referred to as a Nobel Prize for computer science.
	www.berkeley.edu /news/berkeleyan/1999/0901/awards.html (244 words)

	DNW's Archive: forth/complex
		Another revision that uses William Kahan's extended accuracy algorithms.
		William Kahan uses Borda's mouthpiece as an example where the proper treatment of signed zero makes a dramatic difference.
		John von Neumann lecture: The Baleful Effect of Computer Languages and Benchmarks upon Applied Mathematics, Physics and Chemistry by William Kahan.
	www-personal.umich.edu /~williams/archive/forth/complex?N=D (366 words)

	IEEE-754 References
		John Palmer persuaded Intel that it needed an arithmetic standard to prevent different boxes with "Intel" on the outside from computing disparate results inside.
		At Stanford ten years earlier, Palmer had heard a visiting professor, William Kahan, analyze commercially significant arithmetics and assess how much their anomalies inflated the costs of reliable and portable numerical software.
		Kahan had also enhanced the numerical prowess of a successful line of Hewlett-Packard calculators.
	babbage.cs.qc.edu /courses/cs341/IEEE-754references.html (2017 words)

	References
		William M. Kahan ``Branch cuts for complex elementary functions'', In The state of the art in numerical analysis, M.
		William H. Press, Brian P. Flannery, Saul A. Teukolsky, and William T. Vetterling, Numerical Recipes, Cambridge University Press, 2nd ed., 1992.
		William Y. Sit, ``An algorithm for solving parametric linear systems'', J. Symb.
	www.apmaths.uwo.ca /~rcorless/AM563/NOTES/Jan_31_96/node29.html (1364 words)

	EETimes.com
		Less sanguine is William Kahan, a professor of computer science at the University of California at Berkeley who is best known as the father of the IEEE floating-point standard, adopted in 1985.
		However, he claimed that Java defines the semantics of the floating-point formats so rigorously that there is no way for Java to use the third, extended-precision, floating-point format.
		As for critics who claim that floating-point questions are of minor importance, Kahan of Berkeley has a response.
	www.eet.com /news/98/1024news/java.html (1840 words)

	Unconventional Schemes for a Class of Ordinary Differential Equations - with Applications to the Korteweg-de Vries ... (Site not responding. Last check: 2007-10-19)
		Unconventional Schemes for a Class of Ordinary Differential Equations - with Applications to the Korteweg-de Vries (KdV) Equation - Kahan, Li (ResearchIndex)
		Kahan and Ren-Cang Li, Unconventional schemes for a class of ordinary differential equations -- with applications to the Korteweg-de Vries equation.
		@misc{ kahan97unconventional, author = "W. Kahan and R. Li", title = "Unconventional schemes for a class of ordinary differential equations -- with applications to the Korteweg-de Vries equation", text = "W. Kahan and Ren-Cang Li, Unconventional schemes for a class of ordinary differential equations -- with applications to the Korteweg-de Vries equation.
	citeseer.ist.psu.edu /kahan97unconventional.html (673 words)

	On to Hydro
		Following that strategy would linearize the field of doubles, getting rid of both the comparison issue and the equality issue.
		+0.0 == -0.0 ------------ Again based on reading of the William Kahan paper, I have the impression that +0.0 and -0.0 are actually different numbers with different meanings, and are not equal or equivalent.
		The Kahan paper indicates that they are not computationally equivalent.
	www.eros-os.org /pipermail/e-lang/2000-August/003707.html (705 words)

	02.14.2005 - Five UC Berkeley professors elected to prestigious National Academy of Engineering
		In addition, William M. Kahan, professor of computer sciences, was one of 10 foreign associates named to the academy.
		This brings to 87 the total number of UC Berkeley faculty members in the society.
		Academy membership honors those who have made outstanding contributions to the field of engineering research, practice or education.
	www.berkeley.edu /news/media/releases/2005/02/14_nae.shtml (363 words)

	Books by Stanley Kahan - Actors Workbook - 1125600519 spanish audio books (Site not responding. Last check: 2007-10-19)
		William R Derrick Stanley I Grossman Richard D Jones - Introduction Do Differential Equations With Boundary Value Problems: Solutions Manual - 031434764X
		William E Oconnor - Introduction To Airline Economics 6ed - 0275969118
		William Barnier - Introduction To Advanced Mathematics - 0130167509
	isbncheck.com /890777_stanley-kahan_1125600519actorsworkbookspanisha... (191 words)

	Uc Berkeley Law (Site not responding. Last check: 2007-10-19)
		William F. Giauque (B.S. 1920, Ph.D. 1922) - Professor, Nobel laureate (1949)
		William F. Giauque (B.S. 1920, Ph.D. 1922) - Nobel laureate (1949, Chemistry)
		William Kahan - recipient of the 1989 Turing Award
	www.wwwtln.com /finance/183/uc-berkeley-law.html (1001 words)

	DDJ, November 1997
		Noted mathematician and computer scientist William Kahan has played a central role in everything from the design of the 8087 math coprocessor to defining the ANSI/IEEE Standard for binary floating-point arithmetic.
		He takes time out of his schedule to talk with us about the current state of numeric computing.
		Robert continues his examination of in-circuit emulators and the Pentium by looking at the Pentium's ICE Mode.
	www.cs.ubc.ca /local/reading/proceedings/ddj/2000_06/articles/1997/9711/9711toc.htm (421 words)

	Mainframeforum - nulls (Site not responding. Last check: 2007-10-19)
		Morton Kahan, the one primarily responsible for them in IEEE 754 -- or it may have been "The Wrath
		In any event, he is firm in his belief that their use should be discouraged and avoided
		In any event, he is firm in his belief that their use should be discouraged[/q1]
	www.mainframeforum.com /t505051.html (5074 words)

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