William "Velvel" Morton Kahan (born June 5, 1933) is a

Canadian Canadians (french: Canadiens) are people identified with the country of Canada. This connection may be residential, legal, historical or cultural. For most Canadians, many (or all) of these connections exist and are collectively the source of ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

and

computer scientist A computer scientist is a person who is trained in the academic study of computer science. Computer scientists typically work on the theoretical side of computation, as opposed to the hardware side on which computer engineers mainly focus (al ...

, who received the

Turing Award The ACM A. M. Turing Award is an annual prize given by the Association for Computing Machinery (ACM) for contributions of lasting and major technical importance to computer science. It is generally recognized as the highest distinction in compu ...

in 1989 for "''his fundamental contributions to

numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...

''", was named an

ACM Fellow ACM or A.C.M. may refer to: Aviation * AGM-129 ACM, 1990–2012 USAF cruise missile * Air chief marshal * Air combat manoeuvring or dogfighting * Air cycle machine * Arica Airport (Colombia) (IATA: ACM), in Arica, Amazonas, Colombia Computing ...

in 1994, and inducted into the

National Academy of Engineering The National Academy of Engineering (NAE) is an American nonprofit, non-governmental organization. The National Academy of Engineering is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy ...

in 2005.

Biography

Born to a Canadian Jewish family, he attended the

University of Toronto The University of Toronto (UToronto or U of T) is a public research university in Toronto, Ontario, Canada, located on the grounds that surround Queen's Park. It was founded by royal charter in 1827 as King's College, the first institution ...

, 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 The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

. Kahan was the primary architect behind the

IEEE 754-1985 IEEE 754-1985 was an industry standard for representing floating-point numbers in computers, officially adopted in 1985 and superseded in 2008 by IEEE 754-2008, and then again in 2019 by minor revision IEEE 754-2019. During its 23 years, it was the ...

standard for

floating-point 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 b ...

computation (and its radix-independent follow-on,

IEEE 854 The IEEE Standard for Radix-Independent Floating-Point Arithmetic (IEEE 854), was the first Institute of Electrical and Electronics Engineers (IEEE) international standard for floating-point arithmetic with radices other than 2, including radix 1 ...

). 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 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 ...

that led to the current IEEE 754 standard. In the 1980s he developed the program "paranoia", a benchmark that tests for a wide range of potential floating-point bugs. He also developed the Kahan summation algorithm, an important algorithm for minimizing error introduced when adding a sequence of finite-precision

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 r ...

s. He coined the term "

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 oft ...

" for the unknown cost of correctly rounding

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 alge ...

s to some preassigned number of digits. The Davis–Kahan–Weinberger dilation theorem is one of the landmark results in the dilation theory of

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 natural ...

operators and has found applications in many different areas. He is an outspoken advocate of better education of the general computing population about floating-point issues and regularly denounces decisions in the design of computers and programming languages that he believes would impair good floating-point computations. When

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 ...

(HP) introduced the original

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 Hewl ...

pocket scientific calculator, its numerical accuracy in evaluating transcendental functions for some arguments was not optimal. HP worked extensively with Kahan to enhance the accuracy of the algorithms, which led to major improvements. This was documented at the time in the ''

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 for "tall stick") is a charter city i ...

''. He also contributed substantially to the design of the algorithms in the

HP Voyager series The Hewlett-Packard Voyager series of calculators were introduced by Hewlett-Packard in 1981. All members of this series are programmable, use Reverse Polish Notation, and feature continuous memory. Nearly identical in appearance, each model ...

and wrote part of their intermediate and advanced manuals.

References

External links

William Kahan's home page

An oral history of William Kahan
Revision 1.1, March, 2016 *
A Conversation with William Kahan, Dr. Dobb's Journal
November 1, 1997 *

February 20, 1998
IEEE 754 An Interview with William Kahan
April, 1998

Paranoia for modern graphics processing units (GPUs)

754-1985 - IEEE Standard for Binary Floating-Point Arithmetic
1985, Superseded b
IEEE Std 754-2008
{{DEFAULTSORT:Kahan, William 1933 births Living people 20th-century Canadian mathematicians 21st-century Canadian mathematicians Numerical analysts Canadian computer scientists Scientific computing researchers UC Berkeley College of Engineering faculty Turing Award laureates Fellows of the Association for Computing Machinery Scientists from Toronto University of Toronto alumni Canadian expatriate academics in the United States Jewish Canadian scientists

Biography

See also

References

External links