William Kahan
Encyclopedia
William Morton Kahan is a mathematician
and computer scientist
who received the Turing Award
in 1989 for "his fundamental contributions to numerical analysis
", and was named an ACM Fellow in 1994.
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 revision
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. It would go on to detect the infamous Pentium division bug
, and continues to have important uses to this day. He also developed the Kahan summation algorithm
, an important algorithm for minimizing error introduced when adding a sequence of finite precision floating point numbers. He coined the term "The Table-Maker's Dilemma" for the unknown cost of correctly rounding transcendental function
s to some preassigned number of digits.
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 may impair good floating-point computations.
When Hewlett–Packard introduced the original HP-35 pocket scientific calculator, its numerical accuracy, in evaluating transcendental functions, for some arguments, was not optimal. Hewlett–Packard 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.
He also contributed substantially to the design of the algorithms in the HP-10C series, and wrote part of their intermediate and advanced manuals.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and computer scientist
Computer scientist
A computer scientist is a scientist who has acquired knowledge of computer science, the study of the theoretical foundations of information and computation and their application in computer systems....
who received the Turing Award
Turing Award
The Turing Award, in full The ACM A.M. Turing Award, is an annual award given by the Association for Computing Machinery to "an individual selected for contributions of a technical nature made to the computing community. The contributions should be of lasting and major technical importance to the...
in 1989 for "his fundamental contributions to numerical analysis
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
", and was named an ACM Fellow in 1994.
He attended the University of Toronto
University of Toronto
The University of Toronto is a public research university in Toronto, Ontario, Canada, situated on the grounds that surround Queen's Park. It was founded by royal charter in 1827 as King's College, the first institution of higher learning in Upper Canada...
, 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
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
.
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 revision
IEEE 754 revision
IEEE 754-2008 was published in August 2008 and is a significant revision to, and replaces, the IEEE 754-1985 floating point standard...
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. It would go on to detect the infamous Pentium division bug
Pentium FDIV bug
The Pentium FDIV bug was a bug in the Intel P5 Pentium floating point unit . Certain floating point division operations performed with these processors would produce incorrect results...
, and continues to have important uses to this day. He also developed the Kahan summation algorithm
Kahan summation algorithm
In numerical analysis, the Kahan summation algorithm significantly reduces the numerical error in the total obtained by adding a sequence of finite precision floating point numbers, compared to the obvious approach...
, an important algorithm for minimizing error introduced when adding a sequence of finite precision floating point numbers. He coined the term "The Table-Maker's Dilemma" for the unknown cost of correctly rounding transcendental function
Transcendental function
A transcendental function is a function that does not satisfy a polynomial equation whose coefficients are themselves polynomials, in contrast to an algebraic function, which does satisfy such an equation...
s to some preassigned number of digits.
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 may impair good floating-point computations.
When Hewlett–Packard introduced the original HP-35 pocket scientific calculator, its numerical accuracy, in evaluating transcendental functions, for some arguments, was not optimal. Hewlett–Packard 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.
He also contributed substantially to the design of the algorithms in the HP-10C series, and wrote part of their intermediate and advanced manuals.
External links
- William Kahan's home page
- portrait picture of Kahan
- Paranoia for modern graphics processing units (GPUs)
- Paranoia source code in multiple languages
- Richard Karpinski. 1985. Paranoia: A floating-point benchmark. Byte Magazine 10, 2 (Feb.), 223–235
- IEEE 1985. IEEE standard for binary floating-point arithmetic. ACM SIGPLAN Notices 22, 2 (Feb.), 9–25
- An Interview with the Old Man of Floating-Point, 1998-Feb-20 http://www.cs.berkeley.edu/~wkahan/ieee754status/754story.html
- A Conversation with William Kahan, Dr. Dobb's Journal November, 1997
