In
mathematics, the irrational base discrete weighted transform (IBDWT) is a variant of the
fast Fourier transform using an
irrational
Irrationality is cognition, thinking, talking, or acting without inclusion of rationality. It is more specifically described as an action or opinion given through inadequate use of reason, or through emotional distress or cognitive deficiency. T ...
base; it was developed by
Richard Crandall
Richard E. Crandall (December 29, 1947 – December 20, 2012) was an American physicist and computer scientist who made contributions to computational number theory.
Background
Richard Crandall was born in Ann Arbor, Michigan, and spent two years ...
(
Reed College
Reed College is a private liberal arts college in Portland, Oregon. Founded in 1908, Reed is a residential college with a campus in the Eastmoreland neighborhood, with Tudor-Gothic style architecture, and a forested canyon nature preserve at ...
),
Barry Fagin (
Dartmouth College
Dartmouth College (; ) is a private research university in Hanover, New Hampshire. Established in 1769 by Eleazar Wheelock, it is one of the nine colonial colleges chartered before the American Revolution. Although founded to educate Native ...
) and
Joshua Doenias (
NeXT Software) in the early 1990s using
Mathematica.
The IBDWT is used in the
Great Internet Mersenne Prime Search
The Great Internet Mersenne Prime Search (GIMPS) is a collaborative project of volunteers who use freely available software to search for Mersenne prime numbers.
GIMPS was founded in 1996 by George Woltman, who also wrote the Prime95 client and ...
's client
Prime95
Prime95, also distributed as the command-line utility mprime for FreeBSD and Linux, is a freeware application written by George Woltman. It is the official client of the Great Internet Mersenne Prime Search (GIMPS), a volunteer computing projec ...
to perform
FFT multiplication, as well as in other programs implementing
Lucas-Lehmer test, such as CUDALucas and Glucas.
References
*
Richard Crandall
Richard E. Crandall (December 29, 1947 – December 20, 2012) was an American physicist and computer scientist who made contributions to computational number theory.
Background
Richard Crandall was born in Ann Arbor, Michigan, and spent two years ...
,
Barry Fagin: ''Discrete weighted transforms and large-integer arithmetic'', Mathematics of Computation 62, 205, 305-324, January 1994
PDF file
*
Richard Crandall
Richard E. Crandall (December 29, 1947 – December 20, 2012) was an American physicist and computer scientist who made contributions to computational number theory.
Background
Richard Crandall was born in Ann Arbor, Michigan, and spent two years ...
: ''Topics in Advanced Scientific Computation'', TELOS/Springer-Verlag
FFT algorithms
Discrete transforms
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