Irrational base discrete weighted transform
Encyclopedia
In mathematics
, the irrational base discrete weighted transform (IBDWT) is a variant of the fast Fourier transform
using an irrational
base; it was developed by Richard Crandall
(Reed College
), Barry Fagin (Dartmouth College
) and Joshua Doenias (NeXT Software
) in the early 1990s using Mathematica
.
The IBDWT is used in the Great Internet Mersenne Prime Search
's Prime95
client to perform FFT multiplication.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, the irrational base discrete weighted transform (IBDWT) is a variant of the fast Fourier transform
Fast Fourier transform
A fast Fourier transform is an efficient algorithm to compute the discrete Fourier transform and its inverse. "The FFT has been called the most important numerical algorithm of our lifetime ." There are many distinct FFT algorithms involving a wide range of mathematics, from simple...
using an irrational
Irrational number
In mathematics, an irrational number is any real number that cannot be expressed as a ratio a/b, where a and b are integers, with b non-zero, and is therefore not a rational number....
base; it was developed by Richard Crandall
Richard Crandall
Richard E. Crandall is an American Physicist and computer scientist who has made contributions to computational number theory.He is most notable for the development of the irrational base discrete weighted transform, an important method of finding very large primes. He has, at various times, been...
(Reed College
Reed College
Reed College is a private, independent, liberal arts college located in southeast Portland, Oregon. Founded in 1908, Reed is a residential college with a campus located in Portland's Eastmoreland neighborhood, featuring architecture based on the Tudor-Gothic style, and a forested canyon wilderness...
), Barry Fagin (Dartmouth College
Dartmouth College
Dartmouth College is a private, Ivy League university in Hanover, New Hampshire, United States. The institution comprises a liberal arts college, Dartmouth Medical School, Thayer School of Engineering, and the Tuck School of Business, as well as 19 graduate programs in the arts and sciences...
) and Joshua Doenias (NeXT Software
NeXT
Next, Inc. was an American computer company headquartered in Redwood City, California, that developed and manufactured a series of computer workstations intended for the higher education and business markets...
) in the early 1990s using Mathematica
Mathematica
Mathematica is a computational software program used in scientific, engineering, and mathematical fields and other areas of technical computing...
.
The IBDWT is used in the Great Internet Mersenne Prime Search
Great Internet Mersenne Prime Search
The Great Internet Mersenne Prime Search is a collaborative project of volunteers who use freely available computer software to search for Mersenne prime numbers. The project was founded by George Woltman, who also wrote the software Prime95 and MPrime for the project...
's Prime95
Prime95
Prime95 is the name of the Microsoft Windows-based software application written by George Woltman that is used by GIMPS, a distributed computing project dedicated to finding new Mersenne prime numbers....
client to perform FFT multiplication.