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» Multithreaded algorithms for the fast Fourier transform
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FMSD
2002
114views more  FMSD 2002»
13 years 7 months ago
The Correctness of the Fast Fourier Transform: A Structured Proof in ACL2
The powerlists data structure, created by Misra in the early 90s, is well suited to express recursive, data-parallel algorithms. Misra has shown how powerlists can be used to give ...
Ruben Gamboa
ISMVL
2002
IEEE
84views Hardware» more  ISMVL 2002»
14 years 9 days ago
The Role of Super-Fast Transforms in Speeding Up Quantum Computations
We present the role that spectral methods play in the development of the most impressive quantum algorithms, such as the polynomial time number factoring algorithm by Shor. While ...
Zeljko Zilic, Katarzyna Radecka
IPPS
1998
IEEE
13 years 11 months ago
Mechanically Verifying the Correctness of the Fast Fourier Transform in ACL2
In [10], Misra introduced the powerlist data structure, which is well suited to express recursive, data-parallel algorithms. In particular, Misra showed how powerlists could be use...
Ruben Gamboa
ERSHOV
2003
Springer
14 years 18 days ago
A Polymorphic Radix- n Framework for Fast Fourier Transforms
We provide a polymorphic framework for radix-n Fast Fourier Transforms (FFTs) where all known kinds of monomoporhic radix-n algorithms can be obtained by specialization. The framew...
Marcin Zalewski, Sibylle Schupp
ISSAC
2004
Springer
135views Mathematics» more  ISSAC 2004»
14 years 23 days ago
The truncated fourier transform and applications
In this paper, we present a truncated version of the classical Fast Fourier Transform. When applied to polynomial multiplication, this algorithm has the nice property of eliminati...
Joris van der Hoeven