ABSTRACT
Truncated Fourier Transforms (TFTs), first introduced by van der Hoeven, refer to a family of algorithms that attempt to smooth ``jumps'' in complexity exhibited by FFT algorithms. We present an in-place TFT whose time complexity, measured in terms of ring operations, is asymptotically equivalent to existing not-in-place TFT methods. We also describe a transformation that maps between two families of TFT algorithms that use different sets of evaluation points.
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Index Terms
- A new truncated fourier transform algorithm
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An in-place truncated fourier transform and applications to polynomial multiplication
ISSAC '10: Proceedings of the 2010 International Symposium on Symbolic and Algebraic ComputationThe truncated Fourier transform (TFT) was introduced by van der Hoeven in 2004 as a means of smoothing the "jumps" in running time of the ordinary FFT algorithm that occur at power-of-two input sizes. However, the TFT still introduces these jumps in ...
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