FFTs in external or hierarchical memory
The Journal of Supercomputing
On fast multiplication of polynomials over arbitrary algebras
Acta Informatica
Topics in advanced scientific computation
Topics in advanced scientific computation
Modern Computer Algebra
The truncated fourier transform and applications
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Fast arithmetic for triangular sets: From theory to practice
Journal of Symbolic Computation
A cache-friendly truncated FFT
Theoretical Computer Science
Space- and time-efficient polynomial multiplication
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
A new truncated fourier transform algorithm
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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The 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 memory usage. We describe in-place variants of the forward and inverse TFT algorithms, achieving time complexity O(n log n) with only O(1) auxiliary space. As an application, we extend the second author's results on space-restricted FFT-based polynomial multiplication to polynomials of arbitrary degree.