  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.
