Find the next fast size of input data to fft, for zero-padding, etc.

SciPy’s FFT algorithms gain their speed by a recursive divide and conquer strategy. This relies on efficient functions for small prime factors of the input length. Thus, the transforms are fastest when using composites of the prime factors handled by the fft implementation. If there are efficient functions for all radices <= n, then the result will be a number x >= target with only prime factors < n. (Also known as n-smooth numbers)


Length to start searching from. Must be a positive integer.

realbool, optional

True if the FFT involves real input or output (e.g., rfft or hfft but not fft). Defaults to False.


The smallest fast length greater than or equal to target.


The result of this function may change in future as performance considerations change, for example, if new prime factors are added.

Calling fft or ifft with real input data performs an 'R2C' transform internally.


On a particular machine, an FFT of prime length takes 11.4 ms:

>>> from scipy import fft
>>> min_len = 93059  # prime length is worst case for speed
>>> a = np.random.randn(min_len)
>>> b = fft.fft(a)

Zero-padding to the next regular length reduces computation time to 1.6 ms, a speedup of 7.3 times:

>>> fft.next_fast_len(min_len, real=True)
>>> b = fft.fft(a, 93312)

Rounding up to the next power of 2 is not optimal, taking 3.0 ms to compute; 1.9 times longer than the size given by next_fast_len:

>>> b = fft.fft(a, 131072)

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