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

SciPy’s FFTPACK has efficient functions for radix {2, 3, 4, 5}, so this returns the next composite of the prime factors 2, 3, and 5 which is greater than or equal to target. (These are also known as 5-smooth numbers, regular numbers, or Hamming numbers.)


target : int

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


out : int

The first 5-smooth number greater than or equal to target.


New in version 0.18.0.


On a particular machine, an FFT of prime length takes 133 ms:

>>> from scipy import fftpack
>>> min_len = 10007  # prime length is worst case for speed
>>> a = np.random.randn(min_len)
>>> b = fftpack.fft(a)

Zero-padding to the next 5-smooth length reduces computation time to 211 us, a speedup of 630 times:

>>> fftpack.helper.next_fast_len(min_len)
>>> b = fftpack.fft(a, 10125)

Rounding up to the next power of 2 is not optimal, taking 367 us to compute, 1.7 times as long as the 5-smooth size:

>>> b = fftpack.fft(a, 16384)