8000 Merge pull request #11888 from mreineck/add_pocketfft · numpy/numpy@bae3cfa · GitHub
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Merge pull request #11888 from mreineck/add_pocketfft
WIP: Add pocketfft sources to numpy for testing, benchmarks, etc.
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‎doc/release/1.17.0-notes.rst

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Highlights
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==========
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* NumPy's FFT implementation has switched to pocketfft
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New functions
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=============
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Improvements
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============
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replacement of the `fftpack`-based FFT module by the `pocketfft` library
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------------------------------------------------------------------------
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Both implementations have the same ancestor (Fortran77 `FFTPACK` by Paul N.
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Swarztrauber), but `pocketfft` contains additional modifications which
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improve both accuracy and performance in some circumstances. For FFT lengths
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containing large prime factors, `pocketfft` uses Bluestein's algorithm, which
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maintains `O(N log N)` run time complexity instead of deteriorating towards
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`O(N*N)` for prime lengths. Also, accuracy for real-valued FFTs with near-prime
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lengths has improved and is on par with complex-valued FFTs.
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Changes
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=======

‎numpy/fft/README.md

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PocketFFT
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---------
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This is a heavily modified implementation of FFTPack [1,2], with the following
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advantages:
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7< 10000 /td>+
- strictly C99 compliant
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- more accurate twiddle factor computation
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- very fast plan generation
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- worst case complexity for transform sizes with large prime factors is
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`N*log(N)`, because Bluestein's algorithm [3] is used for these cases.
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License
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-------
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3-clause BSD (see LICENSE.md)
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Some code details
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-----------------
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Twiddle factor computation:
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- making use of symmetries to reduce number of sin/cos evaluations
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- all angles are reduced to the range `[0; pi/4]` for higher accuracy
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- an adapted implementation of `sincospi()` is used, which actually computes
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`sin(x)` and `(cos(x)-1)`.
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- if `n` sin/cos pairs are required, the adjusted `sincospi()` is only called
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`2*sqrt(n)` times; the remaining values are obtained by evaluating the
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angle addition theorems in a numerically accurate way.
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Parallel invocation:
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- Plans only contain read-only data; all temporary arrays are allocated and
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deallocated during an individual FFT execution. This means that a single plan
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can be used in several threads at the same time.
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Efficient codelets are available for the factors:
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- 2, 3, 4, 5, 7, 11 for complex-valued FFTs
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- 2, 3, 4, 5 for real-valued FFTs
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Larger prime factors are handled by somewhat less efficient, generic routines.
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For lengths with very large prime factors, Bluestein's algorithm is used, and
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instead of an FFT of length `n`, a convolution of length `n2 >= 2*n-1`
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is performed, where `n2` is chosen to be highly composite.
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[1] Swarztrauber, P. 1982, Vectorizing the Fast Fourier Transforms
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(New York: Academic Press), 51
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[2] https://www.netlib.org/fftpack/
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[3] https://en.wikipedia.org/wiki/Chirp_Z-transform

‎numpy/fft/__init__.py

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# To get sub-modules
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from .info import __doc__
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6-
from .fftpack import *
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from .pocketfft import *
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from .helper import *
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from numpy._pytesttester import PytestTester

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