FFT IFFT

Demo Files:
real_fft_test.spin2 Spin2 speed and accuracy test, tested with PNut-ts and flexspin
fft_demo.spin2 Spin2 example program, tested with Propeller Tool and PNut-ts
comparefftbench.c C example program, tested with flexcc (spin2cpp)

Library Files:
cog_fft_mixed.spin2 The latest version supporting FFT and IFFT from 32 to 16384 points, out-of-place output only.
cog_fft.spin2 The original library with FFT and IFFT support.
cog_ifft_radix4.spin2 New faster library which supports only power of 4 sizes.
inline_fft.spin2 Inline PASM2 FFT for when cogs or memory is limited, or when performance doesn't matter.
sa_fft7.spin2 An independently created FFT library by Mark Tillotson. Has built-in windowing.
dft4.spin2 Discrete Fourier Transform library for educational and testing purposes.

Other Files:
SimplestSerial.spin2
thread_factory.c
thread_factory.h

It's not mentioned in the source files but cog_fft will always modify the source array.
cog_ifft_radix4 will not modify the source array unless INPLACE is active.

Please note that IFFT on cog_fft behaves like forward FFT on cog_ifft_radix4 and dft4, and vice versa. This may cause a spectral inversion. I am investigating.

Performance at 160MHz
cog_fft_mixed, new library 2026-03-14
FFT size: 512 DFT uS: 49233 FFT uS: 419 max_error: 31 avg_error: 11
REAL size: 1024 DFT uS: 196766 FFT uS: 561 max_error: 47 avg_error: 7
FFT size: 1024 DFT uS: 196766 FFT uS: 879 max_error: 53 avg_error: 15
IFFT size: 1024 DFT uS: 196766 FFT uS: 879 max_error: 52 avg_error: 15

New 2026-03-04 radix 4 version
1024 point butterfly run time = 831 us FFT ONLY, no bit reversal
1024 point bit-reversal and butterfly run time = 1132 us IFFT In-Place Algorithm
1024 point bit-reversal and butterfly run time = 1132 us In-Place Algorithm
1024 point bit-reversal and butterfly run time = 879 us IFFT
1024 point bit-reversal and butterfly run time = 879 us Cog
1024 point bit-reversal and butterfly run time = 1965 us Inline
1024 point bit-reversal and butterfly run time = 196803 us Discrete Fourier Transform 4 points at a time

Old cog_fft
1024 point butterfly run time = 1018 us FFT ONLY, no bit reversal
1024 point bit-reversal and butterfly run time = 1328 us IFFT In-Place Algorithm
1024 point bit-reversal and butterfly run time = 1297 us In-Place Algorithm
1024 point bit-reversal and butterfly run time = 1204 us IFFT Out-of-Place Algorithm
1024 point bit-reversal and butterfly run time = 1174 us Out-of-Place Algorithm
1024 point bit-reversal and butterfly run time = 664 us Real Input
1024 point bit-reversal and butterfly run time = 3764 us Inline
1024 point bit-reversal and butterfly run time = 12991 us flexcc -2 comparefftbench.c -O3

The cog_fft IFFT is implemented as an FFT with the inputs and outputs conjugated. That's why it's 2.5% slower. I felt this was an acceptable trade-off between speed, library size, and development effort. The newer cog_ifft_radix4 reverses rotation to compute IFFT with no measurable penalty.