Hi,
In the sample code that you have attached, I see that you are computing a forward FFT with a specific input signal. Were you able to perform the same forward FFT with the same signal on MATLAB and compare the results with what the library produced? Are the results significantly different? It is normal for slight floating point differeces between two implementations of FFT. But if the differences are substantial, then there is some problem and we would have to invetsigate.
It is not clear what kind of help you are looking for. Do you need help with the mathematical aspect of FFT? or do you think that the library is not producing correct results? If you are saying that the library is not producing the right numbers, could you please attach a text file with results from MATLAB and the library showning the difference. Thanks.