Parallel FFT for big integer multiplication. Written in three versions: MPI, OpenMP and CUDA(cufft). It is a course assignment of MPI program design given by Prof. Xiang, 2019 Fall, SMS, Nankai Univ.
大整数乘法的并行FFT，MPI程序设计课程作业，包括MPI、OpenMP、cuFFT三个版本。
For more details, please see the report.
parallel the doacross loop in serial version.
use cuFFT.
For larger data (FFT bits >= 10^8) which cannot be stored in a single processor (and GPU), MPI with distributed memory is a better solution.
Say the total bits is 2^n and we have 2^p processors.
In the first p round butterfly operation, all the processors can work independently, and then each processor needs to share data with a particular processor since p+1 round.
In MPI_FFT.cpp, MPI_Sendrecv is used for data sharing of a pair of processors and MPI_Alltoall is used to swap the positions of all processors bitwisely.
A flaw of these program is the precision of complex numbers in FFT cannot be guaranteed when 2^n is very large. In big integer multiplication where the final result will be rounded integers, the precision does not matter. But for other application of FFT, that may be a problem.