Instability of CUFFT_R2C and CUFFT_C2R

I test the function of CUFFT_R2C and CUFFT_C2R.  Both of them appeare to be unstable.  By increasing the output array size, CUFFT_R2C may work properly.  However, CUFFT_C2R nearly never works unless an exact spectrum calculated by CUFFT_R2C is used.  The test suggests these two functions are terrible.  Instead, CUFFT_C2C is much much more stable.

I employed a random matrix, denoted by $x$, which is of dimension Nx-by-Ny, to test both functions.  As mentioned in cufft documentary, the complex-valued data should be of size (Nx/2+1)-by-Ny. The suggested dimension only worked for Nx and Ny <128.  When Nx=Ny=256. The image spectrum contains conspicuous artifacts shown as follows.  For Nx=Ny=1024, the results are totally garbage.  Though not shown here, the spectrum calculated by use of CUFFT_C2C are very accurate in comparison to the ground truth calculated by use of Matlab.

Left: Testing random image ($x$,256-by-256 pixels); Middle: A quarter of the image spectrum calculated by use of CUFFT_R2C; Right: Errors of the middle image in comparison to ground truth calculated by use of Matlab.

Note that the above error CAN be corrected by increasing the size of the complex-valued data from (Nx/2+1)Ny to NxNy.  According to cufft documentary, it suggests that “Pointers to idata and odata are both required to be aligned to cufftComplex data type in single-precision transforms.”  I have no idea how to ALIGN the data to a data type.  It may imply that the complex-valued data should be of dimension Nx*Ny.  (I am non-native speaker.  I am not going to guess the implications.)

The function CUFFT_C2R is trickier.  Unless I used the image spectrum (of dimensions Nx-by-Ny) calculated by CUFFT_R2C, I always got garbage.  It suggests that not only the first (Nx/2+1)Ny elements, but all NxNy elements affect the results.

In summary, it took me whole weekend.  I got little help from either cufft documentary or the internet.  I will not use CUFFT_C2R or CUFFT_R2C.  If anybody knows the trick, please let me know.  I am concluding here the functions of CUFFT_R2C and CUFFT_C2R are TERRIBLE.