The behaviour of fftw_execute when called inside an OpenMP parallel region - c++

Question

I'm writing a spectral PDE code I'd like to parallelise, using FFTW to do the FFT's. The main loop in the code looks as below. Lets say I have a real space array, u, and a fourier space array, uhat, and I've already constructed plans to go between them outside of this for loop (and outside of any parallel region), as well as calling the needed FFTW initialisation functions for parallelisation of fftw_execute.
for
{
fftw_execute(u_to_uhat)
// do some things with uhat, the fourier space array - for
// example,scale the transform in a for loop
for(int n = 0, n<Nmax,n++)
{
uhat[n] = scale*uhat[n])
}
// transform back
fftw_execute(uhat_to_u)
}
I want to parallelise everything here, including the manipulations of uhat within that second for loop. My question is how should I use openMP #pragmas to do so? Currently I have a parallel region around the inner loop:
fftw_init_threads();
fftw_plan_with_nthreads(omp_get_max_threads());
for
{
fftw_execute(u_to_uhat)
// do some things with uhat, the fourier space array - for
// example,scale the transform in a for loop
#pragma omp parallel for
for(int n = 0, n<Nmax,n++)
{
uhat[n] = scale*uhat[n])
}
// transform back
fftw_execute(uhat_to_u)
}
But as I understand it this creates and destroys a thread block every time I enter this for loop, which is expensive. I'd rather construct the parallel region outside the for loop once:
fftw_init_threads();
fftw_plan_with_nthreads(omp_get_max_threads());
#pragma omp parallel
for
{
fftw_execute(u_to_uhat)
// do some things with uhat, the fourier space array - for
// example,scale the transform in a for loop
#pragma omp for
for(int n = 0, n<Nmax,n++)
{
uhat[n] = scale*uhat[n])
}
// transform back
fftw_execute(uhat_to_u)
}
But then I have to worry about the behaviour of fftw_execute called from within the parallel region. I believe the documentation, section 5.4, says fftw_execute is thread safe (i.e safe to call from within a parallel region). But it doesn't tell me whether fftw_execute creates its own block of threads when called - i.e by putting it in a parallel region, am I just making every existing thread construct a load more threads within the fftw_execute function? Alternately, does it know to use the threads that are already there?
In short Can I call fftw_execute() from inside a parallel region, and can you make it work as one would hope it does - i.e just use the existing threads to do the work, rather than spawning new ones.
Sorry for the long question, I'd really appreciate some advice on this!