[BUG]: Binding an FFTW algorithm gives different results

Problem description

Hello everyone,

As I am not sure if the bug I am seeing comes from pybind, the underlying library FFTW3 or the compiling/linking, I also adress this issue in the fftw3 project

Here is the minimal example that I think illustrates my problem in a practical way.

In the Git repository, we have a function foo() that uses an hard-coded vector of size 300 and computes its DFT using the FFTW3 library. I followed what is in the tutorial but with real-to-complex DFT instead.
This function is duplicated in two sources files : main.c that is built into a Main program, and bindings.cpp that is built into a Python module. Both outputs are built using cmake in a conda environment.

To compare the results, the foo() function prints the FFT plan and the ouput complex array.

When launching the foo function from both module and program, I get differences in the output vector (left is the C program call, right is the Python module call) :

Because the input vector for the FFT is hard-coded, I don't think there is a data corruption from pybind. Any idea why we see this behavior ?

Note : the hard-coded vector has been generated with random numbers with numpy, then scaled to 100.
Note 2: taking a small vector (10 elements) shows no differences.

pybind version: 2.9.2
fftw3 version: 3.3.4

Reproducible example code

[minimal example](https://github.com/robin-cls/fftw3_pybind)

Start with the minimal example, comparing main.c and bindings.cpp and how CMake builds each target in the conda environment. Reproduce the differing FFT outputs for the 300-element input, then compare the FFTW tutorial usage and dependency versions; done means identifying the source of the discrepancy and documenting or correcting it.