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Input and output data are also real or complex-values arrays of any size, with the only restriction on their dimension that the number of points per dimension must be a power of 2. We also implemented a version of fastmult. In order to speed up computation times, we used Cython [@behnel2010cython] to write in Python high-level code and use it to generate a C extension module. Cython is a widely-used dialect of Python that allows to create high-level code and directly compile it to machine code. Cython provides a way to interact with the Python language and extensions, including integrated data types, mathematical functions, list and dictionary comprehensions, lambdas and decorators. It allows for improved performance in numerical code, and is suitable for code that requires the manipulation of arrays (and nested arrays) in a structured manner, as is the case for our implementation of the fastmult algorithm . Implementation details ---------------------- In this implementation, we compile the Cython code to a Python module, called FFTW. The implementation uses a single function, [fftwf]( that takes a complex-values array of the appropriate size as input and then computes the desired fast Fourier transform and returns the result in a similar structure. After calling [fftwf]( we use [fftwf]( to compute the desired real-values output of the fast Fourier transform. At each output point, this function computes the corresponding output value of the FFT, and then stores it into a 2-D array. This means that we have to store a 2-D array, that should match the size of the original input array, with the real-values output in each output point. ![image](figures/flow.png){width="100.00000%"} The problem is that we don’t know the number of output points, which is not known at compile time. Moreover, the actual number



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