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I am seconding Marcus Müller's excellent answer with a recent post on Quora: Why does C code run faster than Python's? Let’s write a simple function that adds up all numbers in an array. "It is the same algorithm, yet they have drastically different performance. I called these functions 1 million times for 1K arrays, the python version took 32 seconds ...


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In Big-O notation, $\mathcal{O}(N\log N)= \mathcal{O}(\frac N2\log N)$, as big-O notation only describes an upper bound for growth up to a constant factor, so your first question is kind of impossible to decide; in practice, the effort for a cleverly implemented real-valued FFT will be less than that of a (normal, complex) FFT. But whether it will be exactly ...


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