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4.1.1 Complex numbers

The default FFTW interface uses double precision for all floating-point numbers, and defines a fftw_complex type to hold complex numbers as:

typedef double fftw_complex[2];

Here, the [0] element holds the real part and the [1] element holds the imaginary part.

Alternatively, if you have a C compiler (such as gcc) that supports the C99 revision of the ANSI C standard, you can use C’s new native complex type (which is binary-compatible with the typedef above). In particular, if you #include <complex.h> before <fftw3.h>, then fftw_complex is defined to be the native complex type and you can manipulate it with ordinary arithmetic (e.g. x = y * (3+4*I), where x and y are fftw_complex and I is the standard symbol for the imaginary unit);

C++ has its own complex<T> template class, defined in the standard <complex> header file. Reportedly, the C++ standards committee has recently agreed to mandate that the storage format used for this type be binary-compatible with the C99 type, i.e. an array T[2] with consecutive real [0] and imaginary [1] parts. (See report WG21/N1388.) Although not part of the official standard as of this writing, the proposal stated that: “This solution has been tested with all current major implementations of the standard library and shown to be working.” To the extent that this is true, if you have a variable complex<double> *x, you can pass it directly to FFTW via reinterpret_cast<fftw_complex*>(x).