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fftw3: Complex numbers

 
 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
 <http://www.open-std.org/jtc1/sc22/WG21/docs/papers/2002/n1388.pdf
 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)'.
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