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cannam@95: <h4 class="subsection">4.1.1 Complex numbers</h4>
cannam@95:
cannam@95: <p>The default FFTW interface uses <code>double</code> precision for all
cannam@95: floating-point numbers, and defines a <code>fftw_complex</code> type to hold
cannam@95: complex numbers as:
cannam@95:
cannam@95: <pre class="example"> typedef double fftw_complex[2];
cannam@95: </pre>
cannam@95: <p><a name="index-fftw_005fcomplex-139"></a>
cannam@95: Here, the <code>[0]</code> element holds the real part and the <code>[1]</code>
cannam@95: element holds the imaginary part.
cannam@95:
cannam@95: <p>Alternatively, if you have a C compiler (such as <code>gcc</code>) that
cannam@95: supports the C99 revision of the ANSI C standard, you can use C's new
cannam@95: native complex type (which is binary-compatible with the typedef above).
cannam@95: In particular, if you <code>#include <complex.h></code> <em>before</em>
cannam@95: <code><fftw3.h></code>, then <code>fftw_complex</code> is defined to be the native
cannam@95: complex type and you can manipulate it with ordinary arithmetic
cannam@95: (e.g. <code>x = y * (3+4*I)</code>, where <code>x</code> and <code>y</code> are
cannam@95: <code>fftw_complex</code> and <code>I</code> is the standard symbol for the
cannam@95: imaginary unit);
cannam@95: <a name="index-C99-140"></a>
cannam@95:
cannam@95: <p>C++ has its own <code>complex<T></code> template class, defined in the
cannam@95: standard <code><complex></code> header file. Reportedly, the C++ standards
cannam@95: committee has recently agreed to mandate that the storage format used
cannam@95: for this type be binary-compatible with the C99 type, i.e. an array
cannam@95: <code>T[2]</code> with consecutive real <code>[0]</code> and imaginary <code>[1]</code>
cannam@95: parts. (See report
cannam@95: <a href="http://www.open-std.org/jtc1/sc22/WG21/docs/papers/2002/n1388.pdf WG21/N1388">http://www.open-std.org/jtc1/sc22/WG21/docs/papers/2002/n1388.pdf WG21/N1388</a>.) Although not part of the official standard as of this
cannam@95: writing, the proposal stated that: “This solution has been tested with
cannam@95: all current major implementations of the standard library and shown to
cannam@95: be working.” To the extent that this is true, if you have a variable
cannam@95: <code>complex<double> *x</code>, you can pass it directly to FFTW via
cannam@95: <code>reinterpret_cast<fftw_complex*>(x)</code>.
cannam@95: <a name="index-C_002b_002b-141"></a><a name="index-portability-142"></a>
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