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Lagrang3
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listed all the API methods
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‎api.tex

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@@ -44,6 +44,205 @@ \section{Detailed API}
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and \verb|halfcomplex_to_real| respectively, where the halfcomplex part is
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represented in an array of $n$ complex numbers, hence keeping redundant values.
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\subsection{Complex \dft}
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\begin{lstlisting}[language=C++]
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template< class Complex = std::complex<double>,
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class Allocator = std::allocator<Complex> >
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class bsl_dft;
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\end{lstlisting}
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The backends \verb|gsl_dft| and \verb|fftw_dft| behave in the same way as
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\verb|bsl_dft|.
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\subsubsection{Member functions}
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\begin{lstlisting}[language=C++]
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template< class Complex, class Allocator >
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constexpr bsl_dft<Complex,Allocator>::bsl_dft(
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unsigned int n, const Allocator& alloc = Allocator{} );
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\end{lstlisting}
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\begin{lstlisting}[language=C++]
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template<class InputIt,
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class OutputIt>
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void forward(InputIt first1, InputIt last1, OutputIt d_first);
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\end{lstlisting}
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\begin{lstlisting}[language=C++]
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template<class InputIt,
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class OutputIt>
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void backward(InputIt first1, InputIt last1, OutputIt d_first);
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\end{lstlisting}
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\begin{lstlisting}[language=C++]
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constexpr std::size_t size() const;
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\end{lstlisting}
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\begin{lstlisting}[language=C++]
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void resize(std::size_t new_size);
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\end{lstlisting}
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\subsubsection{One-time transform methods}
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\begin{lstlisting}[language=C++]
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template<class InputIt,
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class OutputIt>
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void bsl_transform::forward(InputIt first1, InputIt last1, OutputIt d_first);
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\end{lstlisting}
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\begin{lstlisting}[language=C++]
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template<class InputIt,
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class OutputIt>
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void bsl_transform::backward(InputIt first1, InputIt last1, OutputIt d_first);
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\end{lstlisting}
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\subsection{Algebraic \dft}
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\begin{lstlisting}[language=C++]
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template< class T = std::complex<double>,
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class Allocator = std::allocator<T> >
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class bsl_algebraic_dft;
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\end{lstlisting}
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Remark: \gsl\ and \fftw\ libraries do not have the equivalent to this type of
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transform.
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\subsubsection{Member functions}
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\begin{lstlisting}[language=C++]
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template< class T, class Allocator >
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constexpr bsl_algebraic_dft<T,Allocator>::bsl_algebraic_dft(
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unsigned int n, T w, const Allocator& alloc = Allocator{} );
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\end{lstlisting}
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\begin{lstlisting}[language=C++]
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template<class InputIt,
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class OutputIt>
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void forward(InputIt first1, InputIt last1, OutputIt d_first);
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\end{lstlisting}
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\begin{lstlisting}[language=C++]
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template<class InputIt,
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class OutputIt>
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void backward(InputIt first1, InputIt last1, OutputIt d_first);
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\end{lstlisting}
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\begin{lstlisting}[language=C++]
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constexpr std::size_t size() const;
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\end{lstlisting}
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% The fact is that the algebraic_dft does have a resize method, but resizing the
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% DFT here must be followed with a change of the internal root of unity w. A
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% correct resize method here requires two arguments: the new size and the new
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% value of w.
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% \begin{lstlisting}[language=C++]
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% void resize(std::size_t new_size);
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% \end{lstlisting}
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\subsubsection{One-time transform methods}
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\begin{lstlisting}[language=C++]
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template<class InputIt,
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class OutputIt,
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class T>
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void bsl_algebraic_transform::forward(
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InputIt first1, InputIt last1, OutputIt d_first, const T w);
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\end{lstlisting}
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\begin{lstlisting}[language=C++]
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template<class InputIt,
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class OutputIt,
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class T>
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void bsl_algebraic_transform::backward(
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InputIt first1, InputIt last1, OutputIt d_first, const T w);
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\end{lstlisting}
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\subsection{Real \dft}
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\begin{lstlisting}[language=C++]
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template< class Real = double,
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class Allocator = std::allocator<Real> >
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class bsl_rdft;
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\end{lstlisting}
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The backends \verb|gsl_rdft| and \verb|fftw_rdft| behave in the same way as
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\verb|bsl_rdft|.
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\subsubsection{Member functions}
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\begin{lstlisting}[language=C++]
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template< class Real, class Allocator >
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constexpr bsl_rdft<Real,Allocator>::bsl_rdft(
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unsigned int n, const Allocator& alloc = Allocator{} );
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\end{lstlisting}
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\begin{lstlisting}[language=C++]
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template<class InputIt,
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class OutputIt>
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void real_to_halfcomplex(InputIt first1, InputIt last1, OutputIt d_first);
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\end{lstlisting}
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\begin{lstlisting}[language=C++]
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template<class InputIt,
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class OutputIt>
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void real_to_complex(InputIt first1, InputIt last1, OutputIt d_first);
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\end{lstlisting}
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\begin{lstlisting}[language=C++]
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template<class InputIt,
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class OutputIt>
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void halfcomplex_to_real(InputIt first1, InputIt last1, OutputIt d_first);
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\end{lstlisting}
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\begin{lstlisting}[language=C++]
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template<class InputIt,
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class OutputIt>
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void complex_to_real(InputIt first1, InputIt last1, OutputIt d_first);
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\end{lstlisting}
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\begin{lstlisting}[language=C++]
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constexpr std::size_t size() const;
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\end{lstlisting}
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\begin{lstlisting}[language=C++]
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void resize(std::size_t new_size);
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\end{lstlisting}
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\subsubsection{One-time transform methods}
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\begin{lstlisting}[language=C++]
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template<class InputIt,
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class OutputIt>
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void bsl_real_transform::real_to_halfcomplex(
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InputIt first1, InputIt last1, OutputIt d_first);
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\end{lstlisting}
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\begin{lstlisting}[language=C++]
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template<class InputIt,
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class OutputIt>
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void bsl_real_transform::real_to_complex(
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InputIt first1, InputIt last1, OutputIt d_first);
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\end{lstlisting}
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\begin{lstlisting}[language=C++]
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template<class InputIt,
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class OutputIt>
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void bsl_real_transform::halfcomplex_to_real(
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InputIt first1, InputIt last1, OutputIt d_first);
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\end{lstlisting}
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\begin{lstlisting}[language=C++]
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template<class InputIt,
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class OutputIt>
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void bsl_real_transform::complex_to_real(
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InputIt first1, InputIt last1, OutputIt d_first);
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\end{lstlisting}
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\subsection{Convolution}
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\begin{lstlisting}[language=C++]
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template<typename InputIt1,
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typename InputIt2,
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typename OutputIt>
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void bsl_transform::convolution(
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InputIt1 first1, InputIt1 last1, InputIt2 first2, OutputIt d_first);
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\end{lstlisting}
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% template<class RingType = std::complex<double>, class Allocator_t = std::allocator<RingType> >
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% using bsl_dft = detail::complex_dft<detail::bsl_backend,RingType,Allocator_t>;
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%
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% template<class T = double, class Allocator_t = std::allocator<T> >
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% using bsl_rdft = detail::real_dft<detail::bsl_rfft_backend,T,Allocator_t>;
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%
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% template<class RingType = std::complex<double>, class Allocator_t = std::allocator<RingType> >
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% using bsl_algebraic_dft = detail::algebraic_dft<detail::bsl_backend,RingType,Allocator_t>;
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%
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% using bsl_transform = transform< bsl_dft<> >;
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% using bsl_algebraic_transform = transform< bsl_algebraic_dft<> >;
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% using bsl_real_transform = transform< bsl_rdft<> >;
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%proposes the design and implementation of a modern C++ template
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%interface for \dft\ within \boostmath\ library. The implementation will consist
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% %\item (if time permits) with multithreaded capabilities.
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% \end{itemize}
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\subsection{Future outlook}
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Describe the pending issues and plans for improvement:
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\begin{itemize}
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\item Documentation inside boost,
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\item optimization of the Boost routines,
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\item multithreading,
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\item multidimentional transforms,
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\item to work in collaboration with boost.mpi to create distributed memory
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transforms to tacke the $D$-dimentional scalability problem proposing a
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$D-1$ domain decomposition similar to \cite{pippig_13}.
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\end{itemize}

‎future.tex

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\section{Future outlook}
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Describe the pending issues and plans for improvement:
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\begin{itemize}
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\item Documentation inside boost,
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\item optimization of the Boost routines,
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\item multithreading,
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\item multidimentional transforms,
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\item to work in collaboration with Boost.MPI to create distributed memory
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transforms to tacke the $D$-dimentional scalability problem proposing a
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$D-1$ domain decomposition similar to \cite{pippig_13}.
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\end{itemize}

‎gsoc-report.tex

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\input quickstart
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\input state
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\input api
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\input implementation
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\input benchmarks
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\input future
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\bibliography{biblio}
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‎implementation.tex

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\section{Implementation}

‎makefile

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VPATH=plots
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docfiles:=gsoc-report.tex intro.tex state.tex api.tex app_ring.tex \
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quickstart.tex benchmarks.tex
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quickstart.tex benchmarks.tex future.tex
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target:=gsoc-report.pdf
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main:=gsoc-report.tex
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command:=rubber

‎quickstart.tex

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\section{Quickstart}
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Our interface was designed for easy of use. The user can start performing
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Boost.Math.FFT provides an interface to compute Fourier Transforms for different
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types using C++ templates.
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Its design aims to be easy to use.
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For instance the user can start performing
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complex FFTs by just calling one of the \texttt{std::transform}-like routines
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\texttt{forward} or \texttt{backward} that correspond to a Discrete Fourier
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Transform (DFT) in $\Complex^n$ space with the root of unity
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Transform (\dft) in $\Complex^n$ space with the root of unity
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$\exp(-\frac{2\pi}{n} i)$ and $\exp(\frac{2\pi}{n} i)$ respectively.
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See listings \ref{ls:complex_dft_transform}
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\begin{lstlisting}[language=C++,label=ls:complex_dft_transform,caption=Simple complex FFT

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