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\begin{document}
\begin{center}
Answer to the Referee Report\\[2ex] 
{\Large
``Using NFFT 3 -- a software library for various \\ nonequispaced fast
  Fourier transforms'' }\\[2ex] 
by Jens Keiner, Stefan Kunis, and Daniel Potts
\end{center}
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First of all, we thank all three referees for their helpful comments and valuable
suggestions.

\section*{Referee 2}
\label{sect:1}

\begin{itemize}
  \item
    \begin{quote}
      Referee: The performance of the
      library is not comparable to high performance libraries such as FFTW but
      it should still be reasonable for many applications. Improving performance
      would still be desirable of course.
    \end{quote}
    We generally acknowledge that performance and software design improvements
    are desirable. But NFFT 3 is for the major part the result of recent
    research and as such has not been around for a long time.
  \item
    \begin{quote}
      Referee: As I see it, there are 3 'layers' that are relevant for a
      library: 1) underlying theory and algorithms (the math behind it)
      2) the actual implementation (what exact specifications have been used and
      why, some pseudo code, what optimization techniques have been used, which
      algorithms and why, arithmetic cost and performance analysis, maybe other
      analyses, etc.) 3) how to install and use the library (Makefiles,
      concrete code examples) In a library paper I would expect a short version
      of 1) as background, 2) as the focus and then 3) very briefly.
    \end{quote}
    In the terminology of TOMS, this paper is a \emph{research paper} and not a
    \emph{library paper}. The aim of the article is to give a mathematical
    description of the algorithms implemented in the NFFT 3 software library
    with some more mathematical background on the core NFFT algorithm. A second
    goal is to mention some applications of the implemented methods.
    The focus of this paper is not the description of technical details of the
    implementation (code optimizations, software engineering concerns,...) and
    the full programming interface. 
  \item
    \begin{quote}
      Referee:
      As it is right now the authors put the emphasis on 3) (including details
      on how to untar a file that is really way too much) and have some of 2)
      in the appendix, but not enough. Also, the cost and performance analysis
      is far too brief for a library paper.
    \end{quote}
    We have shortened the installation instructions. They have also been moved
    to Appendix A.1.

    As mentioned, our aim is not to describe all details of the implementation.
    But we now summarise performance related tests in Section 5. The focus is
    to observe how the NFFT algorithm does behave in comparison to the
    direct implementation.

    It is nevertheless true that more extensive numerical tests at a
    mature state of the library are desirable. At the current stage, an
    extensive and in-depth performance analysis is not available.
  \item
    \begin{quote}
      Referee:
      Concrete, I recommend (following my above numbering) to have a
      background section on 1), then all relevant details on 2) (some of which are
      not in the paper) and then a very short section, or appendix, on 3). (The
      authors may want to look at some existing library papers of popular
      libraries.) Further, there have to be more details on the relevant
      implementation decisions, optimization techniques performed, and, most
      important, a more extensive evaluation of operations count and runtime
      performance (which should be given also in Gflop/s or pseudo Gflop/s, i.e.,
      a number of ops is stipulated in case the exact one is not available).
    \end{quote}
    Section 2 has been extended to start with the classical discrete Fourier
    transform (DFT) and mention more relevant properties of the NFFT algorithm.
    Details are found in the Appendices A.2 and A.3.
  \item
    \begin{quote}
      Referee: Detailed comments \ldots
    \end{quote}
    In the text, the library is now consistently denoted NFFT 3. We include the
    major version number in the name since earlier versions offered
    substantially less functionality. The rest of the comments have been
    incorporated into the paper and all mentioned mistakes have been fixed.
\end{itemize}

\end{document}
