gsoc-report.tex

% rubber: bibtex.path /home/lagrange/Documents/gsoc/2021/math-fft-report
\documentclass[11pt,a4paper]{article}

\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage[a4paper,margin=1in]{geometry}
\usepackage{graphicx}
\usepackage{subfigure}
\usepackage{hyperref}
\usepackage{bold-extra}
\usepackage{tikz}

\usepackage{listings}
\lstset{basicstyle=\footnotesize\ttfamily,breaklines=true}

\hypersetup{
    colorlinks=false,
    hidelinks=true
}
\bibliographystyle{plain} % FIXME: styles are not found

\newcommand{\fft}{\textsc{fft}}
\newcommand{\dft}{\textsc{dft}}
\newcommand{\dftf}{\textsc{dft}_{\textrm{forward}}}
\newcommand{\dftb}{\textsc{dft}_{\textrm{backward}}}
\newcommand{\cdc}{\textsc{cdc}}
\newcommand{\gsoc}{\textsc{gsoc}}
\newcommand{\ntt}{\textsc{ntt}}
\newcommand{\mpi}{\textsc{mpi}}
\newcommand{\raii}{\textsc{raii}}
\newcommand{\api}{\textsc{api}}
\newcommand{\boost}{\textit{Boost}}
\newcommand{\boostmath}{\textit{Boost.Math}}
\newcommand{\boostfft}{\textit{Boost.Math.FFT}}
\newcommand{\boostmpi}{\textit{Boost.MPI}}
\newcommand{\boostublas}{\textit{Boost.Ublas}}
\newcommand{\fftw}{\textit{FFTW}}
\newcommand{\bsl}{\textit{BSL}}
\newcommand{\cufft}{\textit{CUFFT}}
\newcommand{\gcc}{\textit{GCC}}
\newcommand{\gnu}{\textit{GNU}}
\newcommand{\gsl}{\textit{GSL}}
\newcommand{\alglib}{\textit{ALGLIB}}

\newcommand{\Ring}{\mathcal{R}}
\newcommand{\Order}{\mathcal{O}}
\newcommand{\Complex}{\mathbb{C}}
\newcommand{\hComplex}{\frac{1}{2}\mathbb{C}}
\newcommand{\Real}{\mathbb{R}}
\newcommand{\Integer}{\mathbb{Z}}
\newcommand{\xroot}[1]{$#1^{\mathrm{th}}$-root}
\DeclareMathOperator{\real}{real}
\DeclareMathOperator{\imag}{imag}

\newcommand{\comment}[1]{\textrm{\textit{#1}}}
\newcommand{\function}[1]{\textbf{#1}}
\newcommand{\variable}[1]{\textit{#1}}

\newcommand{\floor}[1]{\lfloor #1 \rfloor}

\newtheorem{example}{Example}
\newtheorem{definition}{Definition}

\title{\gsoc\ 2021\\\boostmath: \fft\ Utilities}
\author{Eduardo Quintana Miranda, Christopher Kormanyos, Janek Kozicki}


\begin{document}

\maketitle
\begin{abstract}
This \gsoc\ project brings Fast Fourier Transform (\fft) capabilities
inside the \boostmath\ library. Answering the need for a C++ library
of this sort, and the lack of \fft\ within \boostmath.
Our main goal is to design a modern C++ template interface for \fft\
that supports multiple types that satisfy the Ring Axioms and specialized
routines for types that represent real and complex numbers.
\end{abstract}

\tableofcontents
\input intro
\input quickstart
\input state
\input api
\input implementation
\input benchmarks
\input future
\input conclusions
    
\bibliography{biblio}

\appendix
\input app_ring

\end{document}