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[kahina_paper2.git] / paper.tex

diff --git a/paper.tex b/paper.tex
index b453915c120e114bbe25f4ad16206f496512d2fc..e90eac414fbfd21eccf62dc297e3b63ef5617415 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -275,7 +275,8 @@ where \verb=DBL_MAX= stands for the maximum representable
 
 
 \subsection{The Ehrlich-Aberth parallel implementation on CUDA}
 
 
 \subsection{The Ehrlich-Aberth parallel implementation on CUDA}

-The algorithm ~\ref{alg1-cuda} shows sketch of the Ehrlich-Aberth method using CUDA.
+%\KG{
+  The algorithm ~\ref{alg1-cuda} shows sketch of the Ehrlich-Aberth method using CUDA.

 The first steps consist in the initialization of the input data like, the polynomial P,derivative of P and the vector solution Z. Then, all data of the root finding problem
 must be copied from the CPU memory to the GPU global memory,because
 the GPUs only work on the data filled in their memories.
 The first steps consist in the initialization of the input data like, the polynomial P,derivative of P and the vector solution Z. Then, all data of the root finding problem
 must be copied from the CPU memory to the GPU global memory,because
 the GPUs only work on the data filled in their memories.


@@ -292,6 +293,9 @@ the normal mode of the EA method as in Eq.~\ref{Eq:EA1} but also with the logari
 
 The algorithm terminates its computations when all the roots have
 converged.
 
 The algorithm terminates its computations when all the roots have
 converged.

+%}
+
+

  %The code is organized as kernels which are parts of codes that are run
 %on GPU devices. Algorithm~\ref{alg1-cuda} describes the CUDA
 %implementation of the Ehrlich-Aberth on a GPU.  This algorithms starts
  %The code is organized as kernels which are parts of codes that are run
 %on GPU devices. Algorithm~\ref{alg1-cuda} describes the CUDA
 %implementation of the Ehrlich-Aberth on a GPU.  This algorithms starts


@@ -326,11 +330,11 @@ Copy $P$, $P'$ and $Z$ from CPU to GPU\;
 }
 Copy $Z$ from GPU to CPU\;
 \end{algorithm}
 }
 Copy $Z$ from GPU to CPU\;
 \end{algorithm}

-\\
+\ \\

 This figure shows the second kernel code
 \begin{figure}[htbp]
 \centering
 This figure shows the second kernel code
 \begin{figure}[htbp]
 \centering

-\includegraphics[angle=+0,width=0.4\textwidth]{code1}
+\includegraphics[angle=+0,width=0.5\textwidth]{code}

 \caption{The Kernel Update code}
 \label{fig:00}
 \end{figure}
 \caption{The Kernel Update code}
 \label{fig:00}
 \end{figure}


@@ -348,6 +352,7 @@ Ehrlich-Aberth method with OpenMP and MPI is presented.
 
 \section{The Ehrlich-Aberth algorithm on multiple GPUs}
 \label{sec4}
 
 \section{The Ehrlich-Aberth algorithm on multiple GPUs}
 \label{sec4}

+\KG{we remind that to manage the CUDA contexts of different GPUs, We investigate two parallel paradigms: OpenMP and MPI. In this section we present the both \textit{OpenMP-CUDA} approach and the \textit{MPI-CUDA} approach} used to implement the Ehrlich-Aberth algorithm on multiple GPUs.

 \subsection{An OpenMP-CUDA approach}
 Our OpenMP-CUDA implementation of EA algorithm is based on the hybrid
 OpenMP and CUDA programming model. This algorithm is presented in
 \subsection{An OpenMP-CUDA approach}
 Our OpenMP-CUDA implementation of EA algorithm is based on the hybrid
 OpenMP and CUDA programming model. This algorithm is presented in


@@ -470,9 +475,10 @@ We study two categories of polynomials: sparse polynomials and full polynomials.
      {\Large \forall \alpha_{i} \in \mathbb{C}, i\in \mathbb{N};  p(x)=\sum^{n}_{i=0} \alpha_{i}.x^{i}} 
 \end{equation}
 
      {\Large \forall \alpha_{i} \in \mathbb{C}, i\in \mathbb{N};  p(x)=\sum^{n}_{i=0} \alpha_{i}.x^{i}} 
 \end{equation}
 

-For our tests, a CPU Intel(R) Xeon(R) CPU
-X5650@2.40GHz and 4 GPUs cards Tesla Kepler K40,are used with CUDA version 7.5. In order to
-evaluate both the GPU and Multi-GPU approaches, we performed a set of
+\KG{For our tests, a CPU Intel(R) Xeon(R) CPU
+X5650@2.40GHz and 4 GPUs cards Tesla Kepler K40,are used with CUDA version 7.5}.
+ 
+ In order to evaluate both the GPU and Multi-GPU approaches, we performed a set of

 experiments on a single GPU and multiple GPUs using OpenMP or MPI with
 the EA algorithm, for both sparse and full polynomials of different
 degrees.  All experimental results obtained are performed with double
 experiments on a single GPU and multiple GPUs using OpenMP or MPI with
 the EA algorithm, for both sparse and full polynomials of different
 degrees.  All experimental results obtained are performed with double