new

[kahina_paper2.git] / paper.tex

diff --git a/paper.tex b/paper.tex
index 4f6ae4b7d84c177500fe5100634c18a2352dd031..c593d34d06505b112c59b80d2b2c991065b59835 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -193,12 +193,13 @@ Using the logarithm  and the exponential operators, we can replace any
 multiplications and divisions with additions and
 subtractions. Consequently, computations manipulate lower values in
 absolute values~\cite{Karimall98}. In practice, the  exponential and
 multiplications and divisions with additions and
 subtractions. Consequently, computations manipulate lower values in
 absolute values~\cite{Karimall98}. In practice, the  exponential and

-logarithm mode is used a root excepts the circle unit, \LZK{Je n'ai pas compris cette phrase!} represented by the radius $R$ evaluated in C language as :
+logarithm mode is used when a root is outisde the circle unit represented by the radius $R$ evaluated in C language with:

 \begin{equation}
 \label{R.EL}
 R = exp(log(DBL\_MAX)/(2*n) );
 \end{equation}
 \begin{equation}
 \label{R.EL}
 R = exp(log(DBL\_MAX)/(2*n) );
 \end{equation}

-where \verb=DBL_MAX= stands for the maximum representable \verb=double= value.
+where \verb=DBL_MAX= stands for the maximum representable
+\verb=double= value and $n$ is the degree of the polynimal.

 
 
 \subsection{The Ehrlich-Aberth parallel implementation on CUDA}
 
 
 \subsection{The Ehrlich-Aberth parallel implementation on CUDA}


@@ -218,7 +219,7 @@ long since it performs all the operations with complex numbers with
 the normal mode of the EA method but also with the
 logarithm-exponential one. Then the error is computed with a final
 kernel (line 7). Finally when the EA method has converged, the roots
 the normal mode of the EA method but also with the
 logarithm-exponential one. Then the error is computed with a final
 kernel (line 7). Finally when the EA method has converged, the roots

-are transferred from the GPU to the CPU.%\LZK{Quand est ce qu'on utilise un normal mode ou logarithm-exponential mode?}
+are transferred from the GPU to the CPU.

 
 \begin{algorithm}[htpb]
 \label{alg1-cuda}
 
 \begin{algorithm}[htpb]
 \label{alg1-cuda}


@@ -309,7 +310,6 @@ Copy $P$, $P'$ from CPU to GPU\;
 
 
 \subsection{A MPI-CUDA approach}
 
 
 \subsection{A MPI-CUDA approach}

-

 Our parallel implementation of EA to find roots of polynomials using a
 CUDA-MPI approach follows a similar approach to the one used in
 CUDA-OpenMP. Each process is responsible to compute its own part of
 Our parallel implementation of EA to find roots of polynomials using a
 CUDA-MPI approach follows a similar approach to the one used in
 CUDA-OpenMP. Each process is responsible to compute its own part of