la figure 3 en noir et blanc....

[kahina_paper1.git] / paper.tex

diff --git a/paper.tex b/paper.tex
index d0913cca27ecbbd96ca8786a92908ef6c5dd80a6..e3dde6e9caa09e9e64e50476180d0bdb7dd8f12c 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -582,8 +582,7 @@ Algorithm~\ref{alg2-cuda} shows a sketch of the Ehrlich-Aberth algorithm using C
 \caption{CUDA Algorithm to find roots with the Ehrlich-Aberth method}
 
 \KwIn{$Z^{0}$ (Initial root's vector), $\varepsilon$ (error tolerance
 \caption{CUDA Algorithm to find roots with the Ehrlich-Aberth method}
 
 \KwIn{$Z^{0}$ (Initial root's vector), $\varepsilon$ (error tolerance

-  threshold), P(Polynomial to solve), Pu (the derivative of P), $n$
-  (Polynomial's degrees), $\Delta z_{max}$ (maximum value of stop condition)}
+  threshold), P(Polynomial to solve), Pu (the derivative of P), $n$ (Polynomial's degrees),$\Delta z_{max}$ (maximum value of stop condition)}

 
 \KwOut {$Z$ (The solution root's vector), $ZPrec$ (the previous solution root's vector)}
 
 
 \KwOut {$Z$ (The solution root's vector), $ZPrec$ (the previous solution root's vector)}
 


@@ -606,7 +605,7 @@ Copy results from GPU memory to CPU memory\;
 \end{algorithm}
 ~\\ 
 
 \end{algorithm}
 ~\\ 
 

-After the initialization step, all data of the root finding problem to be solved must be copied from the CPU memory to the GPU global memory, because the GPUs only access data already present in their memories. Next, all the data-parallel arithmetic operations inside the main loop \verb=(while(...))= are executed as kernels by the GPU. The first kernel named \textit{save} in line 6 of Algorithm~\ref{alg2-cuda} consists in saving the vector of polynomial's root found at the previous time-step in GPU memory, in order to check the convergence of the roots after each iteration (line 8, Algorithm~\ref{alg2-cuda}).
+After the initialization step, all data of the root finding problem to be solved must be copied from the CPU memory to the GPU global memory, because the GPUs only access data already present in their memories. Next, all the data-parallel arithmetic operations inside the main loop \verb=(do ... while(...))= are executed as kernels by the GPU. The first kernel named \textit{save} in line 6 of Algorithm~\ref{alg2-cuda} consists in saving the vector of polynomial's root found at the previous time-step in GPU memory, in order to check the convergence of the roots after each iteration (line 8, Algorithm~\ref{alg2-cuda}).

 
 The second kernel executes the iterative function $H$ and updates
 $d\_Z$, according to Algorithm~\ref{alg3-update}. We notice that the
 
 The second kernel executes the iterative function $H$ and updates
 $d\_Z$, according to Algorithm~\ref{alg3-update}. We notice that the


@@ -617,16 +616,16 @@ exponential logarithm algorithm.
 \begin{algorithm}[H]
 \label{alg3-update}
 %\LinesNumbered
 \begin{algorithm}[H]
 \label{alg3-update}
 %\LinesNumbered

-\caption{Kernel\_update}
+\caption{Kernel update}

 
 \eIf{$(\left|d\_Z\right|<= R)$}{
 
 \eIf{$(\left|d\_Z\right|<= R)$}{

-$kernel\_update((d\_Z,d\_Pcoef,d\_Pdegres,d\_Pucoef,d\_Pudegres)$\;}
+$kernel\_update((d\_Z,d\_P,d\_Pu)$\;}

 {
 {

-$kernel\_update\_ExpoLog((d\_Z,d\_Pcoef,d\_Pdegres,d\_Pucoef,d\_Pudegres))$\;
+$kernel\_update\_ExpoLog((d\_Z,d\_P,\_Pu))$\;

 }
 \end{algorithm}
 
 }
 \end{algorithm}
 

-The first form executes formula \ref{eq:SimplePolynome} if the modulus
+The first form executes formula the EA function Eq.~\ref{Eq:Hi} if the modulus

 of the current complex is less than the a certain value called the
 radius i.e. ($ |z^{k}_{i}|<= R$), else the kernel executes the EA.EL
 function Eq.~\ref{Log_H2}
 of the current complex is less than the a certain value called the
 radius i.e. ($ |z^{k}_{i}|<= R$), else the kernel executes the EA.EL
 function Eq.~\ref{Log_H2}