+Now that the GPU contains the data needed to perform the addition. In sequential
+such addition is achieved out with a loop on all the elements. With a GPU, it
+is possible to perform the addition of all elements of the arrays in parallel
+(if the number of blocks and threads per blocks is sufficient). In
+Listing\ref{ch2:lst:ex1} at the beginning, a simple kernel,
+called \texttt{addition} is defined to compute in parallel the summation of the
+two arrays. With CUDA, a kernel starts with the
+keyword \texttt{\_\_global\_\_} \index{CUDA~keywords!\_\_shared\_\_} which
+indicates that this kernel can be called from the C code. The first instruction
+in this kernel is used to compute the variable \texttt{tid} which represents the
+thread index. This thread index\index{thread index} is computed according to
+the values of the block index (it is a variable of CUDA
+called \texttt{blockIdx}\index{CUDA~keywords!blockIdx}). Blocks of threads can
+be decomposed into 1 dimension, 2 dimensions or 3 dimensions. According to the
+dimension of data manipulated, the appropriate dimension can be useful. In our
+example, only one dimension is used. Then using notation \texttt{.x} we can
+access to the first dimension (\texttt{.y} and \texttt{.z} allow respectively to
+access to the second and third dimension). The
+variable \texttt{blockDim}\index{CUDA~keywords!blockDim} gives the size of each
+block.
+
+
+
+\lstinputlisting[label=ch2:lst:ex1,caption=A simple example]{Chapters/chapter2/ex1.cu}
+
+\section{Second example: using CUBLAS}
+
+The Basic Linear Algebra Subprograms (BLAS) allows programmer to use performant
+routines that are often used. Those routines are heavily used in many scientific
+applications and are very optimzed for vector operations, matrix-vector
+operations and matrix-matrix
+operations~\cite{ch2:journals/ijhpca/Dongarra02}. Some of those operations seems
+to be easy to implement with CUDA. Nevertheless, as soon as a reduction is
+needed, implementing an efficient reduction routines with CUDA is far from being
+simple.
+
+In this second example, we consider that we have two vectors $A$ and $B$. First
+of all we want to compute the sum of both vectors in a vector $C$. Then we want
+to compute the scalar product between $1/C$ and $1/A$. This is just an example
+which has not direct interest except to show how to program it with CUDA.
+
+Listing~\ref{ch2:lst:ex2} shows this example with CUDA. The first kernel for the
+addition of two arrays is exactly the same that the one described in the
+previous example.
+
+The kernel to compute the inverse of the elements of an array is very
+simple. For each thread index, the inverse of the array replaces the initial
+array.
+
+In the main function, the beginning is very similar to the one in the previous
+example. First the number of elements is asked to the user. Then a call
+to \texttt{cublasCreate} allows to initialize the cublas library. It creates an
+handle. Then all the arrays are allocated in the host and the device, as in the
+previous example. Both arrays $A$ and $B$ are initialized. Then the CPU
+computation is performed and the time for this CPU computation is measured. In
+order to compute the same result on the GPU, first of all, data from the CPU
+need to be copied into the memory of the GPU. For that, it is possible to use
+cublas function \texttt{cublasSetVector}.
+
+\lstinputlisting[label=ch2:lst:ex2,caption=A simple example]{Chapters/chapter2/ex2.cu}
+
+
+\putbib[Chapters/chapter2/biblio]
