\chapter{Introduction to CUDA}
\label{chapter2}
-\section{Introduction}\label{intro}
+\section{Introduction}
+\label{ch2:intro}
+
In this chapter we give some simple examples on CUDA programming. The goal is
not to provide an exhaustive presentation of all the functionalities of CUDA but
rather giving some basic elements. Of course, readers that do not know CUDA are
\section{First example}
+\label{ch2:1ex}
This first example is intented to show how to build a very simple example with
CUDA. The goal of this example is to performed the sum of two arrays and
\lstinputlisting[label=ch2:lst:ex1,caption=A simple example]{Chapters/chapter2/ex1.cu}
\section{Second example: using CUBLAS}
+\label{ch2:2ex}
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
+applications and are very optimized for vector operations, matrix-vector
operations and matrix-matrix
-operations~\cite{ch2:journals/ijhpca/Dongarra02}. Some of those operations seems
+operations~\cite{ch2:journals/ijhpca/Dongarra02}. Some of those operations seem
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.
+simple. Roughly speaking, a reduction operation\index{reduction~operation} is an
+operation which combines all the elements of an array and extract a number
+computed with all the elements. For example, a sum, a maximum or a dot product
+are reduction operations.
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
+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.
+which has no 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
+addition of two arrays is exactly the same as the one described in the
previous example.
The kernel to compute the inverse of the elements of an array is very
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
+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}
-
+cublas function \texttt{cublasSetVector}. This function several arguments. More
+precisely, the first argument represents the number of elements to transfer, the
+second arguments is the size of each elements, the third element represents the
+source of the array to transfer (in the GPU), the fourth is an offset between
+each element of the source (usually this value is set to 1), the fifth is the
+destination (in the GPU) and the last is an offset between each element of the
+destination. Then we call the kernel \texttt{addition} which computes the sum of
+all elements of arrays $A$ and $B$. The \texttt{inverse} kernel is called twice,
+once to inverse elements of array $C$ and once for $A$. Finally, we call the
+function \texttt{cublasDdot} which computes the dot product of two vectors. To
+use this routine, we must specify the handle initialized by Cuda, the number of
+elements to consider, then each vector is followed by the offset between every
+element. After the GPU computation, it is possible to check that both
+computation produce the same result.
+
+\lstinputlisting[label=ch2:lst:ex2,caption=A simple example with cublas]{Chapters/chapter2/ex2.cu}
+
+\section{Third example: matrix-matrix multiplication}
+\label{ch2:3ex}
+
+
+
+Matrix-matrix multiplication is an operation which is quite easy to parallelize
+with a GPU. If we consider that a matrix is represented using a two dimensional
+array, A[i][j] represents the the element of the $i^{th}$ row and of the
+$j^{th}$ column. In many case, it is easier to manipulate 1D array instead of 2D
+array. With Cuda, even if it is possible to manipulate 2D arrays, in the
+following we present an example based on 1D array. For sake of simplicity we
+consider we have a squared matrix of size \texttt{size}. So with a 1D
+array, \texttt{A[i*size+j]} allows us to access to the element of the $i^{th}$
+row and of the $j^{th}$ column.
+
+In sequential the matrix multiplication is performed using three loops. Supposing that $A$, $B$ represent two square matrices, the result of the multiplication of $A \times B$ is
+
+On C2070M Tesla card, this code take 37.68ms to perform the multiplication. On a
+Intel Xeon E31245 at 3.30GHz, it takes 2465ms without any parallelization (using
+only one core). Consequently the speed up between the CPU and GPU version is
+about 65 which is very good regarding the difficulty of parallelizing this code.
+
+\lstinputlisting[label=ch2:lst:ex3,caption=simple Matrix-matrix multiplication with cuda]{Chapters/chapter2/ex3.cu}
\putbib[Chapters/chapter2/biblio]
