X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/book_gpu.git/blobdiff_plain/0dee9cd4943e9ee5a8d83e90a8f42842e9cfae15..4eb0d6980c190aa2e92700dd01c5f685405590bd:/BookGPU/Chapters/chapter2/ch2.tex?ds=inline

diff --git a/BookGPU/Chapters/chapter2/ch2.tex b/BookGPU/Chapters/chapter2/ch2.tex
index 804afc2..501e34e 100755
--- a/BookGPU/Chapters/chapter2/ch2.tex
+++ b/BookGPU/Chapters/chapter2/ch2.tex
@@ -1,23 +1,26 @@
-\chapterauthor{Author Name1}{Affiliation text1}
-\chapterauthor{Author Name2}{Affiliation text2}
-
+\chapterauthor{RaphaÃ«l Couturier}{Femto-ST Institute, University of Franche-Comte}
 
 \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
-invited to read other books that are specialized on CUDA programming (for example: \cite{Sanders:2010:CEI}).
+invited  to read  other  books that  are  specialized on  CUDA programming  (for
+example: \cite{ch2:Sanders:2010:CEI}).
 
 
 \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
 putting the  result into a  third array.   A cuda program  consists in a  C code
-which calls CUDA kernels that are executed on a GPU. The listing of this code is in Listing~\ref{ch2:lst:ex1}
+which calls CUDA kernels that are executed on a GPU. The listing of this code is
+in Listing~\ref{ch2:lst:ex1}.
 
 
 As GPUs have  their own memory, the first step consists  in allocating memory on
@@ -47,11 +50,12 @@ 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
+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
@@ -65,5 +69,80 @@ block.
 
 \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  optimized  for  vector  operations,  matrix-vector
+operations                           and                           matrix-matrix
+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. 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
+to compute the  scalar product between $1/C$ and $1/A$. This  is just an example
+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  as  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}.  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.
+
+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]
 
