last font embedded pb corrected

[book_gpu.git] / BookGPU / Chapters / chapter1 / ch1.tex

diff --git a/BookGPU/Chapters/chapter1/ch1.tex b/BookGPU/Chapters/chapter1/ch1.tex
index cf7a8b59e4b4119a7b729931f45a8ad3a4f5913e..6c3f1f1e6d67448a79c761f2d84bbe7905011f81 100755 (executable)
--- a/BookGPU/Chapters/chapter1/ch1.tex
+++ b/BookGPU/Chapters/chapter1/ch1.tex
@@ -1,7 +1,7 @@
 \chapterauthor{Raphaël Couturier}{Femto-ST Institute, University of Franche-Comte}
 
 
 \chapterauthor{Raphaël Couturier}{Femto-ST Institute, University of Franche-Comte}
 
 

-\chapter{Presentation of the GPU architecture and of the CUDA environment}
+\chapter{Presentation of the GPU architecture and of the Cuda environment}

 \label{chapter1}
 
 \section{Introduction}\label{ch1:intro}
 \label{chapter1}
 
 \section{Introduction}\label{ch1:intro}


@@ -9,112 +9,113 @@
 This chapter introduces the Graphics  Processing Unit (GPU) architecture and all
 the concepts needed to understand how GPUs  work and can be used to speed up the
 execution of some algorithms. First of all this chapter gives a brief history of
 This chapter introduces the Graphics  Processing Unit (GPU) architecture and all
 the concepts needed to understand how GPUs  work and can be used to speed up the
 execution of some algorithms. First of all this chapter gives a brief history of

-the development of Graphics card until they can be used in order to make general
-purpose computation.  Then  the architecture of a GPU  is illustrated. There are
-many fundamental differences  between a GPU and a  tradition processor. In order
-to benefit from the power of a GPU, a CUDA programmer needs to use threads. They
-have  some particularities  which enables  the CUDA  model to  be  efficient and
-scalable when some constraints are addressed.
+the development  of Graphics  card until they  have been  used in order  to make
+general   purpose   computation.    Then   the   architecture  of   a   GPU   is
+illustrated.  There  are  many  fundamental  differences between  a  GPU  and  a
+tradition  processor. In  order  to benefit  from the  power  of a  GPU, a  Cuda
+programmer needs to use threads. They have some particularities which enable the
+Cuda model to be efficient and scalable when some constraints are addressed.

 
 
 
 \section{Brief history of Video Card}
 
 
 
 
 \section{Brief history of Video Card}
 

-Video  card or  Graphics card  have been  introduced in  personnal  computers to
-produce  high quality  graphics faster  than classical  Central  Processing Unit
+Video  cards or Graphics  cards have  been introduced  in personal  computers to
+produce  high quality graphics  faster than  classical Central  Processing Units

 (CPU) and  to alleviate CPU from this  task. In general, display  tasks are very
 repetitive and very specific.  Hence,  some manufacturers have produced more and
 (CPU) and  to alleviate CPU from this  task. In general, display  tasks are very
 repetitive and very specific.  Hence,  some manufacturers have produced more and

-more sofisticated video cards, providing 2D accelerations then 3D accelerations,
+more sophisticated video cards, providing 2D accelerations then 3D accelerations,

 then some  light transforms. Video cards  own their own memory  to perform their
 then some  light transforms. Video cards  own their own memory  to perform their

-computation.  From  at least two dedaces,  every personnal computer  has a video
-card which is  simple for desktop computers or  which provides many accelerations
-for game  and/or graphic oriented computers.  In the latter  case, graphic cards
+computation.  For at least two decades, every personal computer has had a video
+card which is simple for  desktop computers or which provides many accelerations
+for game and/or  graphic oriented computers.  In the  latter case, graphic cards

 may be more expensive than a CPU.
 
 may be more expensive than a CPU.
 

-After 2000,  video cards allowed to apply  arithmetics operations simulatenously
-on a  sequence of  pixels, also  later called stream  processing. In  this case,
-information of the  pixels (color, location and other  information) are combined
-in   order  to   produce   a  pixel   color   that  can   be   displayed  on   a
-screen.  Simultaneous  computations  are  provided by  shaders  which  calculate
-rendering effects on graphics hardware  with a high degree of flexibility. These
-shaders handles the stream data with pipelines.
+Since  2000, video  cards have  allowed  users to  apply arithmetic  operations
+simultaneously on a sequence of  pixels, also later called stream processing. In
+this case, the information of the pixels (color, location and other information) are
+combined in order  to produce a pixel  color that can be displayed  on a screen.
+Simultaneous  computations are  provided  by shaders  which calculate  rendering
+effects on  graphics hardware with a  high degree of  flexibility. These shaders
+handles the stream data with pipelines.

 
 
 
 

-Some reasearchers  tried to apply  those operations on other  data, representing
+Some researchers  tried to  apply those operations  on other  data, representing

 something different  from pixels,  and consequently this  resulted in  the first
 uses of video cards for  performing general purpose computation. The programming
 model  was not  easy  to use  at  all and  was very  dependent  of the  hardware
 something different  from pixels,  and consequently this  resulted in  the first
 uses of video cards for  performing general purpose computation. The programming
 model  was not  easy  to use  at  all and  was very  dependent  of the  hardware

-constraints.  More precisely  it consisted  in  using either  DirectX of  OpenGL
+constraints.   More precisely  it consisted  in using  either DirectX  of OpenGL

 functions  providing  an  interface  to  some classical  operations  for  videos
 functions  providing  an  interface  to  some classical  operations  for  videos

-operations  (memory  transfers,   texture  manipulation,  ...).  Floating  point
-operations were  most of  the time unimaginable.   Obviously when  something bad
-happened, programmers had no way (and tools) to detect it.
+operations  (memory  transfers,  texture  manipulation,  ...).   Floating  point
+operations were  most of the  time unimaginable.  Obviously when  something went
+wrong, programmers had no way (and neither the tools) to detect it.

 
 \section{GPGPU}
 
 
 \section{GPGPU}
 

-In order  to benefit from the computing  power of more recent  video cards, CUDA
+In order  to benefit from the computing  power of more recent  video cards, Cuda

 was first proposed in 2007 by  NVidia. It unifies the programming model for some
 of  their most performant  video cards.   Cuda~\cite{ch1:cuda} has  quickly been
 considered by  the scientific community as  a great advance  for general purpose
 was first proposed in 2007 by  NVidia. It unifies the programming model for some
 of  their most performant  video cards.   Cuda~\cite{ch1:cuda} has  quickly been
 considered by  the scientific community as  a great advance  for general purpose

-graphics processing  unit (GPGPU) computing.  Of course  other programming model
+graphics processing unit (GPGPU)  computing.  Of course other programming models

 have been  proposed. The  other well-known alternative  is OpenCL which  aims at
 proposing an alternative to Cuda  and which is multi-platform and portable. This
 is a  great advantage since  it is even  possible to execute OpenCL  programs on
 have been  proposed. The  other well-known alternative  is OpenCL which  aims at
 proposing an alternative to Cuda  and which is multi-platform and portable. This
 is a  great advantage since  it is even  possible to execute OpenCL  programs on

-traditionnal  CPUs.  The  main  drawbacks is  that  it is  less  tight with  the
-hardware and consequently provides  sometimes less efficient programs. Moreover,
-Cuda benefits  from more mature compilation and  optimization procedures.  Other
-less known environment  have been proposed, but most of  them have been stopped,
-for example we  can cited: FireStream by ATI which is  not maintened anymore and
-replaced  by  OpenCL,  BrookGPU  by  Standford  University~\cite{ch1:Buck:2004:BGS}.
+traditional CPUs.  The main drawback is that it is less tight with the hardware
+and  consequently sometimes  provides  less efficient  programs. Moreover,  Cuda
+benefits from  more mature compilation and optimization  procedures.  Other less
+known environments  have been proposed, but  most of them have  been stopped, for
+example  we can  cite: FireStream  by ATI  which is  not maintained  anymore and
+replaced by  OpenCL, BrookGPU by  Standford University~\cite{ch1:Buck:2004:BGS}.

 Another environment based  on pragma (insertion of pragma  directives inside the
 Another environment based  on pragma (insertion of pragma  directives inside the

-code to  help the compiler  to generate efficient  code) is call OpenACC.  For a
+code to  help the compiler to generate  efficient code) is call  OpenACC.  For a

 comparison with OpenCL, interested readers may refer to~\cite{ch1:CMR:12}.
 
 
 
 \section{Architecture of current GPUs}
 
 comparison with OpenCL, interested readers may refer to~\cite{ch1:CMR:12}.
 
 
 
 \section{Architecture of current GPUs}
 

-Architecture  \index{architecture  of  a  GPU}  of current  GPUs  is  constantly
-evolving.    Nevertheless    some    trends    remains   true    through    this
-evolution.  Processing  units  composing a  GPU  are  far  more simpler  than  a
-traditional CPU but it is much easier to integrate many computing units inside a
-GPU card than many  cores inside a CPU. This is due to the  fact that cores of a
-GPU are simpler than  cores of a CPU.  In 2012, the  most powerful GPUs own more
-than     500    cores     and    the     most    powerful     CPUs     have    8
+The architecture  \index{architecture of  a GPU} of  current GPUs  is constantly
+evolving.  Nevertheless  some trends remain constant  throughout this evolution.
+Processing units composing a GPU are  far more simple than a traditional CPU but
+it is much easier to integrate many computing units inside a GPU card than to do
+so with many cores inside a CPU. This is due to the fact that the cores of a GPU are
+simpler than the cores of a CPU.  In  2012, the most powerful GPUs own more than 500
+cores       and       the       most       powerful      CPUs       have       8

 cores. Figure~\ref{ch1:fig:comparison_cpu_gpu} shows  the number of cores inside
 a  CPU  and  inside a  GPU.   In  fact,  in  a  current NVidia  GPU,  there  are
 multiprocessors which have 32 cores (for example on Fermi cards). The core clock
 cores. Figure~\ref{ch1:fig:comparison_cpu_gpu} shows  the number of cores inside
 a  CPU  and  inside a  GPU.   In  fact,  in  a  current NVidia  GPU,  there  are
 multiprocessors which have 32 cores (for example on Fermi cards). The core clock

-of CPU is generally around 3GHz and the one of GPU is about 1.5GHz. Although the
-core clock  of GPU cores is  slower, the amount  of cores inside a  GPU provides
-more computational power. This measure  is commonly represented by the number of
-floating point operation  per seconds. Nowadays most powerful  GPUs provide more
-than 1TFlops, i.e. $10^{12}$ floating point operations per second.  Nevertheless
-GPUs  are  very efficient  to  perform  some operations  but  not  all kinds  of
-operations. They are very efficient to execute repetitive work in which only the
-data change. It  is important to keep in mind that  multiprocessors inside a GPU
-have 32 cores. Later we will see that these 32 cores need to do the same work to
-get maximum performance.
+of CPU is  generally around 3GHz and  the one of GPU is  about 1.5GHz.  Although
+the core clock of GPU cores is slower, the amount of cores inside a GPU provides
+more computational power.  This measure is commonly represented by the number of
+floating point operation  per seconds. Nowadays the most powerful  GPUs provide more
+than   1TFlops,  i.e.    $10^{12}$   floating  point   operations  per   second.
+Nevertheless  GPUs are very  efficient to  perform some  operations but  not all
+kinds of operations. They are very efficient to execute repetitive work in which
+only  the data  change. It  is important  to keep  in mind  that multiprocessors
+inside a GPU have 32 cores. Later we will see that these 32 cores need to do the
+same work to get maximum performance.

 
 \begin{figure}[b!]
 \centerline{\includegraphics[]{Chapters/chapter1/figures/nb_cores_CPU_GPU.pdf}}
 
 \begin{figure}[b!]
 \centerline{\includegraphics[]{Chapters/chapter1/figures/nb_cores_CPU_GPU.pdf}}

-\caption[Comparison of number of cores in a CPU and in a GPU]{Comparison of number of cores in a CPU and in a GPU.}
+\caption{Comparison of number of cores in a CPU and in a GPU.}
+%[Comparison of number of cores in a CPU and in a GPU]

 \label{ch1:fig:comparison_cpu_gpu}
 \end{figure}
 
 \label{ch1:fig:comparison_cpu_gpu}
 \end{figure}
 

-On most powerful  GPU cards, called Fermi, multiprocessors  are called streaming
+On the most powerful  GPU cards, called Fermi, multiprocessors  are called streaming

 multiprocessors  (SM). Each  SM contains  32  cores and  is able  to perform  32
 multiprocessors  (SM). Each  SM contains  32  cores and  is able  to perform  32

-floating point or integer operations on  32bits numbers per clock or 16 floating
-point  on  64bits number  per  clock. SMs  have  their  own registers,  execution
+floating points or integer operations on  32 bits numbers per clock or 16 floating
+points  on  64 bits number  per  clock. SMs  have  their  own registers,  execution

 pipelines and caches.  On Fermi architecture,  there are 64Kb shared memory + L1
 cache  and 32,536 32bits  registers per  SM. More  precisely the  programmer can
 pipelines and caches.  On Fermi architecture,  there are 64Kb shared memory + L1
 cache  and 32,536 32bits  registers per  SM. More  precisely the  programmer can

-decide what amount  of shared memory and  L1 cache SM can use.  The constaint is
-that the sum of both amounts is less or equal to 64Kb.
+decide what amount  of shared memory and  L1 cache SM can use.  The constraint is
+that the sum of both amounts should be less or equal to 64Kb.

 
 Threads are used to  benefit from the important number of cores  of a GPU. Those
 threads    are   different    from    traditional   threads    for   CPU.     In
 chapter~\ref{chapter2},  some  examples of  GPU  programming  will explicit  the
 details of  the GPU  threads. However,  threads are gathered  into blocks  of 32
 
 Threads are used to  benefit from the important number of cores  of a GPU. Those
 threads    are   different    from    traditional   threads    for   CPU.     In
 chapter~\ref{chapter2},  some  examples of  GPU  programming  will explicit  the
 details of  the GPU  threads. However,  threads are gathered  into blocks  of 32

-threads, called ``warp''. Those warps  are important when designing an algorithm
+threads, called ``warps''. Those warps  are important when designing an algorithm

 for GPU.
 
 
 for GPU.
 
 


@@ -123,16 +124,16 @@ everything is optimized  to obtain a low latency  architecture. This is possible
 through  the  use  of  cache  memories. Moreover,  nowadays  CPUs  perform  many
 performance optimizations  such as speculative execution  which roughly speaking
 consists in executing  a small part of  code in advance even if  later this work
 through  the  use  of  cache  memories. Moreover,  nowadays  CPUs  perform  many
 performance optimizations  such as speculative execution  which roughly speaking
 consists in executing  a small part of  code in advance even if  later this work

-reveals to  be useless. In  opposite, GPUs do  not have low latency  memory.  In
-comparison GPUs have ridiculous cache memories. Nevertheless the architecture of
-GPUs  is optimized for  throughtput computation  and it  takes into  account the
-memory latency.
+reveals itself  to be  useless. On the  contrary, GPUs  do not have  low latency
+memory.   In comparison GPUs  have small  cache memories.  Nevertheless the
+architecture of GPUs is optimized  for throughput computation and it takes into
+account the memory latency.

 
 
 
 \begin{figure}[b!]
 \centerline{\includegraphics[scale=0.7]{Chapters/chapter1/figures/low_latency_vs_high_throughput.pdf}}
 
 
 
 \begin{figure}[b!]
 \centerline{\includegraphics[scale=0.7]{Chapters/chapter1/figures/low_latency_vs_high_throughput.pdf}}

-\caption[Comparison of low latency of CPU and highthroughput of GPU]{Comparison of low latency of CPU and highthroughput of GPU.}
+\caption{Comparison of low latency of CPU and high throughput of GPU.}

 \label{ch1:fig:latency_throughput}
 \end{figure}
 
 \label{ch1:fig:latency_throughput}
 \end{figure}
 


@@ -142,86 +143,86 @@ by one with a short memory latency to get the data to process. After some tasks,
 there is  a context switch  that allows the  CPU to run  concurrent applications
 and/or multi-threaded  applications. Memory latencies  are longer in a  GPU, the
 the  principle  to   obtain  a  high  throughput  is  to   have  many  tasks  to
 there is  a context switch  that allows the  CPU to run  concurrent applications
 and/or multi-threaded  applications. Memory latencies  are longer in a  GPU, the
 the  principle  to   obtain  a  high  throughput  is  to   have  many  tasks  to

-compute. Later we  will see that those tasks are called  threads with CUDA. With
+compute. Later we  will see that those tasks are called  threads with Cuda. With

 this  principle, as soon  as a  task is  finished the  next one  is ready  to be
 this  principle, as soon  as a  task is  finished the  next one  is ready  to be

-executed  while the  waiting for  data for  the previous  task is  overlapped by
+executed  while the  wait for  data for  the previous  task is  overlapped by

 computation of other tasks.
 
 
 
 \section{Kinds of parallelism}
 
 computation of other tasks.
 
 
 
 \section{Kinds of parallelism}
 

-Many  kinds  of parallelism  are  avaible according  to  the  type of  hardware.
-Roughtly  speaking, there  are three  classes of  parallelism: instruction-level
+Many  kinds  of parallelism  are  amiable according  to  the  type of  hardware.
+Roughly  speaking, there  are three  classes of  parallelism: instruction-level

 parallelism, data parallelism and task parallelism.
 
 Instruction-level parallelism consists in re-ordering some instructions in order
 to execute  some of them in parallel  without changing the result  of the code.
 parallelism, data parallelism and task parallelism.
 
 Instruction-level parallelism consists in re-ordering some instructions in order
 to execute  some of them in parallel  without changing the result  of the code.

-In  modern CPUs, instruction  pipelines allow  processor to  execute instruction
+In  modern CPUs, instruction  pipelines allow  processor to  execute instructions

 faster.   With   a  pipeline  a  processor  can   execute  multiple  instructions
 simultaneously due  to the fact that  the output of a  task is the  input of the
 next one.
 
 Data parallelism consists  in executing the same program  with different data on
 faster.   With   a  pipeline  a  processor  can   execute  multiple  instructions
 simultaneously due  to the fact that  the output of a  task is the  input of the
 next one.
 
 Data parallelism consists  in executing the same program  with different data on

-different computing  units. Of course, no  depency should exist  between the the
+different computing  units.  Of course,  no dependency should exist  between the

 data. For example, it is easy  to parallelize loops without dependency using the
 data parallelism paradigm. This paradigm  is linked with the Single Instructions
 data. For example, it is easy  to parallelize loops without dependency using the
 data parallelism paradigm. This paradigm  is linked with the Single Instructions

-Multiple Data  (SIMD) architecture. This is  the kind of  parallism providing by
+Multiple Data (SIMD)  architecture. This is the kind  of parallelism provided by

 GPUs.
 
 GPUs.
 

-Taks parallelism is the common parallism  achieved out on clusters and grids and
+Task parallelism is the common parallelism  achieved out on clusters and grids and

 high performance  architectures where different tasks are  executed by different
 computing units.
 
 high performance  architectures where different tasks are  executed by different
 computing units.
 

-\section{CUDA Multithreading}
+\section{Cuda Multithreading}

 
 

-The data parallelism  of CUDA is more precisely based  on the Single Instruction
+The data parallelism  of Cuda is more precisely based  on the Single Instruction

 Multiple Thread (SIMT) model. This is due to the fact that a programmer accesses
 Multiple Thread (SIMT) model. This is due to the fact that a programmer accesses

-to  the cores  by the  intermediate of  threads. In  the CUDA  model,  all cores
+to  the cores  by the  intermediate of  threads. In  the Cuda  model,  all cores

 execute the  same set of  instructions but with  different data. This  model has
 execute the  same set of  instructions but with  different data. This  model has

-similarities with vector programming  model proposed for vector machines through
-the  1970s into  the  90s, notably  the  various Cray  platforms.   On the  CUDA
+similarities with the vector programming  model proposed for vector machines through
+the  1970s into  the  90s, notably  the  various Cray  platforms.   On the  Cuda

 architecture, the  performance is  led by the  use of  a huge number  of threads
 architecture, the  performance is  led by the  use of  a huge number  of threads

-(from thousand upto  to millions). The particularity of the  model is that there
+(from thousands up to  to millions). The particularity of the  model is that there

 is no  context switching as in  CPUs and each  thread has its own  registers. In
 practice,  threads  are executed  by  SM  and are  gathered  into  groups of  32
 is no  context switching as in  CPUs and each  thread has its own  registers. In
 practice,  threads  are executed  by  SM  and are  gathered  into  groups of  32

-threads.  Those  groups  are  call  ``warps''. Each  SM  alternatively  executes
-``active warps''  and warps becoming temporaly  inactive due to  waiting of data
+threads.  Those  groups  are  called  ``warps''. Each  SM  alternatively  executes
+``active warps''  and warps becoming temporarily  inactive due to  waiting of data

 (as shown in Figure~\ref{ch1:fig:latency_throughput}).
 
 (as shown in Figure~\ref{ch1:fig:latency_throughput}).
 

-The key to scalability in the CUDA model is the use of a huge number of threads.
+The key to scalability in the Cuda model is the use of a huge number of threads.

 In practice, threads are not only gathered  in warps but also in thread blocks. A
 In practice, threads are not only gathered  in warps but also in thread blocks. A

-thread block is executed  by only one SM and it cannot  migrate. Typical size of
-thread block is a number power of two (for example: 64, 128, 256 or 512).
+thread block is executed  by only one SM and it cannot  migrate. The typical size of
+a thread block is a number power of two (for example: 64, 128, 256 or 512).

 
 
 
 
 
 

-In this  case, without changing anything inside  a CUDA code, it  is possible to
-run your  code with  a small CUDA  device or  most performant Tesla  CUDA cards.
+In this  case, without changing anything inside  a Cuda code, it  is possible to
+run your  code with  a small Cuda  device or  the most performing Tesla  Cuda cards.

 Blocks are  executed in any order depending  on the number of  SMs available. So
 the  programmer  must  conceive  its  code  having this  issue  in  mind.   This
 Blocks are  executed in any order depending  on the number of  SMs available. So
 the  programmer  must  conceive  its  code  having this  issue  in  mind.   This

-independence between threads blocks provides the scalability of CUDA codes.
+independence between thread blocks provides the scalability of Cuda codes.

 
 \begin{figure}[b!]
 \centerline{\includegraphics[scale=0.65]{Chapters/chapter1/figures/scalability.pdf}}
 
 \begin{figure}[b!]
 \centerline{\includegraphics[scale=0.65]{Chapters/chapter1/figures/scalability.pdf}}

-\caption[Scalability of GPU]{Scalability of GPU.}
+\caption{Scalability of GPU.}

 \label{ch1:fig:scalability}
 \end{figure}
 
 
 A kernel is a function which  contains a block of instructions that are executed
 \label{ch1:fig:scalability}
 \end{figure}
 
 
 A kernel is a function which  contains a block of instructions that are executed

-by the  threads of a GPU.   When the problem considered  is a 2  dimensions or 3
-dimensions  problem,  it is  possible  to group  thread  blocks  into grid.   In
-practice, the number of  thread blocks and the size of thread  block is given in
-parameter  to  each  kernel.   Figure~\ref{ch1:fig:scalability}  illustrates  an
+by the  threads of a GPU.   When the problem considered  is a two  dimensional or three
+dimensional  problem,  it is  possible  to group  thread  blocks  into a grid.   In
+practice, the number of  thread blocks and the size of thread  blocks is given as
+parameters  to  each  kernel.   Figure~\ref{ch1:fig:scalability}  illustrates  an

 example of a kernel composed of 8 thread blocks. Then this kernel is executed on
 example of a kernel composed of 8 thread blocks. Then this kernel is executed on

-a small device containing only 2 SMs.  So in in this case, blocks are executed 2
-by 2 in any order.  If the kernel is executed on a larger CUDA device containing
+a small device containing only 2 SMs.  So in  this case, blocks are executed 2
+by 2 in any order.  If the kernel is executed on a larger Cuda device containing

 4 SMs, blocks are executed 4 by 4 simultaneously.  The execution times should be
 approximately twice faster in the latter  case. Of course, that depends on other
 parameters that will be described later.
 
 4 SMs, blocks are executed 4 by 4 simultaneously.  The execution times should be
 approximately twice faster in the latter  case. Of course, that depends on other
 parameters that will be described later.
 

-Thread blocks provide a way to cooperation  in the sens that threads of the same
+Thread blocks provide a way to cooperation  in the sense that threads of the same

 block   cooperatively    load   and   store   blocks   of    memory   they   all
 use. Synchronizations of threads in the same block are possible (but not between
 threads of different  blocks). Threads of the same block  can also share results
 block   cooperatively    load   and   store   blocks   of    memory   they   all
 use. Synchronizations of threads in the same block are possible (but not between
 threads of different  blocks). Threads of the same block  can also share results


@@ -242,7 +243,7 @@ memory\index{memory~hierarchy!global~memory}.
 As  previously  mentioned each  thread  can access  its  own  registers.  It  is
 important to keep in mind that the  number of registers per block is limited. On
 recent cards,  this number is  limited to 64Kb  per SM.  Access to  registers is
 As  previously  mentioned each  thread  can access  its  own  registers.  It  is
 important to keep in mind that the  number of registers per block is limited. On
 recent cards,  this number is  limited to 64Kb  per SM.  Access to  registers is

-very fast, so when possible it is a good idea to use them.
+very fast, so it is a good idea to use them whenever possible.

 
 Likewise each thread can access local  memory which, in practice, is much slower
 than registers.  Local memory is automatically used by the compiler when all the
 
 Likewise each thread can access local  memory which, in practice, is much slower
 than registers.  Local memory is automatically used by the compiler when all the


@@ -251,7 +252,7 @@ even if this implies to reduce the number of threads per block.
 
 \begin{figure}[hbtp!]
 \centerline{\includegraphics[scale=0.60]{Chapters/chapter1/figures/memory_hierarchy.pdf}}
 
 \begin{figure}[hbtp!]
 \centerline{\includegraphics[scale=0.60]{Chapters/chapter1/figures/memory_hierarchy.pdf}}

-\caption[Memory hierarchy of a GPU]{Memory hierarchy of a GPU.}
+\caption{Memory hierarchy of a GPU.}

 \label{ch1:fig:memory_hierarchy}
 \end{figure}
 
 \label{ch1:fig:memory_hierarchy}
 \end{figure}
 


@@ -284,19 +285,12 @@ GPU.
 
  \section{Conclusion}
 
 
  \section{Conclusion}
 

-In this chapter,  a brief presentation of the video card,  which later have been
+In this chapter,  a brief presentation of the video card,  which has later been

 used to perform computation, has been  given. The architecture of a GPU has been
 illustrated focusing on the particularity of GPUs in term of parallelism, memory
 latency and  threads. In order to design  an efficient algorithm for  GPU, it is
 essential to have all these parameters in mind.
 
 used to perform computation, has been  given. The architecture of a GPU has been
 illustrated focusing on the particularity of GPUs in term of parallelism, memory
 latency and  threads. In order to design  an efficient algorithm for  GPU, it is
 essential to have all these parameters in mind.
 

-%%http://people.maths.ox.ac.uk/gilesm/pp10/lec2_2x2.pdf
-%%https://people.maths.ox.ac.uk/erban/papers/paperCUDA.pdf
-%%http://forum.wttsnxt.com/my_forum/viewtopic.php?f=5&t=9519
-%%http://www.cs.nyu.edu/manycores/cuda_many_cores.pdf
-%%http://www.cc.gatech.edu/~vetter/keeneland/tutorial-2011-04-14/02-cuda-overview.pdf
-%%http://people.maths.ox.ac.uk/~gilesm/cuda/
-

 
 \putbib[Chapters/chapter1/biblio]
 
 
 \putbib[Chapters/chapter1/biblio]