9ème :

[dmems12.git] / dmems12.tex

diff --git a/dmems12.tex b/dmems12.tex
index e5a7838fd0f72e83b1ba3943e1aa6510d4d2f738..314368e8ff8e9cad225c946751adb95aa857a125 100644 (file)
--- a/dmems12.tex
+++ b/dmems12.tex
@@ -1,5 +1,5 @@
 
 

-\documentclass[10pt, conference, compsocconf]{IEEEtran}
+\documentclass[10pt, peerreview, compsocconf]{IEEEtran}

 %\usepackage{latex8}
 %\usepackage{times}
 \usepackage[utf8]{inputenc}
 %\usepackage{latex8}
 %\usepackage{times}
 \usepackage[utf8]{inputenc}


@@ -58,7 +58,7 @@
 
 
 
 
 
 

-\maketitle
+%\maketitle

 
 \thispagestyle{empty}
 
 
 \thispagestyle{empty}
 


@@ -66,9 +66,16 @@
 
   
 
 
   
 

-{\it keywords}: FPGA, cantilever, interferometry.
+

 \end{abstract}
 
 \end{abstract}
 

+\begin{IEEEkeywords}
+FPGA, cantilever, interferometry.
+\end{IEEEkeywords}
+
+
+\IEEEpeerreviewmaketitle
+

 \section{Introduction}
 
 Cantilevers  are  used  inside  atomic  force  microscope (AFM) which  provides  high
 \section{Introduction}
 
 Cantilevers  are  used  inside  atomic  force  microscope (AFM) which  provides  high


@@ -196,68 +203,147 @@ on spline interpolation (see section \ref{algo-spline}). It also
 computes the coefficient used for unwrapping the phase. The second one
 is the acquisition loop, while which images are taken at regular time
 steps. For each image, the phase $\theta$ of all profiles is computed
 computes the coefficient used for unwrapping the phase. The second one
 is the acquisition loop, while which images are taken at regular time
 steps. For each image, the phase $\theta$ of all profiles is computed

-to obtain, after unwrapping, the deflection of cantilevers.
+to obtain, after unwrapping, the deflection of
+cantilevers. Originally, this computation was also done with an
+algorithm based on spline. This article proposes a new version based
+on a least square method.

 
 \subsection{Design goals}
 \label{sec:goals}
 
 
 \subsection{Design goals}
 \label{sec:goals}
 

+The main goal is to implement a computing unit to estimate the
+deflection of about $10\times10$ cantilevers, faster than the stream of
+images coming from the camera. The accuracy of results must be close
+to the maximum precision ever obtained experimentally on the
+architecture, i.e. 0.3nm. Finally, the latency between an image
+entering in the unit and the deflections must be as small as possible
+(NB : future works plan to add some control on the cantilevers).\\
+

 If we put aside some hardware issues like the speed of the link
 between the camera and the computation unit, the time to deserialize
 pixels and to store them in memory, ... the phase computation is
 obviously the bottle-neck of the whole process. For example, if we
 consider the camera actually in use, an exposition time of 2.5ms for
 If we put aside some hardware issues like the speed of the link
 between the camera and the computation unit, the time to deserialize
 pixels and to store them in memory, ... the phase computation is
 obviously the bottle-neck of the whole process. For example, if we
 consider the camera actually in use, an exposition time of 2.5ms for

-$1024\times 1204$ pixels seems the minimum that can be reached. For a
-$10\times 10$ cantilever array, if we neglect the time to extract
-pixels, it implies that computing the deflection of a single
+$1024\times 1204$ pixels seems the minimum that can be reached. For
+100 cantilevers, if we neglect the time to extract pixels, it implies
+that computing the deflection of a single

 cantilever should take less than 25$\mu$s, thus 12.5$\mu$s by phase.\\
 
 In fact, this timing is a very hard constraint. Let consider a very
 small programm that initializes twenty million of doubles in memory
 and then does 1000000 cumulated sums on 20 contiguous values
 (experimental profiles have about this size). On an intel Core 2 Duo
 cantilever should take less than 25$\mu$s, thus 12.5$\mu$s by phase.\\
 
 In fact, this timing is a very hard constraint. Let consider a very
 small programm that initializes twenty million of doubles in memory
 and then does 1000000 cumulated sums on 20 contiguous values
 (experimental profiles have about this size). On an intel Core 2 Duo

-E6650 at 2.33GHz, this program reaches an average of 155Mflops. It
-implies that the phase computation algorithm should not take more than
-$240\times 12.5 = 1937$ floating operations. For integers, it gives
-$3000$ operations.
-
-%% to be continued ...
-
-%% � faire : timing de l'algo spline en C avec atan et tout le bordel.
-
-
+E6650 at 2.33GHz, this program reaches an average of 155Mflops. 
+
+%%Itimplies that the phase computation algorithm should not take more than
+%%$155\times 12.5 = 1937$ floating operations. For integers, it gives $3000$ operations. 
+
+Obviously, some cache effects and optimizations on
+huge amount of computations can drastically increase these
+performances : peak efficiency is about 2.5Gflops for the considered
+CPU. But this is not the case for phase computation that used only few
+tenth of values.\\
+
+In order to evaluate the original algorithm, we translated it in C
+language. As said further, for 20 pixels, it does about 1550
+operations, thus an estimated execution time of $1550/155
+=$10$\mu$s. For a more realistic evaluation, we constructed a file of
+1Mo containing 200 profiles of 20 pixels, equally scattered. This file
+is equivalent to an image stored in a device file representing the
+camera. We obtained an average of 10.5$\mu$s by profile (including I/O
+accesses). It is under are requirements but close to the limit. In
+case of an occasional load of the system, it could be largely
+overtaken. A solution would be to use a real-time operating system but
+another one to search for a more efficient algorithm.
+
+But the main drawback is the latency of such a solution : since each
+profile must be treated one after another, the deflection of 100
+cantilevers takes about $200\times 10.5 = 2.1$ms, which is inadequate
+for an efficient control. An obvious solution is to parallelize the
+computations, for example on a GPU. Nevertheless, the cost to transfer
+profile in GPU memory and to take back results would be prohibitive
+compared to computation time. It is certainly more efficient to
+pipeline the computation. For example, supposing that 200 profiles of
+20 pixels can be pushed sequentially in the pipelined unit cadenced at
+a 100MHz (i.e. a pixel enters in the unit each 10ns), all profiles
+would be treated in $200\times 20\times 10.10^{-9} =$ 40$\mu$s plus
+the latency of the pipeline. This is about 500 times faster than
+actual results.\\
+
+For these reasons, an FPGA as the computation unit is the best choice
+to achieve the required performance. Nevertheless, passing from
+a C code to a pipelined version in VHDL is not obvious at all. As
+explained in the next section, it can even be impossible because of
+some hardware constraints specific to FPGAs.

 
 
 \section{Proposed solution}
 \label{sec:solus}
 
 
 
 \section{Proposed solution}
 \label{sec:solus}
 

-
-\subsection{FPGA constraints}
-
-A field-programmable gate  array (FPGA) is an integrated  circuit designed to be
-configured by  the customer.  A hardware  description language (HDL)  is used to
-configure a  FPGA. FGPAs are  composed of programmable logic  components, called
-logic blocks.  These blocks can be  configured to perform simple (AND, XOR, ...)
-or  complex  combinational  functions.    Logic  blocks  are  interconnected  by
-reconfigurable  links. Modern  FPGAs  contains memory  elements and  multipliers
-which enables to simplify the design and increase the speed. As the most complex
-operation operation on FGPAs is the  multiplier, design of FGPAs should not used
-complex operations. For example, a divider  is not an available operation and it
-should be programmed using simple components.
-
+Project Oscar aims  to provide a hardware and  software architecture to estimate
+and  control the  deflection of  cantilevers. The  hardware part  consists  in a
+high-speed camera,  linked on an embedded  board hosting FPGAs. By  the way, the
+camera output stream can be pushed  directly into the FPGA. The software part is
+mostly the VHDL  code that deserializes the camera  stream, extracts profile and
+computes  the deflection. Before  focusing on  our work  to implement  the phase
+computation, we give some general information about FPGAs and the board we use.
+
+\subsection{FPGAs}
+
+A field-programmable gate array (FPGA) is an integrated circuit
+designed to be configured by the customer. FGPAs are composed of
+programmable logic components, called configurable logic blocks
+(CLB). These blocks mainly contains look-up tables (LUT), flip/flops
+(F/F) and latches, organized in one or more slices connected
+together. Each CLB can be configured to perform simple (AND, XOR, ...)
+or complex combinational functions. They are interconnected by
+reconfigurable links. Modern FPGAs contain memory elements and
+multipliers which enable to simplify the design and to increase the
+performance. Nevertheless, all other complex operations, like
+division, trigonometric functions, $\ldots$ are not available and must
+be done by configuring a set of CLBs.
+
+Since this configuration is not obvious at all, it can be done via a
+framework that synthetize a design written in an hardware description
+language (HDL), and after, that place and route 
+
+ is used to configure a FPGA.

 FGPAs programming  is very different  from classic processors  programming. When
 FGPAs programming  is very different  from classic processors  programming. When

-logic block are programmed and linked  to performed an operation, they cannot be
-reused anymore.  FPGA  are cadenced slowly than classic  processors but they can
-performed pipelined as  well as pipelined operations. A  pipeline provides a way
-manipulate data quickly  since at each clock top to handle  a new data. However,
-using  a  pipeline  consomes more  logics  and  components  since they  are  not
-reusable,  nevertheless it  is probably  the most  efficient technique  on FPGA.
-Parallel  operations   can  be  used   in  order  to  manipulate   several  data
+logic blocks are  programmed and linked to perform an  operation, they cannot be
+reused anymore.  FPGAs are cadenced more slowly than classic processors but they
+can perform pipeline  as well as parallel operations. A  pipeline provides a way
+to  manipulate  data  quickly  since  at   each  clock  top  it  handles  a  new
+data. However, using  a pipeline consumes more logics  and components since they
+are not  reusable. Nevertheless it is  probably the most  efficient technique on
+FPGA.   Parallel operations  can be  used in  order to  manipulate  several data

 simultaneously. When  it is  possible, using  a pipeline is  a good  solution to
 manipulate  new  data  at  each  clock  top  and  using  parallelism  to  handle
 simultaneously. When  it is  possible, using  a pipeline is  a good  solution to
 manipulate  new  data  at  each  clock  top  and  using  parallelism  to  handle

-simultaneously several data streams.
+simultaneously several pipelines in order to handle multiple data streams.
+
+%% parler du VHDL, synthèse et bitstream
+\subsection{The board}

 
 

-%% contraintes imposées par le FPGA : algo pipeline/parallele, pas d'op math complexe, ...
+The board we use is designed by the Armadeus compagny, under the name
+SP Vision. It consists in a development board hosting a i.MX27 ARM
+processor (from Freescale). The board includes all classical
+connectors : USB, Ethernet, ... A Flash memory contains a Linux kernel
+that can be launched after booting the board via u-Boot.

 
 

+The processor is directly connected to a Spartan3A FPGA (from Xilinx)
+via its special interface called WEIM. The Spartan3A is itself
+connected to a Spartan6 FPGA. Thus, it is possible to develop programs
+that communicate between i.MX and Spartan6, using Spartan3 as a
+tunnel. By default, the WEIM interface provides a clock signal at
+100MHz that is connected to dedicated FPGA pins.
+
+The Spartan6 is an LX100 version. It has 15822 slices, equivalent to
+101261 logic cells. There are 268 internal block RAM of 18Kbits, and
+180 dedicated multiply-adders (named DSP48), which is largely enough
+for our project.
+
+Some I/O pins of Spartan6 are connected to two $2\times 17$ headers
+that can be used as user wants. For the project, they will be
+connected to the interface card of the camera.

 
 \subsection{Considered algorithms}
 
 
 \subsection{Considered algorithms}
 


@@ -518,7 +604,7 @@ largely beyond the worst experimental ones.
 
 \begin{figure}[ht]
 \begin{center}
 
 \begin{figure}[ht]
 \begin{center}

-  \includegraphics[width=9cm]{intens-noise20-spl}
+  \includegraphics[width=9cm]{intens-noise20}

 \end{center}
 \caption{Sample of worst profile for N=10}
 \label{fig:noise20}
 \end{center}
 \caption{Sample of worst profile for N=10}
 \label{fig:noise20}


@@ -526,7 +612,7 @@ largely beyond the worst experimental ones.
 
 \begin{figure}[ht]
 \begin{center}
 
 \begin{figure}[ht]
 \begin{center}

-  \includegraphics[width=9cm]{intens-noise60-lsq}
+  \includegraphics[width=9cm]{intens-noise60}

 \end{center}
 \caption{Sample of worst profile for N=30}
 \label{fig:noise60}
 \end{center}
 \caption{Sample of worst profile for N=30}
 \label{fig:noise60}


@@ -538,25 +624,76 @@ to numbers of pixels $M$. For LSQ, it also depends on $nb_s$ and for
 SPL on $N = k\times M$, i.e. the number of interpolated points. 
 
 We assume that $M=20$, $nb_s=1024$, $k=4$, all possible parts are
 SPL on $N = k\times M$, i.e. the number of interpolated points. 
 
 We assume that $M=20$, $nb_s=1024$, $k=4$, all possible parts are

-already in lookup tables and only arithmetic operations (+, -, *, /)
-are taken account. Translating the two algorithms in C code, we obtain
-about 400 operations for LSQ and 1340 (plus the unknown for $atan$)
-for SPL. Even if the result is largely in favor of LSQ, we can notice
-that executing the C code (compiled with \tt{-O3}) of SPL on an
-2.33GHz Core 2 Duo only takes 6.5µs in average, which is under our
-desing goals. The final decision is thus driven by the third criterion.\\
+already in lookup tables and a limited set of operations (+, -, *, /,
+$<$, $>$) is taken account. Translating the two algorithms in C code, we
+obtain about 430 operations for LSQ and 1550 (plus few tenth for
+$atan$) for SPL. This result is largely in favor of LSQ. Nevertheless,
+considering the total number of operations is not really pertinent for
+an FPGA implementation : it mainly depends on the type of operations
+and their
+ordering. The final decision is thus driven by the third criterion.\\

 
 The Spartan 6 used in our architecture has hard constraint : it has no
 
 The Spartan 6 used in our architecture has hard constraint : it has no

-floating point units. Thus, all computations have to be done with
-integers. 
+built-in floating point units. Obviously, it is possible to use some
+existing "black-boxes" for double precision operations. But they have
+a quite long latency. It is much simpler to exclusively use integers,
+with a quantization of all double precision values. Obviously, this
+quantization should not decrease too much the precision of
+results. Furthermore, it should not lead to a design with a huge
+latency because of operations that could not complete during a single
+or few clock cycles. Divisions are in this case and, moreover, they
+need an varying number of clock cycles to complete. Even
+multiplications can be a problem : DSP48 take inputs of 18 bits
+maximum. For larger multiplications, several DSP must be combined,
+increasing the latency.
+
+Nevertheless, the hardest constraint does not come from the FPGA
+characteristics but from the algorithms. Their VHDL implentation will
+be efficient only if they can be fully (or near) pipelined. By the
+way, the choice is quickly done : only a small part of SPL can be.
+Indeed, the computation of spline coefficients implies to solve a
+tridiagonal system $A.m = b$. Values in $A$ and $b$ can be computed
+from incoming pixels intensity but after, the back-solve starts with
+the lastest values, which breaks the pipeline. Moreover, SPL relies on
+interpolating far more points than profile size. Thus, the end
+of SPL works on a larger amount of data than the beginning, which
+also breaks the pipeline.
+
+LSQ has not this problem : all parts except the dichotomial search
+work on the same amount of data, i.e. the profile size. Furthermore,
+LSQ needs less operations than SPL, implying a smaller output
+latency. Consequently, it is the best candidate for phase
+computation. Nevertheless, obtaining a fully pipelined version
+supposes that operations of different parts complete in a single clock
+cycle. It is the case for simulations but it completely fails when
+mapping and routing the design on the Spartan6. By the way,
+extra-latency is generated and there must be idle times between two
+profiles entering into the pipeline.
+
+%%Before obtaining the least bitstream, the crucial question is : how to
+%%translate the C code the LSQ into VHDL ?
+
+
+%\subsection{VHDL design paradigms}
+
+\section{Experimental tests}

 
 

+\subsection{VHDL implementation}

 
 

+% - ecriture d'un code en C avec integer
+% - calcul de la taille max en bit de chaque variable en fonction de la quantization.
+% - tests de quantization : équilibre entre précision et contraintes FPGA
+% - en parallèle : simulink et VHDL à la main
+%
+\subsection{Simulation}

 
 

-\subsection{VHDL design paradigms}
+% ghdl + gtkwave
+% au mieux : une phase tous les 33 cycles, latence de 95 cycles.
+% mais routage/placement impossible.
+\subsection{Bitstream creation}

 
 

-\subsection{VHDL implementation}
+% pas fait mais prévision d'une sortie tous les 480ns avec une latence de 1120

 
 

-\section{Experimental results}

 \label{sec:results}
 
 
 \label{sec:results}