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@ -66,8 +66,6 @@
\tableofcontents \tableofcontents
\todo{Talk of the repo, somewhere}
\pagebreak \pagebreak
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@ -75,24 +73,26 @@
In the previous years, verification and proved software has gathered an In the previous years, verification and proved software has gathered an
increasing interest in the computer science community, as people realised how increasing interest in the computer science community, as people realised how
hard bugs are to track down. But hardware bugs are even more tedious to find hard bugs are to track down, and the little confidence they had in their own
and fix, and can easily lead to disastrous consequences, as those cannot be code. But hardware bugs are even more tedious to find and fix, and can easily
patched on existing hardware. For instance, the well-known Pentium lead to disastrous consequences, as those cannot be patched on existing
``\textsc{fdiv}'' bug~\cite{pratt1995fdiv} that affected a large number of hardware. For instance, the well-known Pentium ``\textsc{fdiv}''
Pentium processors lead to wrong results for some floating point divisions. bug~\cite{pratt1995fdiv} that affected a large number of Pentium processors
Intel had to offer to replace all the defective CPUs, leading to an announced lead to wrong results for some floating point divisions. Intel had to offer to
loss of 475 million dollars~\cite{nicely_fdiv}. Even recently, the Skylake and replace all the defective CPUs, leading to an announced loss of 475 million
Kaby Lake hyperthreading bug had to be patched using microcode, loosing dollars~\cite{nicely_fdiv}. Even recently, the Skylake and Kaby Lake
performance and reliability. hyperthreading bug had to be patched using microcode, losing performance and
reliability.
To avoid such disasters, the industry nowadays uses a wide range of techniques To avoid such disasters, the industry nowadays uses a wide range of techniques
to catch bugs as early as possible --- which, hopefully, is before the product's to catch bugs as early as possible --- which, hopefully, is before the
release date. Among those are \todo{list + cite}, but also proved hardware. On product's release date. Among those are \todo{list + cite}, but also proved
circuits as complex as processors, usually, only sub-components are proved hardware. On circuits as complex as processors, usually, only sub-components
correct in a specified context --- that should, but is not proved to, be are proved correct with respect to a given specification of its behaviour,
respected by the other parts of the circuit. Yet, this trade-off between proved while the circuit is kept in a specified context, \ie{} a set of valid inputs
correctness and engineer's work time already gives a pretty good confidence in and outputs, etc. --- that should, but is not proved to, be respected by the
the circuit. other parts of the circuit. Yet, this trade-off between proved correctness and
engineer's work time already gives a pretty good confidence in the circuit.
In this context, Carl Seger was one of the main developers of fl at Intel, a In this context, Carl Seger was one of the main developers of fl at Intel, a
functional ml-inspired programming language integrating many features useful to functional ml-inspired programming language integrating many features useful to
@ -113,7 +113,7 @@ understand, and make it easier to understand to work more efficiently.
and Mary Sheeran, aiming to develop tools for proved design of FPGA circuits. and Mary Sheeran, aiming to develop tools for proved design of FPGA circuits.
One of the keystones of this project is an open-sourced and publicly available One of the keystones of this project is an open-sourced and publicly available
version of fl, used for the proving part, and is still at the moment under version of fl, used for the proving part, and is still at the moment under
development. heavy development.
My part of the work resided on this ``search and replace'' tool. More My part of the work resided on this ``search and replace'' tool. More
specifically, I focused on writing a C++ library, \emph{isomatch}, which is specifically, I focused on writing a C++ library, \emph{isomatch}, which is
@ -152,7 +152,7 @@ functions for this task.
\vert~&- & \textit{(sub)} \\ \vert~&- & \textit{(sub)} \\
\vert~&\times & \textit{(times)} \\ \vert~&\times & \textit{(times)} \\
\vert~&\div & \textit{(div)} \\ \vert~&\div & \textit{(div)} \\
\vert~&\% & \textit{(mod)} \\ \vert~&\% & \textit{(mod)} \\ % chktex 35
\vert~&\lsl & \textit{(logical shift left)} \\ \vert~&\lsl & \textit{(logical shift left)} \\
\vert~&\lsr & \textit{(logical shift right)} \\ \vert~&\lsr & \textit{(logical shift right)} \\
\vert~&\asr & \textit{(arithmetic shift right)} \\ \vert~&\asr & \textit{(arithmetic shift right)} \\
@ -186,9 +186,31 @@ can be seen as the construction of a circuit by assembling smaller integrated
circuits (ICs), themselves built the same way, etc. A group is composed of circuits (ICs), themselves built the same way, etc. A group is composed of
sub-circuits, input pins and output pins. Each level can of course contain sub-circuits, input pins and output pins. Each level can of course contain
``leaf'' gates, like \textit{and} or \textit{delay} gates. This is important, ``leaf'' gates, like \textit{and} or \textit{delay} gates. This is important,
because it allows the program to work on smaller areas the circuit (\eg{} because it allows the program to work on smaller areas of the circuit (\eg{}
loading in memory only a part of the circuit, etc.). loading in memory only a part of the circuit, etc.).
\emph{Isomatch} comes along with a small parser for a toy ad-hoc language,
designed to allow one to quickly write a test circuit and run the
\emph{isomatch} functions on it. There was no real apparent need for a better
language, or a standard circuit description language (such as VSDL), since the
user will mostly use \emph{isomatch} through fl, and feed it directly with data
read from fl --- which is able to handle \eg{} VSDL\@.
\subsection{Codebases}
Carl Seger's new version of fl is currently being developed as \textbf{VossII},
and is yet to be open-sourced.
My contribution to the project, \textbf{isomatch}, is free software, and is
available on GitHub:
\begin{center}
\raisebox{-0.4\height}{
\includegraphics[height=2em]{../common/github32.png}}
\hspace{1em}
\url{https://github.com/tobast/circuit-isomatch/}
\end{center}
\subsection{Objective} \subsection{Objective}
More precisely, the problems that \emph{isomatch} must solve are the following. More precisely, the problems that \emph{isomatch} must solve are the following.
@ -199,25 +221,25 @@ More precisely, the problems that \emph{isomatch} must solve are the following.
way, with possibly different names, etc.? way, with possibly different names, etc.?
\item\label{prob:match} Given two circuits, \emph{needle} and \item\label{prob:match} Given two circuits, \emph{needle} and
\emph{haystack}, find every (non-overlapping) occurrence of \emph{needle} in \emph{haystack}, find every (non-overlapping) occurrence of
\emph{haystack}. An occurrence is a set $S$ of sub-circuits of \emph{needle} in \emph{haystack}. An occurrence is a set $S$ of
\emph{haystack} such that there is a one-to-one mapping of structurally sub-circuits of \emph{haystack} such that there is a one-to-one mapping
equivalent circuits of $S$ with circuits of \emph{needle}, and those of structurally equivalent circuits of $S$ with circuits of
circuits are connected the same way in both circuits. \emph{needle}, and those circuits are connected the same way in both circuits.
\end{enumerate} \end{enumerate}
Both problems are hard. The first one is an instance of graph isomorphism, as Both problems are hard. The first one is an instance of the graph isomorphism
the actual question is whether there exists a one-to-one mapping between problem, as the actual question is whether there exists a one-to-one mapping
sub-circuits of the two groups, such that every mapped circuit is equal to the between sub-circuits of the two groups, such that every mapped circuit is equal
other (either directly if it is a leaf gate, or recursively with the same to the other (either directly if it is a leaf gate, or recursively with the
procedure); and whether this mapping respects connections (edges) between those same procedure); and whether this mapping respects connections (edges) between
circuits. Graph isomorphism is known to be in NP (given a permutation of the those circuits. Graph isomorphism is known to be in NP (given a permutation of
first graph, it is polynomial to check whether the first is equal to the second the first graph, it is polynomial to check whether the first is equal to the
\wrt{} the permutation), but not known to be in either P or NP-complete. Thus, second \wrt{} the permutation), but not known to be in either P or NP-complete.
since Babai's work on graph isomorphism~\cite{babai2016graph} is only of Thus, since Babai's work on graph isomorphism~\cite{babai2016graph} is only of
theoretical interest, the known algorithms remain in worst-case exponential theoretical interest (at the moment), the known algorithms remain in worst-case
time, and require ad-hoc heuristics for specific kind of graphs to get maximum exponential time, and require ad-hoc heuristics for specific kind of graphs to
efficiency. get maximum efficiency.
The second one is an instance of subgraph isomorphism problem, which is known The second one is an instance of subgraph isomorphism problem, which is known
to be NP-complete~\cite{cook1971complexity}. Even though a few algorithms to be NP-complete~\cite{cook1971complexity}. Even though a few algorithms
@ -231,9 +253,9 @@ The goal of \textit{isomatch} is to be applied to large circuits on-the-fly,
during their conception. Those circuits can (and will probably) be as large as during their conception. Those circuits can (and will probably) be as large as
a full processor, and the software will be operated by a human, working on a full processor, and the software will be operated by a human, working on
their circuit. Thus, \textit{isomatch} must be as fast as possible, since their circuit. Thus, \textit{isomatch} must be as fast as possible, since
matching operation will be executed often, and often multiple times in a row. matching operations will be executed quite often, and often multiple times in a
It must then remain fast enough for the human not to lose too much time, and row. It must then remain fast enough for the human not to lose too much time,
eventually lose patience. and eventually lose patience.
\todo{Mention clean codebase somewhere} \todo{Mention clean codebase somewhere}