path: root/evaluation.tex

\section{Evaluation}
\label{sec:evaluation}

Our evaluation is designed to answer the following three research questions.
\begin{description}
\item[RQ1] How fast is the hardware generated by \vericert{}?
\item[RQ2] How area-efficient is the hardware generated by \vericert{}?
\item[RQ3] How long does \vericert{} take to produce hardware?
\end{description}

\subsection{Experimental Setup}

\paragraph{Choice of HLS tool for comparison.} We compare \vericert{} against \legup{} 5.1 because it is open-source and hence easily accessible, but still produces hardware ``of comparable quality to a commercial high-level synthesis tool''~\cite{canis11_legup}.

\paragraph{Choice and preparation of benchmarks.} We evaluate \vericert{} using the PolyBench/C benchmark suite (version 4.2.1)~\cite{polybench}, which consists of a collection of 30 numerical kernels. PolyBench/C is popular in the HLS context~\cite{choi+18,poly_hls_pouchet2013polyhedral,poly_hls_zhao2017,poly_hls_zuo2013}, since it has affine loop bounds, making it attractive for streaming computation on FPGA architectures.
We were able to use 27 of the 30 programs; three had to be discarded (\texttt{correlation},~\texttt{gramschmidt} and~\texttt{deriche}) because they involve square roots, which require floats, which we do not support. 
% Interestingly, we were also unable to evaluate \texttt{cholesky} on \legup{}, since it produce an error during its HLS compilation. 
%In summary, we evaluate 27 programs from the latest Polybench suite. 

We configured Polybench's parameters so that only integer types are used, since we do not support floats or doubles currently. We use Polybench's smallest datasets for each program to ensure that data can reside within on-chip memories of the FPGA, avoiding any need for off-chip memory accesses.

\vericert{} implements divisions and modulo operations in C using the corresponding built-in Verilog operators. These built-in operators are designed to complete within a single clock cycle, and this causes substantial penalties in clock frequency. Other HLS tools, including LegUp, supply their own multi-cycle division/modulo implementations, and we plan to do the same in future versions of \vericert{}. In the meantime, we have prepared an alternative version of the benchmarks in which each division/modulo operation is overridden with our own implementation that uses repeated division and multiplications by 2. Where this change makes an appreciable difference to the performance results, we give the results for both benchmark sets.

\paragraph{Synthesis setup} The Verilog that is generated by \vericert{} or \legup{} is provided to Intel Quartus v16.0~\cite{quartus}, which synthesises it to a netlist, before placing-and-routing this netlist onto an Intel Arria 10 FPGA device that contains approximately 430000 LUTs.

\subsection{RQ1: How fast is \vericert{}-generated hardware?}

\begin{figure}
\begin{tikzpicture}
\begin{axis}[
    xmode=log,
    ymode=log,
    height=80mm,
    width=80mm,
    xlabel={\legup{} cycle count},
    ylabel={\vericert{} cycle count},
    xmin=1000,
    xmax=10000000,
    ymax=10000000,
    ymin=1000,
    %log ticks with fixed point,
  ]
  
\addplot[draw=none, mark=*, draw opacity=0, fill opacity=0.3]
  table [x=legupcycles, y=vericertcycles, col sep=comma]
  {results/poly.csv};

\addplot[dotted, domain=1000:10000000]{x};
%\addplot[dashed, domain=10:10000]{9.02*x};
  
\end{axis}
\end{tikzpicture}
\caption{A comparison of the cycle count of hardware designs generated by \vericert{} and by \legup{}, where the diagonal represents $y=x$.}
\label{fig:comparison_cycles}
\end{figure}

\begin{figure}
\begin{tikzpicture}
\begin{axis}[
    xmode=log,
    ymode=log,
    height=80mm,
    width=80mm,
    xlabel={\legup{} execution time (ms)},
    ylabel={\vericert{} execution time (ms)},
    xmin=10,
    xmax=1000000,
    ymax=1000000,
    ymin=10,
    %log ticks with fixed point,
  ]
  
\addplot[draw=none, mark=*, draw opacity=0, fill opacity=0.3,color=red]
  table [x expr={\thisrow{legupcycles}/\thisrow{legupfreqMHz}}, y expr={\thisrow{vericertcycles}/\thisrow{vericertfreqMHz}}, col sep=comma]
  {results/poly.csv};
  
\addplot[draw=none, mark=*, draw opacity=0, fill opacity=0.3, color=blue]
  table [x expr={\thisrow{legupcycles}/\thisrow{legupfreqMHz}}, y expr={\thisrow{vericertcycles}/\thisrow{vericertoldfreqMHz}}, col sep=comma]
  {results/poly.csv};

\addplot[dotted, domain=10:1000000]{x};
%\addplot[dashed, domain=10:10000]{9.02*x + 442};
  
\end{axis}
\end{tikzpicture}
\caption{A comparison of the execution time of hardware designs generated by \vericert{} and by \legup{}, where the diagonal represents $y=x$.}
\label{fig:comparison_time}
\end{figure}

%Firstly, before comparing any performance metrics, it is worth highlighting that any Verilog produced by \vericert{} is guaranteed to be \emph{correct}, whilst no such guarantee can be provided by \legup{}.
%This guarantee in itself provides a significant leap in terms of HLS reliability, compared to any other HLS tools available. 

Figure~\ref{fig:comparison_cycles} compares the cycle counts of our 27 programs executed by \vericert{} and \legup{} respectively. 
In most cases, we see that the data points are above the diagonal, which demonstrates that the \legup{}-generated hardware is faster than \vericert{}-generated Verilog.

On average, \legup{} designs are $4.5\times$ faster than \vericert{} designs.
This performance gap is mostly due to \legup{} optimisations such as scheduling and memory analysis, which are designed to extract parallelism from input programs.
%This gap does not represent the performance cost that comes with formally proving a HLS tool.  
%Instead, it is simply a gap between an unoptimised \vericert{} versus an optimised \legup{}.
It is notable that even without \vericert{} performing many optimisations, a few data points are close to the diagonal and even below it.
%We are very encouraged by these data points. 
As we improve \vericert{} by incorporating further  optimisations, this gap should reduce whilst preserving our correctness guarantees.

Cycle count is one factor in calculating execution times; the other is the clock frequency, which determines the duration of each of these cycles. Figure~\ref{fig:comparison_time} compares the execution times of \vericert{} and \legup{}. Across the original Polybench/C benchmarks, we see that \vericert{} designs are about $60\times$ slower than \legup{} designs. This dramatic discrepancy in performance can be largely attributed to th

As mentioned earlier, we modify the Polybench programs to utilise C-based divides and modulos. We had to avoid using the built-in Verilog divides and modulos, since Quartus interprets them as single-cycle operations. This interpretation affects clock frequency drastically. On average, when using the built-in Verilog approach, \vericert{}'s clock frequency was 21MHz, compared to \legup{}'s clock frequency of 247MHz. By moving to the C-based approach, our average clock frequency is now 112MHz. Hence, we reduce the frequency gap from approximately $12\times$ to $2\times$. This gap still exists because \legup{} uses various optimisation tactics and Intel-specific IPs, which requires further engineering effort and testing from our side. 

% The difference in cycle counts shows the degree of  parallelism that \legup{}'s scheduling and memory system can offer. However, their Verilog generation is not guaranteed to be correct. Although the runtime LegUp outputs are tested to be correct for these programs, this does not provide any confidence on the correctness of Verilog generation of any other programs. Our Coq proof mechanisation guarantees that generated Verilog is correct for any input program that uses the subset of \compcert{} instructions that we have proven to be correct.

\subsection{RQ2: How area-efficient is \vericert{}-generated hardware?}

\begin{figure}
\begin{tikzpicture}
\begin{axis}[
    height=80mm,
    width=80mm,
    xlabel={\legup{} resource utilisation (\%)},
    ylabel={\vericert{} resource utilisation (\%)},
    xmin=0, ymin=0,
    xmax=1, ymax=30,
  ]
  
\addplot[draw=none, mark=*, draw opacity=0, fill opacity=0.3]
  table [x expr=(\thisrow{legupluts}/427200*100), y expr=(\thisrow{vericertluts}/427200*100), col sep=comma]
  {results/poly.csv};
  
%   \addplot[dashed, domain=0:1]{x};
  
\end{axis}
\end{tikzpicture}
\caption{A comparison of the resource utilisation of designs generated by \vericert{} and by \legup{}}
\label{fig:comparison_area}
\end{figure}

Figure~\ref{fig:comparison_area} compares the resource utilisation of Polybench programs generated by \vericert{} and \legup{}.
On average, \vericert{} produces hardware that is $21\times$ larger than \legup{} for the same Polybench programs. 
\vericert{} designs are also filling up to 30\% of a large FPGA chip, which indicates that unoptimised Verilog generation can be costly. 
The key reason for this behaviour, is that absence of RAM inference for the \vericert{} designs. 
RAM are dedicated hardware blocks on the FPGA that are customly designed to allow for array synthesis.
Synthesis tools like Quartus generally require array accesses to be in a certain template or form to enable inference of RAM use.
\legup{}'s Verilog generation is tailored to enable RAM inference by Quartus.
\vericert{}'s array accesses in Verilog are more generic, allowing us to target different FPGA synthesis tools and vendors, but underfits for Quartus requirements.
For a fair comparison, we chose Quartus for these experiments because LegUp supports Quartus efficiently. 
% Consequently, on average, \legup{} designs use $XX$ RAMs whereas \vericert{} use none. 
Improving RAM inference is part of our future plans. 

% We see that \vericert{} designs use between 1\% and 30\% of the available logic on the FPGA, averaging at around 10\%, whereas LegUp designs all use less than 1\% of the FPGA, averaging at around 0.45\%. The main reason for this is mainly because RAM is not inferred automatically for the Verilog that is generated by \vericert{}.  Other synthesis tools can infer the RAM correctly for \vericert{} output, so this issue could be solved by either using a different synthesis tool and targeting a different FPGA, or by generating the correct template which allows Quartus to identify the RAM automatically.

\subsection{RQ3: How long does \vericert{} take to produce hardware?}

\begin{figure}
\begin{tikzpicture}
\begin{axis}[
    height=80mm,
    width=80mm,
    xlabel={\legup{} compilation time (s)},
    ylabel={\vericert{} compilation time (s)},
    yticklabel style={
        /pgf/number format/fixed,
        /pgf/number format/precision=2},
    xmin=4.6,
    xmax=5.1,
    ymin=0.06,
    ymax=0.20,
  ]
  
\addplot[draw=none, mark=*, draw opacity=0, fill opacity=0.3] 
  table [x=legupcomptime, y=vericertcomptime, col sep=comma]
  {results/poly.csv};

  %\addplot[dashed, domain=4.5:5.1]{0.1273*x-0.5048};

\end{axis}
\end{tikzpicture}
\caption{A comparison of compilation time for \vericert{} and for \legup{}}
\label{fig:comparison_comptime}
\end{figure}

Figure~\ref{fig:comparison_comptime} compares the compilation times of \vericert{} and by \legup{}, with each data point corresponding to one of the PolyBench/C benchmarks. On average, \vericert{} compilation is about $47\times$ faster than \legup{} compilation. \vericert{} is much faster because it omits many complext time-consuming HLS optimisations performed by \legup{}, such as scheduling and memory analysis. This comparison also shows our approach do not add any significant overheads in compilation time, since we do not invoke verification for every compilation instance.

\NR{Do we want to finish the section off with some highlights or a summary?}

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