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-% !TEX program = xelatex
-\documentclass{article}
-\usepackage{../style}
-\usepackage{../langs}
-\usepackage{disclaimer}
-\usepackage{tikz}
-\usepackage{pgf}
-\usepackage{pgfplots}
-\usepackage{stackengine}
-%% \usepackage{accents}
-\newcommand\barbelow[1]{\stackunder[1.2pt]{#1}{\raisebox{-4mm}{\boldmath$\uparrow$}}}
-
-%% change Console to scala.io.StdIn.readByte()
-
-
-\begin{document}
-
-\section*{Part 10 (Scala)}
-
-\mbox{}\hfill\textit{``If there's one feature that makes Scala, `Scala',}\\
-\mbox{}\hfill\textit{ I would pick implicits.''}\smallskip\\
-\mbox{}\hfill\textit{ --- Martin Odersky (creator of the Scala language)}\bigskip\bigskip
-
-
-\noindent
-This part is about a small (esoteric) programming language called
-brainf***. Actually, we will implement an interpreter for our own version
-of this language called brainf*ck++.\bigskip
-
-\IMPORTANT{This part is worth 10\% and you need to submit it on \cwTEN{} at 4pm.}
-
-\noindent
-Also note that the running time of each part will be restricted to a
-maximum of 30 seconds on my laptop.
-
-\DISCLAIMER{}
-\newpage
-
-\subsection*{Reference Implementation}
-
-As usual, this Scala assignment comes with a reference implementation in
-form of two \texttt{jar}-files. You can download them from KEATS. They
-allow you to run any test cases on your own computer. For example you
-can call Scala on the command line with the option \texttt{-cp bf.jar}
-and then query any function from the \texttt{bf.scala} template file.
-You have to prefix the calls with \texttt{CW10a} and \texttt{CW10b},
-respectively. For example
-
-
-\begin{lstlisting}[language={},xleftmargin=1mm,numbers=none,basicstyle=\ttfamily\small]
-$ scala -cp bf.jar
-scala> import CW10a._
-scala> run(load_bff("sierpinski.bf")) ; ()
- *
- * *
- * *
- * * * *
- * *
- * * * *
- * * * *
- * * * * * * * *
- * *
- * * * *
- * * * *
- * * * * * * * *
- * * * *
- * * * * * * * *
- * * * * * * * *
- * * * * * * * * * * * * * * * *
- * *
- * * * *
- * * * *
- * * * * * * * *
- * * * *
- * * * * * * * *
- * * * * * * * *
- * * * * * * * * * * * * * * * *
- * * * *
- * * * * * * * *
- * * * * * * * *
- * * * * * * * * * * * * * * * *
- * * * * * * * *
- * * * * * * * * * * * * * * * *
- * * * * * * * * * * * * * * * *
-* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
-\end{lstlisting}%$
-
-\newpage
-
-\subsection*{Part A (6 Marks)}
-
-Coming from Java or C++, you might think Scala is a rather esoteric
-programming language. But remember, some serious companies have built
-their business on
-Scala.\footnote{\url{https://en.wikipedia.org/wiki/Scala_(programming_language)\#Companies}}
-I claim functional programming is not a fad. And there are far, far
-more esoteric languages out there. One is called \emph{brainf***}.
-\here{https://esolangs.org/wiki/Brainfuck}
-You
-are asked in this part to implement an interpreter for
-a slight extension of this language.
-
-Urban M\"uller developed the original version of brainf*** in 1993. A close
-relative of this language was already introduced in 1964 by Corado
-B\"ohm, an Italian computer pioneer. The main feature of brainf*** is
-its minimalistic set of instructions---just 8 instructions in total
-and all of which are single characters. Despite the minimalism, this
-language has been shown to be Turing complete\ldots{}if this doesn't
-ring any bell with you: it roughly means that every(!) algorithm can,
-in principle, be implemented in brainf***. It just takes a lot of
-determination and quite a lot of memory resources.
-
-Some relatively sophisticated sample programs in brainf*** are given
-in the file \texttt{bf.scala}, including a brainf*** program for the
-Sierpinski triangle and the Mandelbrot set. There seems to be even a
-dedicated Windows IDE for bf programs, though I am not sure whether
-this is just an elaborate April fools' joke---judge yourself:
-
-\begin{center}
-\url{https://www.microsoft.com/en-us/p/brainf-ck/9nblgggzhvq5}
-\end{center} \bigskip
-
-
-\noindent
-As mentioned above, the original brainf*** has 8 single-character
-commands. Our version of bf++ will contain the commands \texttt{'>'},
-\texttt{'<'}, \texttt{'+'}, \texttt{'-'}, \texttt{'.'}, \texttt{'['}
-and \texttt{']'} from the original, and in addition the commands
-\texttt{'@'}, \texttt{'*'} and \texttt{'\#'}. Every other character
-is considered a comment.
-
-Our interpreter for bf++ operates on memory cells containing
-integers. For this it uses a single memory pointer, called
-\texttt{mp}, that points at each stage to one memory cell.
-
-\begin{center}
-\begin{tikzpicture}
- \draw [line width=1mm, rounded corners] (0,0) rectangle (5, 0.5);
- \draw (0.5, 0) -- (0.5, 0.5);
- \draw (1.0, 0) -- (1.0, 0.5);
-
- \draw (2.5, 0) -- (2.5, 0.5);
- \draw (2.0, 0) -- (2.0, 0.5);
-
- \draw (4.5, 0) -- (4.5, 0.5);
- \draw (4.0, 0) -- (4.0, 0.5);
-
- \draw (1.5,0.25) node {$\cdots$};
- \draw (3.0,0.25) node {$\cdots$};
-
- \draw [->, thick] (2.25, -0.5) -- (2.25, -0.15);
- \draw (2.25,-0.8) node {\texttt{mp}};
-
- \draw (0.7,0.7) node {\sf\footnotesize memory};
-\end{tikzpicture}
-\end{center}
-
-\noindent
-This pointer can be moved forward by one memory cell by using the
-command \texttt{'>'}, and backward by using \texttt{'<'}. The commands
-\texttt{'+'} and \texttt{'-'} increase, respectively decrease, by 1
-the content of the memory cell to which the memory pointer currently
-points to. The command for output in bf++ is \texttt{'.'} whereby output works
-by reading the content of the memory cell to which the memory pointer
-points to and printing it out as an ASCII character.\footnote{In the
- original version of bf, there is also a command for input, but we
- omit it here. All our programs will be ``autonomous''.} The
-commands \texttt{'['} and \texttt{']'} are looping
-constructs. Everything in between \texttt{'['} and \texttt{']'} is
-repeated until a counter (memory cell) reaches zero. A typical
-program in brainf*** looks as follows:
-
-\begin{center}
-\begin{verbatim}
- ++++++++[>++++[>++>+++>+++>+<<<<-]>+>+>->>+[<]<-]>>.>---.++
- +++++..+++.>>.<-.<.+++.------.--------.>>+.>++.
-\end{verbatim}
-\end{center}
-
-\noindent
-This one prints out Hello World\ldots{}obviously \texttt{;o)} We also
-add 3 new commands in the bf++-version of the bf-language. The purpose
-of these commands we explain later.
-
-
-\subsubsection*{Tasks (file bf.scala)}
-
-\begin{itemize}
-\item[(1)] Write a function that takes a filename (a string) as an argument
- and requests the corresponding file from disk. It returns the
- content of the file as a string. If the file does not exists,
- the function should return the empty string.
- \mbox{}\hfill[1 Mark]
-
-\item[(2)] Brainf**k++ memory is represented by a \texttt{Map} from
- integers to integers. The empty memory is represented by
- \texttt{Map()}, that is nothing is stored in the
- memory; \texttt{Map(0 -> 1, 2 -> 3)} stores \texttt{1} at
- memory location \texttt{0}, and at \texttt{2} it stores \texttt{3}. The
- convention is that if we query the memory at a location that is
- \emph{not} defined in the \texttt{Map}, we return \texttt{0}. Write
- a `safe-read' function, \texttt{sread}, that takes a memory (a \texttt{Map}) and
- a memory pointer (an \texttt{Int}) as arguments, and `safely' reads the
- corresponding memory location. If the \texttt{Map} is not defined at
- the memory pointer, \texttt{sread} returns \texttt{0}.
-
- Write another function \texttt{write}, which takes a memory, a
- memory pointer and an integer value as arguments and updates the
- \texttt{Map} with the value at the given memory location. As usual,
- the \texttt{Map} is not updated `in-place' but a new map is created
- with the same data, except the new value is stored at the given memory
- pointer.\hfill[1 Mark]
-
-\item[(3)] Write two functions, \texttt{jumpRight} and
- \texttt{jumpLeft}, that are needed to implement the loop constructs
- in brainf**k++. They take a program (a \texttt{String}) and a program
- counter (an \texttt{Int}) as arguments and move right (respectively
- left) in the string in order to find the \textbf{matching}
- opening/closing bracket. For example, given the following program
- with the program counter indicated by an arrow:
-
- \begin{center}
- \texttt{--[\barbelow{.}.+>--].>.++}
- \end{center}
-
- then the matching closing bracket is in 9th position (counting from 0) and
- \texttt{jumpRight} is supposed to return the position just after this
-
- \begin{center}
- \texttt{--[..+>--]\barbelow{.}>.++}
- \end{center}
-
- meaning it jumps to after the loop. Similarly, if you are in 8th position,
- then \texttt{jumpLeft} is supposed to jump to just after the opening
- bracket (that is jumping to the beginning of the loop):
-
- \begin{center}
- \texttt{--[..+>-\barbelow{-}].>.++}
- \qquad$\stackrel{\texttt{jumpLeft}}{\longrightarrow}$\qquad
- \texttt{--[\barbelow{.}.+>--].>.++}
- \end{center}
-
- Unfortunately we have to take into account that there might be
- other opening and closing brackets on the `way' to find the
- matching bracket. For example in the brain*ck++ program
-
- \begin{center}
- \texttt{--[\barbelow{.}.[+>]--].>.++}
- \end{center}
-
- we do not want to return the index for the \texttt{'-'} in the 9th
- position, but the program counter for \texttt{'.'} in 12th
- position. The easiest to find out whether a bracket is matched is by
- using levels (which are the third argument in \texttt{jumpLeft} and
- \texttt{jumpLeft}). In case of \texttt{jumpRight} you increase the
- level by one whenever you find an opening bracket and decrease by
- one for a closing bracket. Then in \texttt{jumpRight} you are looking
- for the closing bracket on level \texttt{0}. For \texttt{jumpLeft} you
- do the opposite. In this way you can find \textbf{matching} brackets
- in strings such as
-
- \begin{center}
- \texttt{--[\barbelow{.}.[[-]+>[.]]--].>.++}
- \end{center}
-
- for which \texttt{jumpRight} should produce the position:
-
- \begin{center}
- \texttt{--[..[[-]+>[.]]--]\barbelow{.}>.++}
- \end{center}
-
- It is also possible that the position returned by \texttt{jumpRight} or
- \texttt{jumpLeft} is outside the string in cases where there are
- no matching brackets. For example
-
- \begin{center}
- \texttt{--[\barbelow{.}.[[-]+>[.]]--.>.++}
- \qquad$\stackrel{\texttt{jumpRight}}{\longrightarrow}$\qquad
- \texttt{--[..[[-]+>[.]]-->.++\barbelow{\;\phantom{+}}}
- \end{center}
- \hfill[2 Marks]
-
-
-\item[(4)] Write a recursive function \texttt{compute} that runs a
- brain*u*k++ program. It takes a program, a program counter, a memory
- pointer and a memory as arguments. If the program counter is outside
- the program string, the execution stops and \texttt{compute} returns the
- memory. If the program counter is inside the string, it reads the
- corresponding character and updates the program counter \texttt{pc},
- memory pointer \texttt{mp} and memory \texttt{mem} according to the
- rules shown in Figure~\ref{comms}. It then calls recursively
- \texttt{compute} with the updated data. The most convenient way to
- implement the brainf**k++ rules in Scala is to use pattern-matching
- and to calculate a triple consisting of the updated \texttt{pc},
- \texttt{mp} and \texttt{mem}.
-
- Write another function \texttt{run} that calls \texttt{compute} with a
- given brainfu*k++ program and memory, and the program counter and memory pointer
- set to~$0$. Like \texttt{compute}, it returns the memory after the execution
- of the program finishes. You can test your brainf**k++ interpreter with the
- Sierpinski triangle or the Hello world programs (they seem to be particularly
- useful for debugging purposes), or have a look at
-
- \begin{center}
- \url{https://esolangs.org/wiki/Brainfuck}
- \end{center}
-
- \noindent for more bf/bf++-programs and the test cases given in \texttt{bf.scala}.\\
- \mbox{}\hfill[2 Marks]
-
- \begin{figure}[p]
- \begin{center}
- \begin{tabular}{|@{\hspace{0.5mm}}p{0.8cm}|l|}
- \hline
- \hfill\texttt{'>'} & \begin{tabular}[t]{@{}l@{\hspace{2mm}}l@{}}
- $\bullet$ & $\texttt{pc} + 1$\\
- $\bullet$ & $\texttt{mp} + 1$\\
- $\bullet$ & \texttt{mem} unchanged
- \end{tabular}\\\hline
- \hfill\texttt{'<'} & \begin{tabular}[t]{@{}l@{\hspace{2mm}}l@{}}
- $\bullet$ & $\texttt{pc} + 1$\\
- $\bullet$ & $\texttt{mp} - 1$\\
- $\bullet$ & \texttt{mem} unchanged
- \end{tabular}\\\hline
- \hfill\texttt{'+'} & \begin{tabular}[t]{@{}l@{\hspace{2mm}}l@{}}
- $\bullet$ & $\texttt{pc} + 1$\\
- $\bullet$ & $\texttt{mp}$ unchanged\\
- $\bullet$ & \texttt{mem} updated with \texttt{mp -> mem(mp) + 1}\\
- \end{tabular}\\\hline
- \hfill\texttt{'-'} & \begin{tabular}[t]{@{}l@{\hspace{2mm}}l@{}}
- $\bullet$ & $\texttt{pc} + 1$\\
- $\bullet$ & $\texttt{mp}$ unchanged\\
- $\bullet$ & \texttt{mem} updated with \texttt{mp -> mem(mp) - 1}\\
- \end{tabular}\\\hline
- \hfill\texttt{'.'} & \begin{tabular}[t]{@{}l@{\hspace{2mm}}l@{}}
- $\bullet$ & $\texttt{pc} + 1$\\
- $\bullet$ & $\texttt{mp}$ and \texttt{mem} unchanged\\
- $\bullet$ & print out \,\texttt{mem(mp)} as a character\\
- \end{tabular}\\\hline
- %\hfill\texttt{','} & \begin{tabular}[t]{@{}l@{\hspace{2mm}}l@{}}
- % $\bullet$ & $\texttt{pc} + 1$\\
- % $\bullet$ & $\texttt{mp}$ unchanged\\
- % $\bullet$ & \texttt{mem} updated with \texttt{mp -> \textrm{input}}\\
- % \multicolumn{2}{@{}l}{the input is given by \texttt{Console.in.read().toByte}}
- % \end{tabular}\\\hline
- \hfill\texttt{'['} & \begin{tabular}[t]{@{}l@{\hspace{2mm}}l@{}}
- \multicolumn{2}{@{}l}{if \texttt{mem(mp) == 0} then}\\
- $\bullet$ & $\texttt{pc = jumpRight(prog, pc + 1, 0)}$\\
- $\bullet$ & $\texttt{mp}$ and \texttt{mem} unchanged\medskip\\
- \multicolumn{2}{@{}l}{otherwise if \texttt{mem(mp) != 0} then}\\
- $\bullet$ & $\texttt{pc} + 1$\\
- $\bullet$ & $\texttt{mp}$ and \texttt{mem} unchanged\\
- \end{tabular}
- \\\hline
- \hfill\texttt{']'} & \begin{tabular}[t]{@{}l@{\hspace{2mm}}l@{}}
- \multicolumn{2}{@{}l}{if \texttt{mem(mp) != 0} then}\\
- $\bullet$ & $\texttt{pc = jumpLeft(prog, pc - 1, 0)}$\\
- $\bullet$ & $\texttt{mp}$ and \texttt{mem} unchanged\medskip\\
- \multicolumn{2}{@{}l}{otherwise if \texttt{mem(mp) == 0} then}\\
- $\bullet$ & $\texttt{pc} + 1$\\
- $\bullet$ & $\texttt{mp}$ and \texttt{mem} unchanged\\
- \end{tabular}\\\hline
- \hfill\texttt{'*'} & \begin{tabular}[t]{@{}l@{\hspace{2mm}}l@{}}
- $\bullet$ & $\texttt{pc} + 1$\\
- $\bullet$ & $\texttt{mp}$ unchanged\\
- $\bullet$ & \texttt{mem} updated with \texttt{mp -> mem(mp) * mem(mp - 1)}\\
- \multicolumn{2}{@{}l}{this multiplies the content of the memory cells at
- \texttt{mp} and \texttt{mp - 1}}\\
- \multicolumn{2}{@{}l}{and stores the result at \texttt{mp}}
- \end{tabular}\\\hline
- \hfill\texttt{'@'} & \begin{tabular}[t]{@{}l@{\hspace{2mm}}l@{}}
- $\bullet$ & $\texttt{pc} + 1$\\
- $\bullet$ & $\texttt{mp}$ unchanged\\
- $\bullet$ & \texttt{mem} updated with
- \texttt{mem(mp) -> mem(mp - 1)}\\
- \multicolumn{2}{@{}l}{this updates the memory cell having the index stored at \texttt{mem(mp)},}\\
- \multicolumn{2}{@{}l}{with the value stored at \texttt{mem(mp - 1)},}
- \end{tabular}\\\hline
- \hfill\texttt{'\#'} & \begin{tabular}[t]{@{}l@{\hspace{2mm}}l@{}}
- $\bullet$ & $\texttt{pc} + 1$\\
- $\bullet$ & $\texttt{mp}$ and \texttt{mem} unchanged\\
- $\bullet$ & print out \,\texttt{mem(mp)} as a number\\
- \end{tabular}\\\hline
- any other char & \begin{tabular}[t]{@{}l@{\hspace{2mm}}l@{}}
- $\bullet$ & $\texttt{pc} + 1$\\
- $\bullet$ & \texttt{mp} and \texttt{mem} unchanged
- \end{tabular}\\
- \hline
- \end{tabular}
- \\\mbox{}\\[-10mm]\mbox{}
- \end{center}
- \caption{The rules for how commands in the brainf***++ language update the
- program counter \texttt{pc},
- the memory pointer \texttt{mp} and the memory \texttt{mem}.\label{comms}}
- \end{figure}
-\end{itemize}\bigskip
-
-%%\newpage
-
-\subsection*{Part B (4 Marks)}
-
-I am sure you agree while it is fun to marvel at bf++-programs, like the
-Sierpinski triangle or the Mandelbrot program, being interpreted, it
-is much more fun to write a compiler for the bf++-language.
-
-
-\subsubsection*{Tasks (file bfc.scala)}
-
-\begin{itemize}
-\item[(5)] Compilers, in general, attempt to make programs run
- faster by precomputing as much information as possible
- before running the program. In our case we can precompute the
- addresses where we need to jump at the beginning and end of
- loops.
-
- For this write a function \texttt{jtable} that precomputes the ``jump
- table'' for a bf++-program. This function takes a bf++-program
- as an argument and returns a \texttt{Map[Int, Int]}. The
- purpose of this Map is to record the information, in cases
- a pc-position points to a '\texttt{[}' or a '\texttt{]}',
- to which pc-position do we need to jump next?
-
- For example for the program
-
- \begin{center}
- \texttt{+++++[->++++++++++<]>--<+++[->>++++++++++}
- \texttt{<<]>>++<<----------[+>.>.<+<]}
- \end{center}
-
- we obtain the Map (note the precise numbers might differ depending on white
- spaces etc.~in the bf-program):
-
- \begin{center}
- \texttt{Map(69 -> 61, 5 -> 20, 60 -> 70, 27 -> 44, 43 -> 28, 19 -> 6)}
- \end{center}
-
- This Map states that for the '\texttt{[}' on position 5, we need to
- jump to position 20, which is just after the corresponding '\texttt{]}'.
- Similarly, for the '\texttt{]}' on position 19, we need to jump to
- position 6, which is just after the '\texttt{[}' on position 5, and so
- on. The idea is to not calculate this information each time
- we hit a bracket, but just look up this information in the
- \texttt{jtable}.
-
- Then adapt the \texttt{compute} and \texttt{run} functions
- from Part 1 in order to take advantage of the information
- stored in the \texttt{jtable}. This means whenever \texttt{jumpLeft}
- and \texttt{jumpRight} was called previously, you should look
- up the jump address in the \texttt{jtable}. Feel free to reuse
- the function \texttt{jumpLeft} and \texttt{jumpRight} for
- calculating the \texttt{jtable}.\hfill{[1 Mark]}
-
-\item[(6)] Compilers try to eliminate any ``dead'' code that could
- slow down programs and also perform what is often called
- \emph{peephole
- optimisations}.\footnote{\url{https://en.wikipedia.org/wiki/Peephole_optimization}}
- For the latter consider that it is difficult for compilers to
- comprehend what is intended with whole programs, but they are very good
- at finding out what small snippets of code do, and then try to
- generate faster code for such snippets.
-
- In our case, dead code is everything that is not a bf++-command.
- Therefore write a function \texttt{optimise} which deletes such
- dead code from a bf++-program. Moreover this function should replace every substring
- of the form \pcode{[-]} by a new command \texttt{0}.
- The idea is that the loop \pcode{[-]} just resets the
- memory at the current location to 0. It is more efficient
- to do this in a single step, rather than stepwise in a loop as in
- the original bf++-programs.
-
- In the extended \texttt{compute3} and \texttt{run3} functions you should
- implement this command by writing 0 to \pcode{mem(mp)}, that is use
- \pcode{write(mem, mp, 0)} as the rule for the command \texttt{0}.
- The easiest way to modify a string in this way is to use the regular
- expression \pcode{"""[^<>+-.\\[\\]@\#*]"""}, which recognises everything that is
- not a bf++-command. Similarly, the
- regular expression \pcode{"""\\[-\\]"""} finds all occurrences of \pcode{[-]}. By using the Scala method \pcode{.replaceAll} you can replace substrings
- with new strings.\\
- \mbox{}\hfill{[1 Mark]}
-
-\item[(7)] Finally, real compilers try to take advantage of modern
- CPUs which often provide complex operations in hardware that can
- combine many smaller instructions into a single faster instruction.
-
- In our case we can optimise the several single increments performed at a
- memory cell, for example \pcode{++++}, by a single ``increment by
- 4''. For this optimisation we just have to make sure these single
- increments are all next to each other. Similar optimisations should apply
- for the bf-commands \pcode{-}, \pcode{<} and
- \pcode{>}, which can all be replaced by extended versions that take
- the amount of the increment (decrement) into account. We will do
- this by introducing two-character bf++-commands. For example
-
- \begin{center}
- \begin{tabular}{l|l}
- original bf-cmds & replacement\\
- \hline
- \pcode{+} & \pcode{+A}\\
- \pcode{++} & \pcode{+B}\\
- \pcode{+++} & \pcode{+C}\\
- \ldots{} & \ldots{}\\
- \pcode{+++....++} & \pcode{+Z}\\
- \hspace{5mm}(these are 26 \pcode{+}'s)\\
- \end{tabular}
- \end{center}
-
-
- If there are more
- than 26 \pcode{+}'s in a row, then more than one ``two-character''
- bf-commands need to be generated (the idea is that more than
- 26 copies of a single bf++-command in a row is a rare occurrence in
- actual bf++-programs). Similar replacements apply
- for \pcode{-}, \pcode{<} and \pcode{>}, but
- all other bf++-commands should be unaffected by this
- change.
-
- For this write a function \texttt{combine} which replaces sequences
- of repeated increment and decrement commands by appropriate
- two-character commands. In the functions \pcode{compute4} and
- \pcode{run4}, the ``combine'' and the optimisation from (6) should
- be performed. Make sure that when a two-character bf++-command is
- encountered you need to increase the \pcode{pc}-counter by two in
- order to progress to the next command. For example
-
- \begin{center}
- \pcode{combine(optimise(load_bff("benchmark.bf")))}
- \end{center}
-
- generates the improved program
-
- \begin{center}
- \pcode{>A+B[<A+M>A-A]<A[[}\hspace{3mm}\ldots{}
- \end{center}
-
- for the original benchmark program
-
- \begin{center}
- \pcode{>++[<+++++++++++++>-]<[[}\hspace{3mm}\ldots
- \end{center}
-
- As you can see, the compiler bets on saving a lot of time on the
- \pcode{+B} and \pcode{+M} steps so that the optimisations is
- worthwhile overall (of course for the \pcode{>A}'s and so on, the compiler incurs a
- penalty). Luckily, after you have performed all
- optimisations in (5) - (7), you can expect that the
- \pcode{benchmark.bf} program runs four to five times faster.
- You can also test whether your compiler produces the correct result
- by testing for example
-
- \begin{center}
- \pcode{run(load_bff("sierpinski.bf")) == run4(load_bff("sierpinski.bf"))}
- \end{center}
-
- which should return true for all the different compiler stages. \\
- \mbox{}\hfill{[2 Marks]}
-\end{itemize}
-
-\end{document}
-
-
-%%% Local Variables:
-%%% mode: latex
-%%% TeX-master: t
-%%% End: