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\fnote{\copyright{} Christian Urban, King's College London, 2019}


\section*{Handout 9 (LLVM, SSA and CPS)}

Reflecting on our tiny compiler targetting the JVM, the code generation
part was actually not so hard, no? Pretty much just some post-traversal
of the abstract syntax tree, yes? One of the reasons for this ease is
that the JVM is a stack-based virtual machine and it is therefore not
hard to translate deeply-nested arithmetic expressions into a sequence
of instructions manipulating the stack. The problem is that ``real''
CPUs, although supporting stack operations, are not really designed to
be \emph{stack machines}.  The design of CPUs is more like, here is a
chunk of memory---compiler, or better compiler writers, do something
with it. Consequently, modern compilers need to go the extra mile in
order to generate code that is much easier and faster to process by
CPUs. To make this all tractable for this module, we target the LLVM
Intermediate Language. In this way we can take advantage of the tools
coming with LLVM. For example we do not have to worry about things like
register allocations.\bigskip 

\noindent LLVM\footnote{\url{http://llvm.org}} is a beautiful example
that projects from Academia can make a difference in the world. LLVM
started in 2000 as a project by two researchers at the  University of
Illinois at Urbana-Champaign. At the time the behemoth of compilers was
gcc with its myriad of front-ends for other languages (C++, Fortran,
Ada, Go, Objective-C, Pascal etc). The problem was that gcc morphed over
time into a monolithic gigantic piece of m\ldots ehm software, which you
could not mess about in an afternoon. In contrast, LLVM is designed to
be a modular suite of tools with which you could play around easily and
try out something new. LLVM became a big player once Apple hired one of
the original developers (I cannot remember the reason why Apple did not
want to use gcc, but maybe they were also just disgusted by its big
monolithic codebase). Anyway, LLVM is now the big player and gcc is more
or less legacy. This does not mean that programming languages like C and
C++ are dying out any time soon---they are nicely supported by LLVM.

We will target the LLVM Intermediate Language, or Intermediate
Representation (short LLVM-IR). As a result we can benefit from the
modular structure of the LLVM compiler and let for example the compiler
generate code for different CPUs, like X86 or ARM. That means we can be
agnostic about where our code actually runs. We can also be ignorant
about optimising code and allocating memory efficiently. However, what
we have to do is to generate code in \emph{Static Single-Assignment}
format (short SSA), because that is what the LLVM-IR expects from us. 

The idea behind the SSA format is to use very simple variable
assignments where every variable is assigned only once. The assignments
also need to be primitive in the sense that they can be just simple
operations like addition, multiplication, jumps, comparisons and so on.
Say, we have an expression $((1 + a) + (3 + (b * 5)))$, then the
SSA is 
 
\begin{lstlisting}[language=LLVMIR,numbers=left]
let tmp0 = add 1 a in   
let tmp1 = mul b 5 in 
let tmp2 = add 3 tmp1 in 
let tmp3 = add tmp0 tmp2 in
  tmp3 
\end{lstlisting}

\noindent where every variable is used only once (we could not write
\texttt{tmp1 = add 3 tmp1} in Line 3 for example).  There are
sophisticated algorithms for imperative languages, like C, that
efficiently transform a high-level program into SSA format. But we can
ignore them here. We want to compile a functional language and there
things get much more interesting than just sophisticated. We will need
to have a look at CPS translations, where the CPS stands for
Continuation-Passing-Style---basically black programming art or
abracadabra programming. So sit tight.

\subsection*{LLVM-IR}

Before we start, lets first have a look at the \emph{LLVM Intermediate
Representation} in more detail. What is good about our toy Fun language
is that it basically only contains expressions (be they arithmetic
expressions or boolean expressions or if-expressions). The exception are
function definitions. Luckily, for them we can use the mechanism of
defining functions in LLVM-IR. For example the simple Fun program 


\begin{lstlisting}[language=Scala,numbers=none]
def sqr(x) = x * x
\end{lstlisting}

\noindent
can be compiled into the following LLVM-IR function:

\begin{lstlisting}[language=LLVM]
define i32 @sqr(i32 %x) {
   %tmp = mul i32 %x, %x
   ret i32 %tmp
}    
\end{lstlisting}

\noindent First notice that all variable names in the LLVM-IR are
prefixed by \texttt{\%}; function names need to be prefixed with
@-symbol. Also, the LLVM-IR is a fully typed language. The \texttt{i32}
type stands for 32-bit integers. There are also types for 64-bit
integers (\texttt{i64}), chars (\texttt{i8}), floats, arrays and even
pointer types. In the code above, \texttt{sqr} takes an argument of type
\texttt{i32} and produces a result of type \texttt{i32} (the result type
is before the function name, like in C). Each arithmetic operation, like
addition or multiplication, are also prefixed with the type they operate
on. Obviously these types need to match up\ldots{} but since we have in
our programs only integers, \texttt{i32} everywhere will do. 
 
Conveniently, you can use the program \texttt{lli}, which comes with
LLVM, to interpret programs written in the LLVM-IR. So you can easily
check whether the code you produced actually works. To get a running
program that does something interesting you need to add some boilerplate
about printing out numbers and a main-function that is the entrypoint
for the program (see Figure~\ref{lli} for a complete listing). You can
generate a binary for this program using \texttt{llc}-compiler and
\texttt{gcc}---\texttt{llc} can generate an object file and then you can 
use \texttt{gcc} (that is clang) for generating an executable  binary:

\begin{lstlisting}[language=bash,numbers=none]
llc -filetype=obj sqr.ll
gcc sqr.o -o a.out
./a.out
> 25
\end{lstlisting}

\begin{figure}[t]\small 
\lstinputlisting[language=LLVM,numbers=left]{../progs/sqr.ll}
\caption{An LLVM-IR program for calculating the square function. The 
interesting function is \texttt{sqr} in Lines 13 -- 16. The main
function calls \texttt{sqr} and prints out the result. The other
code is boilerplate for printing out integers.\label{lli}}
\end{figure}   


    
\subsection*{Our Own Intermediate Language}

Remember compilers have to solve the problem of bridging the gap between
``high-level'' programs and ``low-level'' hardware. If the gap is too
wide for one step, then a good strategy is to lay a stepping stone
somewhere in between. The LLVM-IR itself is such a stepping stone to
make the task of generating and optimising code easier. Like a real
compiler we will use our own stepping stone which I call the
\emph{K-language}. For this remember expressions (and boolean
expressions) in the Fun language. For convenience the Scala code is
shown on top of Figure~\ref{absfun}. Below is the code for the
K-language. There are two kinds of syntactic entities, namely
\emph{K-values} and \emph{K-expressions}. The central point of the
K-language is the \texttt{KLet}-constructor. For this recall that 
arithmetic expressions such as $((1 + a) + (3 + (b * 5)))$ need
to be broken up into smaller ``atomic'' steps, like so
 
\begin{lstlisting}[language=LLVMIR,numbers=none]
let tmp0 = add 1 a in   
let tmp1 = mul b 5 in 
let tmp2 = add 3 tmp1 in 
let tmp3 = add tmp0 tmp2 in
  tmp3 
\end{lstlisting}

\noindent
Here \texttt{tmp3} will contain the result of what the expression stands
for. In each step we can only perform an ``atomic'' operation, like
addition or multiplication. We could not for example have an
if-condition on the right-hand side of an equals. These constraints
enforced upon us because how the SSA format works in the LLVM-IR. By
having in \texttt{KLet},  first a string (standing for an intermediate
result) and second a value, we can fulfil this constraint---there is no
way we could write anything else than a value. To sum up, K-values are
the atomic operations that can be on the right-hand side of equal-signs.
The K-language is restricted such that it is easy to generate the SSA format 
for the LLVM-IR.



\begin{figure}[p]\small
\begin{lstlisting}[language=Scala,numbers=none]
// Fun-language (expressions)
abstract class Exp 
abstract class BExp 

case class Call(name: String, args: List[Exp]) extends Exp
case class If(a: BExp, e1: Exp, e2: Exp) extends Exp
case class Write(e: Exp) extends Exp
case class Var(s: String) extends Exp
case class Num(i: Int) extends Exp
case class Aop(o: String, a1: Exp, a2: Exp) extends Exp
case class Sequence(e1: Exp, e2: Exp) extends Exp
case class Bop(o: String, a1: Exp, a2: Exp) extends BExp  



// K-language (K-expressions, K-values)
abstract class KExp
abstract class KVal

case class KVar(s: String) extends KVal
case class KNum(i: Int) extends KVal
case class Kop(o: String, v1: KVal, v2: KVal) extends KVal
case class KCall(o: String, vrs: List[KVal]) extends KVal
case class KWrite(v: KVal) extends KVal

case class KIf(x1: String, e1: KExp, e2: KExp) extends KExp
case class KLet(x: String, v: KVal, e: KExp) extends KExp
case class KReturn(v: KVal) extends KExp
\end{lstlisting}
\caption{Abstract syntax trees for the Fun language.\label{absfun}}
\end{figure}



\subsection*{CPS-Translations}





Another reason why it makes sense to go the extra mile is that stack
instructions are very difficult to optimise---you cannot just re-arrange
instructions without messing about with what is calculated on the stack.
Also it is hard to find out if all the calculations on the stack are
actually necessary and not by chance dead code. The JVM has for all this
sophisticated machinery to make such ``high-level'' code still run fast,
but let's say that for the sake of argument we do not want to rely on
it. We want to generate fast code ourselves. This means we have to work
around the intricacies of what instructions CPUs can actually process.

\end{document}


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