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Add the first half of chapter 5: if/then/else. To come: for statement. git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@43546 91177308-0d34-0410-b5e6-96231b3b80d8
2007-10-31 06:30:21 +00:00
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN"
"http://www.w3.org/TR/html4/strict.dtd">
<html>
<head>
<title>Kaleidoscope: Extending the Language: Control Flow</title>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<meta name="author" content="Chris Lattner">
<link rel="stylesheet" href="../llvm.css" type="text/css">
</head>
<body>
<div class="doc_title">Kaleidoscope: Extending the Language: Control Flow</div>
<div class="doc_author">
<p>Written by <a href="mailto:sabre@nondot.org">Chris Lattner</a></p>
</div>
<!-- *********************************************************************** -->
<div class="doc_section"><a name="intro">Part 5 Introduction</a></div>
<!-- *********************************************************************** -->
<div class="doc_text">
<p>Welcome to Part 5 of the "<a href="index.html">Implementing a language with
LLVM</a>" tutorial. Parts 1-4 described the implementation of the simple
Kaleidoscope language and included support for generating LLVM IR, following by
optimizations and a JIT compiler. Unfortunately, as presented, Kaleidoscope is
mostly useless: it has no control flow other than call and return. This means
that you can't have conditional branches in the code, significantly limiting its
power. In this episode of "build that compiler", we'll extend Kaleidoscope to
have an if/then/else expression plus a simple looping construct.</p>
</div>
<!-- *********************************************************************** -->
<div class="doc_section"><a name="ifthen">If/Then/Else</a></div>
<!-- *********************************************************************** -->
<div class="doc_text">
<p>
Extending Kaleidoscope to support if/then/else is quite straight-forward. It
basically requires adding lexer support for this "new" concept to the lexer,
parser, AST, and LLVM code emitter. This example is nice, because it shows how
easy it is to "grow" a language over time, incrementally extending it as new
ideas are discovered.</p>
<p>Before we get going on "how" we do this extension, lets talk about what we
want. The basic idea is that we want to be able to write this sort of thing:
</p>
<div class="doc_code">
<pre>
def fib(x)
if x &lt; 3 then
1
else
fib(x-1)+fib(x-2);
</pre>
</div>
<p>In Kaleidoscope, every construct is an expression: there are no statements.
As such, the if/then/else expression needs to return a value like any other.
Since we're using a mostly functional form, we'll have it evaluate its
conditional, then return the 'then' or 'else' value based on how the condition
was resolved. This is very similar to the C "?:" expression.</p>
<p>The semantics of the if/then/else expression is that it first evaluates the
condition to a boolean equality value: 0.0 is false and everything else is true.
If the condition is true, the first subexpression is evaluated and returned, if
the condition is false, the second subexpression is evaluated and returned.
Since Kaleidoscope allows side-effects, this behavior is important to nail down.
</p>
<p>Now that we know what we want, lets break this down into its constituent
pieces.</p>
</div>
<!-- ======================================================================= -->
<div class="doc_subsubsection"><a name="iflexer">Lexer Extensions for
If/Then/Else</a></div>
<!-- ======================================================================= -->
<div class="doc_text">
<p>The lexer extensions are straight-forward. First we add new enum values
for the relevant tokens:</p>
<div class="doc_code">
<pre>
// control
tok_if = -6, tok_then = -7, tok_else = -8,
</pre>
</div>
<p>Once we have that, we recognize the new keywords in the lexer, pretty simple
stuff:</p>
<div class="doc_code">
<pre>
...
if (IdentifierStr == "def") return tok_def;
if (IdentifierStr == "extern") return tok_extern;
<b>if (IdentifierStr == "if") return tok_if;
if (IdentifierStr == "then") return tok_then;
if (IdentifierStr == "else") return tok_else;</b>
return tok_identifier;
</pre>
</div>
</div>
<!-- ======================================================================= -->
<div class="doc_subsubsection"><a name="ifast">AST Extensions for
If/Then/Else </a></div>
<!-- ======================================================================= -->
<div class="doc_text">
<p>To represent the new expression we add a new AST node for it:</p>
<div class="doc_code">
<pre>
/// IfExprAST - Expression class for if/then/else.
class IfExprAST : public ExprAST {
ExprAST *Cond, *Then, *Else;
public:
IfExprAST(ExprAST *cond, ExprAST *then, ExprAST *_else)
: Cond(cond), Then(then), Else(_else) {}
virtual Value *Codegen();
};
</pre>
</div>
<p>The AST node just has pointers to the various subexpressions.</p>
</div>
<!-- ======================================================================= -->
<div class="doc_subsubsection"><a name="ifparser">Parser Extensions for
If/Then/Else </a></div>
<!-- ======================================================================= -->
<div class="doc_text">
<p>Now that we have the relevant tokens coming from the lexer and we have the
AST node to build, our parsing logic is relatively straight-forward. First we
define a new parsing function:</p>
<div class="doc_code">
<pre>
/// ifexpr ::= 'if' expression 'then' expression 'else' expression
static ExprAST *ParseIfExpr() {
getNextToken(); // eat the if.
// condition.
ExprAST *Cond = ParseExpression();
if (!Cond) return 0;
if (CurTok != tok_then)
return Error("expected then");
getNextToken(); // eat the then
ExprAST *Then = ParseExpression();
if (Then == 0) return 0;
if (CurTok != tok_else)
return Error("expected else");
getNextToken();
ExprAST *Else = ParseExpression();
if (!Else) return 0;
return new IfExprAST(Cond, Then, Else);
}
</pre>
</div>
<p>Next we hook it up as a primary expression:</p>
<div class="doc_code">
<pre>
static ExprAST *ParsePrimary() {
switch (CurTok) {
default: return Error("unknown token when expecting an expression");
case tok_identifier: return ParseIdentifierExpr();
case tok_number: return ParseNumberExpr();
case '(': return ParseParenExpr();
<b>case tok_if: return ParseIfExpr();</b>
}
}
</pre>
</div>
</div>
<!-- ======================================================================= -->
<div class="doc_subsubsection"><a name="ifir">LLVM IR for If/Then/Else</a></div>
<!-- ======================================================================= -->
<div class="doc_text">
<p>Now that we have it parsing and building the AST, the final piece is adding
LLVM code generation support. This is the most interesting part of the
if/then/else example, because this is where it starts to introduce new concepts.
All of the code above has been described in previous chapters fairly thoroughly.
</p>
<p>To motivate the code we want to produce, lets take a look at a simple
example. Consider:</p>
<div class="doc_code">
<pre>
extern foo();
extern bar();
def baz(x) if x then foo() else bar();
</pre>
</div>
<p>If you disable optimizations, the code you'll (soon) get from Kaleidoscope
looks like this:</p>
<div class="doc_code">
<pre>
declare double @foo()
declare double @bar()
define double @baz(double %x) {
entry:
%ifcond = fcmp one double %x, 0.000000e+00
br i1 %ifcond, label %then, label %else
then: ; preds = %entry
%calltmp = call double @foo()
br label %ifcont
else: ; preds = %entry
%calltmp1 = call double @bar()
br label %ifcont
ifcont: ; preds = %else, %then
%iftmp = phi double [ %calltmp, %then ], [ %calltmp1, %else ]
ret double %iftmp
}
</pre>
</div>
<p>To visualize the control flow graph, you can use a nifty feature of the LLVM
'<a href="http://llvm.org/cmds/opt.html">opt</a>' tool. If you put this LLVM IR
into "t.ll" and run "<tt>llvm-as &lt; t.ll | opt -analyze -view-cfg</tt>", <a
href="../ProgrammersManual.html#ViewGraph">a window will pop up</a> and you'll
see this graph:</p>
<center><img src="LangImpl5-cfg.png" alt="Example CFG" width="423"
height="315"></center>
<p>Another way to get this is to call "<tt>F-&gt;viewCFG()</tt>" or
"<tt>F-&gt;viewCFGOnly()</tt>" (where F is a "<tt>Function*</tt>") either by
inserting actual calls into the code and recompiling or by calling these in the
debugger. LLVM has many nice features for visualizing various graphs.</p>
<p>Coming back to the generated code, it is fairly simple: the entry block
evaluates the conditional expression ("x" in our case here) and compares the
result to 0.0 with the "<tt><a href="../LangRef.html#i_fcmp">fcmp</a> one</tt>"
instruction ('one' is "ordered and not equal"). Based on the result of this
expression, the code jumps to either the "then" or "else" blocks, which contain
the expressions for the true/false case.</p>
<p>Once the then/else blocks is finished executing, they both branch back to the
else block to execute the code that happens after the if/then/else. In this
case the only thing left to do is to return to the caller of the function. The
question then becomes: how does the code know which expression to return?</p>
<p>The answer to this question involves an important SSA operation: the
<a href="http://en.wikipedia.org/wiki/Static_single_assignment_form">Phi
operation</a>. If you're not familiar with SSA, <a
href="http://en.wikipedia.org/wiki/Static_single_assignment_form">the wikipedia
article</a> is a good introduction and there are various other introductions to
it available on your favorite search engine. The short version is that
"execution" of the Phi operation requires "remembering" which block control came
from. The Phi operation takes on the value corresponding to the input control
block. In this case, if control comes in from the "then" block, it gets the
value of "calltmp". If control comes from the "else" block, it gets the value
of "calltmp1".</p>
<p>At this point, you are probably starting to think "on no! this means my
simple and elegant front-end will have to start generating SSA form in order to
use LLVM!". Fortunately, this is not the case, and we strongly advise
<em>not</em> implementing an SSA construction algorithm in your front-end
unless there is an amazingly good reason to do so. In practice, there are two
sorts of values that float around in code written in your average imperative
programming language that might need Phi nodes:</p>
<ol>
<li>Code that involves user variables: <tt>x = 1; x = x + 1; </tt></li>
<li>Values that are implicit in the structure of your AST, such as the phi node
in this case.</li>
</ol>
<p>At a future point in this tutorial ("mutable variables"), we'll talk about #1
in depth. For now, just believe me that you don't need SSA construction to
handle them. For #2, you have the choice of using the techniques that we will
describe for #1, or you can insert Phi nodes directly if convenient. In this
case, it is really really easy to generate the Phi node, so we choose to do it
directly.</p>
<p>Okay, enough of the motivation and overview, lets generate code!</p>
</div>
<!-- ======================================================================= -->
<div class="doc_subsubsection"><a name="ifcodegen">Code Generation for
If/Then/Else</a></div>
<!-- ======================================================================= -->
<div class="doc_text">
<p>In order to generate code for this, we implement the <tt>Codegen</tt> method
for <tt>IfExprAST</tt>:</p>
<div class="doc_code">
<pre>
Value *IfExprAST::Codegen() {
Value *CondV = Cond-&gt;Codegen();
if (CondV == 0) return 0;
// Convert condition to a bool by comparing equal to 0.0.
CondV = Builder.CreateFCmpONE(CondV,
ConstantFP::get(Type::DoubleTy, APFloat(0.0)),
"ifcond");
</pre>
</div>
<p>This code is straight-forward and similar to what we saw before. We emit the
expression for the condition, then compare that value to zero to get a truth
value as a 1-bit (bool) value.</p>
<div class="doc_code">
<pre>
Function *TheFunction = Builder.GetInsertBlock()-&gt;getParent();
// Create blocks for the then and else cases. Insert the 'then' block at the
// end of the function.
BasicBlock *ThenBB = new BasicBlock("then", TheFunction);
BasicBlock *ElseBB = new BasicBlock("else");
BasicBlock *MergeBB = new BasicBlock("ifcont");
Builder.CreateCondBr(CondV, ThenBB, ElseBB);
</pre>
</div>
<p>This code creates the basic blocks that are related to the if/then/else
statement, and correspond directly to the blocks in the example above. The
first line of this gets the current Function object that is being built. It
gets this by asking the builder for the current BasicBlock, and asking that
block for its "parent" (the function it is currently embedded into).</p>
<p>Once it has that, it creates three blocks. Note that it passes "TheFunction"
into the constructor for the "then" block. This causes the constructor to
automatically insert the new block onto the end of the specified function. The
other two blocks are created, but aren't yet inserted into the function.</p>
<p>Once the blocks are created, we can emit the conditional branch that chooses
between them. Note that creating new blocks does not implicitly affect the
LLVMBuilder, so it is still inserting into the block that the condition
went into. Also note that it is creating a branch to the "then" block and the
"else" block, even though the "else" block isn't inserted into the function yet.
This is all ok: it is the standard way that LLVM supports forward
references.</p>
<div class="doc_code">
<pre>
// Emit then value.
Builder.SetInsertPoint(ThenBB);
Value *ThenV = Then-&gt;Codegen();
if (ThenV == 0) return 0;
Builder.CreateBr(MergeBB);
// Codegen of 'Then' can change the current block, update ThenBB for the PHI.
ThenBB = Builder.GetInsertBlock();
</pre>
</div>
<p>After the conditional branch is inserted, we move the builder to start
inserting into the "then" block. Strictly speaking, this call moves the
insertion point to be at the end of the specified block. However, since the
"then" block is empty, it also starts out by inserting at the beginning of the
block. :)</p>
<p>Once the insertion point is set, we recursively codegen the "then" expression
from the AST. To finish off the then block, we create an unconditional branch
to the merge block. One interesting (and very important) aspect of the LLVM IR
is that it <a href="../LangRef.html#functionstructure">requires all basic blocks
to be "terminated"</a> with a <a href="../LangRef.html#terminators">control flow
instruction</a> such as return or branch. This means that all control flow,
<em>including fall throughs</em> must be made explicit in the LLVM IR. If you
violate this rule, the verifier will emit an error.</p>
<p>The final line here is quite subtle, but is very important. The basic issue
is that when we create the Phi node in the merge block, we need to set up the
block/value pairs that indicate how the Phi will work. Importantly, the Phi
node expects to have an extry for each predecessor of the block in the CFG. Why
then are we getting the current block when we just set it to ThenBB 5 lines
above? The problem is that the "Then" expression may actually itself change the
block that the Builder is emitting into if, for example, it contains a nested
"if/then/else" expression. Because calling Codegen recursively could
arbitrarily change the notion of the current block, we are required to get an
up-to-date value for code that will set up the Phi node.</p>
<div class="doc_code">
<pre>
// Emit else block.
TheFunction-&gt;getBasicBlockList().push_back(ElseBB);
Builder.SetInsertPoint(ElseBB);
Value *ElseV = Else-&gt;Codegen();
if (ElseV == 0) return 0;
Builder.CreateBr(MergeBB);
// Codegen of 'Else' can change the current block, update ElseBB for the PHI.
ElseBB = Builder.GetInsertBlock();
</pre>
</div>
<p>Code generation for the 'else' block is basically identical to codegen for
the 'then' block. The only significant difference is the first line, which adds
the 'else' block to the function. Recall previously that the 'else' block was
created, but not added to the function. Now that the 'then' and 'else' blocks
are emitted, we can finish up with the merge code:</p>
<div class="doc_code">
<pre>
// Emit merge block.
TheFunction->getBasicBlockList().push_back(MergeBB);
Builder.SetInsertPoint(MergeBB);
PHINode *PN = Builder.CreatePHI(Type::DoubleTy, "iftmp");
PN->addIncoming(ThenV, ThenBB);
PN->addIncoming(ElseV, ElseBB);
return PN;
}
</pre>
</div>
<p>The first two lines here are now familiar: the first adds the "merge" block
to the Function object (it was previously floating, like the else block above).
The second block changes the insertion point so that newly created code will go
into the "merge" block. Once that is done, we need to create the PHI node and
set up the block/value pairs for the PHI.</p>
<p>Finally, the CodeGen function returns the phi node as the value computed by
the if/then/else expression. In our example above, this returned value will
feed into the code for the top-level function, which will create the return
instruction.</p>
<p>Overall, we now have the ability to execution conditional code in
Kaleidoscope. With this extension, Kaleidoscope is a fairly complete language
that can calculate a wide variety of numeric functions. Next up we'll add
another useful expression that is familiar from non-functional languages...</p>
</div>
<!-- *********************************************************************** -->
<div class="doc_section"><a name="for">'for' Loop Expression</a></div>
<!-- *********************************************************************** -->
<div class="doc_text">
add the code for expression code that we'll add, though most of the description is missing. git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@43547 91177308-0d34-0410-b5e6-96231b3b80d8
2007-10-31 06:47:39 +00:00
<p>Now that we know how to add basic control flow constructs to the language,
we have the tools to add more powerful things. Lets add something more
aggressive, a 'for' expression:</p>
<div class="doc_code">
<pre>
# print 100 '*' (ascii 42) characters
extern putchard(char)
for x = 1, x &lt; 100, 1.0 in putchard(42);
</pre>
</div>
<p>This expression defines a new variable ("x" in this case) which iterates from
a starting value, while the condition ("x &lt; 100" in this case) is true,
incrementing by an optional step value ("1.0" in this case). If the step value
is omitted, it defaults to 1.0. While the loop is true, it executes its
body expression. Because we don't have anything better to return, we'll just
define the loop as always returning 0.0. In the future when we have mutable
variables, it will get more useful.</p>
<p>As before, lets talk about the changes that we need to Kaleidoscope to
support this.</p>
</div>
<!-- ======================================================================= -->
<div class="doc_subsubsection"><a name="forlexer">Lexer Extensions for
the 'for' Loop</a></div>
<!-- ======================================================================= -->
<div class="doc_text">
<p>The lexer extensions are the same sort of thing as for if/then/else:</p>
<div class="doc_code">
<pre>
... in enum Token ...
// control
tok_if = -6, tok_then = -7, tok_else = -8,
<b> tok_for = -9, tok_in = -10</b>
... in gettok ...
if (IdentifierStr == "def") return tok_def;
if (IdentifierStr == "extern") return tok_extern;
if (IdentifierStr == "if") return tok_if;
if (IdentifierStr == "then") return tok_then;
if (IdentifierStr == "else") return tok_else;
<b>if (IdentifierStr == "for") return tok_for;
if (IdentifierStr == "in") return tok_in;</b>
return tok_identifier;
</pre>
</div>
</div>
<!-- ======================================================================= -->
<div class="doc_subsubsection"><a name="forast">AST Extensions for
the 'for' Loop</a></div>
<!-- ======================================================================= -->
<div class="doc_text">
<p>The AST node is similarly simple. It basically boils down to capturing
the variable name and the consituent expressions in the node.</p>
<div class="doc_code">
<pre>
/// ForExprAST - Expression class for for/in.
class ForExprAST : public ExprAST {
std::string VarName;
ExprAST *Start, *End, *Step, *Body;
public:
ForExprAST(const std::string &amp;varname, ExprAST *start, ExprAST *end,
ExprAST *step, ExprAST *body)
: VarName(varname), Start(start), End(end), Step(step), Body(body) {}
virtual Value *Codegen();
};
</pre>
</div>
</div>
<!-- ======================================================================= -->
<div class="doc_subsubsection"><a name="forparser">Parser Extensions for
the 'for' Loop</a></div>
<!-- ======================================================================= -->
<div class="doc_text">
<p>The parser code is also fairly standard. The only interesting thing here is
handling of the optional step value. The parser code handles it by checking to
see if the second comma is present. If not, it sets the step value to null in
the AST node:</p>
<div class="doc_code">
<pre>
/// forexpr ::= 'for' identifer '=' expr ',' expr (',' expr)? 'in' expression
static ExprAST *ParseForExpr() {
getNextToken(); // eat the for.
if (CurTok != tok_identifier)
return Error("expected identifier after for");
std::string IdName = IdentifierStr;
getNextToken(); // eat identifer.
if (CurTok != '=')
return Error("expected '=' after for");
getNextToken(); // eat '='.
ExprAST *Start = ParseExpression();
if (Start == 0) return 0;
if (CurTok != ',')
return Error("expected ',' after for start value");
getNextToken();
ExprAST *End = ParseExpression();
if (End == 0) return 0;
// The step value is optional.
ExprAST *Step = 0;
if (CurTok == ',') {
getNextToken();
Step = ParseExpression();
if (Step == 0) return 0;
}
if (CurTok != tok_in)
return Error("expected 'in' after for");
getNextToken(); // eat 'in'.
ExprAST *Body = ParseExpression();
if (Body == 0) return 0;
return new ForExprAST(IdName, Start, End, Step, Body);
}
</pre>
</div>
</div>
<!-- ======================================================================= -->
<div class="doc_subsubsection"><a name="forir">LLVM IR for
the 'for' Loop</a></div>
<!-- ======================================================================= -->
<div class="doc_text">
<p>Now we get to the good part: the LLVM IR we want to generate for this thing.
</p>
</div>
<!-- ======================================================================= -->
<div class="doc_subsubsection"><a name="forcodegen">Code Generation for
the 'for' Loop</a></div>
<!-- ======================================================================= -->
<div class="doc_text">
<div class="doc_code">
<pre>
Value *ForExprAST::Codegen() {
// Output this as:
// ...
// start = startexpr
// goto loop
// loop:
// variable = phi [start, loopheader], [nextvariable, loopend]
// ...
// bodyexpr
// ...
// loopend:
// step = stepexpr
// nextvariable = variable + step
// endcond = endexpr
// br endcond, loop, endloop
// outloop:
// Emit the start code first, without 'variable' in scope.
Value *StartVal = Start-&gt;Codegen();
if (StartVal == 0) return 0;
// Make the new basic block for the loop header, inserting after current
// block.
Function *TheFunction = Builder.GetInsertBlock()-&gt;getParent();
BasicBlock *PreheaderBB = Builder.GetInsertBlock();
BasicBlock *LoopBB = new BasicBlock("loop", TheFunction);
// Insert an explicit fall through from the current block to the LoopBB.
// Start insertion in LoopBB.
Builder.CreateBr(LoopBB);
Builder.SetInsertPoint(LoopBB);
// Start the PHI node with an entry for Start.
PHINode *Variable = Builder.CreatePHI(Type::DoubleTy, VarName.c_str());
Variable-&gt;addIncoming(StartVal, PreheaderBB);
// Within the loop, the variable is defined equal to the PHI node. If it
// shadows an existing variable, we have to restore it, so save it now.
Value *OldVal = NamedValues[VarName];
NamedValues[VarName] = Variable;
// Emit the body of the loop. This, like any other expr, can change the
// current BB. Note that we ignore the value computed by the body, but don't
// allow an error.
if (Body-&gt;Codegen() == 0)
return 0;
// Emit the step value.
Value *StepVal;
if (Step) {
StepVal = Step-&gt;Codegen();
if (StepVal == 0) return 0;
} else {
// If not specified, use 1.0.
StepVal = ConstantFP::get(Type::DoubleTy, APFloat(1.0));
}
Value *NextVar = Builder.CreateAdd(Variable, StepVal, "nextvar");
// When evaluating the end condition, the value of the variable is the
// incremented value.
NamedValues[VarName] = Variable;
// Compute the end condition.
Value *EndCond = End-&gt;Codegen();
if (EndCond == 0) return EndCond;
// Convert condition to a bool by comparing equal to 0.0.
EndCond = Builder.CreateFCmpONE(EndCond,
ConstantFP::get(Type::DoubleTy, APFloat(0.0)),
"loopcond");
// Create the "after loop" block and insert it.
BasicBlock *LoopEndBB = Builder.GetInsertBlock();
BasicBlock *AfterBB = new BasicBlock("afterloop", TheFunction);
// Insert the conditional branch into the end of LoopEndBB.
Builder.CreateCondBr(EndCond, LoopBB, AfterBB);
// Any new code will be inserted in AfterBB.
Builder.SetInsertPoint(AfterBB);
// Add a new entry to the PHI node for the backedge.
Variable-&gt;addIncoming(NextVar, LoopEndBB);
// Restore the unshadowed variable.
if (OldVal)
NamedValues[VarName] = OldVal;
else
NamedValues.erase(VarName);
// for expr always returns 0.0.
return Constant::getNullValue(Type::DoubleTy);
}
</pre>
</div>
Add the first half of chapter 5: if/then/else. To come: for statement. git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@43546 91177308-0d34-0410-b5e6-96231b3b80d8
2007-10-31 06:30:21 +00:00
</div>
<!-- *********************************************************************** -->
<div class="doc_section"><a name="code">Full Code Listing</a></div>
<!-- *********************************************************************** -->
<div class="doc_text">
<p>
Here is the complete code listing for our running example, enhanced with the
if/then/else and for expressions.. To build this example, use:
</p>
<div class="doc_code">
<pre>
# Compile
g++ -g toy.cpp `llvm-config --cppflags --ldflags --libs core jit native` -O3 -o toy
# Run
./toy
</pre>
</div>
<p>Here is the code:</p>
<div class="doc_code">
<pre>
...
</pre>
</div>
</div>
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<a href="mailto:sabre@nondot.org">Chris Lattner</a><br>
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