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6 <title>Kaleidoscope: Extending the Language: Mutable Variables / SSA
7 construction</title>
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15 <div class="doc_title">Kaleidoscope: Extending the Language: Mutable Variables</div>
17 <ul>
18 <li><a href="index.html">Up to Tutorial Index</a></li>
19 <li>Chapter 7
20 <ol>
21 <li><a href="#intro">Chapter 7 Introduction</a></li>
22 <li><a href="#why">Why is this a hard problem?</a></li>
23 <li><a href="#memory">Memory in LLVM</a></li>
24 <li><a href="#kalvars">Mutable Variables in Kaleidoscope</a></li>
25 <li><a href="#adjustments">Adjusting Existing Variables for
26 Mutation</a></li>
27 <li><a href="#assignment">New Assignment Operator</a></li>
28 <li><a href="#localvars">User-defined Local Variables</a></li>
29 <li><a href="#code">Full Code Listing</a></li>
30 </ol>
31 </li>
32 <li><a href="LangImpl8.html">Chapter 8</a>: Conclusion and other useful LLVM
33 tidbits</li>
34 </ul>
36 <div class="doc_author">
37 <p>Written by <a href="mailto:sabre@nondot.org">Chris Lattner</a></p>
38 </div>
40 <!-- *********************************************************************** -->
41 <div class="doc_section"><a name="intro">Chapter 7 Introduction</a></div>
42 <!-- *********************************************************************** -->
44 <div class="doc_text">
46 <p>Welcome to Chapter 7 of the "<a href="index.html">Implementing a language
47 with LLVM</a>" tutorial. In chapters 1 through 6, we've built a very
48 respectable, albeit simple, <a
49 href="http://en.wikipedia.org/wiki/Functional_programming">functional
50 programming language</a>. In our journey, we learned some parsing techniques,
51 how to build and represent an AST, how to build LLVM IR, and how to optimize
52 the resultant code as well as JIT compile it.</p>
54 <p>While Kaleidoscope is interesting as a functional language, the fact that it
55 is functional makes it "too easy" to generate LLVM IR for it. In particular, a
56 functional language makes it very easy to build LLVM IR directly in <a
57 href="http://en.wikipedia.org/wiki/Static_single_assignment_form">SSA form</a>.
58 Since LLVM requires that the input code be in SSA form, this is a very nice
59 property and it is often unclear to newcomers how to generate code for an
60 imperative language with mutable variables.</p>
62 <p>The short (and happy) summary of this chapter is that there is no need for
63 your front-end to build SSA form: LLVM provides highly tuned and well tested
64 support for this, though the way it works is a bit unexpected for some.</p>
66 </div>
68 <!-- *********************************************************************** -->
69 <div class="doc_section"><a name="why">Why is this a hard problem?</a></div>
70 <!-- *********************************************************************** -->
72 <div class="doc_text">
74 <p>
75 To understand why mutable variables cause complexities in SSA construction,
76 consider this extremely simple C example:
77 </p>
79 <div class="doc_code">
80 <pre>
81 int G, H;
82 int test(_Bool Condition) {
83 int X;
84 if (Condition)
85 X = G;
86 else
87 X = H;
88 return X;
90 </pre>
91 </div>
93 <p>In this case, we have the variable "X", whose value depends on the path
94 executed in the program. Because there are two different possible values for X
95 before the return instruction, a PHI node is inserted to merge the two values.
96 The LLVM IR that we want for this example looks like this:</p>
98 <div class="doc_code">
99 <pre>
100 @G = weak global i32 0 ; type of @G is i32*
101 @H = weak global i32 0 ; type of @H is i32*
103 define i32 @test(i1 %Condition) {
104 entry:
105 br i1 %Condition, label %cond_true, label %cond_false
107 cond_true:
108 %X.0 = load i32* @G
109 br label %cond_next
111 cond_false:
112 %X.1 = load i32* @H
113 br label %cond_next
115 cond_next:
116 %X.2 = phi i32 [ %X.1, %cond_false ], [ %X.0, %cond_true ]
117 ret i32 %X.2
119 </pre>
120 </div>
122 <p>In this example, the loads from the G and H global variables are explicit in
123 the LLVM IR, and they live in the then/else branches of the if statement
124 (cond_true/cond_false). In order to merge the incoming values, the X.2 phi node
125 in the cond_next block selects the right value to use based on where control
126 flow is coming from: if control flow comes from the cond_false block, X.2 gets
127 the value of X.1. Alternatively, if control flow comes from cond_true, it gets
128 the value of X.0. The intent of this chapter is not to explain the details of
129 SSA form. For more information, see one of the many <a
130 href="http://en.wikipedia.org/wiki/Static_single_assignment_form">online
131 references</a>.</p>
133 <p>The question for this article is "who places the phi nodes when lowering
134 assignments to mutable variables?". The issue here is that LLVM
135 <em>requires</em> that its IR be in SSA form: there is no "non-ssa" mode for it.
136 However, SSA construction requires non-trivial algorithms and data structures,
137 so it is inconvenient and wasteful for every front-end to have to reproduce this
138 logic.</p>
140 </div>
142 <!-- *********************************************************************** -->
143 <div class="doc_section"><a name="memory">Memory in LLVM</a></div>
144 <!-- *********************************************************************** -->
146 <div class="doc_text">
148 <p>The 'trick' here is that while LLVM does require all register values to be
149 in SSA form, it does not require (or permit) memory objects to be in SSA form.
150 In the example above, note that the loads from G and H are direct accesses to
151 G and H: they are not renamed or versioned. This differs from some other
152 compiler systems, which do try to version memory objects. In LLVM, instead of
153 encoding dataflow analysis of memory into the LLVM IR, it is handled with <a
154 href="../WritingAnLLVMPass.html">Analysis Passes</a> which are computed on
155 demand.</p>
158 With this in mind, the high-level idea is that we want to make a stack variable
159 (which lives in memory, because it is on the stack) for each mutable object in
160 a function. To take advantage of this trick, we need to talk about how LLVM
161 represents stack variables.
162 </p>
164 <p>In LLVM, all memory accesses are explicit with load/store instructions, and
165 it is carefully designed not to have (or need) an "address-of" operator. Notice
166 how the type of the @G/@H global variables is actually "i32*" even though the
167 variable is defined as "i32". What this means is that @G defines <em>space</em>
168 for an i32 in the global data area, but its <em>name</em> actually refers to the
169 address for that space. Stack variables work the same way, except that instead of
170 being declared with global variable definitions, they are declared with the
171 <a href="../LangRef.html#i_alloca">LLVM alloca instruction</a>:</p>
173 <div class="doc_code">
174 <pre>
175 define i32 @example() {
176 entry:
177 %X = alloca i32 ; type of %X is i32*.
179 %tmp = load i32* %X ; load the stack value %X from the stack.
180 %tmp2 = add i32 %tmp, 1 ; increment it
181 store i32 %tmp2, i32* %X ; store it back
183 </pre>
184 </div>
186 <p>This code shows an example of how you can declare and manipulate a stack
187 variable in the LLVM IR. Stack memory allocated with the alloca instruction is
188 fully general: you can pass the address of the stack slot to functions, you can
189 store it in other variables, etc. In our example above, we could rewrite the
190 example to use the alloca technique to avoid using a PHI node:</p>
192 <div class="doc_code">
193 <pre>
194 @G = weak global i32 0 ; type of @G is i32*
195 @H = weak global i32 0 ; type of @H is i32*
197 define i32 @test(i1 %Condition) {
198 entry:
199 %X = alloca i32 ; type of %X is i32*.
200 br i1 %Condition, label %cond_true, label %cond_false
202 cond_true:
203 %X.0 = load i32* @G
204 store i32 %X.0, i32* %X ; Update X
205 br label %cond_next
207 cond_false:
208 %X.1 = load i32* @H
209 store i32 %X.1, i32* %X ; Update X
210 br label %cond_next
212 cond_next:
213 %X.2 = load i32* %X ; Read X
214 ret i32 %X.2
216 </pre>
217 </div>
219 <p>With this, we have discovered a way to handle arbitrary mutable variables
220 without the need to create Phi nodes at all:</p>
222 <ol>
223 <li>Each mutable variable becomes a stack allocation.</li>
224 <li>Each read of the variable becomes a load from the stack.</li>
225 <li>Each update of the variable becomes a store to the stack.</li>
226 <li>Taking the address of a variable just uses the stack address directly.</li>
227 </ol>
229 <p>While this solution has solved our immediate problem, it introduced another
230 one: we have now apparently introduced a lot of stack traffic for very simple
231 and common operations, a major performance problem. Fortunately for us, the
232 LLVM optimizer has a highly-tuned optimization pass named "mem2reg" that handles
233 this case, promoting allocas like this into SSA registers, inserting Phi nodes
234 as appropriate. If you run this example through the pass, for example, you'll
235 get:</p>
237 <div class="doc_code">
238 <pre>
239 $ <b>llvm-as &lt; example.ll | opt -mem2reg | llvm-dis</b>
240 @G = weak global i32 0
241 @H = weak global i32 0
243 define i32 @test(i1 %Condition) {
244 entry:
245 br i1 %Condition, label %cond_true, label %cond_false
247 cond_true:
248 %X.0 = load i32* @G
249 br label %cond_next
251 cond_false:
252 %X.1 = load i32* @H
253 br label %cond_next
255 cond_next:
256 %X.01 = phi i32 [ %X.1, %cond_false ], [ %X.0, %cond_true ]
257 ret i32 %X.01
259 </pre>
260 </div>
262 <p>The mem2reg pass implements the standard "iterated dominance frontier"
263 algorithm for constructing SSA form and has a number of optimizations that speed
264 up (very common) degenerate cases. The mem2reg optimization pass is the answer to dealing
265 with mutable variables, and we highly recommend that you depend on it. Note that
266 mem2reg only works on variables in certain circumstances:</p>
268 <ol>
269 <li>mem2reg is alloca-driven: it looks for allocas and if it can handle them, it
270 promotes them. It does not apply to global variables or heap allocations.</li>
272 <li>mem2reg only looks for alloca instructions in the entry block of the
273 function. Being in the entry block guarantees that the alloca is only executed
274 once, which makes analysis simpler.</li>
276 <li>mem2reg only promotes allocas whose uses are direct loads and stores. If
277 the address of the stack object is passed to a function, or if any funny pointer
278 arithmetic is involved, the alloca will not be promoted.</li>
280 <li>mem2reg only works on allocas of <a
281 href="../LangRef.html#t_classifications">first class</a>
282 values (such as pointers, scalars and vectors), and only if the array size
283 of the allocation is 1 (or missing in the .ll file). mem2reg is not capable of
284 promoting structs or arrays to registers. Note that the "scalarrepl" pass is
285 more powerful and can promote structs, "unions", and arrays in many cases.</li>
287 </ol>
290 All of these properties are easy to satisfy for most imperative languages, and
291 we'll illustrate it below with Kaleidoscope. The final question you may be
292 asking is: should I bother with this nonsense for my front-end? Wouldn't it be
293 better if I just did SSA construction directly, avoiding use of the mem2reg
294 optimization pass? In short, we strongly recommend that you use this technique
295 for building SSA form, unless there is an extremely good reason not to. Using
296 this technique is:</p>
298 <ul>
299 <li>Proven and well tested: llvm-gcc and clang both use this technique for local
300 mutable variables. As such, the most common clients of LLVM are using this to
301 handle a bulk of their variables. You can be sure that bugs are found fast and
302 fixed early.</li>
304 <li>Extremely Fast: mem2reg has a number of special cases that make it fast in
305 common cases as well as fully general. For example, it has fast-paths for
306 variables that are only used in a single block, variables that only have one
307 assignment point, good heuristics to avoid insertion of unneeded phi nodes, etc.
308 </li>
310 <li>Needed for debug info generation: <a href="../SourceLevelDebugging.html">
311 Debug information in LLVM</a> relies on having the address of the variable
312 exposed so that debug info can be attached to it. This technique dovetails
313 very naturally with this style of debug info.</li>
314 </ul>
316 <p>If nothing else, this makes it much easier to get your front-end up and
317 running, and is very simple to implement. Lets extend Kaleidoscope with mutable
318 variables now!
319 </p>
321 </div>
323 <!-- *********************************************************************** -->
324 <div class="doc_section"><a name="kalvars">Mutable Variables in
325 Kaleidoscope</a></div>
326 <!-- *********************************************************************** -->
328 <div class="doc_text">
330 <p>Now that we know the sort of problem we want to tackle, lets see what this
331 looks like in the context of our little Kaleidoscope language. We're going to
332 add two features:</p>
334 <ol>
335 <li>The ability to mutate variables with the '=' operator.</li>
336 <li>The ability to define new variables.</li>
337 </ol>
339 <p>While the first item is really what this is about, we only have variables
340 for incoming arguments as well as for induction variables, and redefining those only
341 goes so far :). Also, the ability to define new variables is a
342 useful thing regardless of whether you will be mutating them. Here's a
343 motivating example that shows how we could use these:</p>
345 <div class="doc_code">
346 <pre>
347 # Define ':' for sequencing: as a low-precedence operator that ignores operands
348 # and just returns the RHS.
349 def binary : 1 (x y) y;
351 # Recursive fib, we could do this before.
352 def fib(x)
353 if (x &lt; 3) then
355 else
356 fib(x-1)+fib(x-2);
358 # Iterative fib.
359 def fibi(x)
360 <b>var a = 1, b = 1, c in</b>
361 (for i = 3, i &lt; x in
362 <b>c = a + b</b> :
363 <b>a = b</b> :
364 <b>b = c</b>) :
367 # Call it.
368 fibi(10);
369 </pre>
370 </div>
373 In order to mutate variables, we have to change our existing variables to use
374 the "alloca trick". Once we have that, we'll add our new operator, then extend
375 Kaleidoscope to support new variable definitions.
376 </p>
378 </div>
380 <!-- *********************************************************************** -->
381 <div class="doc_section"><a name="adjustments">Adjusting Existing Variables for
382 Mutation</a></div>
383 <!-- *********************************************************************** -->
385 <div class="doc_text">
388 The symbol table in Kaleidoscope is managed at code generation time by the
389 '<tt>NamedValues</tt>' map. This map currently keeps track of the LLVM "Value*"
390 that holds the double value for the named variable. In order to support
391 mutation, we need to change this slightly, so that it <tt>NamedValues</tt> holds
392 the <em>memory location</em> of the variable in question. Note that this
393 change is a refactoring: it changes the structure of the code, but does not
394 (by itself) change the behavior of the compiler. All of these changes are
395 isolated in the Kaleidoscope code generator.</p>
398 At this point in Kaleidoscope's development, it only supports variables for two
399 things: incoming arguments to functions and the induction variable of 'for'
400 loops. For consistency, we'll allow mutation of these variables in addition to
401 other user-defined variables. This means that these will both need memory
402 locations.
403 </p>
405 <p>To start our transformation of Kaleidoscope, we'll change the NamedValues
406 map so that it maps to AllocaInst* instead of Value*. Once we do this, the C++
407 compiler will tell us what parts of the code we need to update:</p>
409 <div class="doc_code">
410 <pre>
411 static std::map&lt;std::string, AllocaInst*&gt; NamedValues;
412 </pre>
413 </div>
415 <p>Also, since we will need to create these alloca's, we'll use a helper
416 function that ensures that the allocas are created in the entry block of the
417 function:</p>
419 <div class="doc_code">
420 <pre>
421 /// CreateEntryBlockAlloca - Create an alloca instruction in the entry block of
422 /// the function. This is used for mutable variables etc.
423 static AllocaInst *CreateEntryBlockAlloca(Function *TheFunction,
424 const std::string &amp;VarName) {
425 IRBuilder&lt;&gt; TmpB(&amp;TheFunction-&gt;getEntryBlock(),
426 TheFunction-&gt;getEntryBlock().begin());
427 return TmpB.CreateAlloca(Type::DoubleTy, 0, VarName.c_str());
429 </pre>
430 </div>
432 <p>This funny looking code creates an IRBuilder object that is pointing at
433 the first instruction (.begin()) of the entry block. It then creates an alloca
434 with the expected name and returns it. Because all values in Kaleidoscope are
435 doubles, there is no need to pass in a type to use.</p>
437 <p>With this in place, the first functionality change we want to make is to
438 variable references. In our new scheme, variables live on the stack, so code
439 generating a reference to them actually needs to produce a load from the stack
440 slot:</p>
442 <div class="doc_code">
443 <pre>
444 Value *VariableExprAST::Codegen() {
445 // Look this variable up in the function.
446 Value *V = NamedValues[Name];
447 if (V == 0) return ErrorV("Unknown variable name");
449 <b>// Load the value.
450 return Builder.CreateLoad(V, Name.c_str());</b>
452 </pre>
453 </div>
455 <p>As you can see, this is pretty straightforward. Now we need to update the
456 things that define the variables to set up the alloca. We'll start with
457 <tt>ForExprAST::Codegen</tt> (see the <a href="#code">full code listing</a> for
458 the unabridged code):</p>
460 <div class="doc_code">
461 <pre>
462 Function *TheFunction = Builder.GetInsertBlock()->getParent();
464 <b>// Create an alloca for the variable in the entry block.
465 AllocaInst *Alloca = CreateEntryBlockAlloca(TheFunction, VarName);</b>
467 // Emit the start code first, without 'variable' in scope.
468 Value *StartVal = Start-&gt;Codegen();
469 if (StartVal == 0) return 0;
471 <b>// Store the value into the alloca.
472 Builder.CreateStore(StartVal, Alloca);</b>
475 // Compute the end condition.
476 Value *EndCond = End-&gt;Codegen();
477 if (EndCond == 0) return EndCond;
479 <b>// Reload, increment, and restore the alloca. This handles the case where
480 // the body of the loop mutates the variable.
481 Value *CurVar = Builder.CreateLoad(Alloca);
482 Value *NextVar = Builder.CreateAdd(CurVar, StepVal, "nextvar");
483 Builder.CreateStore(NextVar, Alloca);</b>
485 </pre>
486 </div>
488 <p>This code is virtually identical to the code <a
489 href="LangImpl5.html#forcodegen">before we allowed mutable variables</a>. The
490 big difference is that we no longer have to construct a PHI node, and we use
491 load/store to access the variable as needed.</p>
493 <p>To support mutable argument variables, we need to also make allocas for them.
494 The code for this is also pretty simple:</p>
496 <div class="doc_code">
497 <pre>
498 /// CreateArgumentAllocas - Create an alloca for each argument and register the
499 /// argument in the symbol table so that references to it will succeed.
500 void PrototypeAST::CreateArgumentAllocas(Function *F) {
501 Function::arg_iterator AI = F-&gt;arg_begin();
502 for (unsigned Idx = 0, e = Args.size(); Idx != e; ++Idx, ++AI) {
503 // Create an alloca for this variable.
504 AllocaInst *Alloca = CreateEntryBlockAlloca(F, Args[Idx]);
506 // Store the initial value into the alloca.
507 Builder.CreateStore(AI, Alloca);
509 // Add arguments to variable symbol table.
510 NamedValues[Args[Idx]] = Alloca;
513 </pre>
514 </div>
516 <p>For each argument, we make an alloca, store the input value to the function
517 into the alloca, and register the alloca as the memory location for the
518 argument. This method gets invoked by <tt>FunctionAST::Codegen</tt> right after
519 it sets up the entry block for the function.</p>
521 <p>The final missing piece is adding the mem2reg pass, which allows us to get
522 good codegen once again:</p>
524 <div class="doc_code">
525 <pre>
526 // Set up the optimizer pipeline. Start with registering info about how the
527 // target lays out data structures.
528 OurFPM.add(new TargetData(*TheExecutionEngine-&gt;getTargetData()));
529 <b>// Promote allocas to registers.
530 OurFPM.add(createPromoteMemoryToRegisterPass());</b>
531 // Do simple "peephole" optimizations and bit-twiddling optzns.
532 OurFPM.add(createInstructionCombiningPass());
533 // Reassociate expressions.
534 OurFPM.add(createReassociatePass());
535 </pre>
536 </div>
538 <p>It is interesting to see what the code looks like before and after the
539 mem2reg optimization runs. For example, this is the before/after code for our
540 recursive fib function. Before the optimization:</p>
542 <div class="doc_code">
543 <pre>
544 define double @fib(double %x) {
545 entry:
546 <b>%x1 = alloca double
547 store double %x, double* %x1
548 %x2 = load double* %x1</b>
549 %cmptmp = fcmp ult double %x2, 3.000000e+00
550 %booltmp = uitofp i1 %cmptmp to double
551 %ifcond = fcmp one double %booltmp, 0.000000e+00
552 br i1 %ifcond, label %then, label %else
554 then: ; preds = %entry
555 br label %ifcont
557 else: ; preds = %entry
558 <b>%x3 = load double* %x1</b>
559 %subtmp = sub double %x3, 1.000000e+00
560 %calltmp = call double @fib( double %subtmp )
561 <b>%x4 = load double* %x1</b>
562 %subtmp5 = sub double %x4, 2.000000e+00
563 %calltmp6 = call double @fib( double %subtmp5 )
564 %addtmp = add double %calltmp, %calltmp6
565 br label %ifcont
567 ifcont: ; preds = %else, %then
568 %iftmp = phi double [ 1.000000e+00, %then ], [ %addtmp, %else ]
569 ret double %iftmp
571 </pre>
572 </div>
574 <p>Here there is only one variable (x, the input argument) but you can still
575 see the extremely simple-minded code generation strategy we are using. In the
576 entry block, an alloca is created, and the initial input value is stored into
577 it. Each reference to the variable does a reload from the stack. Also, note
578 that we didn't modify the if/then/else expression, so it still inserts a PHI
579 node. While we could make an alloca for it, it is actually easier to create a
580 PHI node for it, so we still just make the PHI.</p>
582 <p>Here is the code after the mem2reg pass runs:</p>
584 <div class="doc_code">
585 <pre>
586 define double @fib(double %x) {
587 entry:
588 %cmptmp = fcmp ult double <b>%x</b>, 3.000000e+00
589 %booltmp = uitofp i1 %cmptmp to double
590 %ifcond = fcmp one double %booltmp, 0.000000e+00
591 br i1 %ifcond, label %then, label %else
593 then:
594 br label %ifcont
596 else:
597 %subtmp = sub double <b>%x</b>, 1.000000e+00
598 %calltmp = call double @fib( double %subtmp )
599 %subtmp5 = sub double <b>%x</b>, 2.000000e+00
600 %calltmp6 = call double @fib( double %subtmp5 )
601 %addtmp = add double %calltmp, %calltmp6
602 br label %ifcont
604 ifcont: ; preds = %else, %then
605 %iftmp = phi double [ 1.000000e+00, %then ], [ %addtmp, %else ]
606 ret double %iftmp
608 </pre>
609 </div>
611 <p>This is a trivial case for mem2reg, since there are no redefinitions of the
612 variable. The point of showing this is to calm your tension about inserting
613 such blatent inefficiencies :).</p>
615 <p>After the rest of the optimizers run, we get:</p>
617 <div class="doc_code">
618 <pre>
619 define double @fib(double %x) {
620 entry:
621 %cmptmp = fcmp ult double %x, 3.000000e+00
622 %booltmp = uitofp i1 %cmptmp to double
623 %ifcond = fcmp ueq double %booltmp, 0.000000e+00
624 br i1 %ifcond, label %else, label %ifcont
626 else:
627 %subtmp = sub double %x, 1.000000e+00
628 %calltmp = call double @fib( double %subtmp )
629 %subtmp5 = sub double %x, 2.000000e+00
630 %calltmp6 = call double @fib( double %subtmp5 )
631 %addtmp = add double %calltmp, %calltmp6
632 ret double %addtmp
634 ifcont:
635 ret double 1.000000e+00
637 </pre>
638 </div>
640 <p>Here we see that the simplifycfg pass decided to clone the return instruction
641 into the end of the 'else' block. This allowed it to eliminate some branches
642 and the PHI node.</p>
644 <p>Now that all symbol table references are updated to use stack variables,
645 we'll add the assignment operator.</p>
647 </div>
649 <!-- *********************************************************************** -->
650 <div class="doc_section"><a name="assignment">New Assignment Operator</a></div>
651 <!-- *********************************************************************** -->
653 <div class="doc_text">
655 <p>With our current framework, adding a new assignment operator is really
656 simple. We will parse it just like any other binary operator, but handle it
657 internally (instead of allowing the user to define it). The first step is to
658 set a precedence:</p>
660 <div class="doc_code">
661 <pre>
662 int main() {
663 // Install standard binary operators.
664 // 1 is lowest precedence.
665 <b>BinopPrecedence['='] = 2;</b>
666 BinopPrecedence['&lt;'] = 10;
667 BinopPrecedence['+'] = 20;
668 BinopPrecedence['-'] = 20;
669 </pre>
670 </div>
672 <p>Now that the parser knows the precedence of the binary operator, it takes
673 care of all the parsing and AST generation. We just need to implement codegen
674 for the assignment operator. This looks like:</p>
676 <div class="doc_code">
677 <pre>
678 Value *BinaryExprAST::Codegen() {
679 // Special case '=' because we don't want to emit the LHS as an expression.
680 if (Op == '=') {
681 // Assignment requires the LHS to be an identifier.
682 VariableExprAST *LHSE = dynamic_cast&lt;VariableExprAST*&gt;(LHS);
683 if (!LHSE)
684 return ErrorV("destination of '=' must be a variable");
685 </pre>
686 </div>
688 <p>Unlike the rest of the binary operators, our assignment operator doesn't
689 follow the "emit LHS, emit RHS, do computation" model. As such, it is handled
690 as a special case before the other binary operators are handled. The other
691 strange thing is that it requires the LHS to be a variable. It is invalid to
692 have "(x+1) = expr" - only things like "x = expr" are allowed.
693 </p>
695 <div class="doc_code">
696 <pre>
697 // Codegen the RHS.
698 Value *Val = RHS-&gt;Codegen();
699 if (Val == 0) return 0;
701 // Look up the name.
702 Value *Variable = NamedValues[LHSE-&gt;getName()];
703 if (Variable == 0) return ErrorV("Unknown variable name");
705 Builder.CreateStore(Val, Variable);
706 return Val;
708 ...
709 </pre>
710 </div>
712 <p>Once we have the variable, codegen'ing the assignment is straightforward:
713 we emit the RHS of the assignment, create a store, and return the computed
714 value. Returning a value allows for chained assignments like "X = (Y = Z)".</p>
716 <p>Now that we have an assignment operator, we can mutate loop variables and
717 arguments. For example, we can now run code like this:</p>
719 <div class="doc_code">
720 <pre>
721 # Function to print a double.
722 extern printd(x);
724 # Define ':' for sequencing: as a low-precedence operator that ignores operands
725 # and just returns the RHS.
726 def binary : 1 (x y) y;
728 def test(x)
729 printd(x) :
730 x = 4 :
731 printd(x);
733 test(123);
734 </pre>
735 </div>
737 <p>When run, this example prints "123" and then "4", showing that we did
738 actually mutate the value! Okay, we have now officially implemented our goal:
739 getting this to work requires SSA construction in the general case. However,
740 to be really useful, we want the ability to define our own local variables, lets
741 add this next!
742 </p>
744 </div>
746 <!-- *********************************************************************** -->
747 <div class="doc_section"><a name="localvars">User-defined Local
748 Variables</a></div>
749 <!-- *********************************************************************** -->
751 <div class="doc_text">
753 <p>Adding var/in is just like any other other extensions we made to
754 Kaleidoscope: we extend the lexer, the parser, the AST and the code generator.
755 The first step for adding our new 'var/in' construct is to extend the lexer.
756 As before, this is pretty trivial, the code looks like this:</p>
758 <div class="doc_code">
759 <pre>
760 enum Token {
762 <b>// var definition
763 tok_var = -13</b>
767 static int gettok() {
769 if (IdentifierStr == "in") return tok_in;
770 if (IdentifierStr == "binary") return tok_binary;
771 if (IdentifierStr == "unary") return tok_unary;
772 <b>if (IdentifierStr == "var") return tok_var;</b>
773 return tok_identifier;
775 </pre>
776 </div>
778 <p>The next step is to define the AST node that we will construct. For var/in,
779 it looks like this:</p>
781 <div class="doc_code">
782 <pre>
783 /// VarExprAST - Expression class for var/in
784 class VarExprAST : public ExprAST {
785 std::vector&lt;std::pair&lt;std::string, ExprAST*&gt; &gt; VarNames;
786 ExprAST *Body;
787 public:
788 VarExprAST(const std::vector&lt;std::pair&lt;std::string, ExprAST*&gt; &gt; &amp;varnames,
789 ExprAST *body)
790 : VarNames(varnames), Body(body) {}
792 virtual Value *Codegen();
794 </pre>
795 </div>
797 <p>var/in allows a list of names to be defined all at once, and each name can
798 optionally have an initializer value. As such, we capture this information in
799 the VarNames vector. Also, var/in has a body, this body is allowed to access
800 the variables defined by the var/in.</p>
802 <p>With this in place, we can define the parser pieces. The first thing we do is add
803 it as a primary expression:</p>
805 <div class="doc_code">
806 <pre>
807 /// primary
808 /// ::= identifierexpr
809 /// ::= numberexpr
810 /// ::= parenexpr
811 /// ::= ifexpr
812 /// ::= forexpr
813 <b>/// ::= varexpr</b>
814 static ExprAST *ParsePrimary() {
815 switch (CurTok) {
816 default: return Error("unknown token when expecting an expression");
817 case tok_identifier: return ParseIdentifierExpr();
818 case tok_number: return ParseNumberExpr();
819 case '(': return ParseParenExpr();
820 case tok_if: return ParseIfExpr();
821 case tok_for: return ParseForExpr();
822 <b>case tok_var: return ParseVarExpr();</b>
825 </pre>
826 </div>
828 <p>Next we define ParseVarExpr:</p>
830 <div class="doc_code">
831 <pre>
832 /// varexpr ::= 'var' identifier ('=' expression)?
833 // (',' identifier ('=' expression)?)* 'in' expression
834 static ExprAST *ParseVarExpr() {
835 getNextToken(); // eat the var.
837 std::vector&lt;std::pair&lt;std::string, ExprAST*&gt; &gt; VarNames;
839 // At least one variable name is required.
840 if (CurTok != tok_identifier)
841 return Error("expected identifier after var");
842 </pre>
843 </div>
845 <p>The first part of this code parses the list of identifier/expr pairs into the
846 local <tt>VarNames</tt> vector.
848 <div class="doc_code">
849 <pre>
850 while (1) {
851 std::string Name = IdentifierStr;
852 getNextToken(); // eat identifier.
854 // Read the optional initializer.
855 ExprAST *Init = 0;
856 if (CurTok == '=') {
857 getNextToken(); // eat the '='.
859 Init = ParseExpression();
860 if (Init == 0) return 0;
863 VarNames.push_back(std::make_pair(Name, Init));
865 // End of var list, exit loop.
866 if (CurTok != ',') break;
867 getNextToken(); // eat the ','.
869 if (CurTok != tok_identifier)
870 return Error("expected identifier list after var");
872 </pre>
873 </div>
875 <p>Once all the variables are parsed, we then parse the body and create the
876 AST node:</p>
878 <div class="doc_code">
879 <pre>
880 // At this point, we have to have 'in'.
881 if (CurTok != tok_in)
882 return Error("expected 'in' keyword after 'var'");
883 getNextToken(); // eat 'in'.
885 ExprAST *Body = ParseExpression();
886 if (Body == 0) return 0;
888 return new VarExprAST(VarNames, Body);
890 </pre>
891 </div>
893 <p>Now that we can parse and represent the code, we need to support emission of
894 LLVM IR for it. This code starts out with:</p>
896 <div class="doc_code">
897 <pre>
898 Value *VarExprAST::Codegen() {
899 std::vector&lt;AllocaInst *&gt; OldBindings;
901 Function *TheFunction = Builder.GetInsertBlock()-&gt;getParent();
903 // Register all variables and emit their initializer.
904 for (unsigned i = 0, e = VarNames.size(); i != e; ++i) {
905 const std::string &amp;VarName = VarNames[i].first;
906 ExprAST *Init = VarNames[i].second;
907 </pre>
908 </div>
910 <p>Basically it loops over all the variables, installing them one at a time.
911 For each variable we put into the symbol table, we remember the previous value
912 that we replace in OldBindings.</p>
914 <div class="doc_code">
915 <pre>
916 // Emit the initializer before adding the variable to scope, this prevents
917 // the initializer from referencing the variable itself, and permits stuff
918 // like this:
919 // var a = 1 in
920 // var a = a in ... # refers to outer 'a'.
921 Value *InitVal;
922 if (Init) {
923 InitVal = Init-&gt;Codegen();
924 if (InitVal == 0) return 0;
925 } else { // If not specified, use 0.0.
926 InitVal = ConstantFP::get(APFloat(0.0));
929 AllocaInst *Alloca = CreateEntryBlockAlloca(TheFunction, VarName);
930 Builder.CreateStore(InitVal, Alloca);
932 // Remember the old variable binding so that we can restore the binding when
933 // we unrecurse.
934 OldBindings.push_back(NamedValues[VarName]);
936 // Remember this binding.
937 NamedValues[VarName] = Alloca;
939 </pre>
940 </div>
942 <p>There are more comments here than code. The basic idea is that we emit the
943 initializer, create the alloca, then update the symbol table to point to it.
944 Once all the variables are installed in the symbol table, we evaluate the body
945 of the var/in expression:</p>
947 <div class="doc_code">
948 <pre>
949 // Codegen the body, now that all vars are in scope.
950 Value *BodyVal = Body-&gt;Codegen();
951 if (BodyVal == 0) return 0;
952 </pre>
953 </div>
955 <p>Finally, before returning, we restore the previous variable bindings:</p>
957 <div class="doc_code">
958 <pre>
959 // Pop all our variables from scope.
960 for (unsigned i = 0, e = VarNames.size(); i != e; ++i)
961 NamedValues[VarNames[i].first] = OldBindings[i];
963 // Return the body computation.
964 return BodyVal;
966 </pre>
967 </div>
969 <p>The end result of all of this is that we get properly scoped variable
970 definitions, and we even (trivially) allow mutation of them :).</p>
972 <p>With this, we completed what we set out to do. Our nice iterative fib
973 example from the intro compiles and runs just fine. The mem2reg pass optimizes
974 all of our stack variables into SSA registers, inserting PHI nodes where needed,
975 and our front-end remains simple: no "iterated dominance frontier" computation
976 anywhere in sight.</p>
978 </div>
980 <!-- *********************************************************************** -->
981 <div class="doc_section"><a name="code">Full Code Listing</a></div>
982 <!-- *********************************************************************** -->
984 <div class="doc_text">
987 Here is the complete code listing for our running example, enhanced with mutable
988 variables and var/in support. To build this example, use:
989 </p>
991 <div class="doc_code">
992 <pre>
993 # Compile
994 g++ -g toy.cpp `llvm-config --cppflags --ldflags --libs core jit native` -O3 -o toy
995 # Run
996 ./toy
997 </pre>
998 </div>
1000 <p>Here is the code:</p>
1002 <div class="doc_code">
1003 <pre>
1004 #include "llvm/DerivedTypes.h"
1005 #include "llvm/ExecutionEngine/ExecutionEngine.h"
1006 #include "llvm/Module.h"
1007 #include "llvm/ModuleProvider.h"
1008 #include "llvm/PassManager.h"
1009 #include "llvm/Analysis/Verifier.h"
1010 #include "llvm/Target/TargetData.h"
1011 #include "llvm/Transforms/Scalar.h"
1012 #include "llvm/Support/IRBuilder.h"
1013 #include &lt;cstdio&gt;
1014 #include &lt;string&gt;
1015 #include &lt;map&gt;
1016 #include &lt;vector&gt;
1017 using namespace llvm;
1019 //===----------------------------------------------------------------------===//
1020 // Lexer
1021 //===----------------------------------------------------------------------===//
1023 // The lexer returns tokens [0-255] if it is an unknown character, otherwise one
1024 // of these for known things.
1025 enum Token {
1026 tok_eof = -1,
1028 // commands
1029 tok_def = -2, tok_extern = -3,
1031 // primary
1032 tok_identifier = -4, tok_number = -5,
1034 // control
1035 tok_if = -6, tok_then = -7, tok_else = -8,
1036 tok_for = -9, tok_in = -10,
1038 // operators
1039 tok_binary = -11, tok_unary = -12,
1041 // var definition
1042 tok_var = -13
1045 static std::string IdentifierStr; // Filled in if tok_identifier
1046 static double NumVal; // Filled in if tok_number
1048 /// gettok - Return the next token from standard input.
1049 static int gettok() {
1050 static int LastChar = ' ';
1052 // Skip any whitespace.
1053 while (isspace(LastChar))
1054 LastChar = getchar();
1056 if (isalpha(LastChar)) { // identifier: [a-zA-Z][a-zA-Z0-9]*
1057 IdentifierStr = LastChar;
1058 while (isalnum((LastChar = getchar())))
1059 IdentifierStr += LastChar;
1061 if (IdentifierStr == "def") return tok_def;
1062 if (IdentifierStr == "extern") return tok_extern;
1063 if (IdentifierStr == "if") return tok_if;
1064 if (IdentifierStr == "then") return tok_then;
1065 if (IdentifierStr == "else") return tok_else;
1066 if (IdentifierStr == "for") return tok_for;
1067 if (IdentifierStr == "in") return tok_in;
1068 if (IdentifierStr == "binary") return tok_binary;
1069 if (IdentifierStr == "unary") return tok_unary;
1070 if (IdentifierStr == "var") return tok_var;
1071 return tok_identifier;
1074 if (isdigit(LastChar) || LastChar == '.') { // Number: [0-9.]+
1075 std::string NumStr;
1076 do {
1077 NumStr += LastChar;
1078 LastChar = getchar();
1079 } while (isdigit(LastChar) || LastChar == '.');
1081 NumVal = strtod(NumStr.c_str(), 0);
1082 return tok_number;
1085 if (LastChar == '#') {
1086 // Comment until end of line.
1087 do LastChar = getchar();
1088 while (LastChar != EOF &amp;&amp; LastChar != '\n' &amp;&amp; LastChar != '\r');
1090 if (LastChar != EOF)
1091 return gettok();
1094 // Check for end of file. Don't eat the EOF.
1095 if (LastChar == EOF)
1096 return tok_eof;
1098 // Otherwise, just return the character as its ascii value.
1099 int ThisChar = LastChar;
1100 LastChar = getchar();
1101 return ThisChar;
1104 //===----------------------------------------------------------------------===//
1105 // Abstract Syntax Tree (aka Parse Tree)
1106 //===----------------------------------------------------------------------===//
1108 /// ExprAST - Base class for all expression nodes.
1109 class ExprAST {
1110 public:
1111 virtual ~ExprAST() {}
1112 virtual Value *Codegen() = 0;
1115 /// NumberExprAST - Expression class for numeric literals like "1.0".
1116 class NumberExprAST : public ExprAST {
1117 double Val;
1118 public:
1119 NumberExprAST(double val) : Val(val) {}
1120 virtual Value *Codegen();
1123 /// VariableExprAST - Expression class for referencing a variable, like "a".
1124 class VariableExprAST : public ExprAST {
1125 std::string Name;
1126 public:
1127 VariableExprAST(const std::string &amp;name) : Name(name) {}
1128 const std::string &amp;getName() const { return Name; }
1129 virtual Value *Codegen();
1132 /// UnaryExprAST - Expression class for a unary operator.
1133 class UnaryExprAST : public ExprAST {
1134 char Opcode;
1135 ExprAST *Operand;
1136 public:
1137 UnaryExprAST(char opcode, ExprAST *operand)
1138 : Opcode(opcode), Operand(operand) {}
1139 virtual Value *Codegen();
1142 /// BinaryExprAST - Expression class for a binary operator.
1143 class BinaryExprAST : public ExprAST {
1144 char Op;
1145 ExprAST *LHS, *RHS;
1146 public:
1147 BinaryExprAST(char op, ExprAST *lhs, ExprAST *rhs)
1148 : Op(op), LHS(lhs), RHS(rhs) {}
1149 virtual Value *Codegen();
1152 /// CallExprAST - Expression class for function calls.
1153 class CallExprAST : public ExprAST {
1154 std::string Callee;
1155 std::vector&lt;ExprAST*&gt; Args;
1156 public:
1157 CallExprAST(const std::string &amp;callee, std::vector&lt;ExprAST*&gt; &amp;args)
1158 : Callee(callee), Args(args) {}
1159 virtual Value *Codegen();
1162 /// IfExprAST - Expression class for if/then/else.
1163 class IfExprAST : public ExprAST {
1164 ExprAST *Cond, *Then, *Else;
1165 public:
1166 IfExprAST(ExprAST *cond, ExprAST *then, ExprAST *_else)
1167 : Cond(cond), Then(then), Else(_else) {}
1168 virtual Value *Codegen();
1171 /// ForExprAST - Expression class for for/in.
1172 class ForExprAST : public ExprAST {
1173 std::string VarName;
1174 ExprAST *Start, *End, *Step, *Body;
1175 public:
1176 ForExprAST(const std::string &amp;varname, ExprAST *start, ExprAST *end,
1177 ExprAST *step, ExprAST *body)
1178 : VarName(varname), Start(start), End(end), Step(step), Body(body) {}
1179 virtual Value *Codegen();
1182 /// VarExprAST - Expression class for var/in
1183 class VarExprAST : public ExprAST {
1184 std::vector&lt;std::pair&lt;std::string, ExprAST*&gt; &gt; VarNames;
1185 ExprAST *Body;
1186 public:
1187 VarExprAST(const std::vector&lt;std::pair&lt;std::string, ExprAST*&gt; &gt; &amp;varnames,
1188 ExprAST *body)
1189 : VarNames(varnames), Body(body) {}
1191 virtual Value *Codegen();
1194 /// PrototypeAST - This class represents the "prototype" for a function,
1195 /// which captures its argument names as well as if it is an operator.
1196 class PrototypeAST {
1197 std::string Name;
1198 std::vector&lt;std::string&gt; Args;
1199 bool isOperator;
1200 unsigned Precedence; // Precedence if a binary op.
1201 public:
1202 PrototypeAST(const std::string &amp;name, const std::vector&lt;std::string&gt; &amp;args,
1203 bool isoperator = false, unsigned prec = 0)
1204 : Name(name), Args(args), isOperator(isoperator), Precedence(prec) {}
1206 bool isUnaryOp() const { return isOperator &amp;&amp; Args.size() == 1; }
1207 bool isBinaryOp() const { return isOperator &amp;&amp; Args.size() == 2; }
1209 char getOperatorName() const {
1210 assert(isUnaryOp() || isBinaryOp());
1211 return Name[Name.size()-1];
1214 unsigned getBinaryPrecedence() const { return Precedence; }
1216 Function *Codegen();
1218 void CreateArgumentAllocas(Function *F);
1221 /// FunctionAST - This class represents a function definition itself.
1222 class FunctionAST {
1223 PrototypeAST *Proto;
1224 ExprAST *Body;
1225 public:
1226 FunctionAST(PrototypeAST *proto, ExprAST *body)
1227 : Proto(proto), Body(body) {}
1229 Function *Codegen();
1232 //===----------------------------------------------------------------------===//
1233 // Parser
1234 //===----------------------------------------------------------------------===//
1236 /// CurTok/getNextToken - Provide a simple token buffer. CurTok is the current
1237 /// token the parser it looking at. getNextToken reads another token from the
1238 /// lexer and updates CurTok with its results.
1239 static int CurTok;
1240 static int getNextToken() {
1241 return CurTok = gettok();
1244 /// BinopPrecedence - This holds the precedence for each binary operator that is
1245 /// defined.
1246 static std::map&lt;char, int&gt; BinopPrecedence;
1248 /// GetTokPrecedence - Get the precedence of the pending binary operator token.
1249 static int GetTokPrecedence() {
1250 if (!isascii(CurTok))
1251 return -1;
1253 // Make sure it's a declared binop.
1254 int TokPrec = BinopPrecedence[CurTok];
1255 if (TokPrec &lt;= 0) return -1;
1256 return TokPrec;
1259 /// Error* - These are little helper functions for error handling.
1260 ExprAST *Error(const char *Str) { fprintf(stderr, "Error: %s\n", Str);return 0;}
1261 PrototypeAST *ErrorP(const char *Str) { Error(Str); return 0; }
1262 FunctionAST *ErrorF(const char *Str) { Error(Str); return 0; }
1264 static ExprAST *ParseExpression();
1266 /// identifierexpr
1267 /// ::= identifier
1268 /// ::= identifier '(' expression* ')'
1269 static ExprAST *ParseIdentifierExpr() {
1270 std::string IdName = IdentifierStr;
1272 getNextToken(); // eat identifier.
1274 if (CurTok != '(') // Simple variable ref.
1275 return new VariableExprAST(IdName);
1277 // Call.
1278 getNextToken(); // eat (
1279 std::vector&lt;ExprAST*&gt; Args;
1280 if (CurTok != ')') {
1281 while (1) {
1282 ExprAST *Arg = ParseExpression();
1283 if (!Arg) return 0;
1284 Args.push_back(Arg);
1286 if (CurTok == ')') break;
1288 if (CurTok != ',')
1289 return Error("Expected ')' or ',' in argument list");
1290 getNextToken();
1294 // Eat the ')'.
1295 getNextToken();
1297 return new CallExprAST(IdName, Args);
1300 /// numberexpr ::= number
1301 static ExprAST *ParseNumberExpr() {
1302 ExprAST *Result = new NumberExprAST(NumVal);
1303 getNextToken(); // consume the number
1304 return Result;
1307 /// parenexpr ::= '(' expression ')'
1308 static ExprAST *ParseParenExpr() {
1309 getNextToken(); // eat (.
1310 ExprAST *V = ParseExpression();
1311 if (!V) return 0;
1313 if (CurTok != ')')
1314 return Error("expected ')'");
1315 getNextToken(); // eat ).
1316 return V;
1319 /// ifexpr ::= 'if' expression 'then' expression 'else' expression
1320 static ExprAST *ParseIfExpr() {
1321 getNextToken(); // eat the if.
1323 // condition.
1324 ExprAST *Cond = ParseExpression();
1325 if (!Cond) return 0;
1327 if (CurTok != tok_then)
1328 return Error("expected then");
1329 getNextToken(); // eat the then
1331 ExprAST *Then = ParseExpression();
1332 if (Then == 0) return 0;
1334 if (CurTok != tok_else)
1335 return Error("expected else");
1337 getNextToken();
1339 ExprAST *Else = ParseExpression();
1340 if (!Else) return 0;
1342 return new IfExprAST(Cond, Then, Else);
1345 /// forexpr ::= 'for' identifier '=' expr ',' expr (',' expr)? 'in' expression
1346 static ExprAST *ParseForExpr() {
1347 getNextToken(); // eat the for.
1349 if (CurTok != tok_identifier)
1350 return Error("expected identifier after for");
1352 std::string IdName = IdentifierStr;
1353 getNextToken(); // eat identifier.
1355 if (CurTok != '=')
1356 return Error("expected '=' after for");
1357 getNextToken(); // eat '='.
1360 ExprAST *Start = ParseExpression();
1361 if (Start == 0) return 0;
1362 if (CurTok != ',')
1363 return Error("expected ',' after for start value");
1364 getNextToken();
1366 ExprAST *End = ParseExpression();
1367 if (End == 0) return 0;
1369 // The step value is optional.
1370 ExprAST *Step = 0;
1371 if (CurTok == ',') {
1372 getNextToken();
1373 Step = ParseExpression();
1374 if (Step == 0) return 0;
1377 if (CurTok != tok_in)
1378 return Error("expected 'in' after for");
1379 getNextToken(); // eat 'in'.
1381 ExprAST *Body = ParseExpression();
1382 if (Body == 0) return 0;
1384 return new ForExprAST(IdName, Start, End, Step, Body);
1387 /// varexpr ::= 'var' identifier ('=' expression)?
1388 // (',' identifier ('=' expression)?)* 'in' expression
1389 static ExprAST *ParseVarExpr() {
1390 getNextToken(); // eat the var.
1392 std::vector&lt;std::pair&lt;std::string, ExprAST*&gt; &gt; VarNames;
1394 // At least one variable name is required.
1395 if (CurTok != tok_identifier)
1396 return Error("expected identifier after var");
1398 while (1) {
1399 std::string Name = IdentifierStr;
1400 getNextToken(); // eat identifier.
1402 // Read the optional initializer.
1403 ExprAST *Init = 0;
1404 if (CurTok == '=') {
1405 getNextToken(); // eat the '='.
1407 Init = ParseExpression();
1408 if (Init == 0) return 0;
1411 VarNames.push_back(std::make_pair(Name, Init));
1413 // End of var list, exit loop.
1414 if (CurTok != ',') break;
1415 getNextToken(); // eat the ','.
1417 if (CurTok != tok_identifier)
1418 return Error("expected identifier list after var");
1421 // At this point, we have to have 'in'.
1422 if (CurTok != tok_in)
1423 return Error("expected 'in' keyword after 'var'");
1424 getNextToken(); // eat 'in'.
1426 ExprAST *Body = ParseExpression();
1427 if (Body == 0) return 0;
1429 return new VarExprAST(VarNames, Body);
1433 /// primary
1434 /// ::= identifierexpr
1435 /// ::= numberexpr
1436 /// ::= parenexpr
1437 /// ::= ifexpr
1438 /// ::= forexpr
1439 /// ::= varexpr
1440 static ExprAST *ParsePrimary() {
1441 switch (CurTok) {
1442 default: return Error("unknown token when expecting an expression");
1443 case tok_identifier: return ParseIdentifierExpr();
1444 case tok_number: return ParseNumberExpr();
1445 case '(': return ParseParenExpr();
1446 case tok_if: return ParseIfExpr();
1447 case tok_for: return ParseForExpr();
1448 case tok_var: return ParseVarExpr();
1452 /// unary
1453 /// ::= primary
1454 /// ::= '!' unary
1455 static ExprAST *ParseUnary() {
1456 // If the current token is not an operator, it must be a primary expr.
1457 if (!isascii(CurTok) || CurTok == '(' || CurTok == ',')
1458 return ParsePrimary();
1460 // If this is a unary operator, read it.
1461 int Opc = CurTok;
1462 getNextToken();
1463 if (ExprAST *Operand = ParseUnary())
1464 return new UnaryExprAST(Opc, Operand);
1465 return 0;
1468 /// binoprhs
1469 /// ::= ('+' unary)*
1470 static ExprAST *ParseBinOpRHS(int ExprPrec, ExprAST *LHS) {
1471 // If this is a binop, find its precedence.
1472 while (1) {
1473 int TokPrec = GetTokPrecedence();
1475 // If this is a binop that binds at least as tightly as the current binop,
1476 // consume it, otherwise we are done.
1477 if (TokPrec &lt; ExprPrec)
1478 return LHS;
1480 // Okay, we know this is a binop.
1481 int BinOp = CurTok;
1482 getNextToken(); // eat binop
1484 // Parse the unary expression after the binary operator.
1485 ExprAST *RHS = ParseUnary();
1486 if (!RHS) return 0;
1488 // If BinOp binds less tightly with RHS than the operator after RHS, let
1489 // the pending operator take RHS as its LHS.
1490 int NextPrec = GetTokPrecedence();
1491 if (TokPrec &lt; NextPrec) {
1492 RHS = ParseBinOpRHS(TokPrec+1, RHS);
1493 if (RHS == 0) return 0;
1496 // Merge LHS/RHS.
1497 LHS = new BinaryExprAST(BinOp, LHS, RHS);
1501 /// expression
1502 /// ::= unary binoprhs
1504 static ExprAST *ParseExpression() {
1505 ExprAST *LHS = ParseUnary();
1506 if (!LHS) return 0;
1508 return ParseBinOpRHS(0, LHS);
1511 /// prototype
1512 /// ::= id '(' id* ')'
1513 /// ::= binary LETTER number? (id, id)
1514 /// ::= unary LETTER (id)
1515 static PrototypeAST *ParsePrototype() {
1516 std::string FnName;
1518 int Kind = 0; // 0 = identifier, 1 = unary, 2 = binary.
1519 unsigned BinaryPrecedence = 30;
1521 switch (CurTok) {
1522 default:
1523 return ErrorP("Expected function name in prototype");
1524 case tok_identifier:
1525 FnName = IdentifierStr;
1526 Kind = 0;
1527 getNextToken();
1528 break;
1529 case tok_unary:
1530 getNextToken();
1531 if (!isascii(CurTok))
1532 return ErrorP("Expected unary operator");
1533 FnName = "unary";
1534 FnName += (char)CurTok;
1535 Kind = 1;
1536 getNextToken();
1537 break;
1538 case tok_binary:
1539 getNextToken();
1540 if (!isascii(CurTok))
1541 return ErrorP("Expected binary operator");
1542 FnName = "binary";
1543 FnName += (char)CurTok;
1544 Kind = 2;
1545 getNextToken();
1547 // Read the precedence if present.
1548 if (CurTok == tok_number) {
1549 if (NumVal &lt; 1 || NumVal &gt; 100)
1550 return ErrorP("Invalid precedecnce: must be 1..100");
1551 BinaryPrecedence = (unsigned)NumVal;
1552 getNextToken();
1554 break;
1557 if (CurTok != '(')
1558 return ErrorP("Expected '(' in prototype");
1560 std::vector&lt;std::string&gt; ArgNames;
1561 while (getNextToken() == tok_identifier)
1562 ArgNames.push_back(IdentifierStr);
1563 if (CurTok != ')')
1564 return ErrorP("Expected ')' in prototype");
1566 // success.
1567 getNextToken(); // eat ')'.
1569 // Verify right number of names for operator.
1570 if (Kind &amp;&amp; ArgNames.size() != Kind)
1571 return ErrorP("Invalid number of operands for operator");
1573 return new PrototypeAST(FnName, ArgNames, Kind != 0, BinaryPrecedence);
1576 /// definition ::= 'def' prototype expression
1577 static FunctionAST *ParseDefinition() {
1578 getNextToken(); // eat def.
1579 PrototypeAST *Proto = ParsePrototype();
1580 if (Proto == 0) return 0;
1582 if (ExprAST *E = ParseExpression())
1583 return new FunctionAST(Proto, E);
1584 return 0;
1587 /// toplevelexpr ::= expression
1588 static FunctionAST *ParseTopLevelExpr() {
1589 if (ExprAST *E = ParseExpression()) {
1590 // Make an anonymous proto.
1591 PrototypeAST *Proto = new PrototypeAST("", std::vector&lt;std::string&gt;());
1592 return new FunctionAST(Proto, E);
1594 return 0;
1597 /// external ::= 'extern' prototype
1598 static PrototypeAST *ParseExtern() {
1599 getNextToken(); // eat extern.
1600 return ParsePrototype();
1603 //===----------------------------------------------------------------------===//
1604 // Code Generation
1605 //===----------------------------------------------------------------------===//
1607 static Module *TheModule;
1608 static IRBuilder&lt;&gt; Builder;
1609 static std::map&lt;std::string, AllocaInst*&gt; NamedValues;
1610 static FunctionPassManager *TheFPM;
1612 Value *ErrorV(const char *Str) { Error(Str); return 0; }
1614 /// CreateEntryBlockAlloca - Create an alloca instruction in the entry block of
1615 /// the function. This is used for mutable variables etc.
1616 static AllocaInst *CreateEntryBlockAlloca(Function *TheFunction,
1617 const std::string &amp;VarName) {
1618 IRBuilder&lt;&gt; TmpB(&amp;TheFunction-&gt;getEntryBlock(),
1619 TheFunction-&gt;getEntryBlock().begin());
1620 return TmpB.CreateAlloca(Type::DoubleTy, 0, VarName.c_str());
1624 Value *NumberExprAST::Codegen() {
1625 return ConstantFP::get(APFloat(Val));
1628 Value *VariableExprAST::Codegen() {
1629 // Look this variable up in the function.
1630 Value *V = NamedValues[Name];
1631 if (V == 0) return ErrorV("Unknown variable name");
1633 // Load the value.
1634 return Builder.CreateLoad(V, Name.c_str());
1637 Value *UnaryExprAST::Codegen() {
1638 Value *OperandV = Operand-&gt;Codegen();
1639 if (OperandV == 0) return 0;
1641 Function *F = TheModule-&gt;getFunction(std::string("unary")+Opcode);
1642 if (F == 0)
1643 return ErrorV("Unknown unary operator");
1645 return Builder.CreateCall(F, OperandV, "unop");
1649 Value *BinaryExprAST::Codegen() {
1650 // Special case '=' because we don't want to emit the LHS as an expression.
1651 if (Op == '=') {
1652 // Assignment requires the LHS to be an identifier.
1653 VariableExprAST *LHSE = dynamic_cast&lt;VariableExprAST*&gt;(LHS);
1654 if (!LHSE)
1655 return ErrorV("destination of '=' must be a variable");
1656 // Codegen the RHS.
1657 Value *Val = RHS-&gt;Codegen();
1658 if (Val == 0) return 0;
1660 // Look up the name.
1661 Value *Variable = NamedValues[LHSE-&gt;getName()];
1662 if (Variable == 0) return ErrorV("Unknown variable name");
1664 Builder.CreateStore(Val, Variable);
1665 return Val;
1669 Value *L = LHS-&gt;Codegen();
1670 Value *R = RHS-&gt;Codegen();
1671 if (L == 0 || R == 0) return 0;
1673 switch (Op) {
1674 case '+': return Builder.CreateAdd(L, R, "addtmp");
1675 case '-': return Builder.CreateSub(L, R, "subtmp");
1676 case '*': return Builder.CreateMul(L, R, "multmp");
1677 case '&lt;':
1678 L = Builder.CreateFCmpULT(L, R, "cmptmp");
1679 // Convert bool 0/1 to double 0.0 or 1.0
1680 return Builder.CreateUIToFP(L, Type::DoubleTy, "booltmp");
1681 default: break;
1684 // If it wasn't a builtin binary operator, it must be a user defined one. Emit
1685 // a call to it.
1686 Function *F = TheModule-&gt;getFunction(std::string("binary")+Op);
1687 assert(F &amp;&amp; "binary operator not found!");
1689 Value *Ops[] = { L, R };
1690 return Builder.CreateCall(F, Ops, Ops+2, "binop");
1693 Value *CallExprAST::Codegen() {
1694 // Look up the name in the global module table.
1695 Function *CalleeF = TheModule-&gt;getFunction(Callee);
1696 if (CalleeF == 0)
1697 return ErrorV("Unknown function referenced");
1699 // If argument mismatch error.
1700 if (CalleeF-&gt;arg_size() != Args.size())
1701 return ErrorV("Incorrect # arguments passed");
1703 std::vector&lt;Value*&gt; ArgsV;
1704 for (unsigned i = 0, e = Args.size(); i != e; ++i) {
1705 ArgsV.push_back(Args[i]-&gt;Codegen());
1706 if (ArgsV.back() == 0) return 0;
1709 return Builder.CreateCall(CalleeF, ArgsV.begin(), ArgsV.end(), "calltmp");
1712 Value *IfExprAST::Codegen() {
1713 Value *CondV = Cond-&gt;Codegen();
1714 if (CondV == 0) return 0;
1716 // Convert condition to a bool by comparing equal to 0.0.
1717 CondV = Builder.CreateFCmpONE(CondV,
1718 ConstantFP::get(APFloat(0.0)),
1719 "ifcond");
1721 Function *TheFunction = Builder.GetInsertBlock()-&gt;getParent();
1723 // Create blocks for the then and else cases. Insert the 'then' block at the
1724 // end of the function.
1725 BasicBlock *ThenBB = BasicBlock::Create("then", TheFunction);
1726 BasicBlock *ElseBB = BasicBlock::Create("else");
1727 BasicBlock *MergeBB = BasicBlock::Create("ifcont");
1729 Builder.CreateCondBr(CondV, ThenBB, ElseBB);
1731 // Emit then value.
1732 Builder.SetInsertPoint(ThenBB);
1734 Value *ThenV = Then-&gt;Codegen();
1735 if (ThenV == 0) return 0;
1737 Builder.CreateBr(MergeBB);
1738 // Codegen of 'Then' can change the current block, update ThenBB for the PHI.
1739 ThenBB = Builder.GetInsertBlock();
1741 // Emit else block.
1742 TheFunction-&gt;getBasicBlockList().push_back(ElseBB);
1743 Builder.SetInsertPoint(ElseBB);
1745 Value *ElseV = Else-&gt;Codegen();
1746 if (ElseV == 0) return 0;
1748 Builder.CreateBr(MergeBB);
1749 // Codegen of 'Else' can change the current block, update ElseBB for the PHI.
1750 ElseBB = Builder.GetInsertBlock();
1752 // Emit merge block.
1753 TheFunction-&gt;getBasicBlockList().push_back(MergeBB);
1754 Builder.SetInsertPoint(MergeBB);
1755 PHINode *PN = Builder.CreatePHI(Type::DoubleTy, "iftmp");
1757 PN-&gt;addIncoming(ThenV, ThenBB);
1758 PN-&gt;addIncoming(ElseV, ElseBB);
1759 return PN;
1762 Value *ForExprAST::Codegen() {
1763 // Output this as:
1764 // var = alloca double
1765 // ...
1766 // start = startexpr
1767 // store start -&gt; var
1768 // goto loop
1769 // loop:
1770 // ...
1771 // bodyexpr
1772 // ...
1773 // loopend:
1774 // step = stepexpr
1775 // endcond = endexpr
1777 // curvar = load var
1778 // nextvar = curvar + step
1779 // store nextvar -&gt; var
1780 // br endcond, loop, endloop
1781 // outloop:
1783 Function *TheFunction = Builder.GetInsertBlock()-&gt;getParent();
1785 // Create an alloca for the variable in the entry block.
1786 AllocaInst *Alloca = CreateEntryBlockAlloca(TheFunction, VarName);
1788 // Emit the start code first, without 'variable' in scope.
1789 Value *StartVal = Start-&gt;Codegen();
1790 if (StartVal == 0) return 0;
1792 // Store the value into the alloca.
1793 Builder.CreateStore(StartVal, Alloca);
1795 // Make the new basic block for the loop header, inserting after current
1796 // block.
1797 BasicBlock *PreheaderBB = Builder.GetInsertBlock();
1798 BasicBlock *LoopBB = BasicBlock::Create("loop", TheFunction);
1800 // Insert an explicit fall through from the current block to the LoopBB.
1801 Builder.CreateBr(LoopBB);
1803 // Start insertion in LoopBB.
1804 Builder.SetInsertPoint(LoopBB);
1806 // Within the loop, the variable is defined equal to the PHI node. If it
1807 // shadows an existing variable, we have to restore it, so save it now.
1808 AllocaInst *OldVal = NamedValues[VarName];
1809 NamedValues[VarName] = Alloca;
1811 // Emit the body of the loop. This, like any other expr, can change the
1812 // current BB. Note that we ignore the value computed by the body, but don't
1813 // allow an error.
1814 if (Body-&gt;Codegen() == 0)
1815 return 0;
1817 // Emit the step value.
1818 Value *StepVal;
1819 if (Step) {
1820 StepVal = Step-&gt;Codegen();
1821 if (StepVal == 0) return 0;
1822 } else {
1823 // If not specified, use 1.0.
1824 StepVal = ConstantFP::get(APFloat(1.0));
1827 // Compute the end condition.
1828 Value *EndCond = End-&gt;Codegen();
1829 if (EndCond == 0) return EndCond;
1831 // Reload, increment, and restore the alloca. This handles the case where
1832 // the body of the loop mutates the variable.
1833 Value *CurVar = Builder.CreateLoad(Alloca, VarName.c_str());
1834 Value *NextVar = Builder.CreateAdd(CurVar, StepVal, "nextvar");
1835 Builder.CreateStore(NextVar, Alloca);
1837 // Convert condition to a bool by comparing equal to 0.0.
1838 EndCond = Builder.CreateFCmpONE(EndCond,
1839 ConstantFP::get(APFloat(0.0)),
1840 "loopcond");
1842 // Create the "after loop" block and insert it.
1843 BasicBlock *LoopEndBB = Builder.GetInsertBlock();
1844 BasicBlock *AfterBB = BasicBlock::Create("afterloop", TheFunction);
1846 // Insert the conditional branch into the end of LoopEndBB.
1847 Builder.CreateCondBr(EndCond, LoopBB, AfterBB);
1849 // Any new code will be inserted in AfterBB.
1850 Builder.SetInsertPoint(AfterBB);
1852 // Restore the unshadowed variable.
1853 if (OldVal)
1854 NamedValues[VarName] = OldVal;
1855 else
1856 NamedValues.erase(VarName);
1859 // for expr always returns 0.0.
1860 return Constant::getNullValue(Type::DoubleTy);
1863 Value *VarExprAST::Codegen() {
1864 std::vector&lt;AllocaInst *&gt; OldBindings;
1866 Function *TheFunction = Builder.GetInsertBlock()-&gt;getParent();
1868 // Register all variables and emit their initializer.
1869 for (unsigned i = 0, e = VarNames.size(); i != e; ++i) {
1870 const std::string &amp;VarName = VarNames[i].first;
1871 ExprAST *Init = VarNames[i].second;
1873 // Emit the initializer before adding the variable to scope, this prevents
1874 // the initializer from referencing the variable itself, and permits stuff
1875 // like this:
1876 // var a = 1 in
1877 // var a = a in ... # refers to outer 'a'.
1878 Value *InitVal;
1879 if (Init) {
1880 InitVal = Init-&gt;Codegen();
1881 if (InitVal == 0) return 0;
1882 } else { // If not specified, use 0.0.
1883 InitVal = ConstantFP::get(APFloat(0.0));
1886 AllocaInst *Alloca = CreateEntryBlockAlloca(TheFunction, VarName);
1887 Builder.CreateStore(InitVal, Alloca);
1889 // Remember the old variable binding so that we can restore the binding when
1890 // we unrecurse.
1891 OldBindings.push_back(NamedValues[VarName]);
1893 // Remember this binding.
1894 NamedValues[VarName] = Alloca;
1897 // Codegen the body, now that all vars are in scope.
1898 Value *BodyVal = Body-&gt;Codegen();
1899 if (BodyVal == 0) return 0;
1901 // Pop all our variables from scope.
1902 for (unsigned i = 0, e = VarNames.size(); i != e; ++i)
1903 NamedValues[VarNames[i].first] = OldBindings[i];
1905 // Return the body computation.
1906 return BodyVal;
1910 Function *PrototypeAST::Codegen() {
1911 // Make the function type: double(double,double) etc.
1912 std::vector&lt;const Type*&gt; Doubles(Args.size(), Type::DoubleTy);
1913 FunctionType *FT = FunctionType::get(Type::DoubleTy, Doubles, false);
1915 Function *F = Function::Create(FT, Function::ExternalLinkage, Name, TheModule);
1917 // If F conflicted, there was already something named 'Name'. If it has a
1918 // body, don't allow redefinition or reextern.
1919 if (F-&gt;getName() != Name) {
1920 // Delete the one we just made and get the existing one.
1921 F-&gt;eraseFromParent();
1922 F = TheModule-&gt;getFunction(Name);
1924 // If F already has a body, reject this.
1925 if (!F-&gt;empty()) {
1926 ErrorF("redefinition of function");
1927 return 0;
1930 // If F took a different number of args, reject.
1931 if (F-&gt;arg_size() != Args.size()) {
1932 ErrorF("redefinition of function with different # args");
1933 return 0;
1937 // Set names for all arguments.
1938 unsigned Idx = 0;
1939 for (Function::arg_iterator AI = F-&gt;arg_begin(); Idx != Args.size();
1940 ++AI, ++Idx)
1941 AI-&gt;setName(Args[Idx]);
1943 return F;
1946 /// CreateArgumentAllocas - Create an alloca for each argument and register the
1947 /// argument in the symbol table so that references to it will succeed.
1948 void PrototypeAST::CreateArgumentAllocas(Function *F) {
1949 Function::arg_iterator AI = F-&gt;arg_begin();
1950 for (unsigned Idx = 0, e = Args.size(); Idx != e; ++Idx, ++AI) {
1951 // Create an alloca for this variable.
1952 AllocaInst *Alloca = CreateEntryBlockAlloca(F, Args[Idx]);
1954 // Store the initial value into the alloca.
1955 Builder.CreateStore(AI, Alloca);
1957 // Add arguments to variable symbol table.
1958 NamedValues[Args[Idx]] = Alloca;
1963 Function *FunctionAST::Codegen() {
1964 NamedValues.clear();
1966 Function *TheFunction = Proto-&gt;Codegen();
1967 if (TheFunction == 0)
1968 return 0;
1970 // If this is an operator, install it.
1971 if (Proto-&gt;isBinaryOp())
1972 BinopPrecedence[Proto-&gt;getOperatorName()] = Proto-&gt;getBinaryPrecedence();
1974 // Create a new basic block to start insertion into.
1975 BasicBlock *BB = BasicBlock::Create("entry", TheFunction);
1976 Builder.SetInsertPoint(BB);
1978 // Add all arguments to the symbol table and create their allocas.
1979 Proto-&gt;CreateArgumentAllocas(TheFunction);
1981 if (Value *RetVal = Body-&gt;Codegen()) {
1982 // Finish off the function.
1983 Builder.CreateRet(RetVal);
1985 // Validate the generated code, checking for consistency.
1986 verifyFunction(*TheFunction);
1988 // Optimize the function.
1989 TheFPM-&gt;run(*TheFunction);
1991 return TheFunction;
1994 // Error reading body, remove function.
1995 TheFunction-&gt;eraseFromParent();
1997 if (Proto-&gt;isBinaryOp())
1998 BinopPrecedence.erase(Proto-&gt;getOperatorName());
1999 return 0;
2002 //===----------------------------------------------------------------------===//
2003 // Top-Level parsing and JIT Driver
2004 //===----------------------------------------------------------------------===//
2006 static ExecutionEngine *TheExecutionEngine;
2008 static void HandleDefinition() {
2009 if (FunctionAST *F = ParseDefinition()) {
2010 if (Function *LF = F-&gt;Codegen()) {
2011 fprintf(stderr, "Read function definition:");
2012 LF-&gt;dump();
2014 } else {
2015 // Skip token for error recovery.
2016 getNextToken();
2020 static void HandleExtern() {
2021 if (PrototypeAST *P = ParseExtern()) {
2022 if (Function *F = P-&gt;Codegen()) {
2023 fprintf(stderr, "Read extern: ");
2024 F-&gt;dump();
2026 } else {
2027 // Skip token for error recovery.
2028 getNextToken();
2032 static void HandleTopLevelExpression() {
2033 // Evaluate a top level expression into an anonymous function.
2034 if (FunctionAST *F = ParseTopLevelExpr()) {
2035 if (Function *LF = F-&gt;Codegen()) {
2036 // JIT the function, returning a function pointer.
2037 void *FPtr = TheExecutionEngine-&gt;getPointerToFunction(LF);
2039 // Cast it to the right type (takes no arguments, returns a double) so we
2040 // can call it as a native function.
2041 double (*FP)() = (double (*)())FPtr;
2042 fprintf(stderr, "Evaluated to %f\n", FP());
2044 } else {
2045 // Skip token for error recovery.
2046 getNextToken();
2050 /// top ::= definition | external | expression | ';'
2051 static void MainLoop() {
2052 while (1) {
2053 fprintf(stderr, "ready&gt; ");
2054 switch (CurTok) {
2055 case tok_eof: return;
2056 case ';': getNextToken(); break; // ignore top level semicolons.
2057 case tok_def: HandleDefinition(); break;
2058 case tok_extern: HandleExtern(); break;
2059 default: HandleTopLevelExpression(); break;
2066 //===----------------------------------------------------------------------===//
2067 // "Library" functions that can be "extern'd" from user code.
2068 //===----------------------------------------------------------------------===//
2070 /// putchard - putchar that takes a double and returns 0.
2071 extern "C"
2072 double putchard(double X) {
2073 putchar((char)X);
2074 return 0;
2077 /// printd - printf that takes a double prints it as "%f\n", returning 0.
2078 extern "C"
2079 double printd(double X) {
2080 printf("%f\n", X);
2081 return 0;
2084 //===----------------------------------------------------------------------===//
2085 // Main driver code.
2086 //===----------------------------------------------------------------------===//
2088 int main() {
2089 // Install standard binary operators.
2090 // 1 is lowest precedence.
2091 BinopPrecedence['='] = 2;
2092 BinopPrecedence['&lt;'] = 10;
2093 BinopPrecedence['+'] = 20;
2094 BinopPrecedence['-'] = 20;
2095 BinopPrecedence['*'] = 40; // highest.
2097 // Prime the first token.
2098 fprintf(stderr, "ready&gt; ");
2099 getNextToken();
2101 // Make the module, which holds all the code.
2102 TheModule = new Module("my cool jit");
2104 // Create the JIT.
2105 TheExecutionEngine = ExecutionEngine::create(TheModule);
2108 ExistingModuleProvider OurModuleProvider(TheModule);
2109 FunctionPassManager OurFPM(&amp;OurModuleProvider);
2111 // Set up the optimizer pipeline. Start with registering info about how the
2112 // target lays out data structures.
2113 OurFPM.add(new TargetData(*TheExecutionEngine-&gt;getTargetData()));
2114 // Promote allocas to registers.
2115 OurFPM.add(createPromoteMemoryToRegisterPass());
2116 // Do simple "peephole" optimizations and bit-twiddling optzns.
2117 OurFPM.add(createInstructionCombiningPass());
2118 // Reassociate expressions.
2119 OurFPM.add(createReassociatePass());
2120 // Eliminate Common SubExpressions.
2121 OurFPM.add(createGVNPass());
2122 // Simplify the control flow graph (deleting unreachable blocks, etc).
2123 OurFPM.add(createCFGSimplificationPass());
2125 // Set the global so the code gen can use this.
2126 TheFPM = &amp;OurFPM;
2128 // Run the main "interpreter loop" now.
2129 MainLoop();
2131 TheFPM = 0;
2133 // Print out all of the generated code.
2134 TheModule-&gt;dump();
2136 } // Free module provider (and thus the module) and pass manager.
2138 return 0;
2140 </pre>
2141 </div>
2143 <a href="LangImpl8.html">Next: Conclusion and other useful LLVM tidbits</a>
2144 </div>
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