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diff --git a/docs/tutorial/OCamlLangImpl5.html b/docs/tutorial/OCamlLangImpl5.html new file mode 100644 index 00000000000..feeed6a5337 --- /dev/null +++ b/docs/tutorial/OCamlLangImpl5.html @@ -0,0 +1,1560 @@ +<!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"> + <meta name="author" content="Erick Tryzelaar"> + <link rel="stylesheet" href="../_static/llvm.css" type="text/css"> +</head> + +<body> + +<h1>Kaleidoscope: Extending the Language: Control Flow</h1> + +<ul> +<li><a href="index.html">Up to Tutorial Index</a></li> +<li>Chapter 5 + <ol> + <li><a href="#intro">Chapter 5 Introduction</a></li> + <li><a href="#ifthen">If/Then/Else</a> + <ol> + <li><a href="#iflexer">Lexer Extensions</a></li> + <li><a href="#ifast">AST Extensions</a></li> + <li><a href="#ifparser">Parser Extensions</a></li> + <li><a href="#ifir">LLVM IR</a></li> + <li><a href="#ifcodegen">Code Generation</a></li> + </ol> + </li> + <li><a href="#for">'for' Loop Expression</a> + <ol> + <li><a href="#forlexer">Lexer Extensions</a></li> + <li><a href="#forast">AST Extensions</a></li> + <li><a href="#forparser">Parser Extensions</a></li> + <li><a href="#forir">LLVM IR</a></li> + <li><a href="#forcodegen">Code Generation</a></li> + </ol> + </li> + <li><a href="#code">Full Code Listing</a></li> + </ol> +</li> +<li><a href="OCamlLangImpl6.html">Chapter 6</a>: Extending the Language: +User-defined Operators</li> +</ul> + +<div class="doc_author"> + <p> + Written by <a href="mailto:sabre@nondot.org">Chris Lattner</a> + and <a href="mailto:idadesub@users.sourceforge.net">Erick Tryzelaar</a> + </p> +</div> + +<!-- *********************************************************************** --> +<h2><a name="intro">Chapter 5 Introduction</a></h2> +<!-- *********************************************************************** --> + +<div> + +<p>Welcome to Chapter 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, followed 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 'for' loop.</p> + +</div> + +<!-- *********************************************************************** --> +<h2><a name="ifthen">If/Then/Else</a></h2> +<!-- *********************************************************************** --> + +<div> + +<p> +Extending Kaleidoscope to support if/then/else is quite straightforward. 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 add 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 < 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 evaluates the +condition to a boolean equality value: 0.0 is considered to be false and +everything else is considered to be 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> + +<!-- ======================================================================= --> +<h4><a name="iflexer">Lexer Extensions for If/Then/Else</a></h4> +<!-- ======================================================================= --> + + +<div> + +<p>The lexer extensions are straightforward. First we add new variants +for the relevant tokens:</p> + +<div class="doc_code"> +<pre> + (* control *) + | If | Then | Else | For | In +</pre> +</div> + +<p>Once we have that, we recognize the new keywords in the lexer. This is pretty simple +stuff:</p> + +<div class="doc_code"> +<pre> + ... + match Buffer.contents buffer with + | "def" -> [< 'Token.Def; stream >] + | "extern" -> [< 'Token.Extern; stream >] + | "if" -> [< 'Token.If; stream >] + | "then" -> [< 'Token.Then; stream >] + | "else" -> [< 'Token.Else; stream >] + | "for" -> [< 'Token.For; stream >] + | "in" -> [< 'Token.In; stream >] + | id -> [< 'Token.Ident id; stream >] +</pre> +</div> + +</div> + +<!-- ======================================================================= --> +<h4><a name="ifast">AST Extensions for If/Then/Else</a></h4> +<!-- ======================================================================= --> + +<div> + +<p>To represent the new expression we add a new AST variant for it:</p> + +<div class="doc_code"> +<pre> +type expr = + ... + (* variant for if/then/else. *) + | If of expr * expr * expr +</pre> +</div> + +<p>The AST variant just has pointers to the various subexpressions.</p> + +</div> + +<!-- ======================================================================= --> +<h4><a name="ifparser">Parser Extensions for If/Then/Else</a></h4> +<!-- ======================================================================= --> + +<div> + +<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 straightforward. First we +define a new parsing function:</p> + +<div class="doc_code"> +<pre> +let rec parse_primary = parser + ... + (* ifexpr ::= 'if' expr 'then' expr 'else' expr *) + | [< 'Token.If; c=parse_expr; + 'Token.Then ?? "expected 'then'"; t=parse_expr; + 'Token.Else ?? "expected 'else'"; e=parse_expr >] -> + Ast.If (c, t, e) +</pre> +</div> + +<p>Next we hook it up as a primary expression:</p> + +<div class="doc_code"> +<pre> +let rec parse_primary = parser + ... + (* ifexpr ::= 'if' expr 'then' expr 'else' expr *) + | [< 'Token.If; c=parse_expr; + 'Token.Then ?? "expected 'then'"; t=parse_expr; + 'Token.Else ?? "expected 'else'"; e=parse_expr >] -> + Ast.If (c, t, e) +</pre> +</div> + +</div> + +<!-- ======================================================================= --> +<h4><a name="ifir">LLVM IR for If/Then/Else</a></h4> +<!-- ======================================================================= --> + +<div> + +<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 thoroughly described in previous chapters. +</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 < 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> + +<div style="text-align: center"><img src="LangImpl5-cfg.png" alt="Example CFG" width="423" +height="315"></div> + +<p>Another way to get this is to call "<tt>Llvm_analysis.view_function_cfg +f</tt>" or "<tt>Llvm_analysis.view_function_cfg_only f</tt>" (where <tt>f</tt> +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>Getting 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 cases.</p> + +<p>Once the then/else blocks are finished executing, they both branch back to the +'ifcont' 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 "Oh 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 for 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>In <a href="OCamlLangImpl7.html">Chapter 7</a> of 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 this case. 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> + +<!-- ======================================================================= --> +<h4><a name="ifcodegen">Code Generation for If/Then/Else</a></h4> +<!-- ======================================================================= --> + +<div> + +<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> +let rec codegen_expr = function + ... + | Ast.If (cond, then_, else_) -> + let cond = codegen_expr cond in + + (* Convert condition to a bool by comparing equal to 0.0 *) + let zero = const_float double_type 0.0 in + let cond_val = build_fcmp Fcmp.One cond zero "ifcond" builder in +</pre> +</div> + +<p>This code is straightforward 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> + (* Grab the first block so that we might later add the conditional branch + * to it at the end of the function. *) + let start_bb = insertion_block builder in + let the_function = block_parent start_bb in + + let then_bb = append_block context "then" the_function in + position_at_end then_bb builder; +</pre> +</div> + +<p> +As opposed to the <a href="LangImpl5.html">C++ tutorial</a>, we have to build +our basic blocks bottom up since we can't have dangling BasicBlocks. We start +off by saving a pointer to the first block (which might not be the entry +block), which we'll need to build a conditional branch later. We do this by +asking the <tt>builder</tt> for the current BasicBlock. The fourth line +gets the current Function object that is being built. It gets this by the +<tt>start_bb</tt> for its "parent" (the function it is currently embedded +into).</p> + +<p>Once it has that, it creates one block. It is automatically appended into +the function's list of blocks.</p> + +<div class="doc_code"> +<pre> + (* Emit 'then' value. *) + position_at_end then_bb builder; + let then_val = codegen_expr then_ in + + (* Codegen of 'then' can change the current block, update then_bb for the + * phi. We create a new name because one is used for the phi node, and the + * other is used for the conditional branch. *) + let new_then_bb = insertion_block builder in +</pre> +</div> + +<p>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.</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 entry 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' value. *) + let else_bb = append_block context "else" the_function in + position_at_end else_bb builder; + let else_val = codegen_expr else_ in + + (* Codegen of 'else' can change the current block, update else_bb for the + * phi. *) + let new_else_bb = insertion_block builder in +</pre> +</div> + +<p>Code generation for the 'else' block is basically identical to codegen for +the 'then' block.</p> + +<div class="doc_code"> +<pre> + (* Emit merge block. *) + let merge_bb = append_block context "ifcont" the_function in + position_at_end merge_bb builder; + let incoming = [(then_val, new_then_bb); (else_val, new_else_bb)] in + let phi = build_phi incoming "iftmp" builder in +</pre> +</div> + +<p>The first two lines here are now familiar: the first adds the "merge" block +to the Function object. 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> + +<div class="doc_code"> +<pre> + (* Return to the start block to add the conditional branch. *) + position_at_end start_bb builder; + ignore (build_cond_br cond_val then_bb else_bb builder); +</pre> +</div> + +<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 +IRBuilder, so it is still inserting into the block that the condition +went into. This is why we needed to save the "start" block.</p> + +<div class="doc_code"> +<pre> + (* Set a unconditional branch at the end of the 'then' block and the + * 'else' block to the 'merge' block. *) + position_at_end new_then_bb builder; ignore (build_br merge_bb builder); + position_at_end new_else_bb builder; ignore (build_br merge_bb builder); + + (* Finally, set the builder to the end of the merge block. *) + position_at_end merge_bb builder; + + phi +</pre> +</div> + +<p>To finish off the blocks, 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>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 execute 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> + +<!-- *********************************************************************** --> +<h2><a name="for">'for' Loop Expression</a></h2> +<!-- *********************************************************************** --> + +<div> + +<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> + extern putchard(char); + def printstar(n) + for i = 1, i < n, 1.0 in + putchard(42); # ascii 42 = '*' + + # print 100 '*' characters + printstar(100); +</pre> +</div> + +<p>This expression defines a new variable ("i" in this case) which iterates from +a starting value, while the condition ("i < n" 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> + +<!-- ======================================================================= --> +<h4><a name="forlexer">Lexer Extensions for the 'for' Loop</a></h4> +<!-- ======================================================================= --> + +<div> + +<p>The lexer extensions are the same sort of thing as for if/then/else:</p> + +<div class="doc_code"> +<pre> + ... in Token.token ... + (* control *) + | If | Then | Else + <b>| For | In</b> + + ... in Lexer.lex_ident... + match Buffer.contents buffer with + | "def" -> [< 'Token.Def; stream >] + | "extern" -> [< 'Token.Extern; stream >] + | "if" -> [< 'Token.If; stream >] + | "then" -> [< 'Token.Then; stream >] + | "else" -> [< 'Token.Else; stream >] + <b>| "for" -> [< 'Token.For; stream >] + | "in" -> [< 'Token.In; stream >]</b> + | id -> [< 'Token.Ident id; stream >] +</pre> +</div> + +</div> + +<!-- ======================================================================= --> +<h4><a name="forast">AST Extensions for the 'for' Loop</a></h4> +<!-- ======================================================================= --> + +<div> + +<p>The AST variant is just as simple. It basically boils down to capturing +the variable name and the constituent expressions in the node.</p> + +<div class="doc_code"> +<pre> +type expr = + ... + (* variant for for/in. *) + | For of string * expr * expr * expr option * expr +</pre> +</div> + +</div> + +<!-- ======================================================================= --> +<h4><a name="forparser">Parser Extensions for the 'for' Loop</a></h4> +<!-- ======================================================================= --> + +<div> + +<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> +let rec parse_primary = parser + ... + (* forexpr + ::= 'for' identifier '=' expr ',' expr (',' expr)? 'in' expression *) + | [< 'Token.For; + 'Token.Ident id ?? "expected identifier after for"; + 'Token.Kwd '=' ?? "expected '=' after for"; + stream >] -> + begin parser + | [< + start=parse_expr; + 'Token.Kwd ',' ?? "expected ',' after for"; + end_=parse_expr; + stream >] -> + let step = + begin parser + | [< 'Token.Kwd ','; step=parse_expr >] -> Some step + | [< >] -> None + end stream + in + begin parser + | [< 'Token.In; body=parse_expr >] -> + Ast.For (id, start, end_, step, body) + | [< >] -> + raise (Stream.Error "expected 'in' after for") + end stream + | [< >] -> + raise (Stream.Error "expected '=' after for") + end stream +</pre> +</div> + +</div> + +<!-- ======================================================================= --> +<h4><a name="forir">LLVM IR for the 'for' Loop</a></h4> +<!-- ======================================================================= --> + +<div> + +<p>Now we get to the good part: the LLVM IR we want to generate for this thing. +With the simple example above, we get this LLVM IR (note that this dump is +generated with optimizations disabled for clarity): +</p> + +<div class="doc_code"> +<pre> +declare double @putchard(double) + +define double @printstar(double %n) { +entry: + ; initial value = 1.0 (inlined into phi) + br label %loop + +loop: ; preds = %loop, %entry + %i = phi double [ 1.000000e+00, %entry ], [ %nextvar, %loop ] + ; body + %calltmp = call double @putchard(double 4.200000e+01) + ; increment + %nextvar = fadd double %i, 1.000000e+00 + + ; termination test + %cmptmp = fcmp ult double %i, %n + %booltmp = uitofp i1 %cmptmp to double + %loopcond = fcmp one double %booltmp, 0.000000e+00 + br i1 %loopcond, label %loop, label %afterloop + +afterloop: ; preds = %loop + ; loop always returns 0.0 + ret double 0.000000e+00 +} +</pre> +</div> + +<p>This loop contains all the same constructs we saw before: a phi node, several +expressions, and some basic blocks. Lets see how this fits together.</p> + +</div> + +<!-- ======================================================================= --> +<h4><a name="forcodegen">Code Generation for the 'for' Loop</a></h4> +<!-- ======================================================================= --> + +<div> + +<p>The first part of Codegen is very simple: we just output the start expression +for the loop value:</p> + +<div class="doc_code"> +<pre> +let rec codegen_expr = function + ... + | Ast.For (var_name, start, end_, step, body) -> + (* Emit the start code first, without 'variable' in scope. *) + let start_val = codegen_expr start in +</pre> +</div> + +<p>With this out of the way, the next step is to set up the LLVM basic block +for the start of the loop body. In the case above, the whole loop body is one +block, but remember that the body code itself could consist of multiple blocks +(e.g. if it contains an if/then/else or a for/in expression).</p> + +<div class="doc_code"> +<pre> + (* Make the new basic block for the loop header, inserting after current + * block. *) + let preheader_bb = insertion_block builder in + let the_function = block_parent preheader_bb in + let loop_bb = append_block context "loop" the_function in + + (* Insert an explicit fall through from the current block to the + * loop_bb. *) + ignore (build_br loop_bb builder); +</pre> +</div> + +<p>This code is similar to what we saw for if/then/else. Because we will need +it to create the Phi node, we remember the block that falls through into the +loop. Once we have that, we create the actual block that starts the loop and +create an unconditional branch for the fall-through between the two blocks.</p> + +<div class="doc_code"> +<pre> + (* Start insertion in loop_bb. *) + position_at_end loop_bb builder; + + (* Start the PHI node with an entry for start. *) + let variable = build_phi [(start_val, preheader_bb)] var_name builder in +</pre> +</div> + +<p>Now that the "preheader" for the loop is set up, we switch to emitting code +for the loop body. To begin with, we move the insertion point and create the +PHI node for the loop induction variable. Since we already know the incoming +value for the starting value, we add it to the Phi node. Note that the Phi will +eventually get a second value for the backedge, but we can't set it up yet +(because it doesn't exist!).</p> + +<div class="doc_code"> +<pre> + (* 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. *) + let old_val = + try Some (Hashtbl.find named_values var_name) with Not_found -> None + in + Hashtbl.add named_values var_name 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 *) + ignore (codegen_expr body); +</pre> +</div> + +<p>Now the code starts to get more interesting. Our 'for' loop introduces a new +variable to the symbol table. This means that our symbol table can now contain +either function arguments or loop variables. To handle this, before we codegen +the body of the loop, we add the loop variable as the current value for its +name. Note that it is possible that there is a variable of the same name in the +outer scope. It would be easy to make this an error (emit an error and return +null if there is already an entry for VarName) but we choose to allow shadowing +of variables. In order to handle this correctly, we remember the Value that +we are potentially shadowing in <tt>old_val</tt> (which will be None if there is +no shadowed variable).</p> + +<p>Once the loop variable is set into the symbol table, the code recursively +codegen's the body. This allows the body to use the loop variable: any +references to it will naturally find it in the symbol table.</p> + +<div class="doc_code"> +<pre> + (* Emit the step value. *) + let step_val = + match step with + | Some step -> codegen_expr step + (* If not specified, use 1.0. *) + | None -> const_float double_type 1.0 + in + + let next_var = build_add variable step_val "nextvar" builder in +</pre> +</div> + +<p>Now that the body is emitted, we compute the next value of the iteration +variable by adding the step value, or 1.0 if it isn't present. +'<tt>next_var</tt>' will be the value of the loop variable on the next iteration +of the loop.</p> + +<div class="doc_code"> +<pre> + (* Compute the end condition. *) + let end_cond = codegen_expr end_ in + + (* Convert condition to a bool by comparing equal to 0.0. *) + let zero = const_float double_type 0.0 in + let end_cond = build_fcmp Fcmp.One end_cond zero "loopcond" builder in +</pre> +</div> + +<p>Finally, we evaluate the exit value of the loop, to determine whether the +loop should exit. This mirrors the condition evaluation for the if/then/else +statement.</p> + +<div class="doc_code"> +<pre> + (* Create the "after loop" block and insert it. *) + let loop_end_bb = insertion_block builder in + let after_bb = append_block context "afterloop" the_function in + + (* Insert the conditional branch into the end of loop_end_bb. *) + ignore (build_cond_br end_cond loop_bb after_bb builder); + + (* Any new code will be inserted in after_bb. *) + position_at_end after_bb builder; +</pre> +</div> + +<p>With the code for the body of the loop complete, we just need to finish up +the control flow for it. This code remembers the end block (for the phi node), then creates the block for the loop exit ("afterloop"). Based on the value of the +exit condition, it creates a conditional branch that chooses between executing +the loop again and exiting the loop. Any future code is emitted in the +"afterloop" block, so it sets the insertion position to it.</p> + +<div class="doc_code"> +<pre> + (* Add a new entry to the PHI node for the backedge. *) + add_incoming (next_var, loop_end_bb) variable; + + (* Restore the unshadowed variable. *) + begin match old_val with + | Some old_val -> Hashtbl.add named_values var_name old_val + | None -> () + end; + + (* for expr always returns 0.0. *) + const_null double_type +</pre> +</div> + +<p>The final code handles various cleanups: now that we have the +"<tt>next_var</tt>" value, we can add the incoming value to the loop PHI node. +After that, we remove the loop variable from the symbol table, so that it isn't +in scope after the for loop. Finally, code generation of the for loop always +returns 0.0, so that is what we return from <tt>Codegen.codegen_expr</tt>.</p> + +<p>With this, we conclude the "adding control flow to Kaleidoscope" chapter of +the tutorial. In this chapter we added two control flow constructs, and used +them to motivate a couple of aspects of the LLVM IR that are important for +front-end implementors to know. In the next chapter of our saga, we will get +a bit crazier and add <a href="OCamlLangImpl6.html">user-defined operators</a> +to our poor innocent language.</p> + +</div> + +</div> + +<!-- *********************************************************************** --> +<h2><a name="code">Full Code Listing</a></h2> +<!-- *********************************************************************** --> + +<div> + +<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 +ocamlbuild toy.byte +# Run +./toy.byte +</pre> +</div> + +<p>Here is the code:</p> + +<dl> +<dt>_tags:</dt> +<dd class="doc_code"> +<pre> +<{lexer,parser}.ml>: use_camlp4, pp(camlp4of) +<*.{byte,native}>: g++, use_llvm, use_llvm_analysis +<*.{byte,native}>: use_llvm_executionengine, use_llvm_target +<*.{byte,native}>: use_llvm_scalar_opts, use_bindings +</pre> +</dd> + +<dt>myocamlbuild.ml:</dt> +<dd class="doc_code"> +<pre> +open Ocamlbuild_plugin;; + +ocaml_lib ~extern:true "llvm";; +ocaml_lib ~extern:true "llvm_analysis";; +ocaml_lib ~extern:true "llvm_executionengine";; +ocaml_lib ~extern:true "llvm_target";; +ocaml_lib ~extern:true "llvm_scalar_opts";; + +flag ["link"; "ocaml"; "g++"] (S[A"-cc"; A"g++"]);; +dep ["link"; "ocaml"; "use_bindings"] ["bindings.o"];; +</pre> +</dd> + +<dt>token.ml:</dt> +<dd class="doc_code"> +<pre> +(*===----------------------------------------------------------------------=== + * Lexer Tokens + *===----------------------------------------------------------------------===*) + +(* The lexer returns these 'Kwd' if it is an unknown character, otherwise one of + * these others for known things. *) +type token = + (* commands *) + | Def | Extern + + (* primary *) + | Ident of string | Number of float + + (* unknown *) + | Kwd of char + + (* control *) + | If | Then | Else + | For | In +</pre> +</dd> + +<dt>lexer.ml:</dt> +<dd class="doc_code"> +<pre> +(*===----------------------------------------------------------------------=== + * Lexer + *===----------------------------------------------------------------------===*) + +let rec lex = parser + (* Skip any whitespace. *) + | [< ' (' ' | '\n' | '\r' | '\t'); stream >] -> lex stream + + (* identifier: [a-zA-Z][a-zA-Z0-9] *) + | [< ' ('A' .. 'Z' | 'a' .. 'z' as c); stream >] -> + let buffer = Buffer.create 1 in + Buffer.add_char buffer c; + lex_ident buffer stream + + (* number: [0-9.]+ *) + | [< ' ('0' .. '9' as c); stream >] -> + let buffer = Buffer.create 1 in + Buffer.add_char buffer c; + lex_number buffer stream + + (* Comment until end of line. *) + | [< ' ('#'); stream >] -> + lex_comment stream + + (* Otherwise, just return the character as its ascii value. *) + | [< 'c; stream >] -> + [< 'Token.Kwd c; lex stream >] + + (* end of stream. *) + | [< >] -> [< >] + +and lex_number buffer = parser + | [< ' ('0' .. '9' | '.' as c); stream >] -> + Buffer.add_char buffer c; + lex_number buffer stream + | [< stream=lex >] -> + [< 'Token.Number (float_of_string (Buffer.contents buffer)); stream >] + +and lex_ident buffer = parser + | [< ' ('A' .. 'Z' | 'a' .. 'z' | '0' .. '9' as c); stream >] -> + Buffer.add_char buffer c; + lex_ident buffer stream + | [< stream=lex >] -> + match Buffer.contents buffer with + | "def" -> [< 'Token.Def; stream >] + | "extern" -> [< 'Token.Extern; stream >] + | "if" -> [< 'Token.If; stream >] + | "then" -> [< 'Token.Then; stream >] + | "else" -> [< 'Token.Else; stream >] + | "for" -> [< 'Token.For; stream >] + | "in" -> [< 'Token.In; stream >] + | id -> [< 'Token.Ident id; stream >] + +and lex_comment = parser + | [< ' ('\n'); stream=lex >] -> stream + | [< 'c; e=lex_comment >] -> e + | [< >] -> [< >] +</pre> +</dd> + +<dt>ast.ml:</dt> +<dd class="doc_code"> +<pre> +(*===----------------------------------------------------------------------=== + * Abstract Syntax Tree (aka Parse Tree) + *===----------------------------------------------------------------------===*) + +(* expr - Base type for all expression nodes. *) +type expr = + (* variant for numeric literals like "1.0". *) + | Number of float + + (* variant for referencing a variable, like "a". *) + | Variable of string + + (* variant for a binary operator. *) + | Binary of char * expr * expr + + (* variant for function calls. *) + | Call of string * expr array + + (* variant for if/then/else. *) + | If of expr * expr * expr + + (* variant for for/in. *) + | For of string * expr * expr * expr option * expr + +(* proto - This type represents the "prototype" for a function, which captures + * its name, and its argument names (thus implicitly the number of arguments the + * function takes). *) +type proto = Prototype of string * string array + +(* func - This type represents a function definition itself. *) +type func = Function of proto * expr +</pre> +</dd> + +<dt>parser.ml:</dt> +<dd class="doc_code"> +<pre> +(*===---------------------------------------------------------------------=== + * Parser + *===---------------------------------------------------------------------===*) + +(* binop_precedence - This holds the precedence for each binary operator that is + * defined *) +let binop_precedence:(char, int) Hashtbl.t = Hashtbl.create 10 + +(* precedence - Get the precedence of the pending binary operator token. *) +let precedence c = try Hashtbl.find binop_precedence c with Not_found -> -1 + +(* primary + * ::= identifier + * ::= numberexpr + * ::= parenexpr + * ::= ifexpr + * ::= forexpr *) +let rec parse_primary = parser + (* numberexpr ::= number *) + | [< 'Token.Number n >] -> Ast.Number n + + (* parenexpr ::= '(' expression ')' *) + | [< 'Token.Kwd '('; e=parse_expr; 'Token.Kwd ')' ?? "expected ')'" >] -> e + + (* identifierexpr + * ::= identifier + * ::= identifier '(' argumentexpr ')' *) + | [< 'Token.Ident id; stream >] -> + let rec parse_args accumulator = parser + | [< e=parse_expr; stream >] -> + begin parser + | [< 'Token.Kwd ','; e=parse_args (e :: accumulator) >] -> e + | [< >] -> e :: accumulator + end stream + | [< >] -> accumulator + in + let rec parse_ident id = parser + (* Call. *) + | [< 'Token.Kwd '('; + args=parse_args []; + 'Token.Kwd ')' ?? "expected ')'">] -> + Ast.Call (id, Array.of_list (List.rev args)) + + (* Simple variable ref. *) + | [< >] -> Ast.Variable id + in + parse_ident id stream + + (* ifexpr ::= 'if' expr 'then' expr 'else' expr *) + | [< 'Token.If; c=parse_expr; + 'Token.Then ?? "expected 'then'"; t=parse_expr; + 'Token.Else ?? "expected 'else'"; e=parse_expr >] -> + Ast.If (c, t, e) + + (* forexpr + ::= 'for' identifier '=' expr ',' expr (',' expr)? 'in' expression *) + | [< 'Token.For; + 'Token.Ident id ?? "expected identifier after for"; + 'Token.Kwd '=' ?? "expected '=' after for"; + stream >] -> + begin parser + | [< + start=parse_expr; + 'Token.Kwd ',' ?? "expected ',' after for"; + end_=parse_expr; + stream >] -> + let step = + begin parser + | [< 'Token.Kwd ','; step=parse_expr >] -> Some step + | [< >] -> None + end stream + in + begin parser + | [< 'Token.In; body=parse_expr >] -> + Ast.For (id, start, end_, step, body) + | [< >] -> + raise (Stream.Error "expected 'in' after for") + end stream + | [< >] -> + raise (Stream.Error "expected '=' after for") + end stream + + | [< >] -> raise (Stream.Error "unknown token when expecting an expression.") + +(* binoprhs + * ::= ('+' primary)* *) +and parse_bin_rhs expr_prec lhs stream = + match Stream.peek stream with + (* If this is a binop, find its precedence. *) + | Some (Token.Kwd c) when Hashtbl.mem binop_precedence c -> + let token_prec = precedence c in + + (* If this is a binop that binds at least as tightly as the current binop, + * consume it, otherwise we are done. *) + if token_prec < expr_prec then lhs else begin + (* Eat the binop. *) + Stream.junk stream; + + (* Parse the primary expression after the binary operator. *) + let rhs = parse_primary stream in + + (* Okay, we know this is a binop. *) + let rhs = + match Stream.peek stream with + | Some (Token.Kwd c2) -> + (* If BinOp binds less tightly with rhs than the operator after + * rhs, let the pending operator take rhs as its lhs. *) + let next_prec = precedence c2 in + if token_prec < next_prec + then parse_bin_rhs (token_prec + 1) rhs stream + else rhs + | _ -> rhs + in + + (* Merge lhs/rhs. *) + let lhs = Ast.Binary (c, lhs, rhs) in + parse_bin_rhs expr_prec lhs stream + end + | _ -> lhs + +(* expression + * ::= primary binoprhs *) +and parse_expr = parser + | [< lhs=parse_primary; stream >] -> parse_bin_rhs 0 lhs stream + +(* prototype + * ::= id '(' id* ')' *) +let parse_prototype = + let rec parse_args accumulator = parser + | [< 'Token.Ident id; e=parse_args (id::accumulator) >] -> e + | [< >] -> accumulator + in + + parser + | [< 'Token.Ident id; + 'Token.Kwd '(' ?? "expected '(' in prototype"; + args=parse_args []; + 'Token.Kwd ')' ?? "expected ')' in prototype" >] -> + (* success. *) + Ast.Prototype (id, Array.of_list (List.rev args)) + + | [< >] -> + raise (Stream.Error "expected function name in prototype") + +(* definition ::= 'def' prototype expression *) +let parse_definition = parser + | [< 'Token.Def; p=parse_prototype; e=parse_expr >] -> + Ast.Function (p, e) + +(* toplevelexpr ::= expression *) +let parse_toplevel = parser + | [< e=parse_expr >] -> + (* Make an anonymous proto. *) + Ast.Function (Ast.Prototype ("", [||]), e) + +(* external ::= 'extern' prototype *) +let parse_extern = parser + | [< 'Token.Extern; e=parse_prototype >] -> e +</pre> +</dd> + +<dt>codegen.ml:</dt> +<dd class="doc_code"> +<pre> +(*===----------------------------------------------------------------------=== + * Code Generation + *===----------------------------------------------------------------------===*) + +open Llvm + +exception Error of string + +let context = global_context () +let the_module = create_module context "my cool jit" +let builder = builder context +let named_values:(string, llvalue) Hashtbl.t = Hashtbl.create 10 +let double_type = double_type context + +let rec codegen_expr = function + | Ast.Number n -> const_float double_type n + | Ast.Variable name -> + (try Hashtbl.find named_values name with + | Not_found -> raise (Error "unknown variable name")) + | Ast.Binary (op, lhs, rhs) -> + let lhs_val = codegen_expr lhs in + let rhs_val = codegen_expr rhs in + begin + match op with + | '+' -> build_add lhs_val rhs_val "addtmp" builder + | '-' -> build_sub lhs_val rhs_val "subtmp" builder + | '*' -> build_mul lhs_val rhs_val "multmp" builder + | '<' -> + (* Convert bool 0/1 to double 0.0 or 1.0 *) + let i = build_fcmp Fcmp.Ult lhs_val rhs_val "cmptmp" builder in + build_uitofp i double_type "booltmp" builder + | _ -> raise (Error "invalid binary operator") + end + | Ast.Call (callee, args) -> + (* Look up the name in the module table. *) + let callee = + match lookup_function callee the_module with + | Some callee -> callee + | None -> raise (Error "unknown function referenced") + in + let params = params callee in + + (* If argument mismatch error. *) + if Array.length params == Array.length args then () else + raise (Error "incorrect # arguments passed"); + let args = Array.map codegen_expr args in + build_call callee args "calltmp" builder + | Ast.If (cond, then_, else_) -> + let cond = codegen_expr cond in + + (* Convert condition to a bool by comparing equal to 0.0 *) + let zero = const_float double_type 0.0 in + let cond_val = build_fcmp Fcmp.One cond zero "ifcond" builder in + + (* Grab the first block so that we might later add the conditional branch + * to it at the end of the function. *) + let start_bb = insertion_block builder in + let the_function = block_parent start_bb in + + let then_bb = append_block context "then" the_function in + + (* Emit 'then' value. *) + position_at_end then_bb builder; + let then_val = codegen_expr then_ in + + (* Codegen of 'then' can change the current block, update then_bb for the + * phi. We create a new name because one is used for the phi node, and the + * other is used for the conditional branch. *) + let new_then_bb = insertion_block builder in + + (* Emit 'else' value. *) + let else_bb = append_block context "else" the_function in + position_at_end else_bb builder; + let else_val = codegen_expr else_ in + + (* Codegen of 'else' can change the current block, update else_bb for the + * phi. *) + let new_else_bb = insertion_block builder in + + (* Emit merge block. *) + let merge_bb = append_block context "ifcont" the_function in + position_at_end merge_bb builder; + let incoming = [(then_val, new_then_bb); (else_val, new_else_bb)] in + let phi = build_phi incoming "iftmp" builder in + + (* Return to the start block to add the conditional branch. *) + position_at_end start_bb builder; + ignore (build_cond_br cond_val then_bb else_bb builder); + + (* Set a unconditional branch at the end of the 'then' block and the + * 'else' block to the 'merge' block. *) + position_at_end new_then_bb builder; ignore (build_br merge_bb builder); + position_at_end new_else_bb builder; ignore (build_br merge_bb builder); + + (* Finally, set the builder to the end of the merge block. *) + position_at_end merge_bb builder; + + phi + | Ast.For (var_name, start, end_, step, body) -> + (* Emit the start code first, without 'variable' in scope. *) + let start_val = codegen_expr start in + + (* Make the new basic block for the loop header, inserting after current + * block. *) + let preheader_bb = insertion_block builder in + let the_function = block_parent preheader_bb in + let loop_bb = append_block context "loop" the_function in + + (* Insert an explicit fall through from the current block to the + * loop_bb. *) + ignore (build_br loop_bb builder); + + (* Start insertion in loop_bb. *) + position_at_end loop_bb builder; + + (* Start the PHI node with an entry for start. *) + let variable = build_phi [(start_val, preheader_bb)] var_name builder in + + (* 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. *) + let old_val = + try Some (Hashtbl.find named_values var_name) with Not_found -> None + in + Hashtbl.add named_values var_name 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 *) + ignore (codegen_expr body); + + (* Emit the step value. *) + let step_val = + match step with + | Some step -> codegen_expr step + (* If not specified, use 1.0. *) + | None -> const_float double_type 1.0 + in + + let next_var = build_add variable step_val "nextvar" builder in + + (* Compute the end condition. *) + let end_cond = codegen_expr end_ in + + (* Convert condition to a bool by comparing equal to 0.0. *) + let zero = const_float double_type 0.0 in + let end_cond = build_fcmp Fcmp.One end_cond zero "loopcond" builder in + + (* Create the "after loop" block and insert it. *) + let loop_end_bb = insertion_block builder in + let after_bb = append_block context "afterloop" the_function in + + (* Insert the conditional branch into the end of loop_end_bb. *) + ignore (build_cond_br end_cond loop_bb after_bb builder); + + (* Any new code will be inserted in after_bb. *) + position_at_end after_bb builder; + + (* Add a new entry to the PHI node for the backedge. *) + add_incoming (next_var, loop_end_bb) variable; + + (* Restore the unshadowed variable. *) + begin match old_val with + | Some old_val -> Hashtbl.add named_values var_name old_val + | None -> () + end; + + (* for expr always returns 0.0. *) + const_null double_type + +let codegen_proto = function + | Ast.Prototype (name, args) -> + (* Make the function type: double(double,double) etc. *) + let doubles = Array.make (Array.length args) double_type in + let ft = function_type double_type doubles in + let f = + match lookup_function name the_module with + | None -> declare_function name ft the_module + + (* If 'f' conflicted, there was already something named 'name'. If it + * has a body, don't allow redefinition or reextern. *) + | Some f -> + (* If 'f' already has a body, reject this. *) + if block_begin f <> At_end f then + raise (Error "redefinition of function"); + + (* If 'f' took a different number of arguments, reject. *) + if element_type (type_of f) <> ft then + raise (Error "redefinition of function with different # args"); + f + in + + (* Set names for all arguments. *) + Array.iteri (fun i a -> + let n = args.(i) in + set_value_name n a; + Hashtbl.add named_values n a; + ) (params f); + f + +let codegen_func the_fpm = function + | Ast.Function (proto, body) -> + Hashtbl.clear named_values; + let the_function = codegen_proto proto in + + (* Create a new basic block to start insertion into. *) + let bb = append_block context "entry" the_function in + position_at_end bb builder; + + try + let ret_val = codegen_expr body in + + (* Finish off the function. *) + let _ = build_ret ret_val builder in + + (* Validate the generated code, checking for consistency. *) + Llvm_analysis.assert_valid_function the_function; + + (* Optimize the function. *) + let _ = PassManager.run_function the_function the_fpm in + + the_function + with e -> + delete_function the_function; + raise e +</pre> +</dd> + +<dt>toplevel.ml:</dt> +<dd class="doc_code"> +<pre> +(*===----------------------------------------------------------------------=== + * Top-Level parsing and JIT Driver + *===----------------------------------------------------------------------===*) + +open Llvm +open Llvm_executionengine + +(* top ::= definition | external | expression | ';' *) +let rec main_loop the_fpm the_execution_engine stream = + match Stream.peek stream with + | None -> () + + (* ignore top-level semicolons. *) + | Some (Token.Kwd ';') -> + Stream.junk stream; + main_loop the_fpm the_execution_engine stream + + | Some token -> + begin + try match token with + | Token.Def -> + let e = Parser.parse_definition stream in + print_endline "parsed a function definition."; + dump_value (Codegen.codegen_func the_fpm e); + | Token.Extern -> + let e = Parser.parse_extern stream in + print_endline "parsed an extern."; + dump_value (Codegen.codegen_proto e); + | _ -> + (* Evaluate a top-level expression into an anonymous function. *) + let e = Parser.parse_toplevel stream in + print_endline "parsed a top-level expr"; + let the_function = Codegen.codegen_func the_fpm e in + dump_value the_function; + + (* JIT the function, returning a function pointer. *) + let result = ExecutionEngine.run_function the_function [||] + the_execution_engine in + + print_string "Evaluated to "; + print_float (GenericValue.as_float Codegen.double_type result); + print_newline (); + with Stream.Error s | Codegen.Error s -> + (* Skip token for error recovery. *) + Stream.junk stream; + print_endline s; + end; + print_string "ready> "; flush stdout; + main_loop the_fpm the_execution_engine stream +</pre> +</dd> + +<dt>toy.ml:</dt> +<dd class="doc_code"> +<pre> +(*===----------------------------------------------------------------------=== + * Main driver code. + *===----------------------------------------------------------------------===*) + +open Llvm +open Llvm_executionengine +open Llvm_target +open Llvm_scalar_opts + +let main () = + ignore (initialize_native_target ()); + + (* Install standard binary operators. + * 1 is the lowest precedence. *) + Hashtbl.add Parser.binop_precedence '<' 10; + Hashtbl.add Parser.binop_precedence '+' 20; + Hashtbl.add Parser.binop_precedence '-' 20; + Hashtbl.add Parser.binop_precedence '*' 40; (* highest. *) + + (* Prime the first token. *) + print_string "ready> "; flush stdout; + let stream = Lexer.lex (Stream.of_channel stdin) in + + (* Create the JIT. *) + let the_execution_engine = ExecutionEngine.create Codegen.the_module in + let the_fpm = PassManager.create_function Codegen.the_module in + + (* Set up the optimizer pipeline. Start with registering info about how the + * target lays out data structures. *) + TargetData.add (ExecutionEngine.target_data the_execution_engine) the_fpm; + + (* Do simple "peephole" optimizations and bit-twiddling optzn. *) + add_instruction_combination the_fpm; + + (* reassociate expressions. *) + add_reassociation the_fpm; + + (* Eliminate Common SubExpressions. *) + add_gvn the_fpm; + + (* Simplify the control flow graph (deleting unreachable blocks, etc). *) + add_cfg_simplification the_fpm; + + ignore (PassManager.initialize the_fpm); + + (* Run the main "interpreter loop" now. *) + Toplevel.main_loop the_fpm the_execution_engine stream; + + (* Print out all the generated code. *) + dump_module Codegen.the_module +;; + +main () +</pre> +</dd> + +<dt>bindings.c</dt> +<dd class="doc_code"> +<pre> +#include <stdio.h> + +/* putchard - putchar that takes a double and returns 0. */ +extern double putchard(double X) { + putchar((char)X); + return 0; +} +</pre> +</dd> +</dl> + +<a href="OCamlLangImpl6.html">Next: Extending the language: user-defined +operators</a> +</div> + +<!-- *********************************************************************** --> +<hr> +<address> + <a href="http://jigsaw.w3.org/css-validator/check/referer"><img + src="http://jigsaw.w3.org/css-validator/images/vcss" alt="Valid CSS!"></a> + <a href="http://validator.w3.org/check/referer"><img + src="http://www.w3.org/Icons/valid-html401" alt="Valid HTML 4.01!"></a> + + <a href="mailto:sabre@nondot.org">Chris Lattner</a><br> + <a href="mailto:idadesub@users.sourceforge.net">Erick Tryzelaar</a><br> + <a href="http://llvm.org/">The LLVM Compiler Infrastructure</a><br> + Last modified: $Date$ +</address> +</body> +</html> |