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+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN"
+ "http://www.w3.org/TR/html4/strict.dtd">
+
+<html>
+<head>
+ <title>Kaleidoscope: Extending the Language: User-defined Operators</title>
+ <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
+ <meta name="author" content="Chris Lattner">
+ <link rel="stylesheet" href="../llvm.css" type="text/css">
+</head>
+
+<body>
+
+<div class="doc_title">Kaleidoscope: Extending the Language: User-defined Operators</div>
+
+<ul>
+<li><a href="index.html">Up to Tutorial Index</a></li>
+<li>Chapter 6
+ <ol>
+ <li><a href="#intro">Chapter 6 Introduction</a></li>
+ <li><a href="#idea">User-defined Operators: the Idea</a></li>
+ <li><a href="#binary">User-defined Binary Operators</a></li>
+ <li><a href="#unary">User-defined Unary Operators</a></li>
+ <li><a href="#example">Kicking the Tires</a></li>
+ <li><a href="#code">Full Code Listing</a></li>
+ </ol>
+</li>
+<li><a href="LangImpl7.html">Chapter 7</a>: Extending the Language: Mutable
+Variables / SSA Construction</li>
+</ul>
+
+<div class="doc_author">
+ <p>Written by <a href="mailto:sabre@nondot.org">Chris Lattner</a></p>
+</div>
+
+<!-- *********************************************************************** -->
+<div class="doc_section"><a name="intro">Chapter 6 Introduction</a></div>
+<!-- *********************************************************************** -->
+
+<div class="doc_text">
+
+<p>Welcome to Chapter 6 of the "<a href="index.html">Implementing a language
+with LLVM</a>" tutorial. At this point in our tutorial, we now have a fully
+functional language that is fairly minimal, but also useful. There
+is still one big problem with it, however. Our language doesn't have many
+useful operators (like division, logical negation, or even any comparisons
+besides less-than).</p>
+
+<p>This chapter of the tutorial takes a wild digression into adding user-defined
+operators to the simple and beautiful Kaleidoscope language. This digression now gives
+us a simple and ugly language in some ways, but also a powerful one at the same time.
+One of the great things about creating your own language is that you get to
+decide what is good or bad. In this tutorial we'll assume that it is okay to
+use this as a way to show some interesting parsing techniques.</p>
+
+<p>At the end of this tutorial, we'll run through an example Kaleidoscope
+application that <a href="#example">renders the Mandelbrot set</a>. This gives
+an example of what you can build with Kaleidoscope and its feature set.</p>
+
+</div>
+
+<!-- *********************************************************************** -->
+<div class="doc_section"><a name="idea">User-defined Operators: the Idea</a></div>
+<!-- *********************************************************************** -->
+
+<div class="doc_text">
+
+<p>
+The "operator overloading" that we will add to Kaleidoscope is more general than
+languages like C++. In C++, you are only allowed to redefine existing
+operators: you can't programatically change the grammar, introduce new
+operators, change precedence levels, etc. In this chapter, we will add this
+capability to Kaleidoscope, which will let the user round out the set of
+operators that are supported.</p>
+
+<p>The point of going into user-defined operators in a tutorial like this is to
+show the power and flexibility of using a hand-written parser. Thus far, the parser
+we have been implementing uses recursive descent for most parts of the grammar and
+operator precedence parsing for the expressions. See <a
+href="LangImpl2.html">Chapter 2</a> for details. Without using operator
+precedence parsing, it would be very difficult to allow the programmer to
+introduce new operators into the grammar: the grammar is dynamically extensible
+as the JIT runs.</p>
+
+<p>The two specific features we'll add are programmable unary operators (right
+now, Kaleidoscope has no unary operators at all) as well as binary operators.
+An example of this is:</p>
+
+<div class="doc_code">
+<pre>
+# Logical unary not.
+def unary!(v)
+ if v then
+ 0
+ else
+ 1;
+
+# Define &gt; with the same precedence as &lt;.
+def binary&gt; 10 (LHS RHS)
+ RHS &lt; LHS;
+
+# Binary "logical or", (note that it does not "short circuit")
+def binary| 5 (LHS RHS)
+ if LHS then
+ 1
+ else if RHS then
+ 1
+ else
+ 0;
+
+# Define = with slightly lower precedence than relationals.
+def binary= 9 (LHS RHS)
+ !(LHS &lt; RHS | LHS &gt; RHS);
+</pre>
+</div>
+
+<p>Many languages aspire to being able to implement their standard runtime
+library in the language itself. In Kaleidoscope, we can implement significant
+parts of the language in the library!</p>
+
+<p>We will break down implementation of these features into two parts:
+implementing support for user-defined binary operators and adding unary
+operators.</p>
+
+</div>
+
+<!-- *********************************************************************** -->
+<div class="doc_section"><a name="binary">User-defined Binary Operators</a></div>
+<!-- *********************************************************************** -->
+
+<div class="doc_text">
+
+<p>Adding support for user-defined binary operators is pretty simple with our
+current framework. We'll first add support for the unary/binary keywords:</p>
+
+<div class="doc_code">
+<pre>
+enum Token {
+ ...
+ <b>// operators
+ tok_binary = -11, tok_unary = -12</b>
+};
+...
+static int gettok() {
+...
+ if (IdentifierStr == "for") return tok_for;
+ if (IdentifierStr == "in") return tok_in;
+ <b>if (IdentifierStr == "binary") return tok_binary;
+ if (IdentifierStr == "unary") return tok_unary;</b>
+ return tok_identifier;
+</pre>
+</div>
+
+<p>This just adds lexer support for the unary and binary keywords, like we
+did in <a href="LangImpl5.html#iflexer">previous chapters</a>. One nice thing
+about our current AST, is that we represent binary operators with full generalisation
+by using their ASCII code as the opcode. For our extended operators, we'll use this
+same representation, so we don't need any new AST or parser support.</p>
+
+<p>On the other hand, we have to be able to represent the definitions of these
+new operators, in the "def binary| 5" part of the function definition. In our
+grammar so far, the "name" for the function definition is parsed as the
+"prototype" production and into the <tt>PrototypeAST</tt> AST node. To
+represent our new user-defined operators as prototypes, we have to extend
+the <tt>PrototypeAST</tt> AST node like this:</p>
+
+<div class="doc_code">
+<pre>
+/// PrototypeAST - This class represents the "prototype" for a function,
+/// which captures its argument names as well as if it is an operator.
+class PrototypeAST {
+ std::string Name;
+ std::vector&lt;std::string&gt; Args;
+ <b>bool isOperator;
+ unsigned Precedence; // Precedence if a binary op.</b>
+public:
+ PrototypeAST(const std::string &amp;name, const std::vector&lt;std::string&gt; &amp;args,
+ <b>bool isoperator = false, unsigned prec = 0</b>)
+ : Name(name), Args(args), <b>isOperator(isoperator), Precedence(prec)</b> {}
+
+ <b>bool isUnaryOp() const { return isOperator &amp;&amp; Args.size() == 1; }
+ bool isBinaryOp() const { return isOperator &amp;&amp; Args.size() == 2; }
+
+ char getOperatorName() const {
+ assert(isUnaryOp() || isBinaryOp());
+ return Name[Name.size()-1];
+ }
+
+ unsigned getBinaryPrecedence() const { return Precedence; }</b>
+
+ Function *Codegen();
+};
+</pre>
+</div>
+
+<p>Basically, in addition to knowing a name for the prototype, we now keep track
+of whether it was an operator, and if it was, what precedence level the operator
+is at. The precedence is only used for binary operators (as you'll see below,
+it just doesn't apply for unary operators). Now that we have a way to represent
+the prototype for a user-defined operator, we need to parse it:</p>
+
+<div class="doc_code">
+<pre>
+/// prototype
+/// ::= id '(' id* ')'
+<b>/// ::= binary LETTER number? (id, id)</b>
+static PrototypeAST *ParsePrototype() {
+ std::string FnName;
+
+ <b>unsigned Kind = 0; // 0 = identifier, 1 = unary, 2 = binary.
+ unsigned BinaryPrecedence = 30;</b>
+
+ switch (CurTok) {
+ default:
+ return ErrorP("Expected function name in prototype");
+ case tok_identifier:
+ FnName = IdentifierStr;
+ Kind = 0;
+ getNextToken();
+ break;
+ <b>case tok_binary:
+ getNextToken();
+ if (!isascii(CurTok))
+ return ErrorP("Expected binary operator");
+ FnName = "binary";
+ FnName += (char)CurTok;
+ Kind = 2;
+ getNextToken();
+
+ // Read the precedence if present.
+ if (CurTok == tok_number) {
+ if (NumVal &lt; 1 || NumVal &gt; 100)
+ return ErrorP("Invalid precedecnce: must be 1..100");
+ BinaryPrecedence = (unsigned)NumVal;
+ getNextToken();
+ }
+ break;</b>
+ }
+
+ if (CurTok != '(')
+ return ErrorP("Expected '(' in prototype");
+
+ std::vector&lt;std::string&gt; ArgNames;
+ while (getNextToken() == tok_identifier)
+ ArgNames.push_back(IdentifierStr);
+ if (CurTok != ')')
+ return ErrorP("Expected ')' in prototype");
+
+ // success.
+ getNextToken(); // eat ')'.
+
+ <b>// Verify right number of names for operator.
+ if (Kind &amp;&amp; ArgNames.size() != Kind)
+ return ErrorP("Invalid number of operands for operator");
+
+ return new PrototypeAST(FnName, ArgNames, Kind != 0, BinaryPrecedence);</b>
+}
+</pre>
+</div>
+
+<p>This is all fairly straightforward parsing code, and we have already seen
+a lot of similar code in the past. One interesting part about the code above is
+the couple lines that set up <tt>FnName</tt> for binary operators. This builds names
+like "binary@" for a newly defined "@" operator. This then takes advantage of the
+fact that symbol names in the LLVM symbol table are allowed to have any character in
+them, including embedded nul characters.</p>
+
+<p>The next interesting thing to add, is codegen support for these binary operators.
+Given our current structure, this is a simple addition of a default case for our
+existing binary operator node:</p>
+
+<div class="doc_code">
+<pre>
+Value *BinaryExprAST::Codegen() {
+ Value *L = LHS-&gt;Codegen();
+ Value *R = RHS-&gt;Codegen();
+ if (L == 0 || R == 0) return 0;
+
+ switch (Op) {
+ case '+': return Builder.CreateAdd(L, R, "addtmp");
+ case '-': return Builder.CreateSub(L, R, "subtmp");
+ case '*': return Builder.CreateMul(L, R, "multmp");
+ case '&lt;':
+ L = Builder.CreateFCmpULT(L, R, "cmptmp");
+ // Convert bool 0/1 to double 0.0 or 1.0
+ return Builder.CreateUIToFP(L, Type::getDoubleTy(getGlobalContext()),
+ "booltmp");
+ <b>default: break;</b>
+ }
+
+ <b>// If it wasn't a builtin binary operator, it must be a user defined one. Emit
+ // a call to it.
+ Function *F = TheModule-&gt;getFunction(std::string("binary")+Op);
+ assert(F &amp;&amp; "binary operator not found!");
+
+ Value *Ops[] = { L, R };
+ return Builder.CreateCall(F, Ops, Ops+2, "binop");</b>
+}
+
+</pre>
+</div>
+
+<p>As you can see above, the new code is actually really simple. It just does
+a lookup for the appropriate operator in the symbol table and generates a
+function call to it. Since user-defined operators are just built as normal
+functions (because the "prototype" boils down to a function with the right
+name) everything falls into place.</p>
+
+<p>The final piece of code we are missing, is a bit of top-level magic:</p>
+
+<div class="doc_code">
+<pre>
+Function *FunctionAST::Codegen() {
+ NamedValues.clear();
+
+ Function *TheFunction = Proto->Codegen();
+ if (TheFunction == 0)
+ return 0;
+
+ <b>// If this is an operator, install it.
+ if (Proto-&gt;isBinaryOp())
+ BinopPrecedence[Proto->getOperatorName()] = Proto->getBinaryPrecedence();</b>
+
+ // Create a new basic block to start insertion into.
+ BasicBlock *BB = BasicBlock::Create(getGlobalContext(), "entry", TheFunction);
+ Builder.SetInsertPoint(BB);
+
+ if (Value *RetVal = Body-&gt;Codegen()) {
+ ...
+</pre>
+</div>
+
+<p>Basically, before codegening a function, if it is a user-defined operator, we
+register it in the precedence table. This allows the binary operator parsing
+logic we already have in place to handle it. Since we are working on a fully-general operator precedence parser, this is all we need to do to "extend the grammar".</p>
+
+<p>Now we have useful user-defined binary operators. This builds a lot
+on the previous framework we built for other operators. Adding unary operators
+is a bit more challenging, because we don't have any framework for it yet - lets
+see what it takes.</p>
+
+</div>
+
+<!-- *********************************************************************** -->
+<div class="doc_section"><a name="unary">User-defined Unary Operators</a></div>
+<!-- *********************************************************************** -->
+
+<div class="doc_text">
+
+<p>Since we don't currently support unary operators in the Kaleidoscope
+language, we'll need to add everything to support them. Above, we added simple
+support for the 'unary' keyword to the lexer. In addition to that, we need an
+AST node:</p>
+
+<div class="doc_code">
+<pre>
+/// UnaryExprAST - Expression class for a unary operator.
+class UnaryExprAST : public ExprAST {
+ char Opcode;
+ ExprAST *Operand;
+public:
+ UnaryExprAST(char opcode, ExprAST *operand)
+ : Opcode(opcode), Operand(operand) {}
+ virtual Value *Codegen();
+};
+</pre>
+</div>
+
+<p>This AST node is very simple and obvious by now. It directly mirrors the
+binary operator AST node, except that it only has one child. With this, we
+need to add the parsing logic. Parsing a unary operator is pretty simple: we'll
+add a new function to do it:</p>
+
+<div class="doc_code">
+<pre>
+/// unary
+/// ::= primary
+/// ::= '!' unary
+static ExprAST *ParseUnary() {
+ // If the current token is not an operator, it must be a primary expr.
+ if (!isascii(CurTok) || CurTok == '(' || CurTok == ',')
+ return ParsePrimary();
+
+ // If this is a unary operator, read it.
+ int Opc = CurTok;
+ getNextToken();
+ if (ExprAST *Operand = ParseUnary())
+ return new UnaryExprAST(Opc, Operand);
+ return 0;
+}
+</pre>
+</div>
+
+<p>The grammar we add is pretty straightforward here. If we see a unary
+operator when parsing a primary operator, we eat the operator as a prefix and
+parse the remaining piece as another unary operator. This allows us to handle
+multiple unary operators (e.g. "!!x"). Note that unary operators can't have
+ambiguous parses like binary operators can, so there is no need for precedence
+information.</p>
+
+<p>The problem with this function, is that we need to call ParseUnary from somewhere.
+To do this, we change previous callers of ParsePrimary to call ParseUnary
+instead:</p>
+
+<div class="doc_code">
+<pre>
+/// binoprhs
+/// ::= ('+' unary)*
+static ExprAST *ParseBinOpRHS(int ExprPrec, ExprAST *LHS) {
+ ...
+ <b>// Parse the unary expression after the binary operator.
+ ExprAST *RHS = ParseUnary();
+ if (!RHS) return 0;</b>
+ ...
+}
+/// expression
+/// ::= unary binoprhs
+///
+static ExprAST *ParseExpression() {
+ <b>ExprAST *LHS = ParseUnary();</b>
+ if (!LHS) return 0;
+
+ return ParseBinOpRHS(0, LHS);
+}
+</pre>
+</div>
+
+<p>With these two simple changes, we are now able to parse unary operators and build the
+AST for them. Next up, we need to add parser support for prototypes, to parse
+the unary operator prototype. We extend the binary operator code above
+with:</p>
+
+<div class="doc_code">
+<pre>
+/// prototype
+/// ::= id '(' id* ')'
+/// ::= binary LETTER number? (id, id)
+<b>/// ::= unary LETTER (id)</b>
+static PrototypeAST *ParsePrototype() {
+ std::string FnName;
+
+ unsigned Kind = 0; // 0 = identifier, 1 = unary, 2 = binary.
+ unsigned BinaryPrecedence = 30;
+
+ switch (CurTok) {
+ default:
+ return ErrorP("Expected function name in prototype");
+ case tok_identifier:
+ FnName = IdentifierStr;
+ Kind = 0;
+ getNextToken();
+ break;
+ <b>case tok_unary:
+ getNextToken();
+ if (!isascii(CurTok))
+ return ErrorP("Expected unary operator");
+ FnName = "unary";
+ FnName += (char)CurTok;
+ Kind = 1;
+ getNextToken();
+ break;</b>
+ case tok_binary:
+ ...
+</pre>
+</div>
+
+<p>As with binary operators, we name unary operators with a name that includes
+the operator character. This assists us at code generation time. Speaking of,
+the final piece we need to add is codegen support for unary operators. It looks
+like this:</p>
+
+<div class="doc_code">
+<pre>
+Value *UnaryExprAST::Codegen() {
+ Value *OperandV = Operand->Codegen();
+ if (OperandV == 0) return 0;
+
+ Function *F = TheModule->getFunction(std::string("unary")+Opcode);
+ if (F == 0)
+ return ErrorV("Unknown unary operator");
+
+ return Builder.CreateCall(F, OperandV, "unop");
+}
+</pre>
+</div>
+
+<p>This code is similar to, but simpler than, the code for binary operators. It
+is simpler primarily because it doesn't need to handle any predefined operators.
+</p>
+
+</div>
+
+<!-- *********************************************************************** -->
+<div class="doc_section"><a name="example">Kicking the Tires</a></div>
+<!-- *********************************************************************** -->
+
+<div class="doc_text">
+
+<p>It is somewhat hard to believe, but with a few simple extensions we've
+covered in the last chapters, we have grown a real-ish language. With this, we
+can do a lot of interesting things, including I/O, math, and a bunch of other
+things. For example, we can now add a nice sequencing operator (printd is
+defined to print out the specified value and a newline):</p>
+
+<div class="doc_code">
+<pre>
+ready&gt; <b>extern printd(x);</b>
+Read extern: declare double @printd(double)
+ready&gt; <b>def binary : 1 (x y) 0; # Low-precedence operator that ignores operands.</b>
+..
+ready&gt; <b>printd(123) : printd(456) : printd(789);</b>
+123.000000
+456.000000
+789.000000
+Evaluated to 0.000000
+</pre>
+</div>
+
+<p>We can also define a bunch of other "primitive" operations, such as:</p>
+
+<div class="doc_code">
+<pre>
+# Logical unary not.
+def unary!(v)
+ if v then
+ 0
+ else
+ 1;
+
+# Unary negate.
+def unary-(v)
+ 0-v;
+
+# Define &gt; with the same precedence as &gt;.
+def binary&gt; 10 (LHS RHS)
+ RHS &lt; LHS;
+
+# Binary logical or, which does not short circuit.
+def binary| 5 (LHS RHS)
+ if LHS then
+ 1
+ else if RHS then
+ 1
+ else
+ 0;
+
+# Binary logical and, which does not short circuit.
+def binary&amp; 6 (LHS RHS)
+ if !LHS then
+ 0
+ else
+ !!RHS;
+
+# Define = with slightly lower precedence than relationals.
+def binary = 9 (LHS RHS)
+ !(LHS &lt; RHS | LHS &gt; RHS);
+
+</pre>
+</div>
+
+
+<p>Given the previous if/then/else support, we can also define interesting
+functions for I/O. For example, the following prints out a character whose
+"density" reflects the value passed in: the lower the value, the denser the
+character:</p>
+
+<div class="doc_code">
+<pre>
+ready&gt;
+<b>
+extern putchard(char)
+def printdensity(d)
+ if d &gt; 8 then
+ putchard(32) # ' '
+ else if d &gt; 4 then
+ putchard(46) # '.'
+ else if d &gt; 2 then
+ putchard(43) # '+'
+ else
+ putchard(42); # '*'</b>
+...
+ready&gt; <b>printdensity(1): printdensity(2): printdensity(3) :
+ printdensity(4): printdensity(5): printdensity(9): putchard(10);</b>
+*++..
+Evaluated to 0.000000
+</pre>
+</div>
+
+<p>Based on these simple primitive operations, we can start to define more
+interesting things. For example, here's a little function that solves for the
+number of iterations it takes a function in the complex plane to
+converge:</p>
+
+<div class="doc_code">
+<pre>
+# determine whether the specific location diverges.
+# Solve for z = z^2 + c in the complex plane.
+def mandleconverger(real imag iters creal cimag)
+ if iters &gt; 255 | (real*real + imag*imag &gt; 4) then
+ iters
+ else
+ mandleconverger(real*real - imag*imag + creal,
+ 2*real*imag + cimag,
+ iters+1, creal, cimag);
+
+# return the number of iterations required for the iteration to escape
+def mandleconverge(real imag)
+ mandleconverger(real, imag, 0, real, imag);
+</pre>
+</div>
+
+<p>This "z = z<sup>2</sup> + c" function is a beautiful little creature that is the basis
+for computation of the <a
+href="http://en.wikipedia.org/wiki/Mandelbrot_set">Mandelbrot Set</a>. Our
+<tt>mandelconverge</tt> function returns the number of iterations that it takes
+for a complex orbit to escape, saturating to 255. This is not a very useful
+function by itself, but if you plot its value over a two-dimensional plane,
+you can see the Mandelbrot set. Given that we are limited to using putchard
+here, our amazing graphical output is limited, but we can whip together
+something using the density plotter above:</p>
+
+<div class="doc_code">
+<pre>
+# compute and plot the mandlebrot set with the specified 2 dimensional range
+# info.
+def mandelhelp(xmin xmax xstep ymin ymax ystep)
+ for y = ymin, y &lt; ymax, ystep in (
+ (for x = xmin, x &lt; xmax, xstep in
+ printdensity(mandleconverge(x,y)))
+ : putchard(10)
+ )
+
+# mandel - This is a convenient helper function for ploting the mandelbrot set
+# from the specified position with the specified Magnification.
+def mandel(realstart imagstart realmag imagmag)
+ mandelhelp(realstart, realstart+realmag*78, realmag,
+ imagstart, imagstart+imagmag*40, imagmag);
+</pre>
+</div>
+
+<p>Given this, we can try plotting out the mandlebrot set! Lets try it out:</p>
+
+<div class="doc_code">
+<pre>
+ready&gt; <b>mandel(-2.3, -1.3, 0.05, 0.07);</b>
+*******************************+++++++++++*************************************
+*************************+++++++++++++++++++++++*******************************
+**********************+++++++++++++++++++++++++++++****************************
+*******************+++++++++++++++++++++.. ...++++++++*************************
+*****************++++++++++++++++++++++.... ...+++++++++***********************
+***************+++++++++++++++++++++++..... ...+++++++++*********************
+**************+++++++++++++++++++++++.... ....+++++++++********************
+*************++++++++++++++++++++++...... .....++++++++*******************
+************+++++++++++++++++++++....... .......+++++++******************
+***********+++++++++++++++++++.... ... .+++++++*****************
+**********+++++++++++++++++....... .+++++++****************
+*********++++++++++++++........... ...+++++++***************
+********++++++++++++............ ...++++++++**************
+********++++++++++... .......... .++++++++**************
+*******+++++++++..... .+++++++++*************
+*******++++++++...... ..+++++++++*************
+*******++++++....... ..+++++++++*************
+*******+++++...... ..+++++++++*************
+*******.... .... ...+++++++++*************
+*******.... . ...+++++++++*************
+*******+++++...... ...+++++++++*************
+*******++++++....... ..+++++++++*************
+*******++++++++...... .+++++++++*************
+*******+++++++++..... ..+++++++++*************
+********++++++++++... .......... .++++++++**************
+********++++++++++++............ ...++++++++**************
+*********++++++++++++++.......... ...+++++++***************
+**********++++++++++++++++........ .+++++++****************
+**********++++++++++++++++++++.... ... ..+++++++****************
+***********++++++++++++++++++++++....... .......++++++++*****************
+************+++++++++++++++++++++++...... ......++++++++******************
+**************+++++++++++++++++++++++.... ....++++++++********************
+***************+++++++++++++++++++++++..... ...+++++++++*********************
+*****************++++++++++++++++++++++.... ...++++++++***********************
+*******************+++++++++++++++++++++......++++++++*************************
+*********************++++++++++++++++++++++.++++++++***************************
+*************************+++++++++++++++++++++++*******************************
+******************************+++++++++++++************************************
+*******************************************************************************
+*******************************************************************************
+*******************************************************************************
+Evaluated to 0.000000
+ready&gt; <b>mandel(-2, -1, 0.02, 0.04);</b>
+**************************+++++++++++++++++++++++++++++++++++++++++++++++++++++
+***********************++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+*********************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++.
+*******************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++...
+*****************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++.....
+***************++++++++++++++++++++++++++++++++++++++++++++++++++++++++........
+**************++++++++++++++++++++++++++++++++++++++++++++++++++++++...........
+************+++++++++++++++++++++++++++++++++++++++++++++++++++++..............
+***********++++++++++++++++++++++++++++++++++++++++++++++++++........ .
+**********++++++++++++++++++++++++++++++++++++++++++++++.............
+********+++++++++++++++++++++++++++++++++++++++++++..................
+*******+++++++++++++++++++++++++++++++++++++++.......................
+******+++++++++++++++++++++++++++++++++++...........................
+*****++++++++++++++++++++++++++++++++............................
+*****++++++++++++++++++++++++++++...............................
+****++++++++++++++++++++++++++...... .........................
+***++++++++++++++++++++++++......... ...... ...........
+***++++++++++++++++++++++............
+**+++++++++++++++++++++..............
+**+++++++++++++++++++................
+*++++++++++++++++++.................
+*++++++++++++++++............ ...
+*++++++++++++++..............
+*+++....++++................
+*.......... ...........
+*
+*.......... ...........
+*+++....++++................
+*++++++++++++++..............
+*++++++++++++++++............ ...
+*++++++++++++++++++.................
+**+++++++++++++++++++................
+**+++++++++++++++++++++..............
+***++++++++++++++++++++++............
+***++++++++++++++++++++++++......... ...... ...........
+****++++++++++++++++++++++++++...... .........................
+*****++++++++++++++++++++++++++++...............................
+*****++++++++++++++++++++++++++++++++............................
+******+++++++++++++++++++++++++++++++++++...........................
+*******+++++++++++++++++++++++++++++++++++++++.......................
+********+++++++++++++++++++++++++++++++++++++++++++..................
+Evaluated to 0.000000
+ready&gt; <b>mandel(-0.9, -1.4, 0.02, 0.03);</b>
+*******************************************************************************
+*******************************************************************************
+*******************************************************************************
+**********+++++++++++++++++++++************************************************
+*+++++++++++++++++++++++++++++++++++++++***************************************
++++++++++++++++++++++++++++++++++++++++++++++**********************************
+++++++++++++++++++++++++++++++++++++++++++++++++++*****************************
+++++++++++++++++++++++++++++++++++++++++++++++++++++++*************************
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++**********************
++++++++++++++++++++++++++++++++++.........++++++++++++++++++*******************
++++++++++++++++++++++++++++++++.... ......+++++++++++++++++++****************
++++++++++++++++++++++++++++++....... ........+++++++++++++++++++**************
+++++++++++++++++++++++++++++........ ........++++++++++++++++++++************
++++++++++++++++++++++++++++......... .. ...+++++++++++++++++++++**********
+++++++++++++++++++++++++++........... ....++++++++++++++++++++++********
+++++++++++++++++++++++++............. .......++++++++++++++++++++++******
++++++++++++++++++++++++............. ........+++++++++++++++++++++++****
+++++++++++++++++++++++........... ..........++++++++++++++++++++++***
+++++++++++++++++++++........... .........++++++++++++++++++++++*
+++++++++++++++++++............ ...........++++++++++++++++++++
+++++++++++++++++............... .............++++++++++++++++++
+++++++++++++++................. ...............++++++++++++++++
+++++++++++++.................. .................++++++++++++++
++++++++++.................. .................+++++++++++++
+++++++........ . ......... ..++++++++++++
+++............ ...... ....++++++++++
+.............. ...++++++++++
+.............. ....+++++++++
+.............. .....++++++++
+............. ......++++++++
+........... .......++++++++
+......... ........+++++++
+......... ........+++++++
+......... ....+++++++
+........ ...+++++++
+....... ...+++++++
+ ....+++++++
+ .....+++++++
+ ....+++++++
+ ....+++++++
+ ....+++++++
+Evaluated to 0.000000
+ready&gt; <b>^D</b>
+</pre>
+</div>
+
+<p>At this point, you may be starting to realize that Kaleidoscope is a real
+and powerful language. It may not be self-similar :), but it can be used to
+plot things that are!</p>
+
+<p>With this, we conclude the "adding user-defined operators" chapter of the
+tutorial. We have successfully augmented our language, adding the ability to extend the
+language in the library, and we have shown how this can be used to build a simple but
+interesting end-user application in Kaleidoscope. At this point, Kaleidoscope
+can build a variety of applications that are functional and can call functions
+with side-effects, but it can't actually define and mutate a variable itself.
+</p>
+
+<p>Strikingly, variable mutation is an important feature of some
+languages, and it is not at all obvious how to <a href="LangImpl7.html">add
+support for mutable variables</a> without having to add an "SSA construction"
+phase to your front-end. In the next chapter, we will describe how you can
+add variable mutation without building SSA in your front-end.</p>
+
+</div>
+
+<!-- *********************************************************************** -->
+<div class="doc_section"><a name="code">Full Code Listing</a></div>
+<!-- *********************************************************************** -->
+
+<div class="doc_text">
+
+<p>
+Here is the complete code listing for our running example, enhanced with the
+if/then/else and for expressions.. To build this example, use:
+</p>
+
+<div class="doc_code">
+<pre>
+ # Compile
+ g++ -g toy.cpp `llvm-config --cppflags --ldflags --libs core jit native` -O3 -o toy
+ # Run
+ ./toy
+</pre>
+</div>
+
+<p>Here is the code:</p>
+
+<div class="doc_code">
+<pre>
+#include "llvm/DerivedTypes.h"
+#include "llvm/ExecutionEngine/ExecutionEngine.h"
+#include "llvm/ExecutionEngine/JIT.h"
+#include "llvm/LLVMContext.h"
+#include "llvm/Module.h"
+#include "llvm/PassManager.h"
+#include "llvm/Analysis/Verifier.h"
+#include "llvm/Target/TargetData.h"
+#include "llvm/Target/TargetSelect.h"
+#include "llvm/Transforms/Scalar.h"
+#include "llvm/Support/IRBuilder.h"
+#include &lt;cstdio&gt;
+#include &lt;string&gt;
+#include &lt;map&gt;
+#include &lt;vector&gt;
+using namespace llvm;
+
+//===----------------------------------------------------------------------===//
+// Lexer
+//===----------------------------------------------------------------------===//
+
+// The lexer returns tokens [0-255] if it is an unknown character, otherwise one
+// of these for known things.
+enum Token {
+ tok_eof = -1,
+
+ // commands
+ tok_def = -2, tok_extern = -3,
+
+ // primary
+ tok_identifier = -4, tok_number = -5,
+
+ // control
+ tok_if = -6, tok_then = -7, tok_else = -8,
+ tok_for = -9, tok_in = -10,
+
+ // operators
+ tok_binary = -11, tok_unary = -12
+};
+
+static std::string IdentifierStr; // Filled in if tok_identifier
+static double NumVal; // Filled in if tok_number
+
+/// gettok - Return the next token from standard input.
+static int gettok() {
+ static int LastChar = ' ';
+
+ // Skip any whitespace.
+ while (isspace(LastChar))
+ LastChar = getchar();
+
+ if (isalpha(LastChar)) { // identifier: [a-zA-Z][a-zA-Z0-9]*
+ IdentifierStr = LastChar;
+ while (isalnum((LastChar = getchar())))
+ IdentifierStr += LastChar;
+
+ if (IdentifierStr == "def") return tok_def;
+ if (IdentifierStr == "extern") return tok_extern;
+ if (IdentifierStr == "if") return tok_if;
+ if (IdentifierStr == "then") return tok_then;
+ if (IdentifierStr == "else") return tok_else;
+ if (IdentifierStr == "for") return tok_for;
+ if (IdentifierStr == "in") return tok_in;
+ if (IdentifierStr == "binary") return tok_binary;
+ if (IdentifierStr == "unary") return tok_unary;
+ return tok_identifier;
+ }
+
+ if (isdigit(LastChar) || LastChar == '.') { // Number: [0-9.]+
+ std::string NumStr;
+ do {
+ NumStr += LastChar;
+ LastChar = getchar();
+ } while (isdigit(LastChar) || LastChar == '.');
+
+ NumVal = strtod(NumStr.c_str(), 0);
+ return tok_number;
+ }
+
+ if (LastChar == '#') {
+ // Comment until end of line.
+ do LastChar = getchar();
+ while (LastChar != EOF &amp;&amp; LastChar != '\n' &amp;&amp; LastChar != '\r');
+
+ if (LastChar != EOF)
+ return gettok();
+ }
+
+ // Check for end of file. Don't eat the EOF.
+ if (LastChar == EOF)
+ return tok_eof;
+
+ // Otherwise, just return the character as its ascii value.
+ int ThisChar = LastChar;
+ LastChar = getchar();
+ return ThisChar;
+}
+
+//===----------------------------------------------------------------------===//
+// Abstract Syntax Tree (aka Parse Tree)
+//===----------------------------------------------------------------------===//
+
+/// ExprAST - Base class for all expression nodes.
+class ExprAST {
+public:
+ virtual ~ExprAST() {}
+ virtual Value *Codegen() = 0;
+};
+
+/// NumberExprAST - Expression class for numeric literals like "1.0".
+class NumberExprAST : public ExprAST {