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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="../_static/llvm.css" type="text/css">
-</head>
-
-<body>
-
-<h1>Kaleidoscope: Extending the Language: User-defined Operators</h1>
-
-<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>
-
-<!-- *********************************************************************** -->
-<h2><a name="intro">Chapter 6 Introduction</a></h2>
-<!-- *********************************************************************** -->
-
-<div>
-
-<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>
-
-<!-- *********************************************************************** -->
-<h2><a name="idea">User-defined Operators: the Idea</a></h2>
-<!-- *********************************************************************** -->
-
-<div>
-
-<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>
-
-<!-- *********************************************************************** -->
-<h2><a name="binary">User-defined Binary Operators</a></h2>
-<!-- *********************************************************************** -->
-
-<div>
-
-<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.CreateFAdd(L, R, "addtmp");
- case '-': return Builder.CreateFSub(L, R, "subtmp");
- case '*': return Builder.CreateFMul(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[2] = { L, R };
- return Builder.CreateCall(F, Ops, "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>
-
-<!-- *********************************************************************** -->
-<h2><a name="unary">User-defined Unary Operators</a></h2>
-<!-- *********************************************************************** -->
-
-<div>
-
-<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>
-
-<!-- *********************************************************************** -->
-<h2><a name="example">Kicking the Tires</a></h2>
-<!-- *********************************************************************** -->
-
-<div>
-
-<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 &lt;.
-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);
-
-# Define ':' for sequencing: as a low-precedence operator that ignores operands
-# and just returns the RHS.
-def binary : 1 (x y) y;
-</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 "<code>z = z<sup>2</sup> + c</code>" 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 plotting 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>
-
-<!-- *********************************************************************** -->
-<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
-clang++ -g toy.cpp `llvm-config --cppflags --ldflags --libs core jit native` -O3 -o toy
-# Run
-./toy
-</pre>
-</div>
-
-<p>On some platforms, you will need to specify -rdynamic or -Wl,--export-dynamic
-when linking. This ensures that symbols defined in the main executable are
-exported to the dynamic linker and so are available for symbol resolution at
-run time. This is not needed if you compile your support code into a shared
-library, although doing that will cause problems on Windows.</p>
-
-<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/IRBuilder.h"
-#include "llvm/LLVMContext.h"
-#include "llvm/Module.h"
-#include "llvm/PassManager.h"
-#include "llvm/Analysis/Verifier.h"
-#include "llvm/Analysis/Passes.h"
-#include "llvm/DataLayout.h"
-#include "llvm/Transforms/Scalar.h"
-#include "llvm/Support/TargetSelect.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 =