Kaleidoscope: Adding JIT and Optimizer Support

- Up to Tutorial Index
- Chapter 4
  1. Chapter 4 Introduction
  2. Trivial Constant Folding
  3. LLVM Optimization Passes
  4. Adding a JIT Compiler
  5. Full Code Listing
- Chapter 5: Extending the Language: Control Flow

Written by Chris Lattner

Chapter 4 Introduction

Welcome to Chapter 4 of the "Implementing a language with LLVM" tutorial. Chapters 1-3 described the implementation of a simple language and added support for generating LLVM IR. This chapter describes two new techniques: adding optimizer support to your language, and adding JIT compiler support. These additions will demonstrate how to get nice, efficient code for the Kaleidoscope language.

Trivial Constant Folding

Our demonstration for Chapter 3 is elegant and easy to extend. Unfortunately, it does not produce wonderful code. The IRBuilder, however, does give us obvious optimizations when compiling simple code:

    ready> def test(x) 1+2+x;
    Read function definition:
    define double @test(double %x) {
    entry:
            %addtmp = add double 3.000000e+00, %x
            ret double %addtmp
    }

This code is not a literal transcription of the AST built by parsing the input. That would be:

    ready> def test(x) 1+2+x;
    Read function definition:
    define double @test(double %x) {
    entry:
            %addtmp = add double 2.000000e+00, 1.000000e+00
            %addtmp1 = add double %addtmp, %x
            ret double %addtmp1
    }

Constant folding, as seen above, in particular, is a very common and very important optimization: so much so that many language implementors implement constant folding support in their AST representation.

With LLVM, you don't need this support in the AST. Since all calls to build LLVM IR go through the LLVM IR builder, the builder itself checked to see if there was a constant folding opportunity when you call it. If so, it just does the constant fold and return the constant instead of creating an instruction.

Well, that was easy :). In practice, we recommend always using `IRBuilder` when generating code like this. It has no "syntactic overhead" for its use (you don't have to uglify your compiler with constant checks everywhere) and it can dramatically reduce the amount of LLVM IR that is generated in some cases (particular for languages with a macro preprocessor or that use a lot of constants).

On the other hand, the `IRBuilder` is limited by the fact that it does all of its analysis inline with the code as it is built. If you take a slightly more complex example:

    ready> def test(x) (1+2+x)*(x+(1+2));
    ready> Read function definition:
    define double @test(double %x) {
    entry:
            %addtmp = add double 3.000000e+00, %x
            %addtmp1 = add double %x, 3.000000e+00
            %multmp = mul double %addtmp, %addtmp1
            ret double %multmp
    }

In this case, the LHS and RHS of the multiplication are the same value. We'd really like to see this generate "`tmp = x+3; result = tmp*tmp;`" instead of computing "`x+3`" twice.

Unfortunately, no amount of local analysis will be able to detect and correct this. This requires two transformations: reassociation of expressions (to make the add's lexically identical) and Common Subexpression Elimination (CSE) to delete the redundant add instruction. Fortunately, LLVM provides a broad range of optimizations that you can use, in the form of "passes".

LLVM Optimization Passes

LLVM provides many optimization passes, which do many different sorts of things and have different tradeoffs. Unlike other systems, LLVM doesn't hold to the mistaken notion that one set of optimizations is right for all languages and for all situations. LLVM allows a compiler implementor to make complete decisions about what optimizations to use, in which order, and in what situation.

As a concrete example, LLVM supports both "whole module" passes, which look across as large of body of code as they can (often a whole file, but if run at link time, this can be a substantial portion of the whole program). It also supports and includes "per-function" passes which just operate on a single function at a time, without looking at other functions. For more information on passes and how they are run, see the How to Write a Pass document and the List of LLVM Passes.

For Kaleidoscope, we are currently generating functions on the fly, one at a time, as the user types them in. We aren't shooting for the ultimate optimization experience in this setting, but we also want to catch the easy and quick stuff where possible. As such, we will choose to run a few per-function optimizations as the user types the function in. If we wanted to make a "static Kaleidoscope compiler", we would use exactly the code we have now, except that we would defer running the optimizer until the entire file has been parsed.

In order to get per-function optimizations going, we need to set up a FunctionPassManager to hold and organize the LLVM optimizations that we want to run. Once we have that, we can add a set of optimizations to run. The code looks like this:

        ExistingModuleProvider OurModuleProvider(TheModule);
        FunctionPassManager OurFPM(&OurModuleProvider);

        // Set up the optimizer pipeline.  Start with registering info about how the
        // target lays out data structures.
        OurFPM.add(new TargetData(*TheExecutionEngine->getTargetData()));
        // Do simple "peephole" optimizations and bit-twiddling optzns.
        OurFPM.add(createInstructionCombiningPass());
        // Reassociate expressions.
        OurFPM.add(createReassociatePass());
        // Eliminate Common SubExpressions.
        OurFPM.add(createGVNPass());
        // Simplify the control flow graph (deleting unreachable blocks, etc).
        OurFPM.add(createCFGSimplificationPass());

        // Set the global so the code gen can use this.
        TheFPM = &OurFPM;

        // Run the main "interpreter loop" now.
        MainLoop();

This code defines two objects, an `ExistingModuleProvider` and a `FunctionPassManager`. The former is basically a wrapper around our `Module` that the PassManager requires. It provides certain flexibility that we're not going to take advantage of here, so I won't dive into any details about it.

The meat of the matter here, is the definition of "`OurFPM`". It requires a pointer to the `Module` (through the `ModuleProvider`) to construct itself. Once it is set up, we use a series of "add" calls to add a bunch of LLVM passes. The first pass is basically boilerplate, it adds a pass so that later optimizations know how the data structures in the program are layed out. The "`TheExecutionEngine`" variable is related to the JIT, which we will get to in the next section.

In this case, we choose to add 4 optimization passes. The passes we chose here are a pretty standard set of "cleanup" optimizations that are useful for a wide variety of code. I won't delve into what they do but, believe me, they are a good starting place :).

Once the PassManager is set up, we need to make use of it. We do this by running it after our newly created function is constructed (in `FunctionAST::Codegen`), but before it is returned to the client:

      if (Value *RetVal = Body->Codegen()) {
        // Finish off the function.
        Builder.CreateRet(RetVal);

        // Validate the generated code, checking for consistency.
        verifyFunction(*TheFunction);

        // Optimize the function.
        TheFPM->run(*TheFunction);

        return TheFunction;
      }

As you can see, this is pretty straightforward. The `FunctionPassManager` optimizes and updates the LLVM Function* in place, improving (hopefully) its body. With this in place, we can try our test above again:

    ready> def test(x) (1+2+x)*(x+(1+2));
    ready> Read function definition:
    define double @test(double %x) {
    entry:
            %addtmp = add double %x, 3.000000e+00
            %multmp = mul double %addtmp, %addtmp
            ret double %multmp
    }

As expected, we now get our nicely optimized code, saving a floating point add instruction from every execution of this function.

LLVM provides a wide variety of optimizations that can be used in certain circumstances. Some documentation about the various passes is available, but it isn't very complete. Another good source of ideas can come from looking at the passes that `llvm-gcc` or `llvm-ld` run to get started. The "`opt`" tool allows you to experiment with passes from the command line, so you can see if they do anything.

Now that we have reasonable code coming out of our front-end, lets talk about executing it!

Adding a JIT Compiler

Code that is available in LLVM IR can have a wide variety of tools applied to it. For example, you can run optimizations on it (as we did above), you can dump it out in textual or binary forms, you can compile the code to an assembly file (.s) for some target, or you can JIT compile it. The nice thing about the LLVM IR representation is that it is the "common currency" between many different parts of the compiler.

In this section, we'll add JIT compiler support to our interpreter. The basic idea that we want for Kaleidoscope is to have the user enter function bodies as they do now, but immediately evaluate the top-level expressions they type in. For example, if they type in "1 + 2;", we should evaluate and print out 3. If they define a function, they should be able to call it from the command line.

In order to do this, we first declare and initialize the JIT. This is done by adding a global variable and a call in `main`:

    static ExecutionEngine *TheExecutionEngine;
    ...
    int main() {
      ..
      // Create the JIT.
        TheExecutionEngine = EngineBuilder(TheModule).create();
      ..
    }

This creates an abstract "Execution Engine" which can be either a JIT compiler or the LLVM interpreter. LLVM will automatically pick a JIT compiler for you if one is available for your platform, otherwise it will fall back to the interpreter.

Once the `ExecutionEngine` is created, the JIT is ready to be used. There are a variety of APIs that are useful, but the simplest one is the "`getPointerToFunction(F)`" method. This method JIT compiles the specified LLVM Function and returns a function pointer to the generated machine code. In our case, this means that we can change the code that parses a top-level expression to look like this:

    static void HandleTopLevelExpression() {
      // Evaluate a top level expression into an anonymous function.
      if (FunctionAST *F = ParseTopLevelExpr()) {
        if (Function *LF = F->Codegen()) {
          LF->dump();  // Dump the function for exposition purposes.

          // JIT the function, returning a function pointer.
          void *FPtr = TheExecutionEngine->getPointerToFunction(LF);

          // Cast it to the right type (takes no arguments, returns a double) so we
          // can call it as a native function.
          double (*FP)() = (double (*)())FPtr;
          fprintf(stderr, "Evaluated to %f\n", FP());
        }

Recall that we compile top-level expressions into a self-contained LLVM function that takes no arguments and returns the computed double. Because the LLVM JIT compiler matches the native platform ABI, this means that you can just cast the result pointer to a function pointer of that type and call it directly. This means, there is no difference between JIT compiled code and native machine code that is statically linked into your application.

With just these two changes, lets see how Kaleidoscope works now!

    ready> 4+5;
    define double @""() {
    entry:
            ret double 9.000000e+00
    }

    Evaluated to 9.000000

Well this looks like it is basically working. The dump of the function shows the "no argument function that always returns double" that we synthesize for each top level expression that is typed in. This demonstrates very basic functionality, but can we do more?

    ready> def testfunc(x y) x + y*2;
    Read function definition:
    define double @testfunc(double %x, double %y) {
    entry:
            %multmp = mul double %y, 2.000000e+00
            %addtmp = add double %multmp, %x
            ret double %addtmp
    }

    ready> testfunc(4, 10);
    define double @""() {
    entry:
            %calltmp = call double @testfunc( double 4.000000e+00, double 1.000000e+01 )
            ret double %calltmp
    }

    Evaluated to 24.000000

This illustrates that we can now call user code, but there is something a bit subtle going on here. Note that we only invoke the JIT on the anonymous functions that call testfunc, but we never invoked it on testfunc itself.

What actually happened here is that the anonymous function was JIT'd when requested. When the Kaleidoscope app calls through the function pointer that is returned, the anonymous function starts executing. It ends up making the call to the "testfunc" function, and ends up in a stub that invokes the JIT, lazily, on testfunc. Once the JIT finishes lazily compiling testfunc, it returns and the code re-executes the call.

In summary, the JIT will lazily JIT code, on the fly, as it is needed. The JIT provides a number of other more advanced interfaces for things like freeing allocated machine code, rejit'ing functions to update them, etc. However, even with this simple code, we get some surprisingly powerful capabilities - check this out (I removed the dump of the anonymous functions, you should get the idea by now :) :

    ready> extern sin(x);
    Read extern:
    declare double @sin(double)

    ready> extern cos(x);
    Read extern:
    declare double @cos(double)

    ready> sin(1.0);
    Evaluated to 0.841471

    ready> def foo(x) sin(x)*sin(x) + cos(x)*cos(x);
    Read function definition:
    define double @foo(double %x) {
    entry:
            %calltmp = call double @sin( double %x )
            %multmp = mul double %calltmp, %calltmp
            %calltmp2 = call double @cos( double %x )
            %multmp4 = mul double %calltmp2, %calltmp2
            %addtmp = add double %multmp, %multmp4
            ret double %addtmp
    }

    ready> foo(4.0);
    Evaluated to 1.000000

Whoa, how does the JIT know about sin and cos? The answer is surprisingly simple: in this example, the JIT started execution of a function and got to a function call. It realized that the function was not yet JIT compiled and invoked the standard set of routines to resolve the function. In this case, there is no body defined for the function, so the JIT ended up calling "`dlsym("sin")`" on the Kaleidoscope process itself. Since "`sin`" is defined within the JIT's address space, it simply patches up calls in the module to call the libm version of `sin` directly.

The LLVM JIT provides a number of interfaces (look in the `ExecutionEngine.h` file) for controlling how unknown functions get resolved. It allows you to establish explicit mappings between IR objects and addresses (useful for LLVM global variables that you want to map to static tables, for example), allows you to dynamically decide on the fly based on the function name, and even allows you to have the JIT abort itself if any lazy compilation is attempted.

One interesting application of this is that we can now extend the language by writing arbitrary C++ code to implement operations. For example, if we add:

    /// putchard - putchar that takes a double and returns 0.
    extern "C"
    double putchard(double X) {
      putchar((char)X);
      return 0;
    }

Now we can produce simple output to the console by using things like: "`extern putchard(x); putchard(120);`", which prints a lowercase 'x' on the console (120 is the ASCII code for 'x'). Similar code could be used to implement file I/O, console input, and many other capabilities in Kaleidoscope.

This completes the JIT and optimizer chapter of the Kaleidoscope tutorial. At this point, we can compile a non-Turing-complete programming language, optimize and JIT compile it in a user-driven way. Next up we'll look into extending the language with control flow constructs, tackling some interesting LLVM IR issues along the way.

Full Code Listing

Here is the complete code listing for our running example, enhanced with the LLVM JIT and optimizer. To build this example, use:

       # Compile
       g++ -g toy.cpp `llvm-config --cppflags --ldflags --libs core jit native` -O3 -o toy
       # Run
       ./toy

If you are compiling this on Linux, make sure to add the "-rdynamic" option as well. This makes sure that the external functions are resolved properly at runtime.

Here is the code:

    #include "llvm/DerivedTypes.h"
    #include "llvm/ExecutionEngine/ExecutionEngine.h"
    #include "llvm/LLVMContext.h"
    #include "llvm/Module.h"
    #include "llvm/ModuleProvider.h"
    #include "llvm/PassManager.h"
    #include "llvm/Analysis/Verifier.h"
    #include "llvm/Target/TargetData.h"
    #include "llvm/Transforms/Scalar.h"
    #include "llvm/Support/IRBuilder.h"
    #include <cstdio>
    #include <string>
    #include <map>
    #include <vector>
    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,
    };

    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;
        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 && LastChar != '\n' && 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 {
      double Val;
    public:
      NumberExprAST(double val) : Val(val) {}
      virtual Value *Codegen();
    };

    /// VariableExprAST - Expression class for referencing a variable, like "a".
    class VariableExprAST : public ExprAST {
      std::string Name;
    public:
      VariableExprAST(const std::string &name) : Name(name) {}
      virtual Value *Codegen();
    };

    /// BinaryExprAST - Expression class for a binary operator.
    class BinaryExprAST : public ExprAST {
      char Op;
      ExprAST *LHS, *RHS;
    public:
      BinaryExprAST(char op, ExprAST *lhs, ExprAST *rhs)
        : Op(op), LHS(lhs), RHS(rhs) {}
      virtual Value *Codegen();
    };

    /// CallExprAST - Expression class for function calls.
    class CallExprAST : public ExprAST {
      std::string Callee;
      std::vector<ExprAST*> Args;
    public:
      CallExprAST(const std::string &callee, std::vector<ExprAST*> &args)
        : Callee(callee), Args(args) {}
      virtual Value *Codegen();
    };

    /// 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<std::string> Args;
    public:
      PrototypeAST(const std::string &name, const std::vector<std::string> &args)
        : Name(name), Args(args) {}

      Function *Codegen();
    };

    /// FunctionAST - This class represents a function definition itself.
    class FunctionAST {
      PrototypeAST *Proto;
      ExprAST *Body;
    public:
      FunctionAST(PrototypeAST *proto, ExprAST *body)
        : Proto(proto), Body(body) {}

      Function *Codegen();
    };

    //===----------------------------------------------------------------------===//
    // Parser
    //===----------------------------------------------------------------------===//

    /// CurTok/getNextToken - Provide a simple token buffer.  CurTok is the current
    /// token the parser it looking at.  getNextToken reads another token from the
    /// lexer and updates CurTok with its results.
    static int CurTok;
    static int getNextToken() {
      return CurTok = gettok();
    }

    /// BinopPrecedence - This holds the precedence for each binary operator that is
    /// defined.
    static std::map<char, int> BinopPrecedence;

    /// GetTokPrecedence - Get the precedence of the pending binary operator token.
    static int GetTokPrecedence() {
      if (!isascii(CurTok))
        return -1;

      // Make sure it's a declared binop.
      int TokPrec = BinopPrecedence[CurTok];
      if (TokPrec <= 0) return -1;
      return TokPrec;
    }

    /// Error* - These are little helper functions for error handling.
    ExprAST *Error(const char *Str) { fprintf(stderr, "Error: %s\n", Str);return 0;}
    PrototypeAST *ErrorP(const char *Str) { Error(Str); return 0; }
    FunctionAST *ErrorF(const char *Str) { Error(Str); return 0; }

    static ExprAST *ParseExpression();

    /// identifierexpr
    ///   ::= identifier
    ///   ::= identifier '(' expression* ')'
    static ExprAST *ParseIdentifierExpr() {
      std::string IdName = IdentifierStr;

      getNextToken();  // eat identifier.

      if (CurTok != '(') // Simple variable ref.
        return new VariableExprAST(IdName);

      // Call.
      getNextToken();  // eat (
      std::vector<ExprAST*> Args;
      if (CurTok != ')') {
        while (1) {
          ExprAST *Arg = ParseExpression();
          if (!Arg) return 0;
          Args.push_back(Arg);

          if (CurTok == ')') break;

          if (CurTok != ',')
            return Error("Expected ')' or ',' in argument list");
          getNextToken();
        }
      }

      // Eat the ')'.
      getNextToken();

      return new CallExprAST(IdName, Args);
    }

    /// numberexpr ::= number
    static ExprAST *ParseNumberExpr() {
      ExprAST *Result = new NumberExprAST(NumVal);
      getNextToken(); // consume the number
      return Result;
    }

    /// parenexpr ::= '(' expression ')'
    static ExprAST *ParseParenExpr() {
      getNextToken();  // eat (.
      ExprAST *V = ParseExpression();
      if (!V) return 0;

      if (CurTok != ')')
        return Error("expected ')'");
      getNextToken();  // eat ).
      return V;
    }

    /// primary
    ///   ::= identifierexpr
    ///   ::= numberexpr
    ///   ::= parenexpr
    static ExprAST *ParsePrimary() {
      switch (CurTok) {
      default: return Error("unknown token when expecting an expression");
      case tok_identifier: return ParseIdentifierExpr();
      case tok_number:     return ParseNumberExpr();
      case '(':            return ParseParenExpr();
      }
    }

    /// binoprhs
    ///   ::= ('+' primary)*
    static ExprAST *ParseBinOpRHS(int ExprPrec, ExprAST *LHS) {
      // If this is a binop, find its precedence.
      while (1) {
        int TokPrec = GetTokPrecedence();

        // If this is a binop that binds at least as tightly as the current binop,
        // consume it, otherwise we are done.
        if (TokPrec < ExprPrec)
          return LHS;

        // Okay, we know this is a binop.
        int BinOp = CurTok;
        getNextToken();  // eat binop

        // Parse the primary expression after the binary operator.
        ExprAST *RHS = ParsePrimary();
        if (!RHS) return 0;

        // If BinOp binds less tightly with RHS than the operator after RHS, let
        // the pending operator take RHS as its LHS.
        int NextPrec = GetTokPrecedence();
        if (TokPrec < NextPrec) {
          RHS = ParseBinOpRHS(TokPrec+1, RHS);
          if (RHS == 0) return 0;
        }

        // Merge LHS/RHS.
        LHS = new BinaryExprAST(BinOp, LHS, RHS);
      }
    }

    /// expression
    ///   ::= primary binoprhs
    ///
    static ExprAST *ParseExpression() {
      ExprAST *LHS = ParsePrimary();
      if (!LHS) return 0;

      return ParseBinOpRHS(0, LHS);
    }

    /// prototype
    ///   ::= id '(' id* ')'
    static PrototypeAST *ParsePrototype() {
      if (CurTok != tok_identifier)
        return ErrorP("Expected function name in prototype");

      std::string FnName = IdentifierStr;
      getNextToken();

      if (CurTok != '(')
        return ErrorP("Expected '(' in prototype");

      std::vector<std::string> ArgNames;
      while (getNextToken() == tok_identifier)
        ArgNames.push_back(IdentifierStr);
      if (CurTok != ')')
        return ErrorP("Expected ')' in prototype");

      // success.
      getNextToken();  // eat ')'.

      return new PrototypeAST(FnName, ArgNames);
    }

    /// definition ::= 'def' prototype expression
    static FunctionAST *ParseDefinition() {
      getNextToken();  // eat def.
      PrototypeAST *Proto = ParsePrototype();
      if (Proto == 0) return 0;

      if (ExprAST *E = ParseExpression())
        return new FunctionAST(Proto, E);
      return 0;
    }

    /// toplevelexpr ::= expression
    static FunctionAST *ParseTopLevelExpr() {
      if (ExprAST *E = ParseExpression()) {
        // Make an anonymous proto.
        PrototypeAST *Proto = new PrototypeAST("", std::vector<std::string>());
        return new FunctionAST(Proto, E);
      }
      return 0;
    }

    /// external ::= 'extern' prototype
    static PrototypeAST *ParseExtern() {
      getNextToken();  // eat extern.
      return ParsePrototype();
    }

    //===----------------------------------------------------------------------===//
    // Code Generation
    //===----------------------------------------------------------------------===//

    static Module *TheModule;
    static IRBuilder<> Builder(getGlobalContext());
    static std::map<std::string, Value*> NamedValues;
    static FunctionPassManager *TheFPM;

    Value *ErrorV(const char *Str) { Error(Str); return 0; }

    Value *NumberExprAST::Codegen() {
      return ConstantFP::get(getGlobalContext(), APFloat(Val));
    }

    Value *VariableExprAST::Codegen() {
      // Look this variable up in the function.
      Value *V = NamedValues[Name];
      return V ? V : ErrorV("Unknown variable name");
    }

    Value *BinaryExprAST::Codegen() {
      Value *L = LHS->Codegen();
      Value *R = RHS->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 '<':
        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");
      default: return ErrorV("invalid binary operator");
      }
    }

    Value *CallExprAST::Codegen() {
      // Look up the name in the global module table.
      Function *CalleeF = TheModule->getFunction(Callee);
      if (CalleeF == 0)
        return ErrorV("Unknown function referenced");

      // If argument mismatch error.
      if (CalleeF->arg_size() != Args.size())
        return ErrorV("Incorrect # arguments passed");

      std::vector<Value*> ArgsV;
      for (unsigned i = 0, e = Args.size(); i != e; ++i) {
        ArgsV.push_back(Args[i]->Codegen());
        if (ArgsV.back() == 0) return 0;
      }

      return Builder.CreateCall(CalleeF, ArgsV.begin(), ArgsV.end(), "calltmp");
    }

    Function *PrototypeAST::Codegen() {
      // Make the function type:  double(double,double) etc.
      std::vector<const Type*> Doubles(Args.size(), Type::getDoubleTy(getGlobalContext()));
      FunctionType *FT = FunctionType::get(Type::getDoubleTy(getGlobalContext()), Doubles, false);

      Function *F = Function::Create(FT, Function::ExternalLinkage, Name, TheModule);

      // If F conflicted, there was already something named 'Name'.  If it has a
      // body, don't allow redefinition or reextern.
      if (F->getName() != Name) {
        // Delete the one we just made and get the existing one.
        F->eraseFromParent();
        F = TheModule->getFunction(Name);

        // If F already has a body, reject this.
        if (!F->empty()) {
          ErrorF("redefinition of function");
          return 0;
        }

        // If F took a different number of args, reject.
        if (F->arg_size() != Args.size()) {
          ErrorF("redefinition of function with different # args");
          return 0;
        }
      }

      // Set names for all arguments.
      unsigned Idx = 0;
      for (Function::arg_iterator AI = F->arg_begin(); Idx != Args.size();
           ++AI, ++Idx) {
        AI->setName(Args[Idx]);

        // Add arguments to variable symbol table.
        NamedValues[Args[Idx]] = AI;
      }

      return F;
    }

    Function *FunctionAST::Codegen() {
      NamedValues.clear();

      Function *TheFunction = Proto->Codegen();
      if (TheFunction == 0)
        return 0;

      // Create a new basic block to start insertion into.
      BasicBlock *BB = BasicBlock::Create(getGlobalContext(), "entry", TheFunction);
      Builder.SetInsertPoint(BB);

      if (Value *RetVal = Body->Codegen()) {
        // Finish off the function.
        Builder.CreateRet(RetVal);

        // Validate the generated code, checking for consistency.
        verifyFunction(*TheFunction);

        // Optimize the function.
        TheFPM->run(*TheFunction);

        return TheFunction;
      }

      // Error reading body, remove function.
      TheFunction->eraseFromParent();
      return 0;
    }

    //===----------------------------------------------------------------------===//
    // Top-Level parsing and JIT Driver
    //===----------------------------------------------------------------------===//

    static ExecutionEngine *TheExecutionEngine;

    static void HandleDefinition() {
      if (FunctionAST *F = ParseDefinition()) {
        if (Function *LF = F->Codegen()) {
          fprintf(stderr, "Read function definition:");
          LF->dump();
        }
      } else {
        // Skip token for error recovery.
        getNextToken();
      }
    }

    static void HandleExtern() {
      if (PrototypeAST *P = ParseExtern()) {
        if (Function *F = P->Codegen()) {
          fprintf(stderr, "Read extern: ");
          F->dump();
        }
      } else {
        // Skip token for error recovery.
        getNextToken();
      }
    }

    static void HandleTopLevelExpression() {
      // Evaluate a top level expression into an anonymous function.
      if (FunctionAST *F = ParseTopLevelExpr()) {
        if (Function *LF = F->Codegen()) {
          // JIT the function, returning a function pointer.
          void *FPtr = TheExecutionEngine->getPointerToFunction(LF);

          // Cast it to the right type (takes no arguments, returns a double) so we
          // can call it as a native function.
          double (*FP)() = (double (*)())FPtr;
          fprintf(stderr, "Evaluated to %f\n", FP());
        }
      } else {
        // Skip token for error recovery.
        getNextToken();
      }
    }

    /// top ::= definition | external | expression | ';'
    static void MainLoop() {
      while (1) {
        fprintf(stderr, "ready> ");
        switch (CurTok) {
        case tok_eof:    return;
        case ';':        getNextToken(); break;  // ignore top level semicolons.
        case tok_def:    HandleDefinition(); break;
        case tok_extern: HandleExtern(); break;
        default:         HandleTopLevelExpression(); break;
        }
      }
    }

    //===----------------------------------------------------------------------===//
    // "Library" functions that can be "extern'd" from user code.
    //===----------------------------------------------------------------------===//

    /// putchard - putchar that takes a double and returns 0.
    extern "C"
    double putchard(double X) {
      putchar((char)X);
      return 0;
    }

    //===----------------------------------------------------------------------===//
    // Main driver code.
    //===----------------------------------------------------------------------===//

    int main() {
      // Install standard binary operators.
      // 1 is lowest precedence.
      BinopPrecedence['<'] = 10;
      BinopPrecedence['+'] = 20;
      BinopPrecedence['-'] = 20;
      BinopPrecedence['*'] = 40;  // highest.

      // Prime the first token.
      fprintf(stderr, "ready> ");
      getNextToken();

      // Make the module, which holds all the code.
      TheModule = new Module("my cool jit", getGlobalContext());

      // Create the JIT.
      TheExecutionEngine = EngineBuilder(TheModule).create();

      {
        ExistingModuleProvider OurModuleProvider(TheModule);
        FunctionPassManager OurFPM(&OurModuleProvider);

        // Set up the optimizer pipeline.  Start with registering info about how the
        // target lays out data structures.
        OurFPM.add(new TargetData(*TheExecutionEngine->getTargetData()));
        // Do simple "peephole" optimizations and bit-twiddling optzns.
        OurFPM.add(createInstructionCombiningPass());
        // Reassociate expressions.
        OurFPM.add(createReassociatePass());
        // Eliminate Common SubExpressions.
        OurFPM.add(createGVNPass());
        // Simplify the control flow graph (deleting unreachable blocks, etc).
        OurFPM.add(createCFGSimplificationPass());

        // Set the global so the code gen can use this.
        TheFPM = &OurFPM;

        // Run the main "interpreter loop" now.
        MainLoop();

        TheFPM = 0;

        // Print out all of the generated code.
        TheModule->dump();
      }  // Free module provider (and thus the module) and pass manager.

      return 0;
    }

Next: Extending the language: control flow