# 4. Kaleidoscope: Adding JIT and Optimizer Support

## 4.1. 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.

## 4.2. 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 = fadd 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 = fadd double 2.000000e+00, 1.000000e+00
            %addtmp1 = fadd 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 = fadd double 3.000000e+00, %x
            %addtmp1 = fadd double %x, 3.000000e+00
            %multmp = fmul 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”.

## 4.3. 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 addition to the distinction between function and module passes, passes can be divided into transform and analysis passes. Transform passes mutate the IR, and analysis passes compute information that other passes can use. In order to add a transform pass, all analysis passes it depends upon must be registered in advance.

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. We’ll need a new FunctionPassManager for each module that we want to optimize, so we’ll add to a function created in the previous chapter (`InitializeModule()`):

    void InitializeModuleAndManagers(void) {
      // Open a new context and module.
      TheContext = std::make_unique<LLVMContext>();
      TheModule = std::make_unique<Module>("KaleidoscopeJIT", *TheContext);
      TheModule->setDataLayout(TheJIT->getDataLayout());

      // Create a new builder for the module.
      Builder = std::make_unique<IRBuilder<>>(*TheContext);

      // Create new pass and analysis managers.
      TheFPM = std::make_unique<FunctionPassManager>();
      TheLAM = std::make_unique<LoopAnalysisManager>();
      TheFAM = std::make_unique<FunctionAnalysisManager>();
      TheCGAM = std::make_unique<CGSCCAnalysisManager>();
      TheMAM = std::make_unique<ModuleAnalysisManager>();
      ThePIC = std::make_unique<PassInstrumentationCallbacks>();
      TheSI = std::make_unique<StandardInstrumentations>(*TheContext,
                                                        /*DebugLogging*/ true);
      TheSI->registerCallbacks(*ThePIC, TheMAM.get());
      ...

After initializing the global module `TheModule` and the FunctionPassManager, we need to initialize other parts of the framework. The four AnalysisManagers allow us to add analysis passes that run across the four levels of the IR hierarchy. PassInstrumentationCallbacks and StandardInstrumentations are required for the pass instrumentation framework, which allows developers to customize what happens between passes.

Once these managers are set up, we use a series of “addPass” calls to add a bunch of LLVM transform passes:

    // Add transform passes.
    // Do simple "peephole" optimizations and bit-twiddling optzns.
    TheFPM->addPass(InstCombinePass());
    // Reassociate expressions.
    TheFPM->addPass(ReassociatePass());
    // Eliminate Common SubExpressions.
    TheFPM->addPass(GVNPass());
    // Simplify the control flow graph (deleting unreachable blocks, etc).
    TheFPM->addPass(SimplifyCFGPass());

In this case, we choose to add four optimization passes. The passes we choose 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 :).

Next, we register the analysis passes used by the transform passes.

      // Register analysis passes used in these transform passes.
      PassBuilder PB;
      PB.registerModuleAnalyses(*TheMAM);
      PB.registerFunctionAnalyses(*TheFAM);
      PB.crossRegisterProxies(*TheLAM, *TheFAM, *TheCGAM, *TheMAM);
    }

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, *TheFAM);

      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 = fadd double %x, 3.000000e+00
            %multmp = fmul 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 `Clang` runs 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, let’s talk about executing it!

## 4.4. 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 prepare the environment to create code for the current native target and declare and initialize the JIT. This is done by calling some `InitializeNativeTarget\*` functions and adding a global variable `TheJIT`, and initializing it in `main`:

    static std::unique_ptr<KaleidoscopeJIT> TheJIT;
    ...
    int main() {
      InitializeNativeTarget();
      InitializeNativeTargetAsmPrinter();
      InitializeNativeTargetAsmParser();

      // 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();

      TheJIT = std::make_unique<KaleidoscopeJIT>();

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

      return 0;
    }

We also need to setup the data layout for the JIT:

    void InitializeModuleAndPassManager(void) {
      // Open a new context and module.
      TheContext = std::make_unique<LLVMContext>();
      TheModule = std::make_unique<Module>("my cool jit", TheContext);
      TheModule->setDataLayout(TheJIT->getDataLayout());

      // Create a new builder for the module.
      Builder = std::make_unique<IRBuilder<>>(*TheContext);

      // Create a new pass manager attached to it.
      TheFPM = std::make_unique<legacy::FunctionPassManager>(TheModule.get());
      ...

The KaleidoscopeJIT class is a simple JIT built specifically for these tutorials, available inside the LLVM source code at llvm-src/examples/Kaleidoscope/include/KaleidoscopeJIT.h. In later chapters we will look at how it works and extend it with new features, but for now we will take it as given. Its API is very simple: `addModule` adds an LLVM IR module to the JIT, making its functions available for execution (with its memory managed by a `ResourceTracker`); and `lookup` allows us to look up pointers to the compiled code.

We can take this simple API and change our code that parses top-level expressions to look like this:

    static ExitOnError ExitOnErr;
    ...
    static void HandleTopLevelExpression() {
      // Evaluate a top-level expression into an anonymous function.
      if (auto FnAST = ParseTopLevelExpr()) {
        if (FnAST->codegen()) {
          // Create a ResourceTracker to track JIT'd memory allocated to our
          // anonymous expression -- that way we can free it after executing.
          auto RT = TheJIT->getMainJITDylib().createResourceTracker();

          auto TSM = ThreadSafeModule(std::move(TheModule), std::move(TheContext));
          ExitOnErr(TheJIT->addModule(std::move(TSM), RT));
          InitializeModuleAndPassManager();

          // Search the JIT for the __anon_expr symbol.
          auto ExprSymbol = ExitOnErr(TheJIT->lookup("__anon_expr"));
          assert(ExprSymbol && "Function not found");

          // Get the symbol's address and cast it to the right type (takes no
          // arguments, returns a double) so we can call it as a native function.
          double (*FP)() = ExprSymbol.getAddress().toPtr<double (*)()>();
          fprintf(stderr, "Evaluated to %f\n", FP());

          // Delete the anonymous expression module from the JIT.
          ExitOnErr(RT->remove());
        }

If parsing and codegen succeed, the next step is to add the module containing the top-level expression to the JIT. We do this by calling addModule, which triggers code generation for all the functions in the module, and accepts a `ResourceTracker` which can be used to remove the module from the JIT later. Once the module has been added to the JIT it can no longer be modified, so we also open a new module to hold subsequent code by calling `InitializeModuleAndPassManager()`.

Once we’ve added the module to the JIT we need to get a pointer to the final generated code. We do this by calling the JIT’s `lookup` method, and passing the name of the top-level expression function: `__anon_expr`. Since we just added this function, we assert that `lookup` returned a result.

Next, we get the in-memory address of the `__anon_expr` function by calling `getAddress()` on the symbol. 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.

Finally, since we don’t support re-evaluation of top-level expressions, we remove the module from the JIT when we’re done to free the associated memory. Recall, however, that the module we created a few lines earlier (via `InitializeModuleAndPassManager`) is still open and waiting for new code to be added.

With just these two changes, let’s see how Kaleidoscope works now!

    ready> 4+5;
    Read top-level expression:
    define double @0() {
    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 = fmul double %y, 2.000000e+00
      %addtmp = fadd double %multmp, %x
      ret double %addtmp
    }

    ready> testfunc(4, 10);
    Read top-level expression:
    define double @1() {
    entry:
      %calltmp = call double @testfunc(double 4.000000e+00, double 1.000000e+01)
      ret double %calltmp
    }

    Evaluated to 24.000000

    ready> testfunc(5, 10);
    ready> LLVM ERROR: Program used external function 'testfunc' which could not be resolved!

Function definitions and calls also work, but something went very wrong on that last line. The call looks valid, so what happened? As you may have guessed from the API a Module is a unit of allocation for the JIT, and testfunc was part of the same module that contained anonymous expression. When we removed that module from the JIT to free the memory for the anonymous expression, we deleted the definition of `testfunc` along with it. Then, when we tried to call testfunc a second time, the JIT could no longer find it.

The easiest way to fix this is to put the anonymous expression in a separate module from the rest of the function definitions. The JIT will happily resolve function calls across module boundaries, as long as each of the functions called has a prototype, and is added to the JIT before it is called. By putting the anonymous expression in a different module we can delete it without affecting the rest of the functions.

In fact, we’re going to go a step further and put every function in its own module. Doing so allows us to exploit a useful property of the KaleidoscopeJIT that will make our environment more REPL-like: Functions can be added to the JIT more than once (unlike a module where every function must have a unique definition). When you look up a symbol in KaleidoscopeJIT it will always return the most recent definition:

    ready> def foo(x) x + 1;
    Read function definition:
    define double @foo(double %x) {
    entry:
      %addtmp = fadd double %x, 1.000000e+00
      ret double %addtmp
    }

    ready> foo(2);
    Evaluated to 3.000000

    ready> def foo(x) x + 2;
    define double @foo(double %x) {
    entry:
      %addtmp = fadd double %x, 2.000000e+00
      ret double %addtmp
    }

    ready> foo(2);
    Evaluated to 4.000000

To allow each function to live in its own module we’ll need a way to re-generate previous function declarations into each new module we open:

    static std::unique_ptr<KaleidoscopeJIT> TheJIT;

    ...

    Function *getFunction(std::string Name) {
      // First, see if the function has already been added to the current module.
      if (auto *F = TheModule->getFunction(Name))
        return F;

      // If not, check whether we can codegen the declaration from some existing
      // prototype.
      auto FI = FunctionProtos.find(Name);
      if (FI != FunctionProtos.end())
        return FI->second->codegen();

      // If no existing prototype exists, return null.
      return nullptr;
    }

    ...

    Value *CallExprAST::codegen() {
      // Look up the name in the global module table.
      Function *CalleeF = getFunction(Callee);

    ...

    Function *FunctionAST::codegen() {
      // Transfer ownership of the prototype to the FunctionProtos map, but keep a
      // reference to it for use below.
      auto &P = *Proto;
      FunctionProtos[Proto->getName()] = std::move(Proto);
      Function *TheFunction = getFunction(P.getName());
      if (!TheFunction)
        return nullptr;

To enable this, we’ll start by adding a new global, `FunctionProtos`, that holds the most recent prototype for each function. We’ll also add a convenience method, `getFunction()`, to replace calls to `TheModule->getFunction()`. Our convenience method searches `TheModule` for an existing function declaration, falling back to generating a new declaration from FunctionProtos if it doesn’t find one. In `CallExprAST::codegen()` we just need to replace the call to `TheModule->getFunction()`. In `FunctionAST::codegen()` we need to update the FunctionProtos map first, then call `getFunction()`. With this done, we can always obtain a function declaration in the current module for any previously declared function.

We also need to update HandleDefinition and HandleExtern:

    static void HandleDefinition() {
      if (auto FnAST = ParseDefinition()) {
        if (auto *FnIR = FnAST->codegen()) {
          fprintf(stderr, "Read function definition:");
          FnIR->print(errs());
          fprintf(stderr, "\n");
          ExitOnErr(TheJIT->addModule(
              ThreadSafeModule(std::move(TheModule), std::move(TheContext))));
          InitializeModuleAndPassManager();
        }
      } else {
        // Skip token for error recovery.
         getNextToken();
      }
    }

    static void HandleExtern() {
      if (auto ProtoAST = ParseExtern()) {
        if (auto *FnIR = ProtoAST->codegen()) {
          fprintf(stderr, "Read extern: ");
          FnIR->print(errs());
          fprintf(stderr, "\n");
          FunctionProtos[ProtoAST->getName()] = std::move(ProtoAST);
        }
      } else {
        // Skip token for error recovery.
        getNextToken();
      }
    }

In HandleDefinition, we add two lines to transfer the newly defined function to the JIT and open a new module. In HandleExtern, we just need to add one line to add the prototype to FunctionProtos.

Warning

Duplication of symbols in separate modules is not allowed since LLVM-9. That means you can not redefine function in your Kaleidoscope as its shown below. Just skip this part.

The reason is that the newer OrcV2 JIT APIs are trying to stay very close to the static and dynamic linker rules, including rejecting duplicate symbols. Requiring symbol names to be unique allows us to support concurrent compilation for symbols using the (unique) symbol names as keys for tracking.

With these changes made, let’s try our REPL again (I removed the dump of the anonymous functions this time, you should get the idea by now :) :

    ready> def foo(x) x + 1;
    ready> foo(2);
    Evaluated to 3.000000

    ready> def foo(x) x + 2;
    ready> foo(2);
    Evaluated to 4.000000

It works!

Even with this simple code, we get some surprisingly powerful capabilities - check this out:

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

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

    ready> sin(1.0);
    Read top-level expression:
    define double @2() {
    entry:
      ret double 0x3FEAED548F090CEE
    }

    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 = fmul double %calltmp, %calltmp
      %calltmp2 = call double @cos(double %x)
      %multmp4 = fmul double %calltmp2, %calltmp2
      %addtmp = fadd double %multmp, %multmp4
      ret double %addtmp
    }

    ready> foo(4.0);
    Read top-level expression:
    define double @3() {
    entry:
      %calltmp = call double @foo(double 4.000000e+00)
      ret double %calltmp
    }

    Evaluated to 1.000000

Whoa, how does the JIT know about sin and cos? The answer is surprisingly simple: The KaleidoscopeJIT has a straightforward symbol resolution rule that it uses to find symbols that aren’t available in any given module: First it searches all the modules that have already been added to the JIT, from the most recent to the oldest, to find the newest definition. If no definition is found inside the JIT, it falls back to 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. But in some cases this even goes further: as sin and cos are names of standard math functions, the constant folder will directly evaluate the function calls to the correct result when called with constants like in the “`sin(1.0)`” above.

In the future we’ll see how tweaking this symbol resolution rule can be used to enable all sorts of useful features, from security (restricting the set of symbols available to JIT’d code), to dynamic code generation based on symbol names, and even lazy compilation.

One immediate benefit of the symbol resolution rule is that we can now extend the language by writing arbitrary C++ code to implement operations. For example, if we add:

    #ifdef _WIN32
    #define DLLEXPORT __declspec(dllexport)
    #else
    #define DLLEXPORT
    #endif

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

Note, that for Windows we need to actually export the functions because the dynamic symbol loader will use `GetProcAddress` to find the symbols.

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.

## 4.5. 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
    clang++ -g toy.cpp `llvm-config --cxxflags --ldflags --system-libs --libs core orcjit 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 "../include/KaleidoscopeJIT.h"
    #include "llvm/ADT/APFloat.h"
    #include "llvm/ADT/STLExtras.h"
    #include "llvm/IR/BasicBlock.h"
    #include "llvm/IR/Constants.h"
    #include "llvm/IR/DerivedTypes.h"
    #include "llvm/IR/Function.h"
    #include "llvm/IR/IRBuilder.h"
    #include "llvm/IR/LLVMContext.h"
    #include "llvm/IR/Module.h"
    #include "llvm/IR/PassManager.h"
    #include "llvm/IR/Type.h"
    #include "llvm/IR/Verifier.h"
    #include "llvm/Passes/PassBuilder.h"
    #include "llvm/Passes/StandardInstrumentations.h"
    #include "llvm/Support/TargetSelect.h"
    #include "llvm/Target/TargetMachine.h"
    #include "llvm/Transforms/InstCombine/InstCombine.h"
    #include "llvm/Transforms/Scalar.h"
    #include "llvm/Transforms/Scalar/GVN.h"
    #include "llvm/Transforms/Scalar/Reassociate.h"
    #include "llvm/Transforms/Scalar/SimplifyCFG.h"
    #include <algorithm>
    #include <cassert>
    #include <cctype>
    #include <cstdint>
    #include <cstdio>
    #include <cstdlib>
    #include <map>
    #include <memory>
    #include <string>
    #include <vector>

    using namespace llvm;
    using namespace llvm::orc;

    //===----------------------------------------------------------------------===//
    // 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(), nullptr);
        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)
    //===----------------------------------------------------------------------===//

    namespace {

    /// ExprAST - Base class for all expression nodes.
    class ExprAST {
    public:
      virtual ~ExprAST() = default;

      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) {}

      Value *codegen() override;
    };

    /// VariableExprAST - Expression class for referencing a variable, like "a".
    class VariableExprAST : public ExprAST {
      std::string Name;

    public:
      VariableExprAST(const std::string &Name) : Name(Name) {}

      Value *codegen() override;
    };

    /// BinaryExprAST - Expression class for a binary operator.
    class BinaryExprAST : public ExprAST {
      char Op;
      std::unique_ptr<ExprAST> LHS, RHS;

    public:
      BinaryExprAST(char Op, std::unique_ptr<ExprAST> LHS,
                    std::unique_ptr<ExprAST> RHS)
          : Op(Op), LHS(std::move(LHS)), RHS(std::move(RHS)) {}

      Value *codegen() override;
    };

    /// CallExprAST - Expression class for function calls.
    class CallExprAST : public ExprAST {
      std::string Callee;
      std::vector<std::unique_ptr<ExprAST>> Args;

    public:
      CallExprAST(const std::string &Callee,
                  std::vector<std::unique_ptr<ExprAST>> Args)
          : Callee(Callee), Args(std::move(Args)) {}

      Value *codegen() override;
    };

    /// PrototypeAST - This class represents the "prototype" for a function,
    /// which captures its name, and its argument names (thus implicitly the number
    /// of arguments the function takes).
    class PrototypeAST {
      std::string Name;
      std::vector<std::string> Args;

    public:
      PrototypeAST(const std::string &Name, std::vector<std::string> Args)
          : Name(Name), Args(std::move(Args)) {}

      Function *codegen();
      const std::string &getName() const { return Name; }
    };

    /// FunctionAST - This class represents a function definition itself.
    class FunctionAST {
      std::unique_ptr<PrototypeAST> Proto;
      std::unique_ptr<ExprAST> Body;

    public:
      FunctionAST(std::unique_ptr<PrototypeAST> Proto,
                  std::unique_ptr<ExprAST> Body)
          : Proto(std::move(Proto)), Body(std::move(Body)) {}

      Function *codegen();
    };

    } // end anonymous namespace

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

    /// CurTok/getNextToken - Provide a simple token buffer.  CurTok is the current
    /// token the parser is 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;
    }

    /// LogError* - These are little helper functions for error handling.
    std::unique_ptr<ExprAST> LogError(const char *Str) {
      fprintf(stderr, "Error: %s\n", Str);
      return nullptr;
    }

    std::unique_ptr<PrototypeAST> LogErrorP(const char *Str) {
      LogError(Str);
      return nullptr;
    }

    static std::unique_ptr<ExprAST> ParseExpression();

    /// numberexpr ::= number
    static std::unique_ptr<ExprAST> ParseNumberExpr() {
      auto Result = std::make_unique<NumberExprAST>(NumVal);
      getNextToken(); // consume the number
      return std::move(Result);
    }

    /// parenexpr ::= '(' expression ')'
    static std::unique_ptr<ExprAST> ParseParenExpr() {
      getNextToken(); // eat (.
      auto V = ParseExpression();
      if (!V)
        return nullptr;

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

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

      getNextToken(); // eat identifier.

      if (CurTok != '(') // Simple variable ref.
        return std::make_unique<VariableExprAST>(IdName);

      // Call.
      getNextToken(); // eat (
      std::vector<std::unique_ptr<ExprAST>> Args;
      if (CurTok != ')') {
        while (true) {
          if (auto Arg = ParseExpression())
            Args.push_back(std::move(Arg));
          else
            return nullptr;

          if (CurTok == ')')
            break;

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

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

      return std::make_unique<CallExprAST>(IdName, std::move(Args));
    }

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

    /// binoprhs
    ///   ::= ('+' primary)*
    static std::unique_ptr<ExprAST> ParseBinOpRHS(int ExprPrec,
                                                  std::unique_ptr<ExprAST> LHS) {
      // If this is a binop, find its precedence.
      while (true) {
        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.
        auto RHS = ParsePrimary();
        if (!RHS)
          return nullptr;

        // 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, std::move(RHS));
          if (!RHS)
            return nullptr;
        }

        // Merge LHS/RHS.
        LHS =
            std::make_unique<BinaryExprAST>(BinOp, std::move(LHS), std::move(RHS));
      }
    }

    /// expression
    ///   ::= primary binoprhs
    ///
    static std::unique_ptr<ExprAST> ParseExpression() {
      auto LHS = ParsePrimary();
      if (!LHS)
        return nullptr;

      return ParseBinOpRHS(0, std::move(LHS));
    }

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

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

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

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

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

      return std::make_unique<PrototypeAST>(FnName, std::move(ArgNames));
    }

    /// definition ::= 'def' prototype expression
    static std::unique_ptr<FunctionAST> ParseDefinition() {
      getNextToken(); // eat def.
      auto Proto = ParsePrototype();
      if (!Proto)
        return nullptr;

      if (auto E = ParseExpression())
        return std::make_unique<FunctionAST>(std::move(Proto), std::move(E));
      return nullptr;
    }

    /// toplevelexpr ::= expression
    static std::unique_ptr<FunctionAST> ParseTopLevelExpr() {
      if (auto E = ParseExpression()) {
        // Make an anonymous proto.
        auto Proto = std::make_unique<PrototypeAST>("__anon_expr",
                                                     std::vector<std::string>());
        return std::make_unique<FunctionAST>(std::move(Proto), std::move(E));
      }
      return nullptr;
    }

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

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

    static std::unique_ptr<LLVMContext> TheContext;
    static std::unique_ptr<Module> TheModule;
    static std::unique_ptr<IRBuilder<>> Builder;
    static std::map<std::string, Value *> NamedValues;
    static std::unique_ptr<KaleidoscopeJIT> TheJIT;
    static std::unique_ptr<FunctionPassManager> TheFPM;
    static std::unique_ptr<LoopAnalysisManager> TheLAM;
    static std::unique_ptr<FunctionAnalysisManager> TheFAM;
    static std::unique_ptr<CGSCCAnalysisManager> TheCGAM;
    static std::unique_ptr<ModuleAnalysisManager> TheMAM;
    static std::unique_ptr<PassInstrumentationCallbacks> ThePIC;
    static std::unique_ptr<StandardInstrumentations> TheSI;
    static std::map<std::string, std::unique_ptr<PrototypeAST>> FunctionProtos;
    static ExitOnError ExitOnErr;

    Value *LogErrorV(const char *Str) {
      LogError(Str);
      return nullptr;
    }

    Function *getFunction(std::string Name) {
      // First, see if the function has already been added to the current module.
      if (auto *F = TheModule->getFunction(Name))
        return F;

      // If not, check whether we can codegen the declaration from some existing
      // prototype.
      auto FI = FunctionProtos.find(Name);
      if (FI != FunctionProtos.end())
        return FI->second->codegen();

      // If no existing prototype exists, return null.
      return nullptr;
    }

    Value *NumberExprAST::codegen() {
      return ConstantFP::get(*TheContext, APFloat(Val));
    }

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

    Value *BinaryExprAST::codegen() {
      Value *L = LHS->codegen();
      Value *R = RHS->codegen();
      if (!L || !R)
        return nullptr;

      switch (Op) {
      case '+':
        return Builder->CreateFAdd(L, R, "addtmp");
      case '-':
        return Builder->CreateFSub(L, R, "subtmp");
      case '*':
        return Builder->CreateFMul(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(*TheContext), "booltmp");
      default:
        return LogErrorV("invalid binary operator");
      }
    }

    Value *CallExprAST::codegen() {
      // Look up the name in the global module table.
      Function *CalleeF = getFunction(Callee);
      if (!CalleeF)
        return LogErrorV("Unknown function referenced");

      // If argument mismatch error.
      if (CalleeF->arg_size() != Args.size())
        return LogErrorV("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())
          return nullptr;
      }

      return Builder->CreateCall(CalleeF, ArgsV, "calltmp");
    }

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

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

      // Set names for all arguments.
      unsigned Idx = 0;
      for (auto &Arg : F->args())
        Arg.setName(Args[Idx++]);

      return F;
    }

    Function *FunctionAST::codegen() {
      // Transfer ownership of the prototype to the FunctionProtos map, but keep a
      // reference to it for use below.
      auto &P = *Proto;
      FunctionProtos[Proto->getName()] = std::move(Proto);
      Function *TheFunction = getFunction(P.getName());
      if (!TheFunction)
        return nullptr;

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

      // Record the function arguments in the NamedValues map.
      NamedValues.clear();
      for (auto &Arg : TheFunction->args())
        NamedValues[std::string(Arg.getName())] = &Arg;

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

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

        // Run the optimizer on the function.
        TheFPM->run(*TheFunction, *TheFAM);

        return TheFunction;
      }

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

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

    static void InitializeModuleAndManagers() {
      // Open a new context and module.
      TheContext = std::make_unique<LLVMContext>();
      TheModule = std::make_unique<Module>("KaleidoscopeJIT", *TheContext);
      TheModule->setDataLayout(TheJIT->getDataLayout());

      // Create a new builder for the module.
      Builder = std::make_unique<IRBuilder<>>(*TheContext);

      // Create new pass and analysis managers.
      TheFPM = std::make_unique<FunctionPassManager>();
      TheLAM = std::make_unique<LoopAnalysisManager>();
      TheFAM = std::make_unique<FunctionAnalysisManager>();
      TheCGAM = std::make_unique<CGSCCAnalysisManager>();
      TheMAM = std::make_unique<ModuleAnalysisManager>();
      ThePIC = std::make_unique<PassInstrumentationCallbacks>();
      TheSI = std::make_unique<StandardInstrumentations>(*TheContext,
                                                         /*DebugLogging*/ true);
      TheSI->registerCallbacks(*ThePIC, TheMAM.get());

      // Add transform passes.
      // Do simple "peephole" optimizations and bit-twiddling optzns.
      TheFPM->addPass(InstCombinePass());
      // Reassociate expressions.
      TheFPM->addPass(ReassociatePass());
      // Eliminate Common SubExpressions.
      TheFPM->addPass(GVNPass());
      // Simplify the control flow graph (deleting unreachable blocks, etc).
      TheFPM->addPass(SimplifyCFGPass());

      // Register analysis passes used in these transform passes.
      PassBuilder PB;
      PB.registerModuleAnalyses(*TheMAM);
      PB.registerFunctionAnalyses(*TheFAM);
      PB.crossRegisterProxies(*TheLAM, *TheFAM, *TheCGAM, *TheMAM);
    }

    static void HandleDefinition() {
      if (auto FnAST = ParseDefinition()) {
        if (auto *FnIR = FnAST->codegen()) {
          fprintf(stderr, "Read function definition:");
          FnIR->print(errs());
          fprintf(stderr, "\n");
          ExitOnErr(TheJIT->addModule(
              ThreadSafeModule(std::move(TheModule), std::move(TheContext))));
          InitializeModuleAndManagers();
        }
      } else {
        // Skip token for error recovery.
        getNextToken();
      }
    }

    static void HandleExtern() {
      if (auto ProtoAST = ParseExtern()) {
        if (auto *FnIR = ProtoAST->codegen()) {
          fprintf(stderr, "Read extern: ");
          FnIR->print(errs());
          fprintf(stderr, "\n");
          FunctionProtos[ProtoAST->getName()] = std::move(ProtoAST);
        }
      } else {
        // Skip token for error recovery.
        getNextToken();
      }
    }

    static void HandleTopLevelExpression() {
      // Evaluate a top-level expression into an anonymous function.
      if (auto FnAST = ParseTopLevelExpr()) {
        if (FnAST->codegen()) {
          // Create a ResourceTracker to track JIT'd memory allocated to our
          // anonymous expression -- that way we can free it after executing.
          auto RT = TheJIT->getMainJITDylib().createResourceTracker();

          auto TSM = ThreadSafeModule(std::move(TheModule), std::move(TheContext));
          ExitOnErr(TheJIT->addModule(std::move(TSM), RT));
          InitializeModuleAndManagers();

          // Search the JIT for the __anon_expr symbol.
          auto ExprSymbol = ExitOnErr(TheJIT->lookup("__anon_expr"));

          // Get the symbol's address and cast it to the right type (takes no
          // arguments, returns a double) so we can call it as a native function.
          double (*FP)() = ExprSymbol.toPtr<double (*)()>();
          fprintf(stderr, "Evaluated to %f\n", FP());

          // Delete the anonymous expression module from the JIT.
          ExitOnErr(RT->remove());
        }
      } else {
        // Skip token for error recovery.
        getNextToken();
      }
    }

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

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

    #ifdef _WIN32
    #define DLLEXPORT __declspec(dllexport)
    #else
    #define DLLEXPORT
    #endif

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

    /// printd - printf that takes a double prints it as "%f\n", returning 0.
    extern "C" DLLEXPORT double printd(double X) {
      fprintf(stderr, "%f\n", X);
      return 0;
    }

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

    int main() {
      InitializeNativeTarget();
      InitializeNativeTargetAsmPrinter();
      InitializeNativeTargetAsmParser();

      // 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();

      TheJIT = ExitOnErr(KaleidoscopeJIT::Create());

      InitializeModuleAndManagers();

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

      return 0;
    }

Next: Extending the language: control flow