Kaleidoscope: Extending the Language: Mutable Variables / SSA construction

The 'trick' here is that while LLVM does require all register values to be in SSA form, it does not require (or permit) memory objects to be in SSA form. In the example above, note that the loads from G and H are direct accesses to G and H: they are not renamed or versioned. This differs from some other compiler systems, which do try to version memory objects. In LLVM, instead of encoding dataflow analysis of memory into the LLVM IR, it is handled with Analysis Passes which are computed on demand.

With this in mind, the high-level idea is that we want to make a stack variable (which lives in memory, because it is on the stack) for each mutable object in a function. To take advantage of this trick, we need to talk about how LLVM represents stack variables.

In LLVM, all memory accesses are explicit with load/store instructions, and it is carefully designed not to have (or need) an "address-of" operator. Notice how the type of the @G/@H global variables is actually "i32*" even though the variable is defined as "i32". What this means is that @G defines space for an i32 in the global data area, but its name actually refers to the address for that space. Stack variables work the same way, except that instead of being declared with global variable definitions, they are declared with the LLVM alloca instruction:

define i32 @example() {
entry:
	%X = alloca i32           ; type of %X is i32*.
	...
	%tmp = load i32* %X       ; load the stack value %X from the stack.
	%tmp2 = add i32 %tmp, 1   ; increment it
	store i32 %tmp2, i32* %X  ; store it back
	...

This code shows an example of how you can declare and manipulate a stack variable in the LLVM IR. Stack memory allocated with the alloca instruction is fully general: you can pass the address of the stack slot to functions, you can store it in other variables, etc. In our example above, we could rewrite the example to use the alloca technique to avoid using a PHI node:

@G = weak global i32 0   ; type of @G is i32*
@H = weak global i32 0   ; type of @H is i32*

define i32 @test(i1 %Condition) {
entry:
	%X = alloca i32           ; type of %X is i32*.
	br i1 %Condition, label %cond_true, label %cond_false

cond_true:
	%X.0 = load i32* @G
        store i32 %X.0, i32* %X   ; Update X
	br label %cond_next

cond_false:
	%X.1 = load i32* @H
        store i32 %X.1, i32* %X   ; Update X
	br label %cond_next

cond_next:
	%X.2 = load i32* %X       ; Read X
	ret i32 %X.2
}

With this, we have discovered a way to handle arbitrary mutable variables without the need to create Phi nodes at all:

Each mutable variable becomes a stack allocation.
Each read of the variable becomes a load from the stack.
Each update of the variable becomes a store to the stack.
Taking the address of a variable just uses the stack address directly.

While this solution has solved our immediate problem, it introduced another one: we have now apparently introduced a lot of stack traffic for very simple and common operations, a major performance problem. Fortunately for us, the LLVM optimizer has a highly-tuned optimization pass named "mem2reg" that handles this case, promoting allocas like this into SSA registers, inserting Phi nodes as appropriate. If you run this example through the pass, for example, you'll get:

$ llvm-as < example.ll | opt -mem2reg | llvm-dis
@G = weak global i32 0
@H = weak global i32 0

define i32 @test(i1 %Condition) {
entry:
	br i1 %Condition, label %cond_true, label %cond_false

cond_true:
	%X.0 = load i32* @G
	br label %cond_next

cond_false:
	%X.1 = load i32* @H
	br label %cond_next

cond_next:
	%X.01 = phi i32 [ %X.1, %cond_false ], [ %X.0, %cond_true ]
	ret i32 %X.01
}

The mem2reg pass implements the standard "iterated dominance frontier" algorithm for constructing SSA form and has a number of optimizations that speed up (very common) degenerate cases. The mem2reg optimization pass is the answer to dealing with mutable variables, and we highly recommend that you depend on it. Note that mem2reg only works on variables in certain circumstances:

mem2reg is alloca-driven: it looks for allocas and if it can handle them, it promotes them. It does not apply to global variables or heap allocations.
mem2reg only looks for alloca instructions in the entry block of the function. Being in the entry block guarantees that the alloca is only executed once, which makes analysis simpler.
mem2reg only promotes allocas whose uses are direct loads and stores. If the address of the stack object is passed to a function, or if any funny pointer arithmetic is involved, the alloca will not be promoted.
mem2reg only works on allocas of first class values (such as pointers, scalars and vectors), and only if the array size of the allocation is 1 (or missing in the .ll file). mem2reg is not capable of promoting structs or arrays to registers. Note that the "scalarrepl" pass is more powerful and can promote structs, "unions", and arrays in many cases.

All of these properties are easy to satisfy for most imperative languages, and we'll illustrate it below with Kaleidoscope. The final question you may be asking is: should I bother with this nonsense for my front-end? Wouldn't it be better if I just did SSA construction directly, avoiding use of the mem2reg optimization pass? In short, we strongly recommend that you use this technique for building SSA form, unless there is an extremely good reason not to. Using this technique is:

Proven and well tested: llvm-gcc and clang both use this technique for local mutable variables. As such, the most common clients of LLVM are using this to handle a bulk of their variables. You can be sure that bugs are found fast and fixed early.
Extremely Fast: mem2reg has a number of special cases that make it fast in common cases as well as fully general. For example, it has fast-paths for variables that are only used in a single block, variables that only have one assignment point, good heuristics to avoid insertion of unneeded phi nodes, etc.
Needed for debug info generation: Debug information in LLVM relies on having the address of the variable exposed so that debug info can be attached to it. This technique dovetails very naturally with this style of debug info.

If nothing else, this makes it much easier to get your front-end up and running, and is very simple to implement. Lets extend Kaleidoscope with mutable variables now!

Now that we know the sort of problem we want to tackle, lets see what this looks like in the context of our little Kaleidoscope language. We're going to add two features:

The ability to mutate variables with the '=' operator.
The ability to define new variables.

While the first item is really what this is about, we only have variables for incoming arguments as well as for induction variables, and redefining those only goes so far :). Also, the ability to define new variables is a useful thing regardless of whether you will be mutating them. Here's a motivating example that shows how we could use these:

# Define ':' for sequencing: as a low-precedence operator that ignores operands
# and just returns the RHS.
def binary : 1 (x y) y;

# Recursive fib, we could do this before.
def fib(x)
  if (x < 3) then
    1
  else
    fib(x-1)+fib(x-2);

# Iterative fib.
def fibi(x)
  var a = 1, b = 1, c in
  (for i = 3, i < x in 
     c = a + b :
     a = b :
     b = c) :
  b;

# Call it. 
fibi(10);

In order to mutate variables, we have to change our existing variables to use the "alloca trick". Once we have that, we'll add our new operator, then extend Kaleidoscope to support new variable definitions.

The symbol table in Kaleidoscope is managed at code generation time by the 'NamedValues' map. This map currently keeps track of the LLVM "Value*" that holds the double value for the named variable. In order to support mutation, we need to change this slightly, so that it NamedValues holds the memory location of the variable in question. Note that this change is a refactoring: it changes the structure of the code, but does not (by itself) change the behavior of the compiler. All of these changes are isolated in the Kaleidoscope code generator.

At this point in Kaleidoscope's development, it only supports variables for two things: incoming arguments to functions and the induction variable of 'for' loops. For consistency, we'll allow mutation of these variables in addition to other user-defined variables. This means that these will both need memory locations.

To start our transformation of Kaleidoscope, we'll change the NamedValues map so that it maps to AllocaInst* instead of Value*. Once we do this, the C++ compiler will tell us what parts of the code we need to update:

static std::map<std::string, AllocaInst*> NamedValues;

Also, since we will need to create these alloca's, we'll use a helper function that ensures that the allocas are created in the entry block of the function:

/// CreateEntryBlockAlloca - Create an alloca instruction in the entry block of
/// the function.  This is used for mutable variables etc.
static AllocaInst *CreateEntryBlockAlloca(Function *TheFunction,
                                          const std::string &VarName) {
  IRBuilder TmpB(&TheFunction->getEntryBlock(),
                 TheFunction->getEntryBlock().begin());
  return TmpB.CreateAlloca(Type::DoubleTy, 0, VarName.c_str());
}

This funny looking code creates an IRBuilder object that is pointing at the first instruction (.begin()) of the entry block. It then creates an alloca with the expected name and returns it. Because all values in Kaleidoscope are doubles, there is no need to pass in a type to use.

With this in place, the first functionality change we want to make is to variable references. In our new scheme, variables live on the stack, so code generating a reference to them actually needs to produce a load from the stack slot:

Value *VariableExprAST::Codegen() {
  // Look this variable up in the function.
  Value *V = NamedValues[Name];
  if (V == 0) return ErrorV("Unknown variable name");

  // Load the value.
  return Builder.CreateLoad(V, Name.c_str());
}

As you can see, this is pretty straightforward. Now we need to update the things that define the variables to set up the alloca. We'll start with ForExprAST::Codegen (see the full code listing for the unabridged code):

  Function *TheFunction = Builder.GetInsertBlock()->getParent();

  // Create an alloca for the variable in the entry block.
  AllocaInst *Alloca = CreateEntryBlockAlloca(TheFunction, VarName);
  
    // Emit the start code first, without 'variable' in scope.
  Value *StartVal = Start->Codegen();
  if (StartVal == 0) return 0;
  
  // Store the value into the alloca.
  Builder.CreateStore(StartVal, Alloca);
  ...

  // Compute the end condition.
  Value *EndCond = End->Codegen();
  if (EndCond == 0) return EndCond;
  
  // Reload, increment, and restore the alloca.  This handles the case where
  // the body of the loop mutates the variable.
  Value *CurVar = Builder.CreateLoad(Alloca);
  Value *NextVar = Builder.CreateAdd(CurVar, StepVal, "nextvar");
  Builder.CreateStore(NextVar, Alloca);
  ...

This code is virtually identical to the code before we allowed mutable variables. The big difference is that we no longer have to construct a PHI node, and we use load/store to access the variable as needed.

To support mutable argument variables, we need to also make allocas for them. The code for this is also pretty simple:

/// CreateArgumentAllocas - Create an alloca for each argument and register the
/// argument in the symbol table so that references to it will succeed.
void PrototypeAST::CreateArgumentAllocas(Function *F) {
  Function::arg_iterator AI = F->arg_begin();
  for (unsigned Idx = 0, e = Args.size(); Idx != e; ++Idx, ++AI) {
    // Create an alloca for this variable.
    AllocaInst *Alloca = CreateEntryBlockAlloca(F, Args[Idx]);

    // Store the initial value into the alloca.
    Builder.CreateStore(AI, Alloca);

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

For each argument, we make an alloca, store the input value to the function into the alloca, and register the alloca as the memory location for the argument. This method gets invoked by FunctionAST::Codegen right after it sets up the entry block for the function.

The final missing piece is adding the mem2reg pass, which allows us to get good codegen once again:

    // Set up the optimizer pipeline.  Start with registering info about how the
    // target lays out data structures.
    OurFPM.add(new TargetData(*TheExecutionEngine->getTargetData()));
    // Promote allocas to registers.
    OurFPM.add(createPromoteMemoryToRegisterPass());
    // Do simple "peephole" optimizations and bit-twiddling optzns.
    OurFPM.add(createInstructionCombiningPass());
    // Reassociate expressions.
    OurFPM.add(createReassociatePass());

It is interesting to see what the code looks like before and after the mem2reg optimization runs. For example, this is the before/after code for our recursive fib function. Before the optimization:

define double @fib(double %x) {
entry:
	%x1 = alloca double
	store double %x, double* %x1
	%x2 = load double* %x1
	%cmptmp = fcmp ult double %x2, 3.000000e+00
	%booltmp = uitofp i1 %cmptmp to double
	%ifcond = fcmp one double %booltmp, 0.000000e+00
	br i1 %ifcond, label %then, label %else

then:		; preds = %entry
	br label %ifcont

else:		; preds = %entry
	%x3 = load double* %x1
	%subtmp = sub double %x3, 1.000000e+00
	%calltmp = call double @fib( double %subtmp )
	%x4 = load double* %x1
	%subtmp5 = sub double %x4, 2.000000e+00
	%calltmp6 = call double @fib( double %subtmp5 )
	%addtmp = add double %calltmp, %calltmp6
	br label %ifcont

ifcont:		; preds = %else, %then
	%iftmp = phi double [ 1.000000e+00, %then ], [ %addtmp, %else ]
	ret double %iftmp
}

Here there is only one variable (x, the input argument) but you can still see the extremely simple-minded code generation strategy we are using. In the entry block, an alloca is created, and the initial input value is stored into it. Each reference to the variable does a reload from the stack. Also, note that we didn't modify the if/then/else expression, so it still inserts a PHI node. While we could make an alloca for it, it is actually easier to create a PHI node for it, so we still just make the PHI.

Here is the code after the mem2reg pass runs:

define double @fib(double %x) {
entry:
	%cmptmp = fcmp ult double %x, 3.000000e+00
	%booltmp = uitofp i1 %cmptmp to double
	%ifcond = fcmp one double %booltmp, 0.000000e+00
	br i1 %ifcond, label %then, label %else

then:
	br label %ifcont

else:
	%subtmp = sub double %x, 1.000000e+00
	%calltmp = call double @fib( double %subtmp )
	%subtmp5 = sub double %x, 2.000000e+00
	%calltmp6 = call double @fib( double %subtmp5 )
	%addtmp = add double %calltmp, %calltmp6
	br label %ifcont

ifcont:		; preds = %else, %then
	%iftmp = phi double [ 1.000000e+00, %then ], [ %addtmp, %else ]
	ret double %iftmp
}

This is a trivial case for mem2reg, since there are no redefinitions of the variable. The point of showing this is to calm your tension about inserting such blatent inefficiencies :).

After the rest of the optimizers run, we get:

define double @fib(double %x) {
entry:
	%cmptmp = fcmp ult double %x, 3.000000e+00
	%booltmp = uitofp i1 %cmptmp to double
	%ifcond = fcmp ueq double %booltmp, 0.000000e+00
	br i1 %ifcond, label %else, label %ifcont

else:
	%subtmp = sub double %x, 1.000000e+00
	%calltmp = call double @fib( double %subtmp )
	%subtmp5 = sub double %x, 2.000000e+00
	%calltmp6 = call double @fib( double %subtmp5 )
	%addtmp = add double %calltmp, %calltmp6
	ret double %addtmp

ifcont:
	ret double 1.000000e+00
}

Here we see that the simplifycfg pass decided to clone the return instruction into the end of the 'else' block. This allowed it to eliminate some branches and the PHI node.

Now that all symbol table references are updated to use stack variables, we'll add the assignment operator.

With our current framework, adding a new assignment operator is really simple. We will parse it just like any other binary operator, but handle it internally (instead of allowing the user to define it). The first step is to set a precedence:

 int main() {
   // Install standard binary operators.
   // 1 is lowest precedence.
   BinopPrecedence['='] = 2;
   BinopPrecedence['<'] = 10;
   BinopPrecedence['+'] = 20;
   BinopPrecedence['-'] = 20;

Now that the parser knows the precedence of the binary operator, it takes care of all the parsing and AST generation. We just need to implement codegen for the assignment operator. This looks like:

Value *BinaryExprAST::Codegen() {
  // Special case '=' because we don't want to emit the LHS as an expression.
  if (Op == '=') {
    // Assignment requires the LHS to be an identifier.
    VariableExprAST *LHSE = dynamic_cast<VariableExprAST*>(LHS);
    if (!LHSE)
      return ErrorV("destination of '=' must be a variable");

Unlike the rest of the binary operators, our assignment operator doesn't follow the "emit LHS, emit RHS, do computation" model. As such, it is handled as a special case before the other binary operators are handled. The other strange thing is that it requires the LHS to be a variable. It is invalid to have "(x+1) = expr" - only things like "x = expr" are allowed.

    // Codegen the RHS.
    Value *Val = RHS->Codegen();
    if (Val == 0) return 0;

    // Look up the name.
    Value *Variable = NamedValues[LHSE->getName()];
    if (Variable == 0) return ErrorV("Unknown variable name");

    Builder.CreateStore(Val, Variable);
    return Val;
  }
  ...

Once we have the variable, codegen'ing the assignment is straightforward: we emit the RHS of the assignment, create a store, and return the computed value. Returning a value allows for chained assignments like "X = (Y = Z)".

Now that we have an assignment operator, we can mutate loop variables and arguments. For example, we can now run code like this:

# Function to print a double.
extern printd(x);

# Define ':' for sequencing: as a low-precedence operator that ignores operands
# and just returns the RHS.
def binary : 1 (x y) y;

def test(x)
  printd(x) :
  x = 4 :
  printd(x);

test(123);

When run, this example prints "123" and then "4", showing that we did actually mutate the value! Okay, we have now officially implemented our goal: getting this to work requires SSA construction in the general case. However, to be really useful, we want the ability to define our own local variables, lets add this next!

Adding var/in is just like any other other extensions we made to Kaleidoscope: we extend the lexer, the parser, the AST and the code generator. The first step for adding our new 'var/in' construct is to extend the lexer. As before, this is pretty trivial, the code looks like this:

enum Token {
  ...
  // var definition
  tok_var = -13
...
}
...
static int gettok() {
...
    if (IdentifierStr == "in") return tok_in;
    if (IdentifierStr == "binary") return tok_binary;
    if (IdentifierStr == "unary") return tok_unary;
    if (IdentifierStr == "var") return tok_var;
    return tok_identifier;
...

The next step is to define the AST node that we will construct. For var/in, it looks like this:

/// VarExprAST - Expression class for var/in
class VarExprAST : public ExprAST {
  std::vector<std::pair<std::string, ExprAST*> > VarNames;
  ExprAST *Body;
public:
  VarExprAST(const std::vector<std::pair<std::string, ExprAST*> > &varnames,
             ExprAST *body)
  : VarNames(varnames), Body(body) {}
  
  virtual Value *Codegen();
};

var/in allows a list of names to be defined all at once, and each name can optionally have an initializer value. As such, we capture this information in the VarNames vector. Also, var/in has a body, this body is allowed to access the variables defined by the var/in.

With this in place, we can define the parser pieces. The first thing we do is add it as a primary expression:

/// primary
///   ::= identifierexpr
///   ::= numberexpr
///   ::= parenexpr
///   ::= ifexpr
///   ::= forexpr
///   ::= varexpr
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();
  case tok_if:         return ParseIfExpr();
  case tok_for:        return ParseForExpr();
  case tok_var:        return ParseVarExpr();
  }
}

Next we define ParseVarExpr:

/// varexpr ::= 'var' identifier ('=' expression)? 
//                    (',' identifier ('=' expression)?)* 'in' expression
static ExprAST *ParseVarExpr() {
  getNextToken();  // eat the var.

  std::vector<std::pair<std::string, ExprAST*> > VarNames;

  // At least one variable name is required.
  if (CurTok != tok_identifier)
    return Error("expected identifier after var");

The first part of this code parses the list of identifier/expr pairs into the local VarNames vector.

  while (1) {
    std::string Name = IdentifierStr;
    getNextToken();  // eat identifier.

    // Read the optional initializer.
    ExprAST *Init = 0;
    if (CurTok == '=') {
      getNextToken(); // eat the '='.
      
      Init = ParseExpression();
      if (Init == 0) return 0;
    }
    
    VarNames.push_back(std::make_pair(Name, Init));
    
    // End of var list, exit loop.
    if (CurTok != ',') break;
    getNextToken(); // eat the ','.
    
    if (CurTok != tok_identifier)
      return Error("expected identifier list after var");
  }

Once all the variables are parsed, we then parse the body and create the AST node:

  // At this point, we have to have 'in'.
  if (CurTok != tok_in)
    return Error("expected 'in' keyword after 'var'");
  getNextToken();  // eat 'in'.
  
  ExprAST *Body = ParseExpression();
  if (Body == 0) return 0;
  
  return new VarExprAST(VarNames, Body);
}

Now that we can parse and represent the code, we need to support emission of LLVM IR for it. This code starts out with:

Value *VarExprAST::Codegen() {
  std::vector<AllocaInst *> OldBindings;
  
  Function *TheFunction = Builder.GetInsertBlock()->getParent();

  // Register all variables and emit their initializer.
  for (unsigned i = 0, e = VarNames.size(); i != e; ++i) {
    const std::string &VarName = VarNames[i].first;
    ExprAST *Init = VarNames[i].second;

Basically it loops over all the variables, installing them one at a time. For each variable we put into the symbol table, we remember the previous value that we replace in OldBindings.

    // Emit the initializer before adding the variable to scope, this prevents
    // the initializer from referencing the variable itself, and permits stuff
    // like this:
    //  var a = 1 in
    //    var a = a in ...   # refers to outer 'a'.
    Value *InitVal;
    if (Init) {
      InitVal = Init->Codegen();
      if (InitVal == 0) return 0;
    } else { // If not specified, use 0.0.
      InitVal = ConstantFP::get(Type::DoubleTy, APFloat(0.0));
    }
    
    AllocaInst *Alloca = CreateEntryBlockAlloca(TheFunction, VarName);
    Builder.CreateStore(InitVal, Alloca);

    // Remember the old variable binding so that we can restore the binding when
    // we unrecurse.
    OldBindings.push_back(NamedValues[VarName]);
    
    // Remember this binding.
    NamedValues[VarName] = Alloca;
  }

There are more comments here than code. The basic idea is that we emit the initializer, create the alloca, then update the symbol table to point to it. Once all the variables are installed in the symbol table, we evaluate the body of the var/in expression:

  // Codegen the body, now that all vars are in scope.
  Value *BodyVal = Body->Codegen();
  if (BodyVal == 0) return 0;

Finally, before returning, we restore the previous variable bindings:

  // Pop all our variables from scope.
  for (unsigned i = 0, e = VarNames.size(); i != e; ++i)
    NamedValues[VarNames[i].first] = OldBindings[i];

  // Return the body computation.
  return BodyVal;
}

The end result of all of this is that we get properly scoped variable definitions, and we even (trivially) allow mutation of them :).

With this, we completed what we set out to do. Our nice iterative fib example from the intro compiles and runs just fine. The mem2reg pass optimizes all of our stack variables into SSA registers, inserting PHI nodes where needed, and our front-end remains simple: no "iterated dominance frontier" computation anywhere in sight.

Here is the complete code listing for our running example, enhanced with mutable variables and var/in support. To build this example, use:

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

Here is the code:

#include "llvm/DerivedTypes.h"
#include "llvm/ExecutionEngine/ExecutionEngine.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,
  
  // control
  tok_if = -6, tok_then = -7, tok_else = -8,
  tok_for = -9, tok_in = -10,
  
  // operators
  tok_binary = -11, tok_unary = -12,
  
  // var definition
  tok_var = -13
};

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;
    if (IdentifierStr == "var") return tok_var;
    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) {}
  const std::string &getName() const { return Name; }
  virtual Value *Codegen();
};

/// 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();
};

/// 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();
};

/// IfExprAST - Expression class for if/then/else.
class IfExprAST : public ExprAST {
  ExprAST *Cond, *Then, *Else;
public:
  IfExprAST(ExprAST *cond, ExprAST *then, ExprAST *_else)
  : Cond(cond), Then(then), Else(_else) {}
  virtual Value *Codegen();
};

/// ForExprAST - Expression class for for/in.
class ForExprAST : public ExprAST {
  std::string VarName;
  ExprAST *Start, *End, *Step, *Body;
public:
  ForExprAST(const std::string &varname, ExprAST *start, ExprAST *end,
             ExprAST *step, ExprAST *body)
    : VarName(varname), Start(start), End(end), Step(step), Body(body) {}
  virtual Value *Codegen();
};

/// VarExprAST - Expression class for var/in
class VarExprAST : public ExprAST {
  std::vector<std::pair<std::string, ExprAST*> > VarNames;
  ExprAST *Body;
public:
  VarExprAST(const std::vector<std::pair<std::string, ExprAST*> > &varnames,
             ExprAST *body)
  : VarNames(varnames), Body(body) {}
  
  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;
  bool isOperator;
  unsigned Precedence;  // Precedence if a binary op.
public:
  PrototypeAST(const std::string &name, const std::vector<std::string> &args,
               bool isoperator = false, unsigned prec = 0)
  : Name(name), Args(args), isOperator(isoperator), Precedence(prec) {}
  
  bool isUnaryOp() const { return isOperator && Args.size() == 1; }
  bool isBinaryOp() const { return isOperator && Args.size() == 2; }
  
  char getOperatorName() const {
    assert(isUnaryOp() || isBinaryOp());
    return Name[Name.size()-1];
  }
  
  unsigned getBinaryPrecedence() const { return Precedence; }
  
  Function *Codegen();
  
  void CreateArgumentAllocas(Function *F);
};

/// 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 ')'");
      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;
}

/// ifexpr ::= 'if' expression 'then' expression 'else' expression
static ExprAST *ParseIfExpr() {
  getNextToken();  // eat the if.
  
  // condition.
  ExprAST *Cond = ParseExpression();
  if (!Cond) return 0;
  
  if (CurTok != tok_then)
    return Error("expected then");
  getNextToken();  // eat the then
  
  ExprAST *Then = ParseExpression();
  if (Then == 0) return 0;
  
  if (CurTok != tok_else)
    return Error("expected else");
  
  getNextToken();
  
  ExprAST *Else = ParseExpression();
  if (!Else) return 0;
  
  return new IfExprAST(Cond, Then, Else);
}

/// forexpr ::= 'for' identifier '=' expr ',' expr (',' expr)? 'in' expression
static ExprAST *ParseForExpr() {
  getNextToken();  // eat the for.

  if (CurTok != tok_identifier)
    return Error("expected identifier after for");
  
  std::string IdName = IdentifierStr;
  getNextToken();  // eat identifier.
  
  if (CurTok != '=')
    return Error("expected '=' after for");
  getNextToken();  // eat '='.
  
  
  ExprAST *Start = ParseExpression();
  if (Start == 0) return 0;
  if (CurTok != ',')
    return Error("expected ',' after for start value");
  getNextToken();
  
  ExprAST *End = ParseExpression();
  if (End == 0) return 0;
  
  // The step value is optional.
  ExprAST *Step = 0;
  if (CurTok == ',') {
    getNextToken();
    Step = ParseExpression();
    if (Step == 0) return 0;
  }
  
  if (CurTok != tok_in)
    return Error("expected 'in' after for");
  getNextToken();  // eat 'in'.
  
  ExprAST *Body = ParseExpression();
  if (Body == 0) return 0;

  return new ForExprAST(IdName, Start, End, Step, Body);
}

/// varexpr ::= 'var' identifier ('=' expression)? 
//                    (',' identifier ('=' expression)?)* 'in' expression
static ExprAST *ParseVarExpr() {
  getNextToken();  // eat the var.

  std::vector<std::pair<std::string, ExprAST*> > VarNames;

  // At least one variable name is required.
  if (CurTok != tok_identifier)
    return Error("expected identifier after var");
  
  while (1) {
    std::string Name = IdentifierStr;
    getNextToken();  // eat identifier.

    // Read the optional initializer.
    ExprAST *Init = 0;
    if (CurTok == '=') {
      getNextToken(); // eat the '='.
      
      Init = ParseExpression();
      if (Init == 0) return 0;
    }
    
    VarNames.push_back(std::make_pair(Name, Init));
    
    // End of var list, exit loop.
    if (CurTok != ',') break;
    getNextToken(); // eat the ','.
    
    if (CurTok != tok_identifier)
      return Error("expected identifier list after var");
  }
  
  // At this point, we have to have 'in'.
  if (CurTok != tok_in)
    return Error("expected 'in' keyword after 'var'");
  getNextToken();  // eat 'in'.
  
  ExprAST *Body = ParseExpression();
  if (Body == 0) return 0;
  
  return new VarExprAST(VarNames, Body);
}


/// primary
///   ::= identifierexpr
///   ::= numberexpr
///   ::= parenexpr
///   ::= ifexpr
///   ::= forexpr
///   ::= varexpr
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();
  case tok_if:         return ParseIfExpr();
  case tok_for:        return ParseForExpr();
  case tok_var:        return ParseVarExpr();
  }
}

/// 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;
}

/// binoprhs
///   ::= ('+' unary)*
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 unary expression after the binary operator.
    ExprAST *RHS = ParseUnary();
    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
///   ::= unary binoprhs
///
static ExprAST *ParseExpression() {
  ExprAST *LHS = ParseUnary();
  if (!LHS) return 0;
  
  return ParseBinOpRHS(0, LHS);
}

/// prototype
///   ::= id '(' id* ')'
///   ::= binary LETTER number? (id, id)
///   ::= unary LETTER (id)
static PrototypeAST *ParsePrototype() {
  std::string FnName;
  
  int 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;
  case tok_unary:
    getNextToken();
    if (!isascii(CurTok))
      return ErrorP("Expected unary operator");
    FnName = "unary";
    FnName += (char)CurTok;
    Kind = 1;
    getNextToken();
    break;
  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 < 1 || NumVal > 100)
        return ErrorP("Invalid precedecnce: must be 1..100");
      BinaryPrecedence = (unsigned)NumVal;
      getNextToken();
    }
    break;
  }
  
  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 ')'.
  
  // Verify right number of names for operator.
  if (Kind && ArgNames.size() != Kind)
    return ErrorP("Invalid number of operands for operator");
  
  return new PrototypeAST(FnName, ArgNames, Kind != 0, BinaryPrecedence);
}

/// 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;
static std::map<std::string, AllocaInst*> NamedValues;
static FunctionPassManager *TheFPM;

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

/// CreateEntryBlockAlloca - Create an alloca instruction in the entry block of
/// the function.  This is used for mutable variables etc.
static AllocaInst *CreateEntryBlockAlloca(Function *TheFunction,
                                          const std::string &VarName) {
  IRBuilder TmpB(&TheFunction->getEntryBlock(),
                 TheFunction->getEntryBlock().begin());
  return TmpB.CreateAlloca(Type::DoubleTy, 0, VarName.c_str());
}


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

Value *VariableExprAST::Codegen() {
  // Look this variable up in the function.
  Value *V = NamedValues[Name];
  if (V == 0) return ErrorV("Unknown variable name");

  // Load the value.
  return Builder.CreateLoad(V, Name.c_str());
}

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");
}


Value *BinaryExprAST::Codegen() {
  // Special case '=' because we don't want to emit the LHS as an expression.
  if (Op == '=') {
    // Assignment requires the LHS to be an identifier.
    VariableExprAST *LHSE = dynamic_cast<VariableExprAST*>(LHS);
    if (!LHSE)
      return ErrorV("destination of '=' must be a variable");
    // Codegen the RHS.
    Value *Val = RHS->Codegen();
    if (Val == 0) return 0;

    // Look up the name.
    Value *Variable = NamedValues[LHSE->getName()];
    if (Variable == 0) return ErrorV("Unknown variable name");

    Builder.CreateStore(Val, Variable);
    return Val;
  }
  
  
  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::DoubleTy, "booltmp");
  default: break;
  }
  
  // If it wasn't a builtin binary operator, it must be a user defined one. Emit
  // a call to it.
  Function *F = TheModule->getFunction(std::string("binary")+Op);
  assert(F && "binary operator not found!");
  
  Value *Ops[] = { L, R };
  return Builder.CreateCall(F, Ops, Ops+2, "binop");
}

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");
}

Value *IfExprAST::Codegen() {
  Value *CondV = Cond->Codegen();
  if (CondV == 0) return 0;
  
  // Convert condition to a bool by comparing equal to 0.0.
  CondV = Builder.CreateFCmpONE(CondV, 
                                ConstantFP::get(Type::DoubleTy, APFloat(0.0)),
                                "ifcond");
  
  Function *TheFunction = Builder.GetInsertBlock()->getParent();
  
  // Create blocks for the then and else cases.  Insert the 'then' block at the
  // end of the function.
  BasicBlock *ThenBB = new BasicBlock("then", TheFunction);
  BasicBlock *ElseBB = new BasicBlock("else");
  BasicBlock *MergeBB = new BasicBlock("ifcont");
  
  Builder.CreateCondBr(CondV, ThenBB, ElseBB);
  
  // Emit then value.
  Builder.SetInsertPoint(ThenBB);
  
  Value *ThenV = Then->Codegen();
  if (ThenV == 0) return 0;
  
  Builder.CreateBr(MergeBB);
  // Codegen of 'Then' can change the current block, update ThenBB for the PHI.
  ThenBB = Builder.GetInsertBlock();
  
  // Emit else block.
  TheFunction->getBasicBlockList().push_back(ElseBB);
  Builder.SetInsertPoint(ElseBB);
  
  Value *ElseV = Else->Codegen();
  if (ElseV == 0) return 0;
  
  Builder.CreateBr(MergeBB);
  // Codegen of 'Else' can change the current block, update ElseBB for the PHI.
  ElseBB = Builder.GetInsertBlock();
  
  // Emit merge block.
  TheFunction->getBasicBlockList().push_back(MergeBB);
  Builder.SetInsertPoint(MergeBB);
  PHINode *PN = Builder.CreatePHI(Type::DoubleTy, "iftmp");
  
  PN->addIncoming(ThenV, ThenBB);
  PN->addIncoming(ElseV, ElseBB);
  return PN;
}

Value *ForExprAST::Codegen() {
  // Output this as:
  //   var = alloca double
  //   ...
  //   start = startexpr
  //   store start -> var
  //   goto loop
  // loop: 
  //   ...
  //   bodyexpr
  //   ...
  // loopend:
  //   step = stepexpr
  //   endcond = endexpr
  //
  //   curvar = load var
  //   nextvar = curvar + step
  //   store nextvar -> var
  //   br endcond, loop, endloop
  // outloop:
  
  Function *TheFunction = Builder.GetInsertBlock()->getParent();

  // Create an alloca for the variable in the entry block.
  AllocaInst *Alloca = CreateEntryBlockAlloca(TheFunction, VarName);
  
  // Emit the start code first, without 'variable' in scope.
  Value *StartVal = Start->Codegen();
  if (StartVal == 0) return 0;
  
  // Store the value into the alloca.
  Builder.CreateStore(StartVal, Alloca);
  
  // Make the new basic block for the loop header, inserting after current
  // block.
  BasicBlock *PreheaderBB = Builder.GetInsertBlock();
  BasicBlock *LoopBB = new BasicBlock("loop", TheFunction);
  
  // Insert an explicit fall through from the current block to the LoopBB.
  Builder.CreateBr(LoopBB);

  // Start insertion in LoopBB.
  Builder.SetInsertPoint(LoopBB);
  
  // Within the loop, the variable is defined equal to the PHI node.  If it
  // shadows an existing variable, we have to restore it, so save it now.
  AllocaInst *OldVal = NamedValues[VarName];
  NamedValues[VarName] = Alloca;
  
  // Emit the body of the loop.  This, like any other expr, can change the
  // current BB.  Note that we ignore the value computed by the body, but don't
  // allow an error.
  if (Body->Codegen() == 0)
    return 0;
  
  // Emit the step value.
  Value *StepVal;
  if (Step) {
    StepVal = Step->Codegen();
    if (StepVal == 0) return 0;
  } else {
    // If not specified, use 1.0.
    StepVal = ConstantFP::get(Type::DoubleTy, APFloat(1.0));
  }
  
  // Compute the end condition.
  Value *EndCond = End->Codegen();
  if (EndCond == 0) return EndCond;
  
  // Reload, increment, and restore the alloca.  This handles the case where
  // the body of the loop mutates the variable.
  Value *CurVar = Builder.CreateLoad(Alloca, VarName.c_str());
  Value *NextVar = Builder.CreateAdd(CurVar, StepVal, "nextvar");
  Builder.CreateStore(NextVar, Alloca);
  
  // Convert condition to a bool by comparing equal to 0.0.
  EndCond = Builder.CreateFCmpONE(EndCond, 
                                  ConstantFP::get(Type::DoubleTy, APFloat(0.0)),
                                  "loopcond");
  
  // Create the "after loop" block and insert it.
  BasicBlock *LoopEndBB = Builder.GetInsertBlock();
  BasicBlock *AfterBB = new BasicBlock("afterloop", TheFunction);
  
  // Insert the conditional branch into the end of LoopEndBB.
  Builder.CreateCondBr(EndCond, LoopBB, AfterBB);
  
  // Any new code will be inserted in AfterBB.
  Builder.SetInsertPoint(AfterBB);
  
  // Restore the unshadowed variable.
  if (OldVal)
    NamedValues[VarName] = OldVal;
  else
    NamedValues.erase(VarName);

  
  // for expr always returns 0.0.
  return Constant::getNullValue(Type::DoubleTy);
}

Value *VarExprAST::Codegen() {
  std::vector<AllocaInst *> OldBindings;
  
  Function *TheFunction = Builder.GetInsertBlock()->getParent();

  // Register all variables and emit their initializer.
  for (unsigned i = 0, e = VarNames.size(); i != e; ++i) {
    const std::string &VarName = VarNames[i].first;
    ExprAST *Init = VarNames[i].second;
    
    // Emit the initializer before adding the variable to scope, this prevents
    // the initializer from referencing the variable itself, and permits stuff
    // like this:
    //  var a = 1 in
    //    var a = a in ...   # refers to outer 'a'.
    Value *InitVal;
    if (Init) {
      InitVal = Init->Codegen();
      if (InitVal == 0) return 0;
    } else { // If not specified, use 0.0.
      InitVal = ConstantFP::get(Type::DoubleTy, APFloat(0.0));
    }
    
    AllocaInst *Alloca = CreateEntryBlockAlloca(TheFunction, VarName);
    Builder.CreateStore(InitVal, Alloca);

    // Remember the old variable binding so that we can restore the binding when
    // we unrecurse.
    OldBindings.push_back(NamedValues[VarName]);
    
    // Remember this binding.
    NamedValues[VarName] = Alloca;
  }
  
  // Codegen the body, now that all vars are in scope.
  Value *BodyVal = Body->Codegen();
  if (BodyVal == 0) return 0;
  
  // Pop all our variables from scope.
  for (unsigned i = 0, e = VarNames.size(); i != e; ++i)
    NamedValues[VarNames[i].first] = OldBindings[i];

  // Return the body computation.
  return BodyVal;
}


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

/// CreateArgumentAllocas - Create an alloca for each argument and register the
/// argument in the symbol table so that references to it will succeed.
void PrototypeAST::CreateArgumentAllocas(Function *F) {
  Function::arg_iterator AI = F->arg_begin();
  for (unsigned Idx = 0, e = Args.size(); Idx != e; ++Idx, ++AI) {
    // Create an alloca for this variable.
    AllocaInst *Alloca = CreateEntryBlockAlloca(F, Args[Idx]);

    // Store the initial value into the alloca.
    Builder.CreateStore(AI, Alloca);

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


Function *FunctionAST::Codegen() {
  NamedValues.clear();
  
  Function *TheFunction = Proto->Codegen();
  if (TheFunction == 0)
    return 0;
  
  // If this is an operator, install it.
  if (Proto->isBinaryOp())
    BinopPrecedence[Proto->getOperatorName()] = Proto->getBinaryPrecedence();
  
  // Create a new basic block to start insertion into.
  BasicBlock *BB = new BasicBlock("entry", TheFunction);
  Builder.SetInsertPoint(BB);
  
  // Add all arguments to the symbol table and create their allocas.
  Proto->CreateArgumentAllocas(TheFunction);
  
  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();

  if (Proto->isBinaryOp())
    BinopPrecedence.erase(Proto->getOperatorName());
  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;
}

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

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

int main() {
  // Install standard binary operators.
  // 1 is lowest precedence.
  BinopPrecedence['='] = 2;
  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");
  
  // Create the JIT.
  TheExecutionEngine = ExecutionEngine::create(TheModule);

  {
    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()));
    // Promote allocas to registers.
    OurFPM.add(createPromoteMemoryToRegisterPass());
    // 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;
}

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