README.md

Chapter 7: While Statement

Table of Contents

1. Dealing With Back Edges
2. New Node Types
3. Detailed Steps
4. Visualization
5. Nested Loops
6. Loop With Nested If

You can also read this chapter in a linear Git revision history on the linear branch and compare it to the previous chapter.

In this chapter we introduce the while statement.

Here is the complete language grammar for this chapter.

Dealing With Back Edges

The complication introduced by looping constructs is that variables flow back into the body of the loop on iteration. For example:

while(arg < 10) {
    arg = arg + 1;
}
return arg;

The variable arg is assigned a new value inside the body of the loop, and this then flows back into the body of the loop.

In general, we will rewrite the looping construct as follows:

loop_head:
if( !(arg < 10) )
    goto loop_exit;
arg = arg + 1;
goto loop_head;

loop_exit:

Above is for illustration only, we do not have labels and goto statements in the language.

From an SSA¹ point of view, since arg flows back, it requires a phi node at the head. Conceptually we would like the outcome to be:

// arg1 represents incoming arg
//
loop_head:
arg2 = phi(arg1, arg3);
if( !(arg2 < 10) )
    goto loop_exit;
arg3 = arg2 + 1;
goto loop_head;

loop_exit:

Notice that the phi for arg2 refers to arg3, which is not known at the time we parse the while loop predicate. This is the crux of the problem that we need to solve in order to successfully construct the Sea of Nodes graph, which is always in SSA form.

Recall from Chapter 5 that when parsing if statements, we clone the symbol tables as we go past the if predicate. Later we merge the two sets of symbol tables at a Region - creating phis for all names that encountered a change in definition within the two branches of the if statement. In the case of the if statement, the phis are created at the merge point when we already know the definitions that are being merged.

The essential idea for loop constructs is to eagerly create phis for all names in the symbol tables before we enter the loop's if condition, since we do not know which names will be redefined inside the body of the loop. When the loop terminates, we go back and remove unnecessary phis. We call this approach the "eager phi" approach.²

In Chapter 8 we will implement a "lazy phi" approach that creates phis only when we encounter redefinition of a name.

New Node Types

Our list of nodes remains the same as in Chapter 5, however, we create a subtype of Region named Loop to better encapsulate some of the additional logic required. A key aspect of this is to temporarily disable peepholes of the Region and any phis created until we complete parsing the loop body. This is because our phis are not fully constructed until the loop end.

Detailed Steps

1. We start by creating a new subclass of Region, the Loop. The Loop gets two control inputs, the first is the entry point, i.e. the current binding to $ctrl, and second (null) is a placeholder for the back edge that is set after loop is parsed. The absence of a back edge is used as an indicator to switch off peepholes of the region and associated phis.

   ctrl(new LoopNode(ctrl(),null).peephole());

   The newly created region becomes the current control.

2. We duplicate the current Scope node. This involves duplicating all the symbols at every level with the scope, and creating phis for every symbol except the $ctrl binding.

   // Make a new Scope for the body.
   _scope = _scope.dup(true);

   Note that the dup call is given an argument true. This triggers creating phis. The code that creates the phis in the dup() method is shown below.

   // boolean loop=true if this is a loop region
   
   String[] names = reverseNames(); // Get the variable names
   dup.add_def(ctrl());      // Control input is just copied
   for( int i=1; i<nIns(); i++ ) {
      if ( !loop ) { dup.add_def(in(i)); }
      else {
         // Loop region
         // Create a phi node with second input as null - to be filled in
         // by endLoop() below
         dup.add_def(new PhiNode(names[i], ctrl(), in(i), null).peephole());
         // Ensure our node has the same phi in case we created one
         set_def(i, dup.in(i));
      }
   }

   Inside the else block both the duplicated scope and the original scope get the same phi node.

3. Next we set up the if condition, very much like we do with regular ifs.

   // Parse predicate
   var pred = require(parseExpression(), ")");
   // IfNode takes current control and predicate
   IfNode ifNode = (IfNode)new IfNode(ctrl(), pred).<IfNode>keep().peephole();
   // Setup projection nodes
   Node ifT = new ProjNode(ifNode, 0, "True" ).peephole();
   ifNode.unkeep();
   Node ifF = new ProjNode(ifNode, 1, "False").peephole();

4. We make another clone of the current scope. This will be the exit scope that will live after the loop ends, therefore $ctrl in the exit scope is set to the False projection. The exit scope captures any side effects of the loop's predicate.

   // The exit scope, accounting for any side effects in the predicate
   var exit = _scope.dup();
   exit.ctrl(ifF);

5. We now set the control to the True projection and parse the loop body.

   // Parse the true side, which corresponds to loop body
   ctrl(ifT);              // set ctrl token to ifTrue projection
   parseStatement();       // Parse loop body

6. After the loop body is parsed, we go back and process all the phis we created earlier.

   // The true branch loops back, so whatever is current control gets
   // added to head loop as input
   head.endLoop(_scope, exit);

   The endLoop method sets the second control of the loop region to the control from the back edge. It then goes through all the phis and sets the second data input on the phi to the corresponding entry from the loop body; phis that were not used are peepholed and get replaced by the original input.

   Node ctrl = ctrl();
   ctrl.set_def(2,back.ctrl());
   for( int i=1; i<nIns(); i++ ) {
      PhiNode phi = (PhiNode)in(i);
      assert phi.region()==ctrl && phi.in(2)==null;
      phi.set_def(2,back.in(i));
      // Do an eager useless-phi removal
      Node in = phi.peephole();
      if( in != phi )
         phi.subsume(in);
   }

7. Finally, both the original scope (head) we started with, and the duplicate created for the body are killed. At exit the false control is the current control (step 4), and exit scope is set as the current scope.

   // At exit the false control is the current control, and
   // the scope is the exit scope after the exit test.
   return (_scope = exit);

Visualization

The example quoted above is shown below at an intermediate state:

• Three Scopes are shown, reading clockwise, the loop head, exit and the body.

The final graph looks like this:

More Complex Examples

Nested Loops

int sum = 0;
int i = 0;
while(i < arg) {
    i = i + 1;
    int j = 0;
    while( j < arg ) {
        sum = sum + j;
        j = j + 1;
    }
}
return sum;

Loop With Nested If

int a = 1;
int b = 2;
while(a < 10) {
    if (a == 2) a = 3;
    else b = 4;
}
return b;

Footnotes

1. Cytron, R. et al (1991). Efficiently computing static single assignment form and the control dependence graph, in ACM Transactions on Programming Languages and Systems, 13(4):451-490, 1991. ↩

2. Click, C. (1995). Combining Analyses, Combining Optimizations, 103. ↩