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# Chapter 5
In this chapter we extend the language grammar with following features:
* We introduce the `if` statement.
* To support splitting of control flow and merging, we introduce new nodes: `Region` and `Phi`.
* Since we can now have multiple return points, we also introduce the `Stop` node as the termination.
Here is the [complete language grammar](docs/05-grammar.md) for this chapter.
## Recap
Here is a recap of the nodes introduced in previous chapters:
| Node Name | Type | Chapter | Description | Inputs | Value |
|------------|----------------|---------|------------------------------------------------|------------------------------------------------------------------|-------------------------------------------------------------------------|
| MultiNode | Abstract class | 4 | A node that has a tuple result | | A tuple |
| Start | Control | 1 | Start of function, now a MultiNode | An input argument named `arg`. | A tuple with a ctrl token and an `arg` data node |
| Proj | ? | 4 | Projection nodes extract values from MultiNode | A MultiNode and index | Result is the extracted value from the input MultiNode at offset index |
| Bool | Data | 4 | Represents results of a comparison operator | Two data nodes | Result a comparison, represented as integer value where 1=true, 0=false |
| Return | Control | 1 | End of function | Predecessor control node, Data node value | Return value of the function |
| Constant | Data | 1 | Constants such as integer literals | None, however Start node is set as input to enable graph walking | Value of the constant |
| Add | Data | 2 | Add two values | Two data nodes, values are added, order not important | Result of the add operation |
| Sub | Data | 2 | Subtract a value from another | Two data nodes, values are subtracted, order matters | Result of the subtract |
| Mul | Data | 2 | Multiply two values | Two data nodes, values are multiplied, order not important | Result of the multiply |
| Div | Data | 2 | Divide a value by another | Two data nodes, values are divided, order matters | Result of the division |
| UnaryMinus | Data | 2 | Negate a value | One data node, value is negated | Result of the unary minus |
| Scope | ? | 3 | Represents scopes in the graph | All nodes that define variables | None |
## New Nodes
Following new nodes are introduced in this chapter:
| Node Name | Type | Chapter | Description | Inputs | Value |
|-----------|---------|---------|----------------------------------------------------------------------|------------------------------------------------------------------------------------------------|---------------------------------------------------------------|
| If | Control | 5 | Represents an `if` condition, sub type of `MultiNode` | A control node and a data predicate node | A tuple of two values, one for true branch, another for false |
| Region | Control | 5 | Represents a merge point from multiple control flow | An input for each control flow that is merging | None |
| Phi | ? | 5 | Represents the phi function that picks a value based on control flow | A region control node, and multiple data nodes that provide values from multiple control flows | Result is the extracted value depending on control flow taken |
| Stop | Control | 5 | Represents termination of the program | One or more Return nodes | None |
## Parsing of `If` statement
When we parse an `if` statement, the control flow splits at that point. We must track the names being updated in each part of the `if` statement, and then merge them at the end.
This involves following:
* The `IfNode` is created with the current control token, i.e. the node mapped to `$ctrl`, and the predicate expression as inputs.
* We add two `ProjNodes` - one for the `True` branch (call if `ifT`), and the other for the `False` branch (call it `ifF`) - these extract values from the tuple result of the `IfNode`.
* We now create a duplicate of the current `ScopeNode`. The duplicated `ScopeNode` must have all the stack levels as the original, and moreover the new node must be a user of all the names that are currently bound.
* The original `ScopeNode` is saved.
* We set the duplicate `ScopeNode` as current.
* The control token is updated to the `True` projection node `ifT`.
* We parse the true branch of the `if` statement.
* We reset the original `ScopeNode` as current.
* We set control token to the `False` projection node `ifF`.
* If there is an `else` statement we parse it.
* At this point we have two `ScopeNode`s; the original one, potentially updated by the `False` branch, and the duplicate one, potentially updated by the `True` branch.
* We create a `Region` node to represent a merge point.
* We compare the two `ScopeNode`s. We create `Phi` nodes for any names whose bindings differ. The `Phi` nodes take the `Region` node as the control input and the two data nodes from each of the `ScopeNode`s. The name binding is updated to point to the `Phi` node.
* Finally, we set the `Region` node as the control token, and discard the duplicated `ScopeNode`.
## Example
We show the graph for the following code snippet:
```java
int a = 1;
if (arg == 1)
a = arg+2;
else
a = arg-3;
return a;
```
### Before merging
Following shows the graph just before we merge the two branches of the `if` statement in a `Region` node.
* Note the two `ScopeNode`s in the graph.
* One has its `$ctrl` pointing to the `True` projection, while the other has `$ctrl` pointing to `False` projection.
* Note that the binding of `a` is to the `Sub` node in the `False` branch, whereas `a` is bound to the `Add` node in the `True` branch.
* Thus `a` needs a `Phi` node.
### After merging
Below is the graph after we created a `Region` node and merged the two definitions of `a` in a `Phi` node.
* Observe that the duplicate `ScopeNode` has been discarded.
* The binding of `a` is now bound to the `Phi` node.
* The `Phi` node's inputs are the `Region` node and the `Add` node from the `True` branch, and `Sub` node from the `False` branch.
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