# 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 |
|------------|----------------|---------|------------------------------------------------|------------------------------------------------------------------|-------------------------------------------------------------------------|
| Multi | 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 | Merged control |
| Phi | Data | 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 |
## `If` Nodes
`If` node takes in both control and data (predicate expression) and routes the control token to one of the two control flows, represented by the `Proj` nodes.
## `Phi` Nodes
The `Phi` reads in both data and control, and outputs a data value. The control input to the `Phi` points to a `Region` node. The data inputs to the `Phi` are one each for the control inputs to that `Region`.
The result computed by a `Phi` depends both on the data and the matching control input. At most one control input to the `Region` can be active at a time. The `Phi` passes through the data value from the matching input [[1]](#1).
## `Region` Nodes
`Region` nodes were originally introduced to replace Basic Blocks in the IR [[3]](#3). However, we do not assign a `Region` to every node in the graph; we insert a `Region` node at a merge point where it takes control from each predecessor control edge, and produces
a merged control as output. Data flows via `Phi` nodes at these merge points.
## 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.
The implementation follows the description in [[2]](#2).
This involves following:
* We create an `IfNode` with the current control token, i.e. the node mapped to `$ctrl`, and the `if` predicate expression as inputs.
* We add two `ProjNodes` - one for the `True` branch (call if `ifT`), and the other for the `False` branch (call it `ifF`) - these extract values from the tuple result of the `IfNode`.
* We duplicate the current `ScopeNode`. The duplicated `ScopeNode` contains all the stack levels as the original, and moreover the new node is added as a user of all the names that are currently bound.
* The original `ScopeNode` is saved.
* We set the duplicate `ScopeNode` as current.
* We set control token to the `True` projection node `ifT`.
* We parse the true branch of the `if` statement.
* We reset the original `ScopeNode` as current.
* We set control token to the `False` projection node `ifF`.
* If there is an `else` statement we parse it.
* At this point we have two `ScopeNode`s; the original one, potentially updated by the `False` branch, and the duplicate one, potentially updated by the `True` branch.
* We create a `Region` node to represent a merge point.
* We compare the two `ScopeNode`s. We create `Phi` nodes for any names whose bindings differ. The `Phi` nodes take the `Region` node as the control input and the two data nodes from each of the `ScopeNode`s. The name binding is updated to point to the `Phi` node.
* Finally, we set the `Region` node as the control token, and discard the duplicated `ScopeNode`.
## Example
We show the graph for the following code snippet:
```java
int a = 1;
if (arg == 1)
a = arg+2;
else
a = arg-3;
return a;
```
### Before merging
Following shows the graph just before we merge the two branches of the `if` statement in a `Region` node.
* Note the two `ScopeNode`s in the graph.
* One has its `$ctrl` pointing to the `True` projection, while the other has `$ctrl` pointing to `False` projection.
* Note that `a` is bound 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.
* `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.
## References
[1]
Click, C. (1995).
Combining Analyses, Combining Optimizations, 132.
[2]
Click, C. (1995).
Combining Analyses, Combining Optimizations, 102-103.
[3]
Click, C. (1995).
Combining Analyses, Combining Optimizations, 129.