path: root/chapter24/README.md

# Chapter 24: Chaining Relationals and Sparse Conditional Constant Propagation

In this Chapter we allow *chaining* conditionals, e.g. `(60 <= score < 90)`
where `score` in the middle does not have to be repeated.

The main compiler change is Interprocedural Sparse Conditional Constant
Propagation (SCCP): an optimistic type solve which also discovers call-graph
edges. This snapshot still uses the earlier parser/type and memory machinery;
Chapter 25 currently contains the larger incomplete-types SSA redesign and
separate compilation. Independent correctness fixes will move backward first;
see the [backport review queue](../docs/chapter-backports.md).


You can also read [this chapter](https://github.com/SeaOfNodes/Simple/tree/linear-chapter24) in a linear Git revision history on the [linear](https://github.com/SeaOfNodes/Simple/tree/linear) branch and [compare](https://github.com/SeaOfNodes/Simple/compare/linear-chapter23...linear-chapter24) it to the previous chapter.


## Chaining Relational Tests

Chaining relational tests offer a cleaner, more readable way to write chained
comparisons without repeating the same variable.

```java 
if (min <= x && x < max)
```

becomes

```java 
if (min <= x < max)
```

This syntax saves space and makes the condition more intuitive, similar to how
range checks are written in mathematics.  E.g.

```java 
int score = 75;
if (60 <= score < 90) {
    sys.io.p("Pass");
}
```
This checks if score is between 60 (inclusive) and 90 (exclusive), without repeating `score`.

Expressions that mix opposite directions of comparison, like using both 
`<=` and `>=`, are not allowed by Simple's direction rule.

```java
if (a <= b >= c)
```


### Operator direction rules
Stacked comparisons are *only* valid if all the comparison operators
"point" the same way:
- `<` with `<`
- `<` with `<=`
- `>` with `>`
- `>` with `>=`

Equality operators (`==` and `!=`) have their normal, lower precedence; they
are not links in a relational chain.

It is not allowed to mix directions in a single chain:
```java 
if (a <= b >= c) // Invalid
```

Comparisons can be forced into numeric context using booleans.
This is valid but unusual:
```java
return (0 < arg) > 1;
```
Depending on the result of (0 < arg) this will turn into either
```java
return 0 > 1;
```
OR
```java
return 1 > 1;
```
The equality operator is valid in this form, but since it has lower precedence than comparisons,
```java 
a < b == c
```
is parsed as:
```java
(a < b) == c
```
This might not be the intended chained comparison.
A more explicit alternative is: 
```java 
a < b && b == c
```
Comparisons can be chained together in any length, and different comparison operators may be 
mixed freely as long as they point in the same direction.
Each intermediate operand is evaluated once. Later operands are evaluated only
if earlier comparisons succeed, so calls and updates in a chain short-circuit.

E.g:
```
return 0 < arg < arg+1 < 4;
```

### Tricky edge cases
```java 
return 0 != arg != 1;
```

This is parsed by standard precedence rules as:
```java
return ((0 != arg) != 1);
```
not as chained inequality.

```java
return a == b == c;
```
Similarly, this is parsed as:
```java
return ((a == b) == c);
```



## Sparse Conditional Constant Propagation

[SCCP](https://en.wikipedia.org/wiki/Sparse_conditional_constant_propagation)
is the top-down version of the same peephole/constant-folding work we have
been doing all along.  The rules for the algorithm are well known from the 
literature and commonly taught at the college level; 
[example slides](https://www.cse.psu.edu/~gxt29/teaching/cse522s23/slides/08monotoneFramework.pdf).

- We have a lattice already
- We have SSA form already (hence the algorithm is *sparse*)
- We have a mapping from Nodes to Types (`Node._type`)
- We have transfer functions (`Node.compute`) already.

We initialize all `_type` fields to ⊤ (as opposed to ⊥), and place all Nodes on
a worklist.  We pull a Node from the worklist, run the transfer function
`node.compute()`, and if the result changes from `node._type` we update
`node._type` and put its output neighbors on the worklist.  A simplified
version with all asserts and debug helpers removed:

```java
while( (n = code._iter._work.pop()) != null ) {
    Type nval = n.compute();
    if( n._type != nval ) {
        assert n._type.isa(nval);     // Types start high and always fall
        n._type = nval;               // Update type in Node
        code._iter.addAll(n._outputs);// Neighbors might change, need to inspect
    }
}
```

This algorithm always terminates (and generally fairly quickly) and always
reaches a *fixed point*, as "best answer" subject to the limits of our lattice
and transfer functions.  The resulting types are monotonically better than
those found by the peephole rules; we can then run the peephole rules on nodes
with improved types, to see if unrelated peepholes can fire - such as newly
discovered constants replacing computations with ConstantNodes.

Example:

```java
int x0 = 1;          // x0 = 1
while( rand ) {
    x1 = phi(x0,x2); // x1 = BOT = phi(1,BOT)
    x2 = 2 - x1;     // x2 = BOT = 2 - BOT
}
return x2
```

Without SCCP, this small program cannot remove the computation of `x` and hence
the loop either.  A glance at the program tells us `x` must always be a `1` but
the bottom-up (pessimistic) approach decides that since x1 is BOT, x2 must be
BOT so x1 must be BOT.  We need the optimistic approach to break the
stalemate, and just *assume* x1 is `1`, and then we can discover that x2 is
also a `1`.


The algorithm progresses from left to right and stops when no more changes
happen:

|Var|init|x0=1|x1=phi(1,T)|x2=2-x1|x1=phi(1,1)|
|---|----|----|-----------|-------|-----------|
|x0 | T  | 1  | 1         | 1     | 1         |
|x1 | T  | T  | 1         | 1     | 1         |
|x2 | T  | T  | T         | 1     | 1         |



### Conditional 

Since our control flow is in the same graph as our data flow (that's the major
point of Sea-of-Nodes!), we need not do anything special and our algorithm is
*conditional* already.  Again an example is interesting:

Example:

```java
int x0 = 1;          // x0 = 1
while( rand ) {
    x1 = phi(x0,x4); // x1 = BOT = phi(1,BOT)
    if( x1 == 1 )    // Since x1 is BOT, both true and false arms are taken
        x2 = 2 - x1; // x2 = BOT = 2 - BOT
    else x3 = 99;    // x3 = 99
    x4 = phi(x2,x3); // x4 = BOT = phi(BOT,99)
}
return x4
```

Again the algorithm progresses from left to right, although this time not all
paths are reachable.  The `if` result is a pair of Control values, shown as
either `C` if the path is alive or `X` if not.  This is used when we compute
`x4 = phi(x2,x3)`; the `PhiNode` ALSO checks the corresponding control input
from the `if` and only merges alive paths.


|Var|init |x0=1|x1=phi(1,T)| 1 == 1? | x2=2-x1 | x3=99   |x4=phi(C/1,X/99)|x1=phi(1,1)|
|---|-----|----|-----------|---------|---------|---------|----------------|-----------|
|x0 | T   | 1  | 1         | 1       | 1       | 1       | 1              | 1         |
|x1 | T   | T  | 1         | 1       | 1       | 1       | 1              | 1         |
|if | T   | T  | T         | [C,X]   | [C,X]   | [C,X]   | [C,X]          | [C,X]     |
|x2 | T   | T  | T         | T       | 1       | 1       | 1              | 1         |
|x3 | T   | T  | T         | T       | T       | 99      | 99             | 99        |
|x4 | T   | T  | T         | T       | T       | T       | 1              | 1         |

This kind of conditional constant propagation really helps if a condition can
be proven true or false, as this removes a test and branch from the optimized
program.  A common way this happens is with null tests; here is the same
program above, but using null pointers instead of integers:

```java
List head = notNullList();
while( rand ) {
    if( head ) head = new List(head,payload);
    else { head = null; default_action(); }
}
```

Here since `head` starts not-null, it can never be null and the
`default_action` can never happen, and the loop can 
simplify:

```java
List head = notNullList();
while( rand ) {
    head = new List(head,payload);
}
```

### Interprocedural 

In **Simple**, we let our SCCP run interprocedurally, again by (nearly) doing nothing:
`CallNodes` call `FunNodes`, `ReturnNodes` return to `CallEndNodes` and they
pass their type information along in exactly the normal way... except for one issue:
there are no edges between `Calls` and `Funs` (nor `Returns` and `CallEnds`).
Such edges make up a [Call Graph](https://en.wikipedia.org/wiki/Call_graph).

We extend the normal SCCP algorithm to observe when a `Call`s function pointer
input changes - when it picks up new function targets.  There are only a finite
number so we represent them exactly with *function indices* as described in an
early chapter.  (Separate compilation adds a special index for the infinite
unknown functions that are called outside this compilation unit).

Once we observe a new *fidx* at a `Call`, we *link* the `Call` with the `Fun`,
and the `Return` with the `CallEnd`.  Such linkage acts exactly as-if we added
a CFG edge from the `Call` to the `Fun`, and the `Call`s arguments to the
`Fun`s `ParmNodes`.  `FunNodes` extend `RegionNodes` (and `ParmNodes` extend
`PhiNodes`), so this linkage uses the same semantics.  `Fun`s become reachable
when called; `Parm`s merge (*meet*) all calling arguments, and so on.
Similarly, `CallEnd`s merge results from all called functions, computing the
*meet* over all the `Return`s.

This *link* step adds a few checks to our algorithm's inner loop, and also
builds a precise Call Graph, and allows our SCCP to run interprocedurally.
Other than discovering a few new edges as the algorithm proceeds, the core
algorithm is unchanged.  We are guaranteed to terminate with a fixed point
solution, and may discover e.g. certain call parameters are constants (or
e.g. not-null) on all calling paths.