# 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.