# Chapter 24: Chaining Relationals and Sparse Conditional Constant Propagation English | [日本語](README.ja.md) [Previous: Chapter 23](../chapter23/README.md) | [Next: Chapter 25](../chapter25/README.md) 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. Memory follows Chapter 11's lazy partitioning: BulkMemPhi represents whole memory, MemPhi merges precise aliases, and allocations consume and produce partial memory for their instance fields. During SCCP, memory Phis ignore unreachable inputs and allocation results stay high until control reaches them. Chapter 25 retains the larger incomplete-types SSA redesign, private constructor memory, and separate compilation; 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. Here is the [complete language grammar](docs/24-grammar.md) for this 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. The following is SSA pseudocode; `phi` denotes a merge, not Simple syntax. ```text int x0 = 1; // x0 = 1 while( rand ) { x1 = phi(x0,x2); // x1 = BOT = phi(1,BOT) x2 = 2 - x1; // x2 = BOT = 2 - BOT } return x1 ``` Without SCCP, this small program cannot fold the computation of `x`. 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`. Folding the value does not prove the loop terminates or make its condition and side effects removable. 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: Again using SSA pseudocode: ```text 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 x1 ``` 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 earlier 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. ## RegAlloc improvements: try cold loop splits first A loop Phi and its backedge can belong to one live range even though their values must coexist at some instruction. This self-conflict requires splitting the range. Chapter 23 split the Phi's definition and incoming values right away. This chapter first leaves the hot definition/backedge alone and tries the outside-loop copies. If coloring succeeds, it avoids moves on every iteration. Other conflicts, including two-address operations, keep their existing handling. The allocator remembers which Phis have had this chance. If the same Phi self-conflicts again, the next attempt uses the ordinary aggressive splitting. The record uses Phi identity because live ranges are rebuilt each round. It also covers a backedge-only conflict where the first attempt inserts no copy: that attempt must still consume the one permitted delay. A regression checks both the cheaper first attempt and the mandatory fallback. Chapter 21's adjacent-copy forwarding also carries forward: after coloring, a sole use in the next instruction can read the source register when its operand mask permits it and no two-address tie is broken. The table below includes this cleanup and the lazy memory forward port. Cohort 22 now also includes the two zero-move C return ABI checks added since the earlier audit (26 entries instead of 24). Run `make spill-stats`. All rows use **Chapter 24's compiler**, optimizer seed 123, and the same source/target combinations as the earlier cohort tables. These Windows results combine x86 SystemV/Win64 and RISC-V/ARM SystemV, remeasured after the lazy memory forward port. | Program cohort | Compilations | Retained moves | Loop-weighted moves | |---|---:|---:|---:| | Chapter 20 | 39 | 320 | 439 | | Chapter 21 | 52 | 420 | 952 | | Chapter 22 | 26 | 67 | 67 | | Chapter 23 | 30 | 78 | 225 | | Chapter 24 | 67 | 422 | 1,325 | | **Total** | **214** | **1,307** | **3,008** | `_spills` counts retained SplitNodes, including register moves. `_spillScaled` weights those moves by `8^loopDepth`; it is a cost estimate, not measured memory traffic. Diagnostic machine graphs contribute no allocations to this table. The reporter checks allocation legality and native/emulated results even when spill expectations differ, and exits unsuccessfully for either kind of failure. In the original 2026-09-20 allocator audit, before subsequent compiler fixes, the table totaled 1,332 / 2,956. With only the cold-first rule disabled, that compiler and the same programs produced **1,338 moves / 2,962 weighted moves**. The rule saves six of each. A RISC-V MergeSort case adds one move, offset by improvements in other MergeSort cases, Sieve, and an ARM loop case. Aggregate measurements justify accepting that local regression; the improvement here is modest, not universal. On cohorts 20-23 alone in that audit, Chapter 23 produced 933 / 1,745; Chapter 24 produced 900 / 1,614. Only six of each reduction comes from this allocator change. The rest comes from other compiler changes, including SCCP; comparing chapters alone would overstate the heuristic's benefit. The older cohorts retain the 64-bit Person, guarded String, and smaller emulator argument list. Revised Jig, BubbleSort, Newton, and stack-argument inputs belong to cohort 24 alongside this chapter's existing tests. The frozen String workload also exposed a missing null check in the inlining dominator walk; that correctness fix is included on both sides of the heuristic comparison. Area/cost spill ranking remains for Chapter 25. The current function-pointer rule keeps unknown callers whenever an address is used as a value rather than only as a direct call target. This preserves callable bodies without escape analysis, but Phi-selected functions retain general parameter types. The no-return String case now drops its unused hash bodies and needs no splits. Source/target membership remains unchanged; these graph changes are separate from the cold-first allocator comparison above.