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+# SCCP Within a Function
+
+English | [日本語](README.ja.md)
+
+[Previous: Methods and Types](../chapter23/README.md) |
+[Next: SCCP Across Functions](../chapter-interprocedural-sccp/README.md)
+
+This chapter introduces optimistic type analysis within each function. It
+starts with the existing pessimistic peepholes, resets flow types to TOP,
+then propagates reachable control and values to a fixed point. Calls keep
+their conservative interfaces; discovering calls is the next chapter's topic.
+
+The [chapter split](../docs/chapter-split.md) uses names while the chapter
+boundaries settle. This is an independent compiler snapshot, extracted from
+Chapter 24. The numbered snapshot remains a comparison baseline.
+
+## 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:
+
+```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);
+}
+```
+
+## Convergence and calls
+
+Integer ranges can grow one value per loop trip. A loop Phi widens its range
+after a bounded number of such steps. Constants stay precise; above-center
+ranges must remain narrow so they can fall to constants monotonically.
+
+During SCCP, each function retains its unknown-caller Start input. Call edges
+are disconnected, and call results keep the summaries already established by
+pessimistic analysis. Those summaries can be sharper than the written
+signature, so discarding them would lose valid facts. Calls still carry
+whole-memory effects. The solve discovers no new call edges.
+
+After the solve, ordinary peepholes relink calls and apply inlining as before.
+FinalizeIR removes uncalled bodies and detaches calls for scheduling. This
+separates local optimistic analysis from the existing pessimistic call machinery.
+
+`SccpTest` checks a loop fixed point and a function called with 1 and 2: its
+parameter remains general here, while the following chapter infers [1,2].
+
+A recursive function whose return type needs optimistic propagation through
+calls can still report "No defined return type" here. The next chapter adds
+that inference and the widening needed to make it converge; its
+`Chapter24Test.testRecursiveWidening` exercises both recursive data cycles.
+
+## Building and checking
+
+Run `make lib` once for Java test dependencies, then `make tests` in this
+directory. From the repository root, use `make tests CHAPTERS=chapter-sccp`.
+The inherited tests retain their historical class names.
+
+The [grammar](docs/24-grammar.md) includes chained comparisons inherited from
+the extraction baseline. Their planned teaching home is with short-circuit
+expressions. Allocator tuning is covered separately by the planned appendix.