[ty] Optimize TDD atom ordering (#20098)

## Summary

While looking at some logging output that I added to
`ReachabilityConstraintBuilder::add_and_constraint` in order to debug
astral-sh/ty#1091, I noticed that it seemed to
suggest that the TDD was built in an imbalanced way for code like the
following, where we have a sequence of non-nested `if` conditions:

```py
def f(t1, t2, t3, t4, …):
    x = 0
    if t1:
        x = 1
    if t2:
        x = 2
    if t3:
        x = 3
    if t4:
        x = 4
    …
```

To understand this a bit better, I added some code to the
`ReachabilityConstraintBuilder` to render the resulting TDD. On `main`,
we get a tree that looks like the following, where you can see a pattern
of N sub-trees that grow linearly with N (number of `if` statements).
This results in an overall tree structure that has N² nodes (see graph
below):

<img alt="normal order"
src="https://github.com/user-attachments/assets/aab40ce9-e82a-4fcd-823a-811f05f15f66"
/>

If we zoom in to one of these subgraphs, we can see what the problem is.
When we add new constraints that represent combinations like `t1 AND ~t2
AND ~t3 AND t4 AND …`, they start with the evaluation of "early"
conditions (`t1`, `t2`, …). This means that we have to create new
subgraphs for each new `if` condition because there is little sharing
with the previous structure. We evaluate the Boolean condition in a
right-associative way: `t1 AND (~t2 AND (~t3 AND t4)))`:

<img width="500" align="center"
src="https://github.com/user-attachments/assets/31ea7182-9e00-4975-83df-d980464f545d"
/>

If we change the ordering of TDD atoms, we can change that to a
left-associative evaluation: `(((t1 AND ~t2) AND ~t3) AND t4) …`. This
means that we can re-use previous subgraphs `(t1 AND ~t2)`, which
results in a much more compact graph structure overall (note how "late"
conditions are now at the top, and "early" conditions are further down
in the graph):

<img alt="reverse order"
src="https://github.com/user-attachments/assets/96a6b7c1-3d35-4192-a917-0b2d24c6b144"
/>

If we count the number of TDD nodes for a growing number if `if`
statements, we can see that this change results in a slower growth. It's
worth noting that the growth is still superlinear, though:

<img width="800" height="600" alt="plot"
src="https://github.com/user-attachments/assets/22e8394f-e74e-4a9e-9687-0d41f94f2303"
/>

On the actual code from the referenced ticket (the `t_main.py` file
reduced to its main function, with the main function limited to 2000
lines instead of 11000 to allow the version on `main` to run to
completion), the effect is much more dramatic. Instead of 26 million TDD
nodes (`main`), we now only create 250 thousand (this branch), which is
slightly less than 1%.

The change in this PR allows us to build the semantic index and
type-check the problematic `t_main.py` file in
astral-sh/ty#1091 in 9 seconds. This is still
not great, but an obvious improvement compared to running out of memory
after *minutes* of execution.

An open question remains whether this change is beneficial for all kinds
of code patterns, or just this linear sequence of `if` statements. It
does not seem unreasonable to think that referring to "earlier"
conditions is generally a good idea, but I learned from Doug that it's
generally not possible to find a TDD-construction heuristic that is
non-pathological for all kinds of inputs. Fortunately, it seems like
this change here results in performance improvements across *all of our
benchmarks*, which should increase the confidence in this change:

| Benchmark           | Improvement |
|---------------------|-------------------------|
| hydra-zen           | +13%                    |
| DateType            | +5%                     |
| sympy (walltime)    | +4%                     |
| attrs               | +4%                     |
| pydantic (walltime) | +2%                     |
| pandas (walltime)   | +2%                     |
| altair (walltime)   | +2%                     |
| static-frame        | +2%                     |
| anyio               | +1%                     |
| freqtrade           | +1%                     |
| colour-science      | +1%                     |
| tanjun              | +1%                     |

closes astral-sh/ty#1091

---------

Co-authored-by: Douglas Creager <[email protected]>

Author: sharkdp

crates/ty_python_semantic/src/semantic_index/reachability_constraints.rs

@@ -424,9 +424,26 @@ impl ReachabilityConstraintsBuilder {
         }
     }
 
-    /// Returns whether `a` or `b` has a "larger" atom. TDDs are ordered such that interior nodes
-    /// can only have edges to "larger" nodes. Terminals are considered to have a larger atom than
-    /// any internal node, since they are leaf nodes.
+    /// Implements the ordering that determines which level a TDD node appears at.
+    ///
+    /// Each interior node checks the value of a single variable (for us, a `Predicate`).
+    /// TDDs are ordered such that every path from the root of the graph to the leaves must
+    /// check each variable at most once, and must check each variable in the same order.
+    ///
+    /// We can choose any ordering that we want, as long as it's consistent — with the
+    /// caveat that terminal nodes must always be last in the ordering, since they are the
+    /// leaf nodes of the graph.
+    ///
+    /// We currently compare interior nodes by looking at the Salsa IDs of each variable's
+    /// `Predicate`, since this is already available and easy to compare. We also _reverse_
+    /// the comparison of those Salsa IDs. The Salsa IDs are assigned roughly sequentially
+    /// while traversing the source code. Reversing the comparison means `Predicate`s that
+    /// appear later in the source will tend to be placed "higher" (closer to the root) in
+    /// the TDD graph. We have found empirically that this leads to smaller TDD graphs [1],
+    /// since there are often repeated combinations of `Predicate`s from earlier in the
+    /// file.
+    ///
+    /// [1]: https://github.com/astral-sh/ruff/pull/20098
     fn cmp_atoms(
         &self,
         a: ScopedReachabilityConstraintId,
@@ -439,7 +456,12 @@ impl ReachabilityConstraintsBuilder {
         } else if b.is_terminal() {
             Ordering::Less
         } else {
-            self.interiors[a].atom.cmp(&self.interiors[b].atom)
+            // See https://github.com/astral-sh/ruff/pull/20098 for an explanation of why this
+            // ordering is reversed.
+            self.interiors[a]
+                .atom
+                .cmp(&self.interiors[b].atom)
+                .reverse()
         }
     }