feat: Hoist constant allocation outside of loops (#6158)

# Description

## Problem\*

Avoids the runtime cost of reinitializing constants inside loops.

## Summary\*



## Additional Context



## Documentation\*

Check one:
- [x] No documentation needed.
- [ ] Documentation included in this PR.
- [ ] **[For Experimental Features]** Documentation to be submitted in a
separate PR.

# PR Checklist\*

- [x] I have tested the changes locally.
- [x] I have formatted the changes with [Prettier](https://prettier.io/)
and/or `cargo fmt` on default settings.

compiler/noirc_evaluator/src/brillig/brillig_gen/constant_allocation.rs

@@ -1,7 +1,7 @@
 //! This module analyzes the usage of constants in a given function and decides an allocation point for them.
 //! The allocation point will be the common dominator of all the places where the constant is used.
 //! By allocating in the common dominator, we can cache the constants for all subsequent uses.
-use fxhash::FxHashMap as HashMap;
+use fxhash::{FxHashMap as HashMap, FxHashSet as HashSet};
 
 use crate::ssa::ir::{
     basic_block::BasicBlockId,
@@ -26,20 +26,23 @@ pub(crate) struct ConstantAllocation {
     constant_usage: HashMap<ValueId, HashMap<BasicBlockId, Vec<InstructionLocation>>>,
     allocation_points: HashMap<BasicBlockId, HashMap<InstructionLocation, Vec<ValueId>>>,
     dominator_tree: DominatorTree,
+    blocks_within_loops: HashSet<BasicBlockId>,
 }
 
 impl ConstantAllocation {
     pub(crate) fn from_function(func: &Function) -> Self {
         let cfg = ControlFlowGraph::with_function(func);
         let post_order = PostOrder::with_function(func);
-        let dominator_tree = DominatorTree::with_cfg_and_post_order(&cfg, &post_order);
+        let mut dominator_tree = DominatorTree::with_cfg_and_post_order(&cfg, &post_order);
+        let blocks_within_loops = find_all_blocks_within_loops(func, &cfg, &mut dominator_tree);
         let mut instance = ConstantAllocation {
             constant_usage: HashMap::default(),
             allocation_points: HashMap::default(),
             dominator_tree,
+            blocks_within_loops,
         };
         instance.collect_constant_usage(func);
-        instance.decide_allocation_points();
+        instance.decide_allocation_points(func);
 
         instance
     }
@@ -95,16 +98,16 @@ impl ConstantAllocation {
         }
     }
 
-    fn decide_allocation_points(&mut self) {
+    fn decide_allocation_points(&mut self, func: &Function) {
         for (constant_id, usage_in_blocks) in self.constant_usage.iter() {
             let block_ids: Vec<_> = usage_in_blocks.iter().map(|(block_id, _)| *block_id).collect();
 
-            let common_dominator = self.common_dominator(&block_ids);
+            let allocation_point = self.decide_allocation_point(*constant_id, &block_ids, func);
 
-            // If the common dominator is one of the places where it's used, we take the first usage in the common dominator.
-            // Otherwise, we allocate it at the terminator of the common dominator.
+            // If the allocation point is one of the places where it's used, we take the first usage in the allocation point.
+            // Otherwise, we allocate it at the terminator of the allocation point.
             let location = if let Some(locations_in_common_dominator) =
-                usage_in_blocks.get(&common_dominator)
+                usage_in_blocks.get(&allocation_point)
             {
                 *locations_in_common_dominator
                     .first()
@@ -114,29 +117,105 @@ impl ConstantAllocation {
             };
 
             self.allocation_points
-                .entry(common_dominator)
+                .entry(allocation_point)
                 .or_default()
                 .entry(location)
                 .or_default()
                 .push(*constant_id);
         }
     }
 
-    fn common_dominator(&self, block_ids: &[BasicBlockId]) -> BasicBlockId {
-        if block_ids.len() == 1 {
-            return block_ids[0];
-        }
-
-        let mut common_dominator = block_ids[0];
+    fn decide_allocation_point(
+        &self,
+        constant_id: ValueId,
+        blocks_where_is_used: &[BasicBlockId],
+        func: &Function,
+    ) -> BasicBlockId {
+        // Find the common dominator of all the blocks where the constant is used.
+        let common_dominator = if blocks_where_is_used.len() == 1 {
+            blocks_where_is_used[0]
+        } else {
+            let mut common_dominator = blocks_where_is_used[0];
+
+            for block_id in blocks_where_is_used.iter().skip(1) {
+                common_dominator =
+                    self.dominator_tree.common_dominator(common_dominator, *block_id);
+            }
 
-        for block_id in block_ids.iter().skip(1) {
-            common_dominator = self.dominator_tree.common_dominator(common_dominator, *block_id);
+            common_dominator
+        };
+        // If the value only contains constants, it's safe to hoist outside of any loop
+        if func.dfg.is_constant(constant_id) {
+            self.exit_loops(common_dominator)
+        } else {
+            common_dominator
         }
+    }
 
-        common_dominator
+    /// Returns the nearest dominator that is outside of any loop.
+    fn exit_loops(&self, block: BasicBlockId) -> BasicBlockId {
+        let mut current_block = block;
+        while self.blocks_within_loops.contains(&current_block) {
+            current_block = self
+                .dominator_tree
+                .immediate_dominator(current_block)
+                .expect("No dominator found when trying to allocate a constant outside of a loop");
+        }
+        current_block
     }
 }
 
 pub(crate) fn is_constant_value(id: ValueId, dfg: &DataFlowGraph) -> bool {
     matches!(&dfg[dfg.resolve(id)], Value::NumericConstant { .. } | Value::Array { .. })
 }
+
+/// For a given function, finds all the blocks that are within loops
+fn find_all_blocks_within_loops(
+    func: &Function,
+    cfg: &ControlFlowGraph,
+    dominator_tree: &mut DominatorTree,
+) -> HashSet<BasicBlockId> {
+    let mut blocks_in_loops = HashSet::default();
+    for block_id in func.reachable_blocks() {
+        let block = &func.dfg[block_id];
+        let successors = block.successors();
+        for successor_id in successors {
+            if dominator_tree.dominates(successor_id, block_id) {
+                blocks_in_loops.extend(find_blocks_in_loop(successor_id, block_id, cfg));
+            }
+        }
+    }
+
+    blocks_in_loops
+}
+
+/// Return each block that is in a loop starting in the given header block.
+/// Expects back_edge_start -> header to be the back edge of the loop.
+fn find_blocks_in_loop(
+    header: BasicBlockId,
+    back_edge_start: BasicBlockId,
+    cfg: &ControlFlowGraph,
+) -> HashSet<BasicBlockId> {
+    let mut blocks = HashSet::default();
+    blocks.insert(header);
+
+    let mut insert = |block, stack: &mut Vec<BasicBlockId>| {
+        if !blocks.contains(&block) {
+            blocks.insert(block);
+            stack.push(block);
+        }
+    };
+
+    // Starting from the back edge of the loop, each predecessor of this block until
+    // the header is within the loop.
+    let mut stack = vec![];
+    insert(back_edge_start, &mut stack);
+
+    while let Some(block) = stack.pop() {
+        for predecessor in cfg.predecessors(block) {
+            insert(predecessor, &mut stack);
+        }
+    }
+
+    blocks
+}

compiler/noirc_evaluator/src/brillig/brillig_gen/variable_liveness.rs

@@ -570,28 +570,34 @@ mod test {
         let liveness = VariableLiveness::from_function(func, &constants);
 
         assert!(liveness.get_live_in(&func.entry_block()).is_empty());
-        assert_eq!(liveness.get_live_in(&b1), &FxHashSet::from_iter([v0, v1, v3, v4].into_iter()));
+        assert_eq!(
+            liveness.get_live_in(&b1),
+            &FxHashSet::from_iter([v0, v1, v3, v4, twenty_seven, one].into_iter())
+        );
         assert_eq!(liveness.get_live_in(&b3), &FxHashSet::from_iter([v3].into_iter()));
-        assert_eq!(liveness.get_live_in(&b2), &FxHashSet::from_iter([v0, v1, v3, v4].into_iter()));
+        assert_eq!(
+            liveness.get_live_in(&b2),
+            &FxHashSet::from_iter([v0, v1, v3, v4, twenty_seven, one].into_iter())
+        );
         assert_eq!(
             liveness.get_live_in(&b4),
-            &FxHashSet::from_iter([v0, v1, v3, v4, v6, v7].into_iter())
+            &FxHashSet::from_iter([v0, v1, v3, v4, v6, v7, twenty_seven, one].into_iter())
         );
         assert_eq!(
             liveness.get_live_in(&b6),
-            &FxHashSet::from_iter([v0, v1, v3, v4, one].into_iter())
+            &FxHashSet::from_iter([v0, v1, v3, v4, twenty_seven, one].into_iter())
         );
         assert_eq!(
             liveness.get_live_in(&b5),
-            &FxHashSet::from_iter([v0, v1, v3, v4, v6, v7, one].into_iter())
+            &FxHashSet::from_iter([v0, v1, v3, v4, v6, v7, twenty_seven, one].into_iter())
         );
         assert_eq!(
             liveness.get_live_in(&b7),
-            &FxHashSet::from_iter([v0, v1, v3, v4, v6, v7, one].into_iter())
+            &FxHashSet::from_iter([v0, v1, v3, v4, v6, v7, twenty_seven, one].into_iter())
         );
         assert_eq!(
             liveness.get_live_in(&b8),
-            &FxHashSet::from_iter([v0, v1, v3, v4, v6, v7, one].into_iter())
+            &FxHashSet::from_iter([v0, v1, v3, v4, v6, v7, twenty_seven, one].into_iter())
         );
 
         let block_3 = &func.dfg[b3];