feat: remove 'single use' intermediate variables (noir-lang#6268)

# Description

## Problem\*

Resolves noir-lang#6085 

## Summary\*
This PR tries to benefit from Barretenberg's 'big-add gates' support,
which was enabled by PR
AztecProtocol/aztec-packages#8960
It's a simple optimisation which removes intermediate variables usually
created by the CSatTransformer if they are not re-used elsewhere.
The PR assumes that the backend is able to handle infinite width, but
still requires the CSatTransformer, which is not really consistent. I
plan to make follow-up PRs to get rid of this (but I can't guarantee it
will work).



## Additional Context
I tested the optimisation on all 'execution_sucess' test cases. In most
cases, there were no change at all, while in some cases we would win one
or two (10 max) on the circuit size.
However, in a few cases, listed below in the form "test case: circuit
size with 'intermediate var' optimisation vs no optimisation", it can be
more significant:

7_function: 2955 vs 2992
bit_shifts_runtime: 5451 vs 5761
eddsa: 65805 vs 70406
hashmap: 135023 vs 150661
nested_array_dynamic: 12594 vs 12922
nested_array_in_slice: 5371 vs 5449
poseidon_bn254_hash: 1028 vs 1060
poseidon_bn254_hash_width_3: 1028 vs 1495
poseidonsponge_x5_254: 1244 vs 1307
regression_5252: 76491 vs 83862
sha256_var_size_regression: 74093 vs 74529
sha2_byte: 93998 vs 94006
slice_dynamic_index: 6308 vs 6419
slices: 3835 vs 3874
to_be_bytes: 135 vs 143
to_bytes_consistent: 6 vs 51
to_bytes_integration: 434 vs 484
u128: 4662 vs 4707
u16_support: 3023 vs 3057



## 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.

Co-authored-by: Tom French <[email protected]>

acvm-repo/acir/src/circuit/opcodes/black_box_function_call.rs

@@ -1,3 +1,5 @@
+use std::collections::HashSet;
+
 use crate::native_types::Witness;
 use crate::{AcirField, BlackBoxFunc};
 
@@ -389,6 +391,16 @@ impl<F: Copy> BlackBoxFuncCall<F> {
             BlackBoxFuncCall::BigIntToLeBytes { outputs, .. } => outputs.to_vec(),
         }
     }
+
+    pub fn get_input_witnesses(&self) -> HashSet<Witness> {
+        let mut result = HashSet::new();
+        for input in self.get_inputs_vec() {
+            if let ConstantOrWitnessEnum::Witness(w) = input.input() {
+                result.insert(w);
+            }
+        }
+        result
+    }
 }
 
 const ABBREVIATION_LIMIT: usize = 5;

acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs

@@ -0,0 +1,202 @@
+use std::collections::{HashMap, HashSet};
+
+use acir::{
+    circuit::{brillig::BrilligInputs, directives::Directive, opcodes::BlockId, Circuit, Opcode},
+    native_types::{Expression, Witness},
+    AcirField,
+};
+
+pub(crate) struct MergeExpressionsOptimizer {
+    resolved_blocks: HashMap<BlockId, HashSet<Witness>>,
+}
+
+impl MergeExpressionsOptimizer {
+    pub(crate) fn new() -> Self {
+        MergeExpressionsOptimizer { resolved_blocks: HashMap::new() }
+    }
+    /// This pass analyzes the circuit and identifies intermediate variables that are
+    /// only used in two gates. It then merges the gate that produces the
+    /// intermediate variable into the second one that uses it
+    /// Note: This pass is only relevant for backends that can handle unlimited width
+    pub(crate) fn eliminate_intermediate_variable<F: AcirField>(
+        &mut self,
+        circuit: &Circuit<F>,
+        acir_opcode_positions: Vec<usize>,
+    ) -> (Vec<Opcode<F>>, Vec<usize>) {
+        // Keep track, for each witness, of the gates that use it
+        let circuit_inputs = circuit.circuit_arguments();
+        self.resolved_blocks = HashMap::new();
+        let mut used_witness: HashMap<Witness, HashSet<usize>> = HashMap::new();
+        for (i, opcode) in circuit.opcodes.iter().enumerate() {
+            let witnesses = self.witness_inputs(opcode);
+            if let Opcode::MemoryInit { block_id, .. } = opcode {
+                self.resolved_blocks.insert(*block_id, witnesses.clone());
+            }
+            for w in witnesses {
+                // We do not simplify circuit inputs
+                if !circuit_inputs.contains(&w) {
+                    used_witness.entry(w).or_default().insert(i);
+                }
+            }
+        }
+
+        let mut modified_gates: HashMap<usize, Opcode<F>> = HashMap::new();
+        let mut new_circuit = Vec::new();
+        let mut new_acir_opcode_positions = Vec::new();
+        // For each opcode, try to get a target opcode to merge with
+        for (i, opcode) in circuit.opcodes.iter().enumerate() {
+            if !matches!(opcode, Opcode::AssertZero(_)) {
+                new_circuit.push(opcode.clone());
+                new_acir_opcode_positions.push(acir_opcode_positions[i]);
+                continue;
+            }
+            let opcode = modified_gates.get(&i).unwrap_or(opcode).clone();
+            let mut to_keep = true;
+            let input_witnesses = self.witness_inputs(&opcode);
+            for w in input_witnesses.clone() {
+                let empty_gates = HashSet::new();
+                let gates_using_w = used_witness.get(&w).unwrap_or(&empty_gates);
+                // We only consider witness which are used in exactly two arithmetic gates
+                if gates_using_w.len() == 2 {
+                    let gates_using_w: Vec<_> = gates_using_w.iter().collect();
+                    let mut b = *gates_using_w[1];
+                    if b == i {
+                        b = *gates_using_w[0];
+                    } else {
+                        // sanity check
+                        assert!(i == *gates_using_w[0]);
+                    }
+                    let second_gate = modified_gates.get(&b).unwrap_or(&circuit.opcodes[b]).clone();
+                    if let (Opcode::AssertZero(expr_define), Opcode::AssertZero(expr_use)) =
+                        (opcode.clone(), second_gate)
+                    {
+                        if let Some(expr) = Self::merge(&expr_use, &expr_define, w) {
+                            // sanity check
+                            assert!(i < b);
+                            modified_gates.insert(b, Opcode::AssertZero(expr));
+                            to_keep = false;
+                            // Update the 'used_witness' map to account for the merge.
+                            for w2 in Self::expr_wit(&expr_define) {
+                                if !circuit_inputs.contains(&w2) {
+                                    let mut v = used_witness[&w2].clone();
+                                    v.insert(b);
+                                    v.remove(&i);
+                                    used_witness.insert(w2, v);
+                                }
+                            }
+                            // We need to stop here and continue with the next opcode
+                            // because the merge invalidate the current opcode
+                            break;
+                        }
+                    }
+                }
+            }
+
+            if to_keep {
+                if modified_gates.contains_key(&i) {
+                    new_circuit.push(modified_gates[&i].clone());
+                } else {
+                    new_circuit.push(opcode.clone());
+                }
+                new_acir_opcode_positions.push(acir_opcode_positions[i]);
+            }
+        }
+        (new_circuit, new_acir_opcode_positions)
+    }
+
+    fn expr_wit<F>(expr: &Expression<F>) -> HashSet<Witness> {
+        let mut result = HashSet::new();
+        result.extend(expr.mul_terms.iter().flat_map(|i| vec![i.1, i.2]));
+        result.extend(expr.linear_combinations.iter().map(|i| i.1));
+        result
+    }
+
+    fn brillig_input_wit<F>(&self, input: &BrilligInputs<F>) -> HashSet<Witness> {
+        let mut result = HashSet::new();
+        match input {
+            BrilligInputs::Single(expr) => {
+                result.extend(Self::expr_wit(expr));
+            }
+            BrilligInputs::Array(exprs) => {
+                for expr in exprs {
+                    result.extend(Self::expr_wit(expr));
+                }
+            }
+            BrilligInputs::MemoryArray(block_id) => {
+                let witnesses = self.resolved_blocks.get(block_id).expect("Unknown block id");
+                result.extend(witnesses);
+            }
+        }
+        result
+    }
+
+    // Returns the input witnesses used by the opcode
+    fn witness_inputs<F: AcirField>(&self, opcode: &Opcode<F>) -> HashSet<Witness> {
+        let mut witnesses = HashSet::new();
+        match opcode {
+            Opcode::AssertZero(expr) => Self::expr_wit(expr),
+            Opcode::BlackBoxFuncCall(bb_func) => bb_func.get_input_witnesses(),
+            Opcode::Directive(Directive::ToLeRadix { a, .. }) => Self::expr_wit(a),
+            Opcode::MemoryOp { block_id: _, op, predicate } => {
+                //index et value, et predicate
+                let mut witnesses = HashSet::new();
+                witnesses.extend(Self::expr_wit(&op.index));
+                witnesses.extend(Self::expr_wit(&op.value));
+                if let Some(p) = predicate {
+                    witnesses.extend(Self::expr_wit(p));
+                }
+                witnesses
+            }
+
+            Opcode::MemoryInit { block_id: _, init, block_type: _ } => {
+                init.iter().cloned().collect()
+            }
+            Opcode::BrilligCall { inputs, .. } => {
+                for i in inputs {
+                    witnesses.extend(self.brillig_input_wit(i));
+                }
+                witnesses
+            }
+            Opcode::Call { id: _, inputs, outputs: _, predicate } => {
+                for i in inputs {
+                    witnesses.insert(*i);
+                }
+                if let Some(p) = predicate {
+                    witnesses.extend(Self::expr_wit(p));
+                }
+                witnesses
+            }
+        }
+    }
+
+    // Merge 'expr' into 'target' via Gaussian elimination on 'w'
+    // Returns None if the expressions cannot be merged
+    fn merge<F: AcirField>(
+        target: &Expression<F>,
+        expr: &Expression<F>,
+        w: Witness,
+    ) -> Option<Expression<F>> {
+        // Check that the witness is not part of multiplication terms
+        for m in &target.mul_terms {
+            if m.1 == w || m.2 == w {
+                return None;
+            }
+        }
+        for m in &expr.mul_terms {
+            if m.1 == w || m.2 == w {
+                return None;
+            }
+        }
+
+        for k in &target.linear_combinations {
+            if k.1 == w {
+                for i in &expr.linear_combinations {
+                    if i.1 == w {
+                        return Some(target.add_mul(-(k.0 / i.0), expr));
+                    }
+                }
+            }
+        }
+        None
+    }
+}

acvm-repo/acvm/src/compiler/optimizers/mod.rs

@@ -5,10 +5,12 @@ use acir::{
 
 // mod constant_backpropagation;
 mod general;
+mod merge_expressions;
 mod redundant_range;
 mod unused_memory;
 
 pub(crate) use general::GeneralOptimizer;
+pub(crate) use merge_expressions::MergeExpressionsOptimizer;
 pub(crate) use redundant_range::RangeOptimizer;
 use tracing::info;
 

acvm-repo/acvm/src/compiler/transformers/mod.rs

@@ -10,7 +10,9 @@ mod csat;
 pub(crate) use csat::CSatTransformer;
 pub use csat::MIN_EXPRESSION_WIDTH;
 
-use super::{transform_assert_messages, AcirTransformationMap};
+use super::{
+    optimizers::MergeExpressionsOptimizer, transform_assert_messages, AcirTransformationMap,
+};
 
 /// Applies [`ProofSystemCompiler`][crate::ProofSystemCompiler] specific optimizations to a [`Circuit`].
 pub fn transform<F: AcirField>(
@@ -166,6 +168,16 @@ pub(super) fn transform_internal<F: AcirField>(
         // The transformer does not add new public inputs
         ..acir
     };
-
+    let mut merge_optimizer = MergeExpressionsOptimizer::new();
+    let (opcodes, new_acir_opcode_positions) =
+        merge_optimizer.eliminate_intermediate_variable(&acir, new_acir_opcode_positions);
+    // n.b. we do not update current_witness_index after the eliminate_intermediate_variable pass, the real index could be less.
+    let acir = Circuit {
+        current_witness_index,
+        expression_width,
+        opcodes,
+        // The optimizer does not add new public inputs
+        ..acir
+    };
     (acir, new_acir_opcode_positions)
 }