feat: Optimize euclidean division acir-gen (#3121)

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

Author: TomAFrench

compiler/noirc_evaluator/src/ssa/acir_gen/acir_ir/generated_acir.rs

@@ -440,9 +440,30 @@ impl GeneratedAcir {
         //
         // When the predicate is 0, the equation always passes.
         // When the predicate is 1, the rhs must not be 0.
-        let rhs_is_zero = self.is_zero(rhs);
-        let rhs_is_not_zero = self.mul_with_witness(&rhs_is_zero.into(), predicate);
-        self.assert_is_zero(rhs_is_not_zero);
+        let rhs_is_nonzero_const = rhs.is_const() && !rhs.is_zero();
+        if !rhs_is_nonzero_const {
+            match predicate.to_const() {
+                Some(predicate) if predicate.is_zero() => {
+                    // If predicate is known to be inactive, we don't need to lay down constraints.
+                }
+
+                Some(predicate) if predicate.is_one() => {
+                    // If the predicate is known to be active, we simply assert that an inverse must exist.
+                    // This implies that `rhs != 0`.
+                    let unsafe_inverse = self.brillig_inverse(rhs.clone());
+                    let rhs_has_inverse =
+                        self.mul_with_witness(rhs, &unsafe_inverse.into()) - FieldElement::one();
+                    self.assert_is_zero(rhs_has_inverse);
+                }
+
+                _ => {
+                    // Otherwise we must handle both potential cases.
+                    let rhs_is_zero = self.is_zero(rhs);
+                    let rhs_is_not_zero = self.mul_with_witness(&rhs_is_zero.into(), predicate);
+                    self.assert_is_zero(rhs_is_not_zero);
+                }
+            }
+        }
 
         // maximum bit size for q and for [r and rhs]
         let mut max_q_bits = max_bit_size;