feat: skip inverting field elements with values +-1 in ACVM

acvm-repo/acvm/src/pwg/arithmetic.rs

@@ -59,7 +59,7 @@ impl ExpressionSolver {
                             Ok(())
                         }
                     } else {
-                        let assignment = -total_sum / (q + b);
+                        let assignment = -quick_invert(total_sum, q + b);
                         insert_value(&w1, assignment, initial_witness)
                     }
                 } else {
@@ -88,7 +88,7 @@ impl ExpressionSolver {
                         Ok(())
                     }
                 } else {
-                    let assignment = -(total_sum / partial_prod);
+                    let assignment = -quick_invert(total_sum, partial_prod);
                     insert_value(&unknown_var, assignment, initial_witness)
                 }
             }
@@ -122,7 +122,7 @@ impl ExpressionSolver {
                         Ok(())
                     }
                 } else {
-                    let assignment = -(total_sum / coeff);
+                    let assignment = -quick_invert(total_sum, coeff);
                     insert_value(&unknown_var, assignment, initial_witness)
                 }
             }
@@ -248,11 +248,34 @@ impl ExpressionSolver {
     }
 }
 
+/// A wrapper around field division which skips the inversion if the denominator
+/// is ±1.
+///
+/// Field inversion is the most significant cost of solving [`Opcode::AssertZero`][acir::circuit::opcodes::Opcode::AssertZero]
+/// opcodes, we can avoid this in the situation
+fn quick_invert<F: AcirField>(numerator: F, denominator: F) -> F {
+    if denominator == F::one() {
+        numerator
+    } else if denominator == -F::one() {
+        -numerator
+    } else {
+        numerator / denominator
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;
     use acir::FieldElement;
 
+    #[test]
+    /// Sanity check for the special cases of [`quick_invert`]
+    fn quick_invert_matches_slow_invert() {
+        let numerator = FieldElement::from_be_bytes_reduce("hello_world".as_bytes());
+        assert_eq!(quick_invert(numerator, FieldElement::one()), numerator / FieldElement::one());
+        assert_eq!(quick_invert(numerator, -FieldElement::one()), numerator / -FieldElement::one());
+    }
+
     #[test]
     fn solves_simple_assignment() {
         let a = Witness(0);