Minor changes and documentation

src/arithmetic.rs

@@ -440,8 +440,8 @@ pub fn lagrange_interpolate<F: Field>(points: &[F], evals: &[F]) -> Vec<F> {
     } else {
         let mut interpolation_polys = vec![];
         for (j, x_j) in points.iter().enumerate() {
-            let mut tmp: Vec<F> = Vec::with_capacity(points.len() + 1);
+            let mut tmp: Vec<F> = Vec::with_capacity(points.len());
-            let mut product = Vec::with_capacity(points.len() + 1);
+            let mut product = Vec::with_capacity(points.len() - 1);
             tmp.push(F::one());
             for (k, x_k) in points.iter().enumerate() {
                 if k != j {
@@ -459,6 +459,8 @@ pub fn lagrange_interpolate<F: Field>(points: &[F], evals: &[F]) -> Vec<F> {
                     std::mem::swap(&mut tmp, &mut product);
                 }
             }
+            assert_eq!(tmp.len(), points.len());
+            assert_eq!(product.len(), points.len() - 1);
             interpolation_polys.push(tmp);
         }
         let mut final_poly = vec![F::zero(); points.len()];

src/poly/multiopen/prover.rs

@@ -40,6 +40,9 @@ impl<C: CurveAffine> Proof<C> {
         // x_4 challenge.
         let mut q_polys: Vec<Option<Polynomial<C::Scalar, Coeff>>> = vec![None; point_sets.len()];
         let mut q_blinds = vec![Blind(C::Scalar::zero()); point_sets.len()];
+
+        // A vec of vecs of evals. The outer vec corresponds to the point set,
+        // while the inner vec corresponds to the points in a particular set.
         let mut q_eval_sets: Vec<Vec<_>> = vec![Vec::new(); point_sets.len()];
         for (set_idx, point_set) in point_sets.iter().enumerate() {
             q_eval_sets[set_idx] = vec![C::Scalar::zero(); point_set.len()];
@@ -66,6 +69,8 @@ impl<C: CurveAffine> Proof<C> {
                     });
                 q_blinds[set_idx] *= x_4;
                 q_blinds[set_idx] += blind;
+                // Each polynomial is evaluated at a set of points. For each set,
+                // we collapse each polynomial's evals pointwise.
                 for (eval_idx, &eval) in evals.iter().enumerate() {
                     q_eval_sets[set_idx][eval_idx] *= &x_4;
                     q_eval_sets[set_idx][eval_idx] += &eval;
@@ -142,7 +147,7 @@ impl<C: CurveAffine> Proof<C> {
                 (f_poly.clone(), f_blind),
                 |(f_poly, f_blind), (poly, blind)| {
                     (
-                        f_poly * x_7 + &poly.clone().unwrap(),
+                        f_poly * x_7 + poly.as_ref().unwrap(),
                         Blind((f_blind.0 * &x_7) + &blind.0),
                     )
                 },

src/poly/multiopen/verifier.rs

@@ -17,9 +17,9 @@ struct CommitmentData<C: CurveAffine> {
     evals: Vec<C::Scalar>,
 }
 
-impl<'a, C: CurveAffine> Proof<C> {
+impl<C: CurveAffine> Proof<C> {
     /// Verify a multi-opening proof
-    pub fn verify<I, HBase: Hasher<C::Base>, HScalar: Hasher<C::Scalar>>(
+    pub fn verify<'a, I, HBase: Hasher<C::Base>, HScalar: Hasher<C::Scalar>>(
         &self,
         params: &'a Params<C>,
         transcript: &mut HBase,
@@ -43,6 +43,9 @@ impl<'a, C: CurveAffine> Proof<C> {
         // Compress the commitments and expected evaluations at x_3 together.
         // using the challenge x_4
         let mut q_commitments: Vec<_> = vec![params.empty_msm(); point_sets.len()];
+
+        // A vec of vecs of evals. The outer vec corresponds to the point set,
+        // while the inner vec corresponds to the points in a particular set.
         let mut q_eval_sets: Vec<Vec<C::Scalar>> = vec![Vec::new(); point_sets.len()];
         for (set_idx, point_set) in point_sets.iter().enumerate() {
             q_eval_sets[set_idx] = vec![C::Scalar::zero(); point_set.len()];
@@ -57,6 +60,8 @@ impl<'a, C: CurveAffine> Proof<C> {
                 }
             };
 
+            // Each commitment corresponds to evaluations at a set of points.
+            // For each set, we collapse each commitment's evals pointwise.
             for (commitment, commitment_data) in commitment_map {
                 accumulate(
                     commitment_data.set_index,      // set_idx,