Merge pull request #712 from mir-protocol/comment_batch_opening

Document batch opening function

plonky2/src/fri/oracle.rs

@@ -180,7 +180,15 @@ impl<F: RichField + Extendable<D>, C: GenericConfig<D, F = F>, const D: usize>
         // Final low-degree polynomial that goes into FRI.
         let mut final_poly = PolynomialCoeffs::empty();
 
+        // Each batch `i` consists of an opening point `z_i` and polynomials `{f_ij}_j` to be opened at that point.
+        // For each batch, we compute the composition polynomial `F_i = sum alpha^j f_ij`,
+        // where `alpha` is a random challenge in the extension field.
+        // The final polynomial is then computed as `final_poly = sum_i alpha^(k_i) (F_i(X) - F_i(z_i))/(X-z_i)`
+        // where the `k_i`s are chosen such that each power of `alpha` appears only once in the final sum.
+        // There are usually two batches for the openings at `zeta` and `g * zeta`.
+        // The oracles used in Plonky2 are given in `FRI_ORACLES` in `plonky2/src/plonk/plonk_common.rs`.
         for FriBatchInfo { point, polynomials } in &instance.batches {
+            // Collect the coefficients of all the polynomials in `polynomials`.
             let polys_coeff = polynomials.iter().map(|fri_poly| {
                 &oracles[fri_poly.oracle_index].polynomials[fri_poly.polynomial_index]
             });

plonky2/src/fri/structure.rs

@@ -42,7 +42,7 @@ pub struct FriBatchInfoTarget<const D: usize> {
 
 #[derive(Copy, Clone, Debug)]
 pub struct FriPolynomialInfo {
-    /// Index into `FriInstanceInfoTarget`'s `oracles` list.
+    /// Index into `FriInstanceInfo`'s `oracles` list.
     pub oracle_index: usize,
     /// Index of the polynomial within the oracle.
     pub polynomial_index: usize,