BaseFold: Add and reimplement some utility functions.

[yczhangsjtu]

Extracting small PRs from #294

There was an implementation of Iterator for iterating through a FieldType. Turns out that it can be replaced with existing tools in iter_tools. This proposes the new implementation.

Also added some other utility functions for type conversion between FieldType and Vec<E>, to avoid match field_type everywhere.

[matthiasgoergens]

Thanks for breaking down the big PR into more digestible chunks!

[matthiasgoergens]

Could you please add in the PR description why we are making this refactoring?

Just a quick note about what task becomes easier or simpler with the new organisation?

Thanks!

[hero78119]

does the Either::Left and Either::Right here is nessesary? Because return type are the same, here somehow Either is a bit over design

[yczhangsjtu]

No the return types are not the same. They are both iterators over BaseField but different types of Iterator.

[yczhangsjtu]

What's the standard solution for this? The Either is some solution I found on the internet after many fruitless fightings with the compiler. Any better suggestions are welcome. I'm really not an expert in rust iterators.

[hero78119]

Another option is rely on runtime dispatch.

diff --git a/mpcs/src/util.rs b/mpcs/src/util.rs
index 7688b53e..6edd82d4 100644
--- a/mpcs/src/util.rs
+++ b/mpcs/src/util.rs
@@ -182,10 +182,10 @@ pub fn field_type_as_ext<E: ExtensionField>(values: &FieldType<E>) -> &Vec<E> {

 pub fn field_type_iter_base<E: ExtensionField>(
     values: &FieldType<E>,
-) -> impl Iterator<Item = &E::BaseField> + '_ {
+) -> Box<dyn Iterator<Item = &E::BaseField> + '_> {
     match values {
-        FieldType::Ext(coeffs) => Either::Left(coeffs.iter().flat_map(|x| x.as_bases())),
-        FieldType::Base(coeffs) => Either::Right(coeffs.iter()),
+        FieldType::Ext(coeffs) => Box::new(coeffs.iter().flat_map(|x| x.as_bases())),
+        FieldType::Base(coeffs) => Box::new(coeffs.iter()),
         _ => unreachable!(),
     }
 }

After reading document in Either, I think static dispatch via Either is better, and either already implement iterator so it's truly works this purpose. So LGTM under this scope! 👍

[hero78119]

👍