chore: folding at i demands witness caching at i+1 and i+2

Make folding, in the main thread, be the driving force that demands
caching witnesses for the next two MultiFrames.

src/proof/nova.rs

@@ -13,6 +13,7 @@ use nova::{
 };
 use once_cell::sync::OnceCell;
 use pasta_curves::pallas;
+use rayon::iter::{IntoParallelIterator, ParallelIterator};
 use serde::{Deserialize, Serialize};
 use std::{
     marker::PhantomData,
@@ -297,24 +298,34 @@ impl<'a, F: CurveCycleEquipped, C: Coprocessor<F>> RecursiveSNARKTrait<F, C1LEM<
             .is_parallel()
         {
             let cc = steps.into_iter().map(Mutex::new).collect::<Vec<_>>();
+            let (folding_idx_sender, folding_idx_receiver) =
+                std::sync::mpsc::channel::<Option<usize>>();
 
             std::thread::scope(|s| {
                 s.spawn(|| {
-                    // Skip the very first circuit's witness, so `prove_step` can begin immediately.
-                    // That circuit's witness will not be cached and will just be computed on-demand.
-                    cc.iter().skip(1).for_each(|mf| {
-                        mf.lock()
-                            .unwrap()
-                            .cache_witness(store)
-                            .expect("witness caching failed");
-                    });
+                    for folding_idx in folding_idx_receiver {
+                        if let Some(folding_idx) = folding_idx {
+                            [1, 2].into_par_iter().for_each(|shift| {
+                                if let Some(mf) = cc.get(folding_idx + shift) {
+                                    mf.lock()
+                                        .unwrap()
+                                        .cache_witness(store)
+                                        .expect("witness caching failed");
+                                }
+                            });
+                        } else {
+                            return;
+                        }
+                    }
                 });
 
                 for (i, step) in cc.iter().enumerate() {
+                    folding_idx_sender.send(Some(i)).unwrap();
                     let mut step = step.lock().unwrap();
                     prove_step(i, &step, &mut recursive_snark_option);
                     step.clear_cached_witness();
                 }
+                folding_idx_sender.send(None).unwrap();
                 recursive_snark_option
             })
         } else {

src/proof/supernova.rs

@@ -11,7 +11,9 @@ use nova::{
     },
 };
 use once_cell::sync::OnceCell;
-use rayon::iter::{IndexedParallelIterator, IntoParallelRefIterator, ParallelIterator};
+use rayon::iter::{
+    IndexedParallelIterator, IntoParallelIterator, IntoParallelRefIterator, ParallelIterator,
+};
 use serde::{Deserialize, Serialize};
 use std::{
     marker::PhantomData,
@@ -260,24 +262,11 @@ impl<'a, F: CurveCycleEquipped, C: Coprocessor<F>> RecursiveSNARKTrait<F, C1LEM<
                 .into_iter()
                 .map(|mf| (mf.program_counter() == 0, Mutex::new(mf)))
                 .collect::<Vec<_>>();
+            let (folding_idx_sender, folding_idx_receiver) =
+                std::sync::mpsc::channel::<Option<usize>>();
 
             std::thread::scope(|s| {
                 s.spawn(|| {
-                    // Skip the very first circuit's witness, so `prove_step` can begin immediately.
-                    // That circuit's witness will not be cached and will just be computed on-demand.
-
-                    // There are many MultiFrames with PC = 0, each with several inner frames and heavy internal
-                    // parallelism for witness generation. So we do it like on Nova's pipeline.
-                    cc.iter()
-                        .skip(1)
-                        .filter(|(is_zero_pc, _)| *is_zero_pc)
-                        .for_each(|(_, mf)| {
-                            mf.lock()
-                                .unwrap()
-                                .cache_witness(store)
-                                .expect("witness caching failed");
-                        });
-
                     // There shouldn't be as many MultiFrames with PC != 0 and they only have one inner frame, each with
                     // poor internal parallelism for witness generation, so we can generate their witnesses in parallel.
                     // This is mimicking the behavior we had in the Nova pipeline before #941 so...
@@ -294,11 +283,33 @@ impl<'a, F: CurveCycleEquipped, C: Coprocessor<F>> RecursiveSNARKTrait<F, C1LEM<
                         });
                 });
 
+                s.spawn(|| {
+                    for folding_idx in folding_idx_receiver {
+                        if let Some(folding_idx) = folding_idx {
+                            [1, 2].into_par_iter().for_each(|shift| {
+                                if let Some((is_zero_pc, mf)) = cc.get(folding_idx + shift) {
+                                    // We're already generating witnesses for MultiFrames with PC != 0 in parallel
+                                    if *is_zero_pc {
+                                        mf.lock()
+                                            .unwrap()
+                                            .cache_witness(store)
+                                            .expect("witness caching failed");
+                                    }
+                                }
+                            });
+                        } else {
+                            return;
+                        }
+                    }
+                });
+
                 for (i, (_, step)) in cc.iter().enumerate() {
+                    folding_idx_sender.send(Some(i)).unwrap();
                     let mut step = step.lock().unwrap();
                     prove_step(i, &step, &mut recursive_snark_option);
                     step.clear_cached_witness();
                 }
+                folding_idx_sender.send(None).unwrap();
                 recursive_snark_option
             })
         } else {