Benchmark computation commitments (#201)

* feat; benchmark compressed SNARK with computational commitments

- labeled types for compressed SNARKs in benchmarks, both with and without computational commitments, enhancing the functionality.
- Extended benchmark testing to include compressed SNARK with computational commtiments

* fix: use flat sampling mode for computational commitments, reduce circuit sizes

benches/compressed-snark.rs

@@ -17,8 +17,12 @@ type G1 = pasta_curves::pallas::Point;
 type G2 = pasta_curves::vesta::Point;
 type EE1 = nova_snark::provider::ipa_pc::EvaluationEngine<G1>;
 type EE2 = nova_snark::provider::ipa_pc::EvaluationEngine<G2>;
+// SNARKs without computational commitments
 type S1 = nova_snark::spartan::snark::RelaxedR1CSSNARK<G1, EE1>;
 type S2 = nova_snark::spartan::snark::RelaxedR1CSSNARK<G2, EE2>;
+// SNARKs with computational commitments
+type SS1 = nova_snark::spartan::ppsnark::RelaxedR1CSSNARK<G1, EE1>;
+type SS2 = nova_snark::spartan::ppsnark::RelaxedR1CSSNARK<G2, EE2>;
 type C1 = NonTrivialTestCircuit<<G1 as Group>::Scalar>;
 type C2 = TrivialTestCircuit<<G2 as Group>::Scalar>;
 
@@ -31,13 +35,13 @@ cfg_if::cfg_if! {
     criterion_group! {
       name = compressed_snark;
       config = Criterion::default().warm_up_time(Duration::from_millis(3000)).with_profiler(pprof::criterion::PProfProfiler::new(100, pprof::criterion::Output::Flamegraph(None)));
-      targets = bench_compressed_snark
+      targets = bench_compressed_snark, bench_compressed_snark_with_computational_commitments
     }
   } else {
     criterion_group! {
       name = compressed_snark;
       config = Criterion::default().warm_up_time(Duration::from_millis(3000));
-      targets = bench_compressed_snark
+      targets = bench_compressed_snark, bench_compressed_snark_with_computational_commitments
     }
   }
 }
@@ -129,6 +133,93 @@ fn bench_compressed_snark(c: &mut Criterion) {
   }
 }
 
+fn bench_compressed_snark_with_computational_commitments(c: &mut Criterion) {
+  let num_samples = 10;
+  let num_cons_verifier_circuit_primary = 9819;
+  // we vary the number of constraints in the step circuit
+  for &num_cons_in_augmented_circuit in [9819, 16384, 32768, 65536, 131072, 262144].iter() {
+    // number of constraints in the step circuit
+    let num_cons = num_cons_in_augmented_circuit - num_cons_verifier_circuit_primary;
+
+    let mut group = c.benchmark_group(format!(
+      "CompressedSNARK-Commitments-StepCircuitSize-{num_cons}"
+    ));
+    group
+      .sampling_mode(SamplingMode::Flat)
+      .sample_size(num_samples);
+
+    let c_primary = NonTrivialTestCircuit::new(num_cons);
+    let c_secondary = TrivialTestCircuit::default();
+
+    // Produce public parameters
+    let pp = PublicParams::<G1, G2, C1, C2>::setup(c_primary.clone(), c_secondary.clone());
+
+    // Produce prover and verifier keys for CompressedSNARK
+    let (pk, vk) = CompressedSNARK::<_, _, _, _, SS1, SS2>::setup(&pp).unwrap();
+
+    // produce a recursive SNARK
+    let num_steps = 3;
+    let mut recursive_snark: RecursiveSNARK<G1, G2, C1, C2> = RecursiveSNARK::new(
+      &pp,
+      &c_primary,
+      &c_secondary,
+      vec![<G1 as Group>::Scalar::from(2u64)],
+      vec![<G2 as Group>::Scalar::from(2u64)],
+    );
+
+    for i in 0..num_steps {
+      let res = recursive_snark.prove_step(
+        &pp,
+        &c_primary,
+        &c_secondary,
+        vec![<G1 as Group>::Scalar::from(2u64)],
+        vec![<G2 as Group>::Scalar::from(2u64)],
+      );
+      assert!(res.is_ok());
+
+      // verify the recursive snark at each step of recursion
+      let res = recursive_snark.verify(
+        &pp,
+        i + 1,
+        &[<G1 as Group>::Scalar::from(2u64)],
+        &[<G2 as Group>::Scalar::from(2u64)],
+      );
+      assert!(res.is_ok());
+    }
+
+    // Bench time to produce a compressed SNARK
+    group.bench_function("Prove", |b| {
+      b.iter(|| {
+        assert!(CompressedSNARK::<_, _, _, _, SS1, SS2>::prove(
+          black_box(&pp),
+          black_box(&pk),
+          black_box(&recursive_snark)
+        )
+        .is_ok());
+      })
+    });
+    let res = CompressedSNARK::<_, _, _, _, SS1, SS2>::prove(&pp, &pk, &recursive_snark);
+    assert!(res.is_ok());
+    let compressed_snark = res.unwrap();
+
+    // Benchmark the verification time
+    group.bench_function("Verify", |b| {
+      b.iter(|| {
+        assert!(black_box(&compressed_snark)
+          .verify(
+            black_box(&vk),
+            black_box(num_steps),
+            black_box(vec![<G1 as Group>::Scalar::from(2u64)]),
+            black_box(vec![<G2 as Group>::Scalar::from(2u64)]),
+          )
+          .is_ok());
+      })
+    });
+
+    group.finish();
+  }
+}
+
 #[derive(Clone, Debug, Default)]
 struct NonTrivialTestCircuit<F: PrimeField> {
   num_cons: usize,