enabling batch opening and mock tests (#80)

- add mock circuits
- add vanilla and jellyfish plonk gates
- performance tuning

pcs/benches/bench.rs

@@ -0,0 +1,88 @@
+use ark_bls12_381::{Bls12_381, Fr};
+use ark_ff::UniformRand;
+use ark_poly::{DenseMultilinearExtension, MultilinearExtension};
+use ark_std::{rc::Rc, test_rng};
+use pcs::{
+    prelude::{MultilinearKzgPCS, PCSError, PolynomialCommitmentScheme},
+    StructuredReferenceString,
+};
+use std::time::Instant;
+
+fn main() -> Result<(), PCSError> {
+    bench_pcs()
+}
+
+fn bench_pcs() -> Result<(), PCSError> {
+    let mut rng = test_rng();
+
+    // normal polynomials
+    let uni_params = MultilinearKzgPCS::<Bls12_381>::gen_srs_for_testing(&mut rng, 18)?;
+
+    for nv in 4..19 {
+        let repetition = if nv < 10 {
+            100
+        } else if nv < 20 {
+            50
+        } else {
+            10
+        };
+
+        let poly = Rc::new(DenseMultilinearExtension::rand(nv, &mut rng));
+        let (ml_ck, ml_vk) = uni_params.0.trim(nv)?;
+        let (uni_ck, uni_vk) = uni_params.1.trim(nv)?;
+        let ck = (ml_ck, uni_ck);
+        let vk = (ml_vk, uni_vk);
+
+        let point: Vec<_> = (0..nv).map(|_| Fr::rand(&mut rng)).collect();
+
+        // commit
+        let com = {
+            let start = Instant::now();
+            for _ in 0..repetition {
+                let _commit = MultilinearKzgPCS::commit(&ck, &poly)?;
+            }
+
+            println!(
+                "KZG commit for {} variables: {} ns",
+                nv,
+                start.elapsed().as_nanos() / repetition as u128
+            );
+
+            MultilinearKzgPCS::commit(&ck, &poly)?
+        };
+
+        // open
+        let (proof, value) = {
+            let start = Instant::now();
+            for _ in 0..repetition {
+                let _open = MultilinearKzgPCS::open(&ck, &poly, &point)?;
+            }
+
+            println!(
+                "KZG open for {} variables: {} ns",
+                nv,
+                start.elapsed().as_nanos() / repetition as u128
+            );
+            MultilinearKzgPCS::open(&ck, &poly, &point)?
+        };
+
+        // verify
+        {
+            let start = Instant::now();
+            for _ in 0..repetition {
+                assert!(MultilinearKzgPCS::verify(
+                    &vk, &com, &point, &value, &proof
+                )?);
+            }
+            println!(
+                "KZG verify for {} variables: {} ns",
+                nv,
+                start.elapsed().as_nanos() / repetition as u128
+            );
+        }
+
+        println!("====================================");
+    }
+
+    Ok(())
+}