feat(bellman): declare naive main gate (#28)

This PR introduces a new main gate type that has only 3 columns without
support for custom gates and lookup.

crates/bellman/src/plonk/better_better_cs/cs.rs

@@ -1,4 +1,3 @@
-use crate::bit_vec::BitVec;
 use crate::pairing::ff::{Field, PrimeField, PrimeFieldRepr};
 use crate::pairing::{CurveAffine, CurveProjective, Engine};
 
@@ -146,6 +145,7 @@ pub trait Gate<E: Engine>: GateInternal<E> + Sized + Clone + std::hash::Hash + s
     }
 }
 
+use bit_vec::BitVec;
 use serde::{Deserialize, Serialize};
 use smallvec::SmallVec;
 
@@ -665,6 +665,16 @@ pub trait ConstraintSystem<E: Engine> {
     fn get_current_aux_gate_number(&self) -> usize;
 }
 
+#[derive(Clone, Copy, PartialEq, Eq, Debug)]
+pub struct PlonkCsWidth3Params;
+impl<E: Engine> PlonkConstraintSystemParams<E> for PlonkCsWidth3Params {
+    const STATE_WIDTH: usize = 3;
+    const WITNESS_WIDTH: usize = 0;
+    const HAS_WITNESS_POLYNOMIALS: bool = false;
+    const HAS_CUSTOM_GATES: bool = false;
+    const CAN_ACCESS_NEXT_TRACE_STEP: bool = false;
+}
+
 #[derive(Clone, Copy, PartialEq, Eq, Debug)]
 pub struct PlonkCsWidth4WithNextStepParams;
 impl<E: Engine> PlonkConstraintSystemParams<E> for PlonkCsWidth4WithNextStepParams {
@@ -2043,7 +2053,7 @@ impl_assembly! {
             non_residues.push(E::Fr::one());
             non_residues.extend(make_non_residues::<E::Fr>(P::STATE_WIDTH - 1));
 
-            assert_eq!(non_residues.len(), 4);
+            assert_eq!(non_residues.len(), P::STATE_WIDTH);
 
             let mut sigmas = vec![];
             for i in 0..P::STATE_WIDTH {

crates/bellman/src/plonk/better_better_cs/gates/mod.rs

@@ -18,4 +18,5 @@ use crate::plonk::cs::variable::*;
 use crate::plonk::fft::cooley_tukey_ntt::*;
 
 pub mod main_gate_with_d_next;
+pub mod naive_main_gate;
 pub mod selector_optimized_with_d_next;