optimize the non-native arithmetic and hashing costs by using 4 limbs instead of 8 (#102)

src/bellperson/mod.rs

@@ -354,14 +354,14 @@ mod tests {
 
     // First create the shape
     let mut cs: ShapeCS<G> = ShapeCS::new();
-    let _ = synthesize_add(&mut cs, &a_val, &b_val, &c_val, 32, 8);
+    let _ = synthesize_add(&mut cs, &a_val, &b_val, &c_val, 64, 4);
     let shape = cs.r1cs_shape();
     let gens = cs.r1cs_gens();
     println!("Add mod constraint no: {}", cs.num_constraints());
 
     // Now get the assignment
     let mut cs: SatisfyingAssignment<G> = SatisfyingAssignment::new();
-    let _ = synthesize_add(&mut cs, &a_val, &b_val, &c_val, 32, 8);
+    let _ = synthesize_add(&mut cs, &a_val, &b_val, &c_val, 64, 4);
     let (inst, witness) = cs.r1cs_instance_and_witness(&shape, &gens).unwrap();
 
     // Make sure that this is satisfiable

src/circuit.rs

@@ -379,7 +379,7 @@ mod tests {
     let mut cs: ShapeCS<G1> = ShapeCS::new();
     let _ = circuit1.synthesize(&mut cs);
     let (shape1, gens1) = (cs.r1cs_shape(), cs.r1cs_gens());
-    assert_eq!(cs.num_constraints(), 20584);
+    assert_eq!(cs.num_constraints(), 20122);
 
     // Initialize the shape and gens for the secondary
     let circuit2: NovaAugmentedCircuit<G1, TrivialTestCircuit<<G1 as Group>::Base>> =
@@ -392,7 +392,7 @@ mod tests {
     let mut cs: ShapeCS<G2> = ShapeCS::new();
     let _ = circuit2.synthesize(&mut cs);
     let (shape2, gens2) = (cs.r1cs_shape(), cs.r1cs_gens());
-    assert_eq!(cs.num_constraints(), 21124);
+    assert_eq!(cs.num_constraints(), 20654);
 
     // Execute the base case for the primary
     let zero1 = <<G2 as Group>::Base as Field>::zero();

src/constants.rs

@@ -1,4 +1,4 @@
 pub(crate) const NUM_CHALLENGE_BITS: usize = 128;
 pub(crate) const NUM_HASH_BITS: usize = 250;
-pub(crate) const BN_LIMB_WIDTH: usize = 32;
-pub(crate) const BN_N_LIMBS: usize = 8;
+pub(crate) const BN_LIMB_WIDTH: usize = 64;
+pub(crate) const BN_N_LIMBS: usize = 4;

src/poseidon.rs

@@ -9,7 +9,7 @@ use bellperson::{
 };
 use core::marker::PhantomData;
 use ff::{PrimeField, PrimeFieldBits};
-use generic_array::typenum::{U27, U32};
+use generic_array::typenum::{U19, U24};
 use neptune::{
   circuit::poseidon_hash,
   poseidon::{Poseidon, PoseidonConstants},
@@ -22,8 +22,8 @@ pub struct PoseidonConstantsCircuit
 where
   Scalar: PrimeField,
 {
-  constants27: PoseidonConstants<Scalar, U27>,
-  constants32: PoseidonConstants<Scalar, U32>,
+  constants19: PoseidonConstants<Scalar, U19>,
+  constants24: PoseidonConstants<Scalar, U24>,
 }
 
 impl<Scalar> ROConstantsTrait<Scalar> for PoseidonConstantsCircuit<Scalar>
@@ -33,11 +33,11 @@ where
   /// Generate Poseidon constants for the arities that Nova uses
   #[allow(clippy::new_without_default)]
   fn new() -> Self {
-    let constants27 = PoseidonConstants::<Scalar, U27>::new_with_strength(Strength::Standard);
-    let constants32 = PoseidonConstants::<Scalar, U32>::new_with_strength(Strength::Standard);
+    let constants19 = PoseidonConstants::<Scalar, U19>::new_with_strength(Strength::Standard);
+    let constants24 = PoseidonConstants::<Scalar, U24>::new_with_strength(Strength::Standard);
     Self {
-      constants27,
-      constants32,
+      constants19,
+      constants24,
     }
   }
 }
@@ -78,11 +78,11 @@ where
   /// Compute a challenge by hashing the current state
   fn squeeze(&self, num_bits: usize) -> Scalar {
     let hash = match self.state.len() {
-      27 => {
-        Poseidon::<Base, U27>::new_with_preimage(&self.state, &self.constants.constants27).hash()
+      19 => {
+        Poseidon::<Base, U19>::new_with_preimage(&self.state, &self.constants.constants19).hash()
       }
-      32 => {
-        Poseidon::<Base, U32>::new_with_preimage(&self.state, &self.constants.constants32).hash()
+      24 => {
+        Poseidon::<Base, U24>::new_with_preimage(&self.state, &self.constants.constants24).hash()
       }
       _ => {
         panic!(
@@ -145,15 +145,15 @@ where
     CS: ConstraintSystem<Scalar>,
   {
     let hash = match self.state.len() {
-      27 => poseidon_hash(
+      19 => poseidon_hash(
         cs.namespace(|| "Poseidon hash"),
         self.state.clone(),
-        &self.constants.constants27,
+        &self.constants.constants19,
       )?,
-      32 => poseidon_hash(
+      24 => poseidon_hash(
         cs.namespace(|| "Posideon hash"),
         self.state.clone(),
-        &self.constants.constants32,
+        &self.constants.constants24,
       )?,
       _ => {
         panic!(
@@ -199,7 +199,7 @@ mod tests {
     let mut ro: PoseidonRO<S, B> = PoseidonRO::new(constants.clone());
     let mut ro_gadget: PoseidonROCircuit<S> = PoseidonROCircuit::new(constants);
     let mut cs: SatisfyingAssignment<G> = SatisfyingAssignment::new();
-    for i in 0..27 {
+    for i in 0..19 {
       let num = S::random(&mut csprng);
       ro.absorb(num);
       let num_gadget =