Ppsnark refactorings (#208)

* refactor: Refactor row/col vector construction for efficiency

- Optimized the creation of `row` and `col` in `R1CSShapeSparkRepr::new` using map and unzip methods.
- Updated `R1CSShapeSparkRepr::evaluation_oracles` to create `E_row` and `E_col` using the same logic for consistency.

* refactor: Refactor and optimize `R1CSShapeSparkRepr` initialization

- Updated method for zero padding in `val_B` and `val_C` using `std::iter::repeat`, to need one vector allocation instead of two
- Functionality and outputs remain unchanged.

* refactor: Refactor polynomial struct in SumCheck to use generic Scalar type

- Updated `CompressedUniPoly` and `UniPoly` structs in `sumcheck.rs` to use the generic `Scalar` type.
- Adapted all methods within these structs to accommodate the `Scalar` type instead of `G: Group` type.
- Modified the type of `cubic_polys` in `ppsnark.rs` to `CompressedUniPoly<G::Scalar>`.

* refactor: Eliminate most instances of resize

resize in Rust may cause reallocation of the memory, which is an expensive operation. This is particularly true when the vector is resized to a larger size.

src/spartan/ppsnark.rs

@@ -119,51 +119,34 @@ impl R1CSShapeSparkRepr {
       max(total_nz, max(2 * S.num_vars, S.num_cons)).next_power_of_two()
     };
 
-    let row = {
-      let mut r = S
-        .A
-        .iter()
-        .chain(S.B.iter())
-        .chain(S.C.iter())
-        .map(|(r, _, _)| *r)
-        .collect::<Vec<usize>>();
-      r.resize(N, 0usize);
-      r
-    };
+    let (mut row, mut col) = (vec![0usize; N], vec![0usize; N]);
 
-    let col = {
-      let mut c = S
-        .A
-        .iter()
-        .chain(S.B.iter())
-        .chain(S.C.iter())
-        .map(|(_, c, _)| *c)
-        .collect::<Vec<usize>>();
-      c.resize(N, 0usize);
-      c
-    };
+    for (i, (r, c, _)) in S.A.iter().chain(S.B.iter()).chain(S.C.iter()).enumerate() {
+      row[i] = *r;
+      col[i] = *c;
+    }
 
     let val_A = {
-      let mut val = S.A.iter().map(|(_, _, v)| *v).collect::<Vec<G::Scalar>>();
-      val.resize(N, G::Scalar::ZERO);
+      let mut val = vec![G::Scalar::ZERO; N];
+      for (i, (_, _, v)) in S.A.iter().enumerate() {
+        val[i] = *v;
+      }
       val
     };
 
     let val_B = {
-      // prepend zeros
-      let mut val = vec![G::Scalar::ZERO; S.A.len()];
-      val.extend(S.B.iter().map(|(_, _, v)| *v).collect::<Vec<G::Scalar>>());
-      // append zeros
-      val.resize(N, G::Scalar::ZERO);
+      let mut val = vec![G::Scalar::ZERO; N];
+      for (i, (_, _, v)) in S.B.iter().enumerate() {
+        val[S.A.len() + i] = *v;
+      }
       val
     };
 
     let val_C = {
-      // prepend zeros
-      let mut val = vec![G::Scalar::ZERO; S.A.len() + S.B.len()];
-      val.extend(S.C.iter().map(|(_, _, v)| *v).collect::<Vec<G::Scalar>>());
-      // append zeros
-      val.resize(N, G::Scalar::ZERO);
+      let mut val = vec![G::Scalar::ZERO; N];
+      for (i, (_, _, v)) in S.C.iter().enumerate() {
+        val[S.A.len() + S.B.len() + i] = *v;
+      }
       val
     };
 
@@ -265,29 +248,30 @@ impl R1CSShapeSparkRepr {
 
     let mem_row = EqPolynomial::new(r_x_padded).evals();
     let mem_col = {
-      let mut z = z.to_vec();
-      z.resize(self.N, G::Scalar::ZERO);
-      z
+      let mut val = vec![G::Scalar::ZERO; self.N];
+      for (i, v) in z.iter().enumerate() {
+        val[i] = *v;
+      }
+      val
     };
 
-    let mut E_row = S
-      .A
-      .iter()
-      .chain(S.B.iter())
-      .chain(S.C.iter())
-      .map(|(r, _, _)| mem_row[*r])
-      .collect::<Vec<G::Scalar>>();
-
-    let mut E_col = S
-      .A
-      .iter()
-      .chain(S.B.iter())
-      .chain(S.C.iter())
-      .map(|(_, c, _)| mem_col[*c])
-      .collect::<Vec<G::Scalar>>();
+    let (E_row, E_col) = {
+      let mut E_row = vec![mem_row[0]; self.N]; // we place mem_row[0] since resized row is appended with 0s
+      let mut E_col = vec![mem_col[0]; self.N];
 
-    E_row.resize(self.N, mem_row[0]); // we place mem_row[0] since resized row is appended with 0s
-    E_col.resize(self.N, mem_col[0]);
+      for (i, (val_r, val_c)) in S
+        .A
+        .iter()
+        .chain(S.B.iter())
+        .chain(S.C.iter())
+        .map(|(r, c, _)| (mem_row[*r], mem_col[*c]))
+        .enumerate()
+      {
+        E_row[i] = val_r;
+        E_col[i] = val_c;
+      }
+      (E_row, E_col)
+    };
 
     (mem_row, mem_col, E_row, E_col)
   }
@@ -862,7 +846,7 @@ impl> RelaxedR1CSSNARK
 
     let mut e = claim;
     let mut r: Vec<G::Scalar> = Vec::new();
-    let mut cubic_polys: Vec<CompressedUniPoly<G>> = Vec::new();
+    let mut cubic_polys: Vec<CompressedUniPoly<G::Scalar>> = Vec::new();
     let num_rounds = mem.size().log_2();
     for _i in 0..num_rounds {
       let mut evals: Vec<Vec<G::Scalar>> = Vec::new();
@@ -999,8 +983,13 @@ impl> RelaxedR1CSSNARKTrait
       Bz.resize(pk.S_repr.N, G::Scalar::ZERO);
       Cz.resize(pk.S_repr.N, G::Scalar::ZERO);
 
-      let mut E = W.E.clone();
-      E.resize(pk.S_repr.N, G::Scalar::ZERO);
+      let E = {
+        let mut val = vec![G::Scalar::ZERO; pk.S_repr.N];
+        for (i, w_e) in W.E.iter().enumerate() {
+          val[i] = *w_e;
+        }
+        val
+      };
 
       (Az, Bz, Cz, E)
     };

src/spartan/sumcheck.rs

@@ -3,19 +3,18 @@
 use super::polynomial::MultilinearPolynomial;
 use crate::errors::NovaError;
 use crate::traits::{Group, TranscriptEngineTrait, TranscriptReprTrait};
-use core::marker::PhantomData;
-use ff::Field;
+use ff::{Field, PrimeField};
 use rayon::prelude::*;
 use serde::{Deserialize, Serialize};
 
 #[derive(Clone, Debug, Serialize, Deserialize)]
 #[serde(bound = "")]
 pub(crate) struct SumcheckProof<G: Group> {
-  compressed_polys: Vec<CompressedUniPoly<G>>,
+  compressed_polys: Vec<CompressedUniPoly<G::Scalar>>,
 }
 
 impl<G: Group> SumcheckProof<G> {
-  pub fn new(compressed_polys: Vec<CompressedUniPoly<G>>) -> Self {
+  pub fn new(compressed_polys: Vec<CompressedUniPoly<G::Scalar>>) -> Self {
     Self { compressed_polys }
   }
 
@@ -101,7 +100,7 @@ impl SumcheckProof {
     F: Fn(&G::Scalar, &G::Scalar) -> G::Scalar + Sync,
   {
     let mut r: Vec<G::Scalar> = Vec::new();
-    let mut polys: Vec<CompressedUniPoly<G>> = Vec::new();
+    let mut polys: Vec<CompressedUniPoly<G::Scalar>> = Vec::new();
     let mut claim_per_round = *claim;
     for _ in 0..num_rounds {
       let poly = {
@@ -150,7 +149,7 @@ impl SumcheckProof {
   {
     let mut e = *claim;
     let mut r: Vec<G::Scalar> = Vec::new();
-    let mut quad_polys: Vec<CompressedUniPoly<G>> = Vec::new();
+    let mut quad_polys: Vec<CompressedUniPoly<G::Scalar>> = Vec::new();
 
     for _j in 0..num_rounds {
       let mut evals: Vec<(G::Scalar, G::Scalar)> = Vec::new();
@@ -204,7 +203,7 @@ impl SumcheckProof {
     F: Fn(&G::Scalar, &G::Scalar, &G::Scalar, &G::Scalar) -> G::Scalar + Sync,
   {
     let mut r: Vec<G::Scalar> = Vec::new();
-    let mut polys: Vec<CompressedUniPoly<G>> = Vec::new();
+    let mut polys: Vec<CompressedUniPoly<G::Scalar>> = Vec::new();
     let mut claim_per_round = *claim;
 
     for _ in 0..num_rounds {
@@ -288,25 +287,24 @@ impl SumcheckProof {
 // ax^2 + bx + c stored as vec![a,b,c]
 // ax^3 + bx^2 + cx + d stored as vec![a,b,c,d]
 #[derive(Debug)]
-pub struct UniPoly<G: Group> {
-  coeffs: Vec<G::Scalar>,
+pub struct UniPoly<Scalar: PrimeField> {
+  coeffs: Vec<Scalar>,
 }
 
 // ax^2 + bx + c stored as vec![a,c]
 // ax^3 + bx^2 + cx + d stored as vec![a,c,d]
 #[derive(Clone, Debug, Serialize, Deserialize)]
-pub struct CompressedUniPoly<G: Group> {
-  coeffs_except_linear_term: Vec<G::Scalar>,
-  _p: PhantomData<G>,
+pub struct CompressedUniPoly<Scalar: PrimeField> {
+  coeffs_except_linear_term: Vec<Scalar>,
 }
 
-impl<G: Group> UniPoly<G> {
-  pub fn from_evals(evals: &[G::Scalar]) -> Self {
+impl<Scalar: PrimeField> UniPoly<Scalar> {
+  pub fn from_evals(evals: &[Scalar]) -> Self {
     // we only support degree-2 or degree-3 univariate polynomials
     assert!(evals.len() == 3 || evals.len() == 4);
     let coeffs = if evals.len() == 3 {
       // ax^2 + bx + c
-      let two_inv = G::Scalar::from(2).invert().unwrap();
+      let two_inv = Scalar::from(2).invert().unwrap();
 
       let c = evals[0];
       let a = two_inv * (evals[2] - evals[1] - evals[1] + c);
@@ -314,8 +312,8 @@ impl UniPoly {
       vec![c, b, a]
     } else {
       // ax^3 + bx^2 + cx + d
-      let two_inv = G::Scalar::from(2).invert().unwrap();
-      let six_inv = G::Scalar::from(6).invert().unwrap();
+      let two_inv = Scalar::from(2).invert().unwrap();
+      let six_inv = Scalar::from(6).invert().unwrap();
 
       let d = evals[0];
       let a = six_inv
@@ -338,18 +336,18 @@ impl UniPoly {
     self.coeffs.len() - 1
   }
 
-  pub fn eval_at_zero(&self) -> G::Scalar {
+  pub fn eval_at_zero(&self) -> Scalar {
     self.coeffs[0]
   }
 
-  pub fn eval_at_one(&self) -> G::Scalar {
+  pub fn eval_at_one(&self) -> Scalar {
     (0..self.coeffs.len())
       .into_par_iter()
       .map(|i| self.coeffs[i])
-      .reduce(|| G::Scalar::ZERO, |a, b| a + b)
+      .reduce(|| Scalar::ZERO, |a, b| a + b)
   }
 
-  pub fn evaluate(&self, r: &G::Scalar) -> G::Scalar {
+  pub fn evaluate(&self, r: &Scalar) -> Scalar {
     let mut eval = self.coeffs[0];
     let mut power = *r;
     for coeff in self.coeffs.iter().skip(1) {
@@ -359,27 +357,26 @@ impl UniPoly {
     eval
   }
 
-  pub fn compress(&self) -> CompressedUniPoly<G> {
+  pub fn compress(&self) -> CompressedUniPoly<Scalar> {
     let coeffs_except_linear_term = [&self.coeffs[0..1], &self.coeffs[2..]].concat();
     assert_eq!(coeffs_except_linear_term.len() + 1, self.coeffs.len());
     CompressedUniPoly {
       coeffs_except_linear_term,
-      _p: Default::default(),
     }
   }
 }
 
-impl<G: Group> CompressedUniPoly<G> {
+impl<Scalar: PrimeField> CompressedUniPoly<Scalar> {
   // we require eval(0) + eval(1) = hint, so we can solve for the linear term as:
   // linear_term = hint - 2 * constant_term - deg2 term - deg3 term
-  pub fn decompress(&self, hint: &G::Scalar) -> UniPoly<G> {
+  pub fn decompress(&self, hint: &Scalar) -> UniPoly<Scalar> {
     let mut linear_term =
       *hint - self.coeffs_except_linear_term[0] - self.coeffs_except_linear_term[0];
     for i in 1..self.coeffs_except_linear_term.len() {
       linear_term -= self.coeffs_except_linear_term[i];
     }
 
-    let mut coeffs: Vec<G::Scalar> = Vec::new();
+    let mut coeffs: Vec<Scalar> = Vec::new();
     coeffs.push(self.coeffs_except_linear_term[0]);
     coeffs.push(linear_term);
     coeffs.extend(&self.coeffs_except_linear_term[1..]);
@@ -388,7 +385,7 @@ impl CompressedUniPoly {
   }
 }
 
-impl<G: Group> TranscriptReprTrait<G> for UniPoly<G> {
+impl<G: Group> TranscriptReprTrait<G> for UniPoly<G::Scalar> {
   fn to_transcript_bytes(&self) -> Vec<u8> {
     let coeffs = self.compress().coeffs_except_linear_term;
     coeffs.as_slice().to_transcript_bytes()