test: add evaluation unit test

Author: huitseeker

Cargo.toml

@@ -45,6 +45,7 @@ cfg-if = "1.0.0"
 once_cell = "1.18.0"
 anyhow = "1.0.72"
 rand = "0.8.4"
+rand_xorshift = "0.3.0"
 
 [target.'cfg(any(target_arch = "x86_64", target_arch = "aarch64"))'.dependencies]
 pasta-msm = { git="https://github.com/lurk-lab/pasta-msm", branch="dev", version = "0.1.4" }

ThirdPartyNotices.txt

@@ -52,3 +52,212 @@ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLI
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src/spartan/polys/multilinear.rs

@@ -213,6 +213,7 @@ mod tests {
 
   use super::*;
   use pasta_curves::Fp;
+  use rand_core::SeedableRng;
 
   fn make_mlp<F: PrimeField>(len: usize, value: F) -> MultilinearPolynomial<F> {
     MultilinearPolynomial {
@@ -335,4 +336,115 @@ mod tests {
     test_evaluation_with::<provider::bn256_grumpkin::bn256::Scalar>();
     test_evaluation_with::<provider::secp_secq::secp256k1::Scalar>();
   }
+
+  pub fn partial_eval<F: PrimeField>(
+    poly: &MultilinearPolynomial<F>,
+    point: &[F],
+  ) -> MultilinearPolynomial<F> {
+    // Get size of partial evaluation point u = (u_0,...,u_{m-1})
+    let m = point.len();
+
+    // Assert that the size of the polynomial being evaluated is a power of 2 greater than (1 << m)
+    assert!(poly.Z.len().is_power_of_two());
+    assert!(poly.Z.len() >= 1 << m);
+    let n = poly.Z.len().trailing_zeros() as usize;
+
+    // Partial evaluation is done in m rounds l = 0,...,m-1.
+    let mut n_l = 1 << (n - 1);
+
+    // Temporary buffer of half the size of the polynomial
+    let mut tmp = vec![F::ZERO; n_l];
+
+    let prev = &poly.Z;
+
+    // Evaluate variable X_{n-1} at u_{m-1}
+    let u_l = point[m - 1];
+    for i in 0..n_l {
+      tmp[i] = prev[i] + u_l * (prev[i + n_l] - prev[i]);
+    }
+
+    // Evaluate m-1 variables X_{n-l-1}, ..., X_{n-2} at m-1 remaining values u_0,...,u_{m-2})
+    for l in 1..m {
+      n_l = 1 << (n - l - 1);
+      let u_l = point[m - l - 1];
+      for i in 0..n_l {
+        tmp[i] = tmp[i] + u_l * (tmp[i + n_l] - tmp[i]);
+      }
+    }
+    tmp.truncate(1 << (poly.num_vars - m));
+
+    MultilinearPolynomial::new(tmp)
+  }
+
+  fn make_rand_mlp<F: PrimeField, R: RngCore>(
+    var_count: usize,
+    mut rng: &mut R,
+  ) -> MultilinearPolynomial<F> {
+    let eqpoly = EqPolynomial::new(
+      std::iter::from_fn(|| Some(F::random(&mut rng)))
+        .take(var_count)
+        .collect::<Vec<_>>(),
+    );
+    MultilinearPolynomial::new(eqpoly.evals())
+  }
+
+  fn partial_evaluate_mle_with<F: PrimeField>() {
+    // Initialize a random polynomial
+    let n = 5;
+    let mut rng = rand_xorshift::XorShiftRng::from_seed([0u8; 16]);
+    let poly = make_rand_mlp::<F, _>(n, &mut rng);
+
+    // Define a random multivariate evaluation point u = (u_0, u_1, u_2, u_3, u_4)
+    let u_0 = F::random(&mut rng);
+    let u_1 = F::random(&mut rng);
+    let u_2 = F::random(&mut rng);
+    let u_3 = F::random(&mut rng);
+    let u_4 = F::random(&mut rng);
+    let u_challenge = vec![u_4, u_3, u_2, u_1, u_0];
+
+    // Directly computing v = p(u_0,...,u_4) and comparing it with the result of
+    // first computing the partial evaluation in the last 3 variables
+    // g(X_0,X_1) = p(X_0,X_1,u_2,u_3,u_4), then v = g(u_0,u_1)
+
+    // Compute v = p(u_0,...,u_4)
+    let v_expected = poly.evaluate(&u_challenge[..]);
+
+    // Compute g(X_0,X_1) = p(X_0,X_1,u_2,u_3,u_4), then v = g(u_0,u_1)
+    let u_part_1 = vec![u_1, u_0]; // note the endianness difference
+    let u_part_2 = vec![u_2, u_3, u_4];
+    let partial_evaluated_poly = partial_eval(&poly, &u_part_2);
+    let v_result = partial_evaluated_poly.evaluate(&u_part_1);
+
+    assert_eq!(v_result, v_expected);
+  }
+
+  #[test]
+  fn test_partial_evaluate_mle() {
+    partial_evaluate_mle_with::<Fp>();
+    partial_evaluate_mle_with::<bn256::Scalar>();
+    partial_evaluate_mle_with::<secp256k1::Scalar>();
+  }
+
+  fn partial_and_evaluate_with<F: PrimeField>() {
+    for _i in 0..50 {
+      // Initialize a random polynomial
+      let n = 7;
+      let mut rng = rand_xorshift::XorShiftRng::from_seed([0u8; 16]);
+      let poly = make_rand_mlp::<F, _>(n, &mut rng);
+
+      // draw a random point
+      let pt: Vec<_> = std::iter::from_fn(|| Some(F::random(&mut rng)))
+        .take(n)
+        .collect();
+      let rev_pt: Vec<_> = pt.iter().cloned().rev().collect();
+      assert_eq!(poly.evaluate(&pt), partial_eval(&poly, &rev_pt).Z[0])
+    }
+  }
+
+  #[test]
+  fn test_partial_and_evaluate() {
+    partial_and_evaluate_with::<Fp>();
+    partial_and_evaluate_with::<bn256::Scalar>();
+    partial_and_evaluate_with::<secp256k1::Scalar>();
+  }
 }