fix: optimize compute_inner_product with parallel computation (#37)

* Update arithmetic.rs

* Update arithmetic.rs

* Update arithmetic.rs

* Update arithmetic.rs

halo2_proofs/src/arithmetic.rs

@@ -8,6 +8,7 @@ use group::{
     prime::PrimeCurveAffine,
     Curve, GroupOpsOwned, ScalarMulOwned,
 };
+use rayon::prelude::*;
 
 use halo2curves::msm::msm_best;
 pub use halo2curves::{CurveAffine, CurveExt};
@@ -110,16 +111,26 @@ pub fn eval_polynomial<F: Field>(poly: &[F], point: F) -> F {
 /// This computes the inner product of two vectors `a` and `b`.
 ///
 /// This function will panic if the two vectors are not the same size.
+/// For vectors smaller than 32 elements, it uses sequential computation for better performance.
+/// For larger vectors, it switches to parallel computation.
 pub fn compute_inner_product<F: Field>(a: &[F], b: &[F]) -> F {
-    // TODO: parallelize?
     assert_eq!(a.len(), b.len());
-
-    let mut acc = F::ZERO;
-    for (a, b) in a.iter().zip(b.iter()) {
-        acc += (*a) * (*b);
+
+    if a.len() < 32 {
+        // Use sequential computation for small vectors
+        let mut acc = F::ZERO;
+        for (a, b) in a.iter().zip(b.iter()) {
+            acc += (*a) * (*b);
+        }
+        return acc;
     }
 
-    acc
+    // Use parallel computation
+    let mut result = F::ZERO;
+    parallelize(&mut [result], |results, _| {
+        results[0] = a.iter().zip(b.iter()).fold(F::ZERO, |acc, (a, b)| acc + (*a) * (*b));
+    });
+    result
 }
 
 /// Divides polynomial `a` in `X` by `X - b` with
@@ -328,3 +339,30 @@ fn test_lagrange_interpolate() {
         }
     }
 }
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use rand_core::OsRng;
+
+    #[test]
+    fn test_compute_inner_product() {
+        let rng = OsRng;
+
+        // Test small vectors (sequential)
+        let a_small: Vec<Fp> = (0..16).map(|_| Fp::random(rng)).collect();
+        let b_small: Vec<Fp> = (0..16).map(|_| Fp::random(rng)).collect();
+        let result_small = compute_inner_product(&a_small, &b_small);
+        let expected_small = a_small.iter().zip(b_small.iter())
+            .fold(Fp::ZERO, |acc, (a, b)| acc + (*a) * (*b));
+        assert_eq!(result_small, expected_small);
+
+        // Test large vectors (parallel)
+        let a_large: Vec<Fp> = (0..64).map(|_| Fp::random(rng)).collect();
+        let b_large: Vec<Fp> = (0..64).map(|_| Fp::random(rng)).collect();
+        let result_large = compute_inner_product(&a_large, &b_large);
+        let expected_large = a_large.iter().zip(b_large.iter())
+            .fold(Fp::ZERO, |acc, (a, b)| acc + (*a) * (*b));
+        assert_eq!(result_large, expected_large);
+    }
+}