From 82837b2f77490a86fdad2fc1bd9771931fb81d04 Mon Sep 17 00:00:00 2001
From: Ben Hamlin <protob3n@gmail.com>
Date: Wed, 15 Feb 2023 08:06:58 -0800
Subject: [PATCH] Multilinear extension evaluation speedup (#603)

* Reduce # multiplications in dense ml extension eval

* Reduce # multiplications in sparse ml extension eval

* Eliminate extra vector allocation in precompute_eq

* Add entry to changelog on mul reduction in eval functions
---
 CHANGELOG.md                                            | 2 ++
 poly/src/evaluations/multivariate/multilinear/dense.rs  | 4 +++-
 poly/src/evaluations/multivariate/multilinear/sparse.rs | 9 ++++-----
 3 files changed, 9 insertions(+), 6 deletions(-)

diff --git a/CHANGELOG.md b/CHANGELOG.md
index a734c6005..a39633574 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -2,6 +2,8 @@
 
 ## Pending
 
+- (`ark-poly`) Reduce the number of field multiplications performed by `SparseMultilinearExtension::evaluate` and `DenseMultilinearExtension::evaluate`
+
 ### Breaking changes
 
 ### Features
diff --git a/poly/src/evaluations/multivariate/multilinear/dense.rs b/poly/src/evaluations/multivariate/multilinear/dense.rs
index d2efa8a8d..e4525899a 100644
--- a/poly/src/evaluations/multivariate/multilinear/dense.rs
+++ b/poly/src/evaluations/multivariate/multilinear/dense.rs
@@ -119,7 +119,9 @@ impl<F: Field> MultilinearExtension<F> for DenseMultilinearExtension<F> {
         for i in 1..dim + 1 {
             let r = partial_point[i - 1];
             for b in 0..(1 << (nv - i)) {
-                poly[b] = poly[b << 1] * (F::one() - r) + poly[(b << 1) + 1] * r;
+                let left = poly[b << 1];
+                let right = poly[(b << 1) + 1];
+                poly[b] = left + r * (right - left);
             }
         }
         Self::from_evaluations_slice(nv - dim, &poly[..(1 << (nv - dim))])
diff --git a/poly/src/evaluations/multivariate/multilinear/sparse.rs b/poly/src/evaluations/multivariate/multilinear/sparse.rs
index 68b4726d2..f4f8040ca 100644
--- a/poly/src/evaluations/multivariate/multilinear/sparse.rs
+++ b/poly/src/evaluations/multivariate/multilinear/sparse.rs
@@ -102,15 +102,14 @@ impl<F: Field> SparseMultilinearExtension<F> {
 /// utility: precompute f(x) = eq(g,x)
 fn precompute_eq<F: Field>(g: &[F]) -> Vec<F> {
     let dim = g.len();
-    let mut dp = Vec::with_capacity(1 << dim);
-    dp.resize(1 << dim, F::zero());
+    let mut dp = vec![F::zero(); 1 << dim];
     dp[0] = F::one() - g[0];
     dp[1] = g[0];
     for i in 1..dim {
-        let dp_prev = dp[0..(1 << i)].to_vec();
         for b in 0..(1 << i) {
-            dp[b] = dp_prev[b] * (F::one() - g[i]);
-            dp[b + (1 << i)] = dp_prev[b] * g[i];
+            let prev = dp[b];
+            dp[b + (1 << i)] = prev * g[i];
+            dp[b] = prev - dp[b + (1 << i)];
         }
     }
     dp