Implement Polynomial for MultilinearExtension (#691)

Co-authored-by: Antonio Mejías Gil <[email protected]>

CHANGELOG.md

@@ -12,6 +12,8 @@
 
 ### Features
 
+- [\#691](https://github.com/arkworks-rs/algebra/pull/691) (`ark-poly`) Implement `Polynomial` for `SparseMultilinearExtension` and `DenseMultilinearExtension`.
+
 ### Improvements
 
 ### Bugfixes

poly/README.md

@@ -120,7 +120,7 @@ let g: DenseMultilinearExtension<Fq> = DenseMultilinearExtension::from_evaluatio
 );
 // when evaluated at any point within the Boolean hypercube, f and g should be equal
 let point_within_hypercube = &vec![Fq::from(0), Fq::from(1), Fq::from(1)];
-assert_eq!(f.evaluate(&point_within_hypercube), g.evaluate(&point_within_hypercube).unwrap());
+assert_eq!(f.evaluate(&point_within_hypercube), g.evaluate(&point_within_hypercube));
 
 // We can also define a MLE g'(x_0, x_1, x_2) by providing the list of non-zero evaluations:
 let g_prime: SparseMultilinearExtension<Fq> = SparseMultilinearExtension::from_evaluations(
@@ -135,7 +135,7 @@ let g_prime: SparseMultilinearExtension<Fq> = SparseMultilinearExtension::from_e
 );
 // at any random point (X0, X1, X2), g == g' with negligible probability, unless they are the same function
 let random_point = &vec![Fq::from(123), Fq::from(456), Fq::from(789)];
-assert_eq!(g_prime.evaluate(&random_point).unwrap(), g.evaluate(&random_point).unwrap());
+assert_eq!(g_prime.evaluate(&random_point), g.evaluate(&random_point));
 
 ```
 

poly/benches/dense_multilinear.rs

@@ -2,7 +2,7 @@
 extern crate criterion;
 
 use ark_ff::Field;
-use ark_poly::{DenseMultilinearExtension, MultilinearExtension};
+use ark_poly::{DenseMultilinearExtension, MultilinearExtension, Polynomial};
 use ark_std::{ops::Range, test_rng};
 use ark_test_curves::bls12_381;
 use criterion::{black_box, BenchmarkId, Criterion};
@@ -40,7 +40,7 @@ fn evaluation_op_bench<F: Field>(c: &mut Criterion) {
         group.bench_with_input(BenchmarkId::from_parameter(nv), &nv, |b, &nv| {
             let poly = DenseMultilinearExtension::<F>::rand(nv, &mut rng);
             let point: Vec<_> = (0..nv).map(|_| F::rand(&mut rng)).collect();
-            b.iter(|| black_box(poly.evaluate(&point).unwrap()))
+            b.iter(|| black_box(poly.evaluate(&point)))
         });
     }
     group.finish();

poly/benches/sparse_multilinear.rs

@@ -2,7 +2,7 @@
 extern crate criterion;
 
 use ark_ff::Field;
-use ark_poly::{MultilinearExtension, SparseMultilinearExtension};
+use ark_poly::{Polynomial, SparseMultilinearExtension};
 use ark_std::{ops::Range, test_rng};
 use ark_test_curves::bls12_381;
 use criterion::{black_box, BenchmarkId, Criterion};
@@ -72,7 +72,7 @@ fn evaluation_op_bench<F: Field>(c: &mut Criterion) {
                     &mut rng,
                 );
                 let point: Vec<_> = (0..nv).map(|_| F::rand(&mut rng)).collect();
-                b.iter(|| black_box(poly.evaluate(&point).unwrap()))
+                b.iter(|| black_box(poly.evaluate(&point)))
             },
         );
     }

poly/src/evaluations/multivariate/multilinear/dense.rs

@@ -1,6 +1,9 @@
 //! Multilinear polynomial represented in dense evaluation form.
 
-use crate::evaluations::multivariate::multilinear::{swap_bits, MultilinearExtension};
+use crate::{
+    evaluations::multivariate::multilinear::{swap_bits, MultilinearExtension},
+    Polynomial,
+};
 use ark_ff::{Field, Zero};
 use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
 use ark_std::{
@@ -86,32 +89,6 @@ impl<F: Field> MultilinearExtension<F> for DenseMultilinearExtension<F> {
         self.num_vars
     }
 
-    /// Evaluate the dense MLE at the given point
-    /// # Example
-    /// ```
-    /// use ark_test_curves::bls12_381::Fr;
-    /// # use ark_poly::{MultilinearExtension, DenseMultilinearExtension};
-    /// # use ark_ff::One;
-    ///
-    /// // The two-variate polynomial x_0 + 3 * x_0 * x_1 + 2 evaluates to [2, 3, 2, 6]
-    /// // in the two-dimensional hypercube with points [00, 10, 01, 11]
-    /// let mle = DenseMultilinearExtension::from_evaluations_vec(
-    ///     2, vec![2, 3, 2, 6].iter().map(|x| Fr::from(*x as u64)).collect()
-    /// );
-    ///
-    /// // By the uniqueness of MLEs, `mle` is precisely the above polynomial, which
-    /// // takes the value 54 at the point (1, 17)
-    /// let eval = mle.evaluate(&[Fr::one(), Fr::from(17)]).unwrap();
-    /// assert_eq!(eval, Fr::from(54));
-    /// ```
-    fn evaluate(&self, point: &[F]) -> Option<F> {
-        if point.len() == self.num_vars {
-            Some(self.fix_variables(point)[0])
-        } else {
-            None
-        }
-    }
-
     fn rand<R: Rng>(num_vars: usize, rng: &mut R) -> Self {
         Self::from_evaluations_vec(
             num_vars,
@@ -307,9 +284,40 @@ impl<F: Field> Zero for DenseMultilinearExtension<F> {
     }
 }
 
+impl<F: Field> Polynomial<F> for DenseMultilinearExtension<F> {
+    type Point = Vec<F>;
+
+    fn degree(&self) -> usize {
+        self.num_vars
+    }
+
+    /// Evaluate the dense MLE at the given point
+    /// # Example
+    /// ```
+    /// use ark_test_curves::bls12_381::Fr;
+    /// # use ark_poly::{MultilinearExtension, DenseMultilinearExtension, Polynomial};
+    /// # use ark_ff::One;
+    ///
+    /// // The two-variate polynomial x_0 + 3 * x_0 * x_1 + 2 evaluates to [2, 3, 2, 6]
+    /// // in the two-dimensional hypercube with points [00, 10, 01, 11]
+    /// let mle = DenseMultilinearExtension::from_evaluations_vec(
+    ///     2, vec![2, 3, 2, 6].iter().map(|x| Fr::from(*x as u64)).collect()
+    /// );
+    ///
+    /// // By the uniqueness of MLEs, `mle` is precisely the above polynomial, which
+    /// // takes the value 54 at the point (1, 17)
+    /// let eval = mle.evaluate(&[Fr::one(), Fr::from(17)].into());
+    /// assert_eq!(eval, Fr::from(54));
+    /// ```
+    fn evaluate(&self, point: &Self::Point) -> F {
+        assert!(point.len() == self.num_vars);
+        self.fix_variables(&point)[0]
+    }
+}
+
 #[cfg(test)]
 mod tests {
-    use crate::{DenseMultilinearExtension, MultilinearExtension};
+    use crate::{DenseMultilinearExtension, MultilinearExtension, Polynomial};
     use ark_ff::{Field, Zero};
     use ark_std::{ops::Neg, test_rng, vec::Vec, UniformRand};
     use ark_test_curves::bls12_381::Fr;
@@ -340,7 +348,7 @@ mod tests {
             let point: Vec<_> = (0..10).map(|_| Fr::rand(&mut rng)).collect();
             assert_eq!(
                 evaluate_data_array(&poly.evaluations, &point),
-                poly.evaluate(&point).unwrap()
+                poly.evaluate(&point)
             )
         }
     }
@@ -390,32 +398,32 @@ mod tests {
             let point: Vec<_> = (0..NV).map(|_| Fr::rand(&mut rng)).collect();
             let poly1 = DenseMultilinearExtension::rand(NV, &mut rng);
             let poly2 = DenseMultilinearExtension::rand(NV, &mut rng);
-            let v1 = poly1.evaluate(&point).unwrap();
-            let v2 = poly2.evaluate(&point).unwrap();
+            let v1 = poly1.evaluate(&point);
+            let v2 = poly2.evaluate(&point);
             // test add
-            assert_eq!((&poly1 + &poly2).evaluate(&point).unwrap(), v1 + v2);
+            assert_eq!((&poly1 + &poly2).evaluate(&point), v1 + v2);
             // test sub
-            assert_eq!((&poly1 - &poly2).evaluate(&point).unwrap(), v1 - v2);
+            assert_eq!((&poly1 - &poly2).evaluate(&point), v1 - v2);
             // test negate
-            assert_eq!(poly1.clone().neg().evaluate(&point).unwrap(), -v1);
+            assert_eq!(poly1.clone().neg().evaluate(&point), -v1);
             // test add assign
             {
                 let mut poly1 = poly1.clone();
                 poly1 += &poly2;
-                assert_eq!(poly1.evaluate(&point).unwrap(), v1 + v2)
+                assert_eq!(poly1.evaluate(&point), v1 + v2)
             }
             // test sub assign
             {
                 let mut poly1 = poly1.clone();
                 poly1 -= &poly2;
-                assert_eq!(poly1.evaluate(&point).unwrap(), v1 - v2)
+                assert_eq!(poly1.evaluate(&point), v1 - v2)
             }
             // test add assign with scalar
             {
                 let mut poly1 = poly1.clone();
                 let scalar = Fr::rand(&mut rng);
                 poly1 += (scalar, &poly2);
-                assert_eq!(poly1.evaluate(&point).unwrap(), v1 + scalar * v2)
+                assert_eq!(poly1.evaluate(&point), v1 + scalar * v2)
             }
             // test additive identity
             {
@@ -428,7 +436,7 @@ mod tests {
                     let mut zero = DenseMultilinearExtension::zero();
                     let scalar = Fr::rand(&mut rng);
                     zero += (scalar, &poly1);
-                    assert_eq!(zero.evaluate(&point).unwrap(), scalar * v1);
+                    assert_eq!(zero.evaluate(&point), scalar * v1);
                 }
             }
         }

poly/src/evaluations/multivariate/multilinear/mod.rs

@@ -16,6 +16,8 @@ use ark_ff::{Field, Zero};
 use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
 use ark_std::rand::Rng;
 
+use crate::Polynomial;
+
 /// This trait describes an interface for the multilinear extension
 /// of an array.
 /// The latter is a multilinear polynomial represented in terms of its
@@ -39,14 +41,11 @@ pub trait MultilinearExtension<F: Field>:
     + for<'a> AddAssign<(F, &'a Self)>
     + for<'a> SubAssign<&'a Self>
     + Index<usize>
+    + Polynomial<F, Point = Vec<F>>
 {
     /// Returns the number of variables in `self`
     fn num_vars(&self) -> usize;
 
-    /// Evaluates `self` at the given the vector `point` in slice.
-    /// If the number of variables does not match, return `None`.
-    fn evaluate(&self, point: &[F]) -> Option<F>;
-
     /// Outputs an `l`-variate multilinear extension where value of evaluations
     /// are sampled uniformly at random.
     fn rand<R: Rng>(num_vars: usize, rng: &mut R) -> Self;

poly/src/evaluations/multivariate/multilinear/sparse.rs

@@ -2,7 +2,7 @@
 
 use crate::{
     evaluations::multivariate::multilinear::swap_bits, DenseMultilinearExtension,
-    MultilinearExtension,
+    MultilinearExtension, Polynomial,
 };
 use ark_ff::{Field, Zero};
 use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
@@ -120,14 +120,6 @@ impl<F: Field> MultilinearExtension<F> for SparseMultilinearExtension<F> {
         self.num_vars
     }
 
-    fn evaluate(&self, point: &[F]) -> Option<F> {
-        if point.len() == self.num_vars {
-            Some(self.fix_variables(point)[0])
-        } else {
-            None
-        }
-    }
-
     /// Outputs an `l`-variate multilinear extension where value of evaluations
     /// are sampled uniformly at random. The number of nonzero entries is
     /// `sqrt(2^num_vars)` and indices of those nonzero entries are distributed
@@ -227,6 +219,19 @@ impl<F: Field> Index<usize> for SparseMultilinearExtension<F> {
     }
 }
 
+impl<F: Field> Polynomial<F> for SparseMultilinearExtension<F> {
+    type Point = Vec<F>;
+
+    fn degree(&self) -> usize {
+        self.num_vars
+    }
+
+    fn evaluate(&self, point: &Self::Point) -> F {
+        assert!(point.len() == self.num_vars);
+        self.fix_variables(point)[0]
+    }
+}
+
 impl<F: Field> Add for SparseMultilinearExtension<F> {
     type Output = SparseMultilinearExtension<F>;
 
@@ -399,7 +404,8 @@ fn hashmap_to_treemap<F: Field>(map: &HashMap<usize, F>) -> BTreeMap<usize, F> {
 #[cfg(test)]
 mod tests {
     use crate::{
-        evaluations::multivariate::multilinear::MultilinearExtension, SparseMultilinearExtension,
+        evaluations::multivariate::multilinear::MultilinearExtension, Polynomial,
+        SparseMultilinearExtension,
     };
     use ark_ff::{One, Zero};
     use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
@@ -453,7 +459,7 @@ mod tests {
         let mut rng = test_rng();
         let ev1 = Fr::rand(&mut rng);
         let poly1 = SparseMultilinearExtension::from_evaluations(0, &vec![(0, ev1)]);
-        assert_eq!(poly1.evaluate(&[]).unwrap(), ev1);
+        assert_eq!(poly1.evaluate(&[].into()), ev1);
 
         // test single-variate polynomial
         let ev2 = vec![Fr::rand(&mut rng), Fr::rand(&mut rng)];
@@ -462,7 +468,7 @@ mod tests {
 
         let x = Fr::rand(&mut rng);
         assert_eq!(
-            poly2.evaluate(&[x]).unwrap(),
+            poly2.evaluate(&[x].into()),
             x * ev2[1] + (Fr::one() - x) * ev2[0]
         );
 
@@ -471,7 +477,7 @@ mod tests {
         let poly2 = SparseMultilinearExtension::from_evaluations(1, &vec![(1, ev3)]);
 
         let x = Fr::rand(&mut rng);
-        assert_eq!(poly2.evaluate(&[x]).unwrap(), x * ev3);
+        assert_eq!(poly2.evaluate(&[x].into()), x * ev3);
     }
 
     #[test]
@@ -500,32 +506,32 @@ mod tests {
             let point: Vec<_> = (0..NV).map(|_| Fr::rand(&mut rng)).collect();
             let poly1 = SparseMultilinearExtension::rand(NV, &mut rng);
             let poly2 = SparseMultilinearExtension::rand(NV, &mut rng);
-            let v1 = poly1.evaluate(&point).unwrap();
-            let v2 = poly2.evaluate(&point).unwrap();
+            let v1 = poly1.evaluate(&point);
+            let v2 = poly2.evaluate(&point);
             // test add
-            assert_eq!((&poly1 + &poly2).evaluate(&point).unwrap(), v1 + v2);
+            assert_eq!((&poly1 + &poly2).evaluate(&point), v1 + v2);
             // test sub
-            assert_eq!((&poly1 - &poly2).evaluate(&point).unwrap(), v1 - v2);
+            assert_eq!((&poly1 - &poly2).evaluate(&point), v1 - v2);
             // test negate
-            assert_eq!(poly1.clone().neg().evaluate(&point).unwrap(), -v1);
+            assert_eq!(poly1.clone().neg().evaluate(&point), -v1);
             // test add assign
             {
                 let mut poly1 = poly1.clone();
                 poly1 += &poly2;
-                assert_eq!(poly1.evaluate(&point).unwrap(), v1 + v2)
+                assert_eq!(poly1.evaluate(&point), v1 + v2)
             }
             // test sub assign
             {
                 let mut poly1 = poly1.clone();
                 poly1 -= &poly2;
-                assert_eq!(poly1.evaluate(&point).unwrap(), v1 - v2)
+                assert_eq!(poly1.evaluate(&point), v1 - v2)
             }
             // test add assign with scalar
             {
                 let mut poly1 = poly1.clone();
                 let scalar = Fr::rand(&mut rng);
                 poly1 += (scalar, &poly2);
-                assert_eq!(poly1.evaluate(&point).unwrap(), v1 + scalar * v2)
+                assert_eq!(poly1.evaluate(&point), v1 + scalar * v2)
             }
             // test additive identity
             {
@@ -538,7 +544,7 @@ mod tests {
                     let mut zero = SparseMultilinearExtension::zero();
                     let scalar = Fr::rand(&mut rng);
                     zero += (scalar, &poly1);
-                    assert_eq!(zero.evaluate(&point).unwrap(), scalar * v1);
+                    assert_eq!(zero.evaluate(&point), scalar * v1);
                 }
             }
         }
@@ -551,29 +557,29 @@ mod tests {
             let mut poly = SparseMultilinearExtension::rand(10, &mut rng);
             let mut point: Vec<_> = (0..10).map(|_| Fr::rand(&mut rng)).collect();
 
-            let expected = poly.evaluate(&point).unwrap();
+            let expected = poly.evaluate(&point);
 
             poly = poly.relabel(2, 2, 1); // should have no effect
-            assert_eq!(expected, poly.evaluate(&point).unwrap());
+            assert_eq!(expected, poly.evaluate(&point));
 
             poly = poly.relabel(3, 4, 1); // should switch 3 and 4
             point.swap(3, 4);
-            assert_eq!(expected, poly.evaluate(&point).unwrap());
+            assert_eq!(expected, poly.evaluate(&point));
 
             poly = poly.relabel(7, 5, 1);
             point.swap(7, 5);
-            assert_eq!(expected, poly.evaluate(&point).unwrap());
+            assert_eq!(expected, poly.evaluate(&point));
 
             poly = poly.relabel(2, 5, 3);
             point.swap(2, 5);
             point.swap(3, 6);
             point.swap(4, 7);
-            assert_eq!(expected, poly.evaluate(&point).unwrap());
+            assert_eq!(expected, poly.evaluate(&point));
 
             poly = poly.relabel(7, 0, 2);
             point.swap(0, 7);
             point.swap(1, 8);
-            assert_eq!(expected, poly.evaluate(&point).unwrap());
+            assert_eq!(expected, poly.evaluate(&point));
         }
     }