Add Field::sum_of_products method

Closes #79.

CHANGELOG.md

@@ -6,6 +6,8 @@ and this library adheres to Rust's notion of
 [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
 ## [Unreleased]
+### Added
+- `ff::Field::sum_of_products`
 
 ## [0.11.0] - 2021-09-02
 ### Added

src/lib.rs

@@ -124,6 +124,21 @@ pub trait Field:
 
         res
     }
+
+    /// Returns `pairs.into_iter().fold(Self::zero(), |acc, (a_i, b_i)| acc + a_i * b_i)`.
+    ///
+    /// This computes the "dot product" or "inner product" `a ⋅ b` of two equal-length
+    /// sequences of elements `a` and `b`, such that `pairs = a.zip(b)`.
+    ///
+    /// The provided implementation of this trait method uses the direct calculation given
+    /// above. Implementations of `Field` should override this to use more efficient
+    /// methods that take advantage of their internal representation, such as interleaving
+    /// or sharing modular reductions.
+    fn sum_of_products<'a, I: IntoIterator<Item = (&'a Self, &'a Self)> + Clone>(pairs: I) -> Self {
+        pairs
+            .into_iter()
+            .fold(Self::zero(), |acc, (a_i, b_i)| acc + (*a_i * b_i))
+    }
 }
 
 /// This represents an element of a prime field.

tests/derive.rs

@@ -21,6 +21,47 @@ mod fermat {
     struct Fermat65537Field([u64; 1]);
 }
 
+#[test]
+fn sum_of_products() {
+    use ff::{Field, PrimeField};
+
+    let one = Bls381K12Scalar::one();
+
+    // [1, 2, 3, 4]
+    let values: Vec<_> = (0..4)
+        .scan(one, |acc, _| {
+            let ret = *acc;
+            *acc += &one;
+            Some(ret)
+        })
+        .collect();
+
+    // We'll pair each value with itself.
+    let expected = Bls381K12Scalar::from_str_vartime("30").unwrap();
+
+    // Check that we can produce the necessary input from two iterators.
+    assert_eq!(
+        // Directly produces (&v, &v)
+        Bls381K12Scalar::sum_of_products(values.iter().zip(values.iter())),
+        expected,
+    );
+
+    // Check that we can produce the necessary input from an iterator of values.
+    assert_eq!(
+        // Maps &v to (&v, &v)
+        Bls381K12Scalar::sum_of_products(values.iter().map(|v| (v, v))),
+        expected,
+    );
+
+    // Check that we can produce the necessary input from an iterator of tuples.
+    let tuples: Vec<_> = values.into_iter().map(|v| (v, v)).collect();
+    assert_eq!(
+        // Maps &(a, b) to (&a, &b)
+        Bls381K12Scalar::sum_of_products(tuples.iter().map(|(a, b)| (a, b))),
+        expected,
+    );
+}
+
 #[test]
 fn batch_inversion() {
     use ff::{BatchInverter, Field};