field: add Sum trait

Also tighten the ops::Neg bound to specify that the output needs to be
Self. Otherwise this bound is not really that useful.

Author: apoelstra

src/primitives/field.rs

@@ -2,7 +2,7 @@
 
 //! Generic Field Traits
 
-use core::{fmt, hash, ops};
+use core::{fmt, hash, iter, ops};
 
 /// A generic field.
 pub trait Field:
@@ -13,6 +13,8 @@ pub trait Field:
     + hash::Hash
     + fmt::Debug
     + fmt::Display
+    + iter::Sum
+    + for<'a> iter::Sum<&'a Self>
     + ops::Add<Self, Output = Self>
     + ops::Sub<Self, Output = Self>
     + ops::AddAssign
@@ -29,7 +31,7 @@ pub trait Field:
     + for<'a> ops::MulAssign<&'a Self>
     + for<'a> ops::Div<&'a Self, Output = Self>
     + for<'a> ops::DivAssign<&'a Self>
-    + ops::Neg
+    + ops::Neg<Output = Self>
 {
     /// The zero constant of the field.
     const ZERO: Self;
@@ -362,6 +364,19 @@ macro_rules! impl_ops_for_fe {
                 self._neg()
             }
         }
+
+        // sum
+        impl core::iter::Sum for $op {
+            fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
+                iter.fold(crate::primitives::Field::ZERO, |i, acc| i + acc)
+            }
+        }
+
+        impl<'s> core::iter::Sum<&'s Self> for $op {
+            fn sum<I: Iterator<Item = &'s Self>>(iter: I) -> Self {
+                iter.fold(crate::primitives::Field::ZERO, |i, acc| i + acc)
+            }
+        }
     };
 }
 pub(super) use impl_ops_for_fe;

src/primitives/polynomial.rs

@@ -90,8 +90,7 @@ impl<F: Field> Polynomial<F> {
         let mut cand = F::ONE;
         let mut eval = self.clone();
         for _ in 0..F::MULTIPLICATIVE_ORDER {
-            let sum = eval.inner.iter().cloned().fold(F::ZERO, F::add);
-            if sum == F::ZERO {
+            if eval.inner.iter().sum::<F>() == F::ZERO {
                 ret.push(cand.clone());
             }