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    use crate::iter;
    use crate::num::Wrapping;
    use crate::ops::{Add, Mul};

    /// Trait to represent types that can be created by summing up an iterator.
    ///
    /// This trait is used to implement the [`sum`] method on iterators. Types which
    /// implement the trait can be generated by the [`sum`] method. Like
    /// [`FromIterator`] this trait should rarely be called directly and instead
    /// interacted with through [`Iterator::sum`].
    ///
    /// [`sum`]: ../../std/iter/trait.Sum.html#tymethod.sum
    /// [`FromIterator`]: ../../std/iter/trait.FromIterator.html
    /// [`Iterator::sum`]: ../../std/iter/trait.Iterator.html#method.sum
    #[stable(feature = "iter_arith_traits", since = "1.12.0")]
    pub trait Sum<A = Self>: Sized {
        /// Method which takes an iterator and generates `Self` from the elements by
        /// "summing up" the items.
        #[stable(feature = "iter_arith_traits", since = "1.12.0")]
        fn sum<I: Iterator<Item = A>>(iter: I) -> Self;
    }

    /// Trait to represent types that can be created by multiplying elements of an
    /// iterator.
    ///
    /// This trait is used to implement the [`product`] method on iterators. Types
    /// which implement the trait can be generated by the [`product`] method. Like
    /// [`FromIterator`] this trait should rarely be called directly and instead
    /// interacted with through [`Iterator::product`].
    ///
    /// [`product`]: ../../std/iter/trait.Product.html#tymethod.product
    /// [`FromIterator`]: ../../std/iter/trait.FromIterator.html
    /// [`Iterator::product`]: ../../std/iter/trait.Iterator.html#method.product
    #[stable(feature = "iter_arith_traits", since = "1.12.0")]
    pub trait Product<A = Self>: Sized {
        /// Method which takes an iterator and generates `Self` from the elements by
        /// multiplying the items.
        #[stable(feature = "iter_arith_traits", since = "1.12.0")]
        fn product<I: Iterator<Item = A>>(iter: I) -> Self;
    }

    // N.B., explicitly use Add and Mul here to inherit overflow checks
    macro_rules! integer_sum_product {
        (@impls $zero:expr, $one:expr, #[$attr:meta], $($a:ty)*) => ($(
            #[$attr]
            impl Sum for $a {
                fn sum<I: Iterator<Item=$a>>(iter: I) -> $a {
                    iter.fold($zero, Add::add)
                }
            }

            #[$attr]
            impl Product for $a {
                fn product<I: Iterator<Item=$a>>(iter: I) -> $a {
                    iter.fold($one, Mul::mul)
                }
            }

            #[$attr]
            impl<'a> Sum<&'a $a> for $a {
                fn sum<I: Iterator<Item=&'a $a>>(iter: I) -> $a {
                    iter.fold($zero, Add::add)
                }
            }

            #[$attr]
            impl<'a> Product<&'a $a> for $a {
                fn product<I: Iterator<Item=&'a $a>>(iter: I) -> $a {
                    iter.fold($one, Mul::mul)
                }
            }
        )*);
        ($($a:ty)*) => (
            integer_sum_product!(@impls 0, 1,
                    #[stable(feature = "iter_arith_traits", since = "1.12.0")],
                    $($a)*);
            integer_sum_product!(@impls Wrapping(0), Wrapping(1),
                    #[stable(feature = "wrapping_iter_arith", since = "1.14.0")],
                    $(Wrapping<$a>)*);
        );
    }

    macro_rules! float_sum_product {
        ($($a:ident)*) => ($(
            #[stable(feature = "iter_arith_traits", since = "1.12.0")]
            impl Sum for $a {
                fn sum<I: Iterator<Item=$a>>(iter: I) -> $a {
                    iter.fold(0.0, Add::add)
                }
            }

            #[stable(feature = "iter_arith_traits", since = "1.12.0")]
            impl Product for $a {
                fn product<I: Iterator<Item=$a>>(iter: I) -> $a {
                    iter.fold(1.0, Mul::mul)
                }
            }

            #[stable(feature = "iter_arith_traits", since = "1.12.0")]
            impl<'a> Sum<&'a $a> for $a {
                fn sum<I: Iterator<Item=&'a $a>>(iter: I) -> $a {
                    iter.fold(0.0, Add::add)
                }
            }

            #[stable(feature = "iter_arith_traits", since = "1.12.0")]
            impl<'a> Product<&'a $a> for $a {
                fn product<I: Iterator<Item=&'a $a>>(iter: I) -> $a {
                    iter.fold(1.0, Mul::mul)
                }
            }
        )*)
    }

    integer_sum_product! { i8 i16 i32 i64 i128 isize u8 u16 u32 u64 u128 usize }
    float_sum_product! { f32 f64 }

    #[stable(feature = "iter_arith_traits_result", since = "1.16.0")]
    impl<T, U, E> Sum<Result<U, E>> for Result<T, E>
    where
        T: Sum<U>,
    {
        /// Takes each element in the `Iterator`: if it is an `Err`, no further
        /// elements are taken, and the `Err` is returned. Should no `Err` occur,
        /// the sum of all elements is returned.
        ///
        /// # Examples
        ///
        /// This sums up every integer in a vector, rejecting the sum if a negative
        /// element is encountered:
        ///
        /// ```
        /// let v = vec![1, 2];
        /// let res: Result<i32, &'static str> = v.iter().map(|&x: &i32|
        ///     if x < 0 { Err("Negative element found") }
        ///     else { Ok(x) }
        /// ).sum();
        /// assert_eq!(res, Ok(3));
        /// ```
        fn sum<I>(iter: I) -> Result<T, E>
        where
            I: Iterator<Item = Result<U, E>>,
        {
            iter::process_results(iter, |i| i.sum())
        }
    }

    #[stable(feature = "iter_arith_traits_result", since = "1.16.0")]
    impl<T, U, E> Product<Result<U, E>> for Result<T, E>
    where
        T: Product<U>,
    {
        /// Takes each element in the `Iterator`: if it is an `Err`, no further
        /// elements are taken, and the `Err` is returned. Should no `Err` occur,
        /// the product of all elements is returned.
        fn product<I>(iter: I) -> Result<T, E>
        where
            I: Iterator<Item = Result<U, E>>,
        {
            iter::process_results(iter, |i| i.product())
        }
    }

    #[stable(feature = "iter_arith_traits_option", since = "1.37.0")]
    impl<T, U> Sum<Option<U>> for Option<T>
    where
        T: Sum<U>,
    {
        /// Takes each element in the `Iterator`: if it is a `None`, no further
        /// elements are taken, and the `None` is returned. Should no `None` occur,
        /// the sum of all elements is returned.
        ///
        /// # Examples
        ///
        /// This sums up the position of the character 'a' in a vector of strings,
        /// if a word did not have the character 'a' the operation returns `None`:
        ///
        /// ```
        /// let words = vec!["have", "a", "great", "day"];
        /// let total: Option<usize> = words.iter().map(|w| w.find('a')).sum();
        /// assert_eq!(total, Some(5));
        /// ```
        fn sum<I>(iter: I) -> Option<T>
        where
            I: Iterator<Item = Option<U>>,
        {
            iter.map(|x| x.ok_or(())).sum::<Result<_, _>>().ok()
        }
    }

    #[stable(feature = "iter_arith_traits_option", since = "1.37.0")]
    impl<T, U> Product<Option<U>> for Option<T>
    where
        T: Product<U>,
    {
        /// Takes each element in the `Iterator`: if it is a `None`, no further
        /// elements are taken, and the `None` is returned. Should no `None` occur,
        /// the product of all elements is returned.
        fn product<I>(iter: I) -> Option<T>
        where
            I: Iterator<Item = Option<U>>,
        {
            iter.map(|x| x.ok_or(())).product::<Result<_, _>>().ok()
        }
    }