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    // Copyright 2013-2016 The Rust Project Developers. See the COPYRIGHT
    // file at the top-level directory of this distribution and at
    // http://rust-lang.org/COPYRIGHT.
    //
    // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
    // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
    // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
    // option. This file may not be copied, modified, or distributed
    // except according to those terms.
    use ops::{Mul, Add, Try};
    use num::Wrapping;

    use super::LoopState;

    /// Conversion from an `Iterator`.
    ///
    /// By implementing `FromIterator` for a type, you define how it will be
    /// created from an iterator. This is common for types which describe a
    /// collection of some kind.
    ///
    /// `FromIterator`'s [`from_iter`] is rarely called explicitly, and is instead
    /// used through [`Iterator`]'s [`collect`] method. See [`collect`]'s
    /// documentation for more examples.
    ///
    /// [`from_iter`]: #tymethod.from_iter
    /// [`Iterator`]: trait.Iterator.html
    /// [`collect`]: trait.Iterator.html#method.collect
    ///
    /// See also: [`IntoIterator`].
    ///
    /// [`IntoIterator`]: trait.IntoIterator.html
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// use std::iter::FromIterator;
    ///
    /// let five_fives = std::iter::repeat(5).take(5);
    ///
    /// let v = Vec::from_iter(five_fives);
    ///
    /// assert_eq!(v, vec![5, 5, 5, 5, 5]);
    /// ```
    ///
    /// Using [`collect`] to implicitly use `FromIterator`:
    ///
    /// ```
    /// let five_fives = std::iter::repeat(5).take(5);
    ///
    /// let v: Vec<i32> = five_fives.collect();
    ///
    /// assert_eq!(v, vec![5, 5, 5, 5, 5]);
    /// ```
    ///
    /// Implementing `FromIterator` for your type:
    ///
    /// ```
    /// use std::iter::FromIterator;
    ///
    /// // A sample collection, that's just a wrapper over Vec<T>
    /// #[derive(Debug)]
    /// struct MyCollection(Vec<i32>);
    ///
    /// // Let's give it some methods so we can create one and add things
    /// // to it.
    /// impl MyCollection {
    ///     fn new() -> MyCollection {
    ///         MyCollection(Vec::new())
    ///     }
    ///
    ///     fn add(&mut self, elem: i32) {
    ///         self.0.push(elem);
    ///     }
    /// }
    ///
    /// // and we'll implement FromIterator
    /// impl FromIterator<i32> for MyCollection {
    ///     fn from_iter<I: IntoIterator<Item=i32>>(iter: I) -> Self {
    ///         let mut c = MyCollection::new();
    ///
    ///         for i in iter {
    ///             c.add(i);
    ///         }
    ///
    ///         c
    ///     }
    /// }
    ///
    /// // Now we can make a new iterator...
    /// let iter = (0..5).into_iter();
    ///
    /// // ... and make a MyCollection out of it
    /// let c = MyCollection::from_iter(iter);
    ///
    /// assert_eq!(c.0, vec![0, 1, 2, 3, 4]);
    ///
    /// // collect works too!
    ///
    /// let iter = (0..5).into_iter();
    /// let c: MyCollection = iter.collect();
    ///
    /// assert_eq!(c.0, vec![0, 1, 2, 3, 4]);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    #[rustc_on_unimplemented(
        message="a collection of type `{Self}` cannot be built from an iterator \
                 over elements of type `{A}`",
        label="a collection of type `{Self}` cannot be built from `std::iter::Iterator<Item={A}>`",
    )]
    pub trait FromIterator<A>: Sized {
        /// Creates a value from an iterator.
        ///
        /// See the [module-level documentation] for more.
        ///
        /// [module-level documentation]: index.html
        ///
        /// # Examples
        ///
        /// Basic usage:
        ///
        /// ```
        /// use std::iter::FromIterator;
        ///
        /// let five_fives = std::iter::repeat(5).take(5);
        ///
        /// let v = Vec::from_iter(five_fives);
        ///
        /// assert_eq!(v, vec![5, 5, 5, 5, 5]);
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        fn from_iter<T: IntoIterator<Item=A>>(iter: T) -> Self;
    }

    /// Conversion into an `Iterator`.
    ///
    /// By implementing `IntoIterator` for a type, you define how it will be
    /// converted to an iterator. This is common for types which describe a
    /// collection of some kind.
    ///
    /// One benefit of implementing `IntoIterator` is that your type will [work
    /// with Rust's `for` loop syntax](index.html#for-loops-and-intoiterator).
    ///
    /// See also: [`FromIterator`].
    ///
    /// [`FromIterator`]: trait.FromIterator.html
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// let v = vec![1, 2, 3];
    /// let mut iter = v.into_iter();
    ///
    /// assert_eq!(Some(1), iter.next());
    /// assert_eq!(Some(2), iter.next());
    /// assert_eq!(Some(3), iter.next());
    /// assert_eq!(None, iter.next());
    /// ```
    /// Implementing `IntoIterator` for your type:
    ///
    /// ```
    /// // A sample collection, that's just a wrapper over Vec<T>
    /// #[derive(Debug)]
    /// struct MyCollection(Vec<i32>);
    ///
    /// // Let's give it some methods so we can create one and add things
    /// // to it.
    /// impl MyCollection {
    ///     fn new() -> MyCollection {
    ///         MyCollection(Vec::new())
    ///     }
    ///
    ///     fn add(&mut self, elem: i32) {
    ///         self.0.push(elem);
    ///     }
    /// }
    ///
    /// // and we'll implement IntoIterator
    /// impl IntoIterator for MyCollection {
    ///     type Item = i32;
    ///     type IntoIter = ::std::vec::IntoIter<i32>;
    ///
    ///     fn into_iter(self) -> Self::IntoIter {
    ///         self.0.into_iter()
    ///     }
    /// }
    ///
    /// // Now we can make a new collection...
    /// let mut c = MyCollection::new();
    ///
    /// // ... add some stuff to it ...
    /// c.add(0);
    /// c.add(1);
    /// c.add(2);
    ///
    /// // ... and then turn it into an Iterator:
    /// for (i, n) in c.into_iter().enumerate() {
    ///     assert_eq!(i as i32, n);
    /// }
    /// ```
    ///
    /// It is common to use `IntoIterator` as a trait bound. This allows
    /// the input collection type to change, so long as it is still an
    /// iterator. Additional bounds can be specified by restricting on
    /// `Item`:
    ///
    /// ```rust
    /// fn collect_as_strings<T>(collection: T) -> Vec<String>
    ///     where T: IntoIterator,
    ///           T::Item : std::fmt::Debug,
    /// {
    ///     collection
    ///         .into_iter()
    ///         .map(|item| format!("{:?}", item))
    ///         .collect()
    /// }
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    pub trait IntoIterator {
        /// The type of the elements being iterated over.
        #[stable(feature = "rust1", since = "1.0.0")]
        type Item;

        /// Which kind of iterator are we turning this into?
        #[stable(feature = "rust1", since = "1.0.0")]
        type IntoIter: Iterator<Item=Self::Item>;

        /// Creates an iterator from a value.
        ///
        /// See the [module-level documentation] for more.
        ///
        /// [module-level documentation]: index.html
        ///
        /// # Examples
        ///
        /// Basic usage:
        ///
        /// ```
        /// let v = vec![1, 2, 3];
        /// let mut iter = v.into_iter();
        ///
        /// assert_eq!(Some(1), iter.next());
        /// assert_eq!(Some(2), iter.next());
        /// assert_eq!(Some(3), iter.next());
        /// assert_eq!(None, iter.next());
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        fn into_iter(self) -> Self::IntoIter;
    }

    #[stable(feature = "rust1", since = "1.0.0")]
    impl<I: Iterator> IntoIterator for I {
        type Item = I::Item;
        type IntoIter = I;

        fn into_iter(self) -> I {
            self
        }
    }

    /// Extend a collection with the contents of an iterator.
    ///
    /// Iterators produce a series of values, and collections can also be thought
    /// of as a series of values. The `Extend` trait bridges this gap, allowing you
    /// to extend a collection by including the contents of that iterator. When
    /// extending a collection with an already existing key, that entry is updated
    /// or, in the case of collections that permit multiple entries with equal
    /// keys, that entry is inserted.
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// // You can extend a String with some chars:
    /// let mut message = String::from("The first three letters are: ");
    ///
    /// message.extend(&['a', 'b', 'c']);
    ///
    /// assert_eq!("abc", &message[29..32]);
    /// ```
    ///
    /// Implementing `Extend`:
    ///
    /// ```
    /// // A sample collection, that's just a wrapper over Vec<T>
    /// #[derive(Debug)]
    /// struct MyCollection(Vec<i32>);
    ///
    /// // Let's give it some methods so we can create one and add things
    /// // to it.
    /// impl MyCollection {
    ///     fn new() -> MyCollection {
    ///         MyCollection(Vec::new())
    ///     }
    ///
    ///     fn add(&mut self, elem: i32) {
    ///         self.0.push(elem);
    ///     }
    /// }
    ///
    /// // since MyCollection has a list of i32s, we implement Extend for i32
    /// impl Extend<i32> for MyCollection {
    ///
    ///     // This is a bit simpler with the concrete type signature: we can call
    ///     // extend on anything which can be turned into an Iterator which gives
    ///     // us i32s. Because we need i32s to put into MyCollection.
    ///     fn extend<T: IntoIterator<Item=i32>>(&mut self, iter: T) {
    ///
    ///         // The implementation is very straightforward: loop through the
    ///         // iterator, and add() each element to ourselves.
    ///         for elem in iter {
    ///             self.add(elem);
    ///         }
    ///     }
    /// }
    ///
    /// let mut c = MyCollection::new();
    ///
    /// c.add(5);
    /// c.add(6);
    /// c.add(7);
    ///
    /// // let's extend our collection with three more numbers
    /// c.extend(vec![1, 2, 3]);
    ///
    /// // we've added these elements onto the end
    /// assert_eq!("MyCollection([5, 6, 7, 1, 2, 3])", format!("{:?}", c));
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    pub trait Extend<A> {
        /// Extends a collection with the contents of an iterator.
        ///
        /// As this is the only method for this trait, the [trait-level] docs
        /// contain more details.
        ///
        /// [trait-level]: trait.Extend.html
        ///
        /// # Examples
        ///
        /// Basic usage:
        ///
        /// ```
        /// // You can extend a String with some chars:
        /// let mut message = String::from("abc");
        ///
        /// message.extend(['d', 'e', 'f'].iter());
        ///
        /// assert_eq!("abcdef", &message);
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        fn extend<T: IntoIterator<Item=A>>(&mut self, iter: T);
    }

    #[stable(feature = "extend_for_unit", since = "1.28.0")]
    impl Extend<()> for () {
        fn extend<T: IntoIterator<Item = ()>>(&mut self, iter: T) {
            iter.into_iter().for_each(drop)
        }
    }

    /// An iterator able to yield elements from both ends.
    ///
    /// Something that implements `DoubleEndedIterator` has one extra capability
    /// over something that implements [`Iterator`]: the ability to also take
    /// `Item`s from the back, as well as the front.
    ///
    /// It is important to note that both back and forth work on the same range,
    /// and do not cross: iteration is over when they meet in the middle.
    ///
    /// In a similar fashion to the [`Iterator`] protocol, once a
    /// `DoubleEndedIterator` returns `None` from a `next_back()`, calling it again
    /// may or may not ever return `Some` again. `next()` and `next_back()` are
    /// interchangeable for this purpose.
    ///
    /// [`Iterator`]: trait.Iterator.html
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// let numbers = vec![1, 2, 3, 4, 5, 6];
    ///
    /// let mut iter = numbers.iter();
    ///
    /// assert_eq!(Some(&1), iter.next());
    /// assert_eq!(Some(&6), iter.next_back());
    /// assert_eq!(Some(&5), iter.next_back());
    /// assert_eq!(Some(&2), iter.next());
    /// assert_eq!(Some(&3), iter.next());
    /// assert_eq!(Some(&4), iter.next());
    /// assert_eq!(None, iter.next());
    /// assert_eq!(None, iter.next_back());
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    pub trait DoubleEndedIterator: Iterator {
        /// Removes and returns an element from the end of the iterator.
        ///
        /// Returns `None` when there are no more elements.
        ///
        /// The [trait-level] docs contain more details.
        ///
        /// [trait-level]: trait.DoubleEndedIterator.html
        ///
        /// # Examples
        ///
        /// Basic usage:
        ///
        /// ```
        /// let numbers = vec![1, 2, 3, 4, 5, 6];
        ///
        /// let mut iter = numbers.iter();
        ///
        /// assert_eq!(Some(&1), iter.next());
        /// assert_eq!(Some(&6), iter.next_back());
        /// assert_eq!(Some(&5), iter.next_back());
        /// assert_eq!(Some(&2), iter.next());
        /// assert_eq!(Some(&3), iter.next());
        /// assert_eq!(Some(&4), iter.next());
        /// assert_eq!(None, iter.next());
        /// assert_eq!(None, iter.next_back());
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        fn next_back(&mut self) -> Option<Self::Item>;

        /// This is the reverse version of [`try_fold()`]: it takes elements
        /// starting from the back of the iterator.
        ///
        /// [`try_fold()`]: trait.Iterator.html#method.try_fold
        ///
        /// # Examples
        ///
        /// Basic usage:
        ///
        /// ```
        /// let a = ["1", "2", "3"];
        /// let sum = a.iter()
        ///     .map(|&s| s.parse::<i32>())
        ///     .try_rfold(0, |acc, x| x.and_then(|y| Ok(acc + y)));
        /// assert_eq!(sum, Ok(6));
        /// ```
        ///
        /// Short-circuiting:
        ///
        /// ```
        /// let a = ["1", "rust", "3"];
        /// let mut it = a.iter();
        /// let sum = it
        ///     .by_ref()
        ///     .map(|&s| s.parse::<i32>())
        ///     .try_rfold(0, |acc, x| x.and_then(|y| Ok(acc + y)));
        /// assert!(sum.is_err());
        ///
        /// // Because it short-circuited, the remaining elements are still
        /// // available through the iterator.
        /// assert_eq!(it.next_back(), Some(&"1"));
        /// ```
        #[inline]
        #[stable(feature = "iterator_try_fold", since = "1.27.0")]
        fn try_rfold<B, F, R>(&mut self, init: B, mut f: F) -> R where
            Self: Sized, F: FnMut(B, Self::Item) -> R, R: Try<Ok=B>
        {
            let mut accum = init;
            while let Some(x) = self.next_back() {
                accum = f(accum, x)?;
            }
            Try::from_ok(accum)
        }

        /// An iterator method that reduces the iterator's elements to a single,
        /// final value, starting from the back.
        ///
        /// This is the reverse version of [`fold()`]: it takes elements starting from
        /// the back of the iterator.
        ///
        /// `rfold()` takes two arguments: an initial value, and a closure with two
        /// arguments: an 'accumulator', and an element. The closure returns the value that
        /// the accumulator should have for the next iteration.
        ///
        /// The initial value is the value the accumulator will have on the first
        /// call.
        ///
        /// After applying this closure to every element of the iterator, `rfold()`
        /// returns the accumulator.
        ///
        /// This operation is sometimes called 'reduce' or 'inject'.
        ///
        /// Folding is useful whenever you have a collection of something, and want
        /// to produce a single value from it.
        ///
        /// [`fold()`]: trait.Iterator.html#method.fold
        ///
        /// # Examples
        ///
        /// Basic usage:
        ///
        /// ```
        /// let a = [1, 2, 3];
        ///
        /// // the sum of all of the elements of a
        /// let sum = a.iter()
        ///            .rfold(0, |acc, &x| acc + x);
        ///
        /// assert_eq!(sum, 6);
        /// ```
        ///
        /// This example builds a string, starting with an initial value
        /// and continuing with each element from the back until the front:
        ///
        /// ```
        /// let numbers = [1, 2, 3, 4, 5];
        ///
        /// let zero = "0".to_string();
        ///
        /// let result = numbers.iter().rfold(zero, |acc, &x| {
        ///     format!("({} + {})", x, acc)
        /// });
        ///
        /// assert_eq!(result, "(1 + (2 + (3 + (4 + (5 + 0)))))");
        /// ```
        #[inline]
        #[stable(feature = "iter_rfold", since = "1.27.0")]
        fn rfold<B, F>(mut self, accum: B, mut f: F) -> B where
            Self: Sized, F: FnMut(B, Self::Item) -> B,
        {
            self.try_rfold(accum, move |acc, x| Ok::<B, !>(f(acc, x))).unwrap()
        }

        /// Searches for an element of an iterator from the back that satisfies a predicate.
        ///
        /// `rfind()` takes a closure that returns `true` or `false`. It applies
        /// this closure to each element of the iterator, starting at the end, and if any
        /// of them return `true`, then `rfind()` returns [`Some(element)`]. If they all return
        /// `false`, it returns [`None`].
        ///
        /// `rfind()` is short-circuiting; in other words, it will stop processing
        /// as soon as the closure returns `true`.
        ///
        /// Because `rfind()` takes a reference, and many iterators iterate over
        /// references, this leads to a possibly confusing situation where the
        /// argument is a double reference. You can see this effect in the
        /// examples below, with `&&x`.
        ///
        /// [`Some(element)`]: ../../std/option/enum.Option.html#variant.Some
        /// [`None`]: ../../std/option/enum.Option.html#variant.None
        ///
        /// # Examples
        ///
        /// Basic usage:
        ///
        /// ```
        /// let a = [1, 2, 3];
        ///
        /// assert_eq!(a.iter().rfind(|&&x| x == 2), Some(&2));
        ///
        /// assert_eq!(a.iter().rfind(|&&x| x == 5), None);
        /// ```
        ///
        /// Stopping at the first `true`:
        ///
        /// ```
        /// let a = [1, 2, 3];
        ///
        /// let mut iter = a.iter();
        ///
        /// assert_eq!(iter.rfind(|&&x| x == 2), Some(&2));
        ///
        /// // we can still use `iter`, as there are more elements.
        /// assert_eq!(iter.next_back(), Some(&1));
        /// ```
        #[inline]
        #[stable(feature = "iter_rfind", since = "1.27.0")]
        fn rfind<P>(&mut self, mut predicate: P) -> Option<Self::Item> where
            Self: Sized,
            P: FnMut(&Self::Item) -> bool
        {
            self.try_rfold((), move |(), x| {
                if predicate(&x) { LoopState::Break(x) }
                else { LoopState::Continue(()) }
            }).break_value()
        }
    }

    #[stable(feature = "rust1", since = "1.0.0")]
    impl<'a, I: DoubleEndedIterator + ?Sized> DoubleEndedIterator for &'a mut I {
        fn next_back(&mut self) -> Option<I::Item> { (**self).next_back() }
    }

    /// An iterator that knows its exact length.
    ///
    /// Many [`Iterator`]s don't know how many times they will iterate, but some do.
    /// If an iterator knows how many times it can iterate, providing access to
    /// that information can be useful. For example, if you want to iterate
    /// backwards, a good start is to know where the end is.
    ///
    /// When implementing an `ExactSizeIterator`, you must also implement
    /// [`Iterator`]. When doing so, the implementation of [`size_hint`] *must*
    /// return the exact size of the iterator.
    ///
    /// [`Iterator`]: trait.Iterator.html
    /// [`size_hint`]: trait.Iterator.html#method.size_hint
    ///
    /// The [`len`] method has a default implementation, so you usually shouldn't
    /// implement it. However, you may be able to provide a more performant
    /// implementation than the default, so overriding it in this case makes sense.
    ///
    /// [`len`]: #method.len
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// // a finite range knows exactly how many times it will iterate
    /// let five = 0..5;
    ///
    /// assert_eq!(5, five.len());
    /// ```
    ///
    /// In the [module level docs][moddocs], we implemented an [`Iterator`],
    /// `Counter`. Let's implement `ExactSizeIterator` for it as well:
    ///
    /// [moddocs]: index.html
    ///
    /// ```
    /// # struct Counter {
    /// #     count: usize,
    /// # }
    /// # impl Counter {
    /// #     fn new() -> Counter {
    /// #         Counter { count: 0 }
    /// #     }
    /// # }
    /// # impl Iterator for Counter {
    /// #     type Item = usize;
    /// #     fn next(&mut self) -> Option<usize> {
    /// #         self.count += 1;
    /// #         if self.count < 6 {
    /// #             Some(self.count)
    /// #         } else {
    /// #             None
    /// #         }
    /// #     }
    /// # }
    /// impl ExactSizeIterator for Counter {
    ///     // We can easily calculate the remaining number of iterations.
    ///     fn len(&self) -> usize {
    ///         5 - self.count
    ///     }
    /// }
    ///
    /// // And now we can use it!
    ///
    /// let counter = Counter::new();
    ///
    /// assert_eq!(5, counter.len());
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    pub trait ExactSizeIterator: Iterator {
        /// Returns the exact number of times the iterator will iterate.
        ///
        /// This method has a default implementation, so you usually should not
        /// implement it directly. However, if you can provide a more efficient
        /// implementation, you can do so. See the [trait-level] docs for an
        /// example.
        ///
        /// This function has the same safety guarantees as the [`size_hint`]
        /// function.
        ///
        /// [trait-level]: trait.ExactSizeIterator.html
        /// [`size_hint`]: trait.Iterator.html#method.size_hint
        ///
        /// # Examples
        ///
        /// Basic usage:
        ///
        /// ```
        /// // a finite range knows exactly how many times it will iterate
        /// let five = 0..5;
        ///
        /// assert_eq!(5, five.len());
        /// ```
        #[inline]
        #[stable(feature = "rust1", since = "1.0.0")]
        fn len(&self) -> usize {
            let (lower, upper) = self.size_hint();
            // Note: This assertion is overly defensive, but it checks the invariant
            // guaranteed by the trait. If this trait were rust-internal,
            // we could use debug_assert!; assert_eq! will check all Rust user
            // implementations too.
            assert_eq!(upper, Some(lower));
            lower
        }

        /// Returns whether the iterator is empty.
        ///
        /// This method has a default implementation using `self.len()`, so you
        /// don't need to implement it yourself.
        ///
        /// # Examples
        ///
        /// Basic usage:
        ///
        /// ```
        /// #![feature(exact_size_is_empty)]
        ///
        /// let mut one_element = std::iter::once(0);
        /// assert!(!one_element.is_empty());
        ///
        /// assert_eq!(one_element.next(), Some(0));
        /// assert!(one_element.is_empty());
        ///
        /// assert_eq!(one_element.next(), None);
        /// ```
        #[inline]
        #[unstable(feature = "exact_size_is_empty", issue = "35428")]
        fn is_empty(&self) -> bool {
            self.len() == 0
        }
    }

    #[stable(feature = "rust1", since = "1.0.0")]
    impl<I: ExactSizeIterator + ?Sized> ExactSizeIterator for &mut I {
        fn len(&self) -> usize {
            (**self).len()
        }
        fn is_empty(&self) -> bool {
            (**self).is_empty()
        }
    }

    /// 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;
    }

    // NB: 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, |a, b| a + b)
                }
            }

            #[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, |a, b| a * b)
                }
            }

            #[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, |a, b| a + *b)
                }
            }

            #[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, |a, b| a * *b)
                }
            }
        )*)
    }

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

    /// An iterator adapter that produces output as long as the underlying
    /// iterator produces `Result::Ok` values.
    ///
    /// If an error is encountered, the iterator stops and the error is
    /// stored. The error may be recovered later via `reconstruct`.
    struct ResultShunt<I, E> {
        iter: I,
        error: Option<E>,
    }

    impl<I, T, E> ResultShunt<I, E>
        where I: Iterator<Item = Result<T, E>>
    {
        /// Process the given iterator as if it yielded a `T` instead of a
        /// `Result<T, _>`. Any errors will stop the inner iterator and
        /// the overall result will be an error.
        pub fn process<F, U>(iter: I, mut f: F) -> Result<U, E>
            where F: FnMut(&mut Self) -> U
        {
            let mut shunt = ResultShunt::new(iter);
            let value = f(shunt.by_ref());
            shunt.reconstruct(value)
        }

        fn new(iter: I) -> Self {
            ResultShunt {
                iter,
                error: None,
            }
        }

        /// Consume the adapter and rebuild a `Result` value. This should
        /// *always* be called, otherwise any potential error would be
        /// lost.
        fn reconstruct<U>(self, val: U) -> Result<U, E> {
            match self.error {
                None => Ok(val),
                Some(e) => Err(e),
            }
        }
    }

    impl<I, T, E> Iterator for ResultShunt<I, E>
        where I: Iterator<Item = Result<T, E>>
    {
        type Item = T;

        fn next(&mut self) -> Option<Self::Item> {
            match self.iter.next() {
                Some(Ok(v)) => Some(v),
                Some(Err(e)) => {
                    self.error = Some(e);
                    None
                }
                None => None,
            }
        }

        fn size_hint(&self) -> (usize, Option<usize>) {
            if self.error.is_some() {
                (0, Some(0))
            } else {
                let (_, upper) = self.iter.size_hint();
                (0, upper)
            }
        }
    }

    #[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>>,
        {
            ResultShunt::process(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>>,
        {
            ResultShunt::process(iter, |i| i.product())
        }
    }

    /// An iterator that always continues to yield `None` when exhausted.
    ///
    /// Calling next on a fused iterator that has returned `None` once is guaranteed
    /// to return [`None`] again. This trait should be implemented by all iterators
    /// that behave this way because it allows optimizing [`Iterator::fuse`].
    ///
    /// Note: In general, you should not use `FusedIterator` in generic bounds if
    /// you need a fused iterator. Instead, you should just call [`Iterator::fuse`]
    /// on the iterator. If the iterator is already fused, the additional [`Fuse`]
    /// wrapper will be a no-op with no performance penalty.
    ///
    /// [`None`]: ../../std/option/enum.Option.html#variant.None
    /// [`Iterator::fuse`]: ../../std/iter/trait.Iterator.html#method.fuse
    /// [`Fuse`]: ../../std/iter/struct.Fuse.html
    #[stable(feature = "fused", since = "1.26.0")]
    pub trait FusedIterator: Iterator {}

    #[stable(feature = "fused", since = "1.26.0")]
    impl<I: FusedIterator + ?Sized> FusedIterator for &mut I {}

    /// An iterator that reports an accurate length using size_hint.
    ///
    /// The iterator reports a size hint where it is either exact
    /// (lower bound is equal to upper bound), or the upper bound is [`None`].
    /// The upper bound must only be [`None`] if the actual iterator length is
    /// larger than [`usize::MAX`]. In that case, the lower bound must be
    /// [`usize::MAX`], resulting in a [`.size_hint`] of `(usize::MAX, None)`.
    ///
    /// The iterator must produce exactly the number of elements it reported
    /// or diverge before reaching the end.
    ///
    /// # Safety
    ///
    /// This trait must only be implemented when the contract is upheld.
    /// Consumers of this trait must inspect [`.size_hint`]’s upper bound.
    ///
    /// [`None`]: ../../std/option/enum.Option.html#variant.None
    /// [`usize::MAX`]: ../../std/usize/constant.MAX.html
    /// [`.size_hint`]: ../../std/iter/trait.Iterator.html#method.size_hint
    #[unstable(feature = "trusted_len", issue = "37572")]
    pub unsafe trait TrustedLen : Iterator {}

    #[unstable(feature = "trusted_len", issue = "37572")]
    unsafe impl<I: TrustedLen + ?Sized> TrustedLen for &mut I {}

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