//! A type that can be treated as a difference.
//!
//! Differential dataflow most commonly tracks the counts associated with records in a multiset, but it
//! generalizes to tracking any map from the records to an Abelian group. The most common generalization
//! is when we maintain both a count and another accumulation, for example height. The differential
//! dataflow collections would then track for each record the total of counts and heights, which allows
//! us to track something like the average.

use std::ops::{AddAssign, Neg};

use ::Data;

#[deprecated]
pub use self::Abelian as Diff;

/// A type with addition and a test for zero.
///
/// These traits are currently the minimal requirements for a type to be a "difference" in differential
/// dataflow. Addition allows differential dataflow to compact multiple updates to the same data, and
/// the test for zero allows differential dataflow to retire updates that have no effect. There is no
/// requirement that the test for zero ever return true, and the zero value does not need to inhabit the
/// type.
///
/// There is a light presumption of commutativity here, in that while we will largely perform addition
/// in order of timestamps, for many types of timestamps there is no total order and consequently no
/// obvious order to respect. Non-commutative semigroups should be used with care.
pub trait Semigroup : for<'a> AddAssign<&'a Self> + ::std::marker::Sized + Data + Clone {
    /// Returns true if the element is the additive identity.
    ///
    /// This is primarily used by differential dataflow to know when it is safe to delete an update.
    /// When a difference accumulates to zero, the difference has no effect on any accumulation and can
    /// be removed.
    ///
    /// A semigroup is not obligated to have a zero element, and this method could always return
    /// false in such a setting.
    fn is_zero(&self) -> bool;
}

impl Semigroup for isize {
    #[inline] fn is_zero(&self) -> bool { self == &0 }
}

impl Semigroup for i128 {
    #[inline] fn is_zero(&self) -> bool { self == &0 }
}

impl Semigroup for i64 {
    #[inline] fn is_zero(&self) -> bool { self == &0 }
}

impl Semigroup for i32 {
    #[inline] fn is_zero(&self) -> bool { self == &0 }
}

impl Semigroup for i16 {
    #[inline] fn is_zero(&self) -> bool { self == &0 }
}

impl Semigroup for i8 {
    #[inline] fn is_zero(&self) -> bool { self == &0 }
}


/// A semigroup with an explicit zero element.
pub trait Monoid : Semigroup {
    /// A zero element under the semigroup addition operator.
    fn zero() -> Self;
}

impl Monoid for isize {
    #[inline] fn zero() -> Self { 0 }
}

impl Monoid for i128 {
    #[inline] fn zero() -> Self { 0 }
}

impl Monoid for i64 {
    #[inline] fn zero() -> Self { 0 }
}

impl Monoid for i32 {
    #[inline] fn zero() -> Self { 0 }
}

impl Monoid for i16 {
    #[inline] fn zero() -> Self { 0 }
}

impl Monoid for i8 {
    #[inline] fn zero() -> Self { 0 }
}


/// A `Monoid` with negation.
///
/// This trait extends the requirements of `Semigroup` to include a negation operator.
/// Several differential dataflow operators require negation in order to retract prior outputs, but
/// not quite as many as you might imagine.
pub trait Abelian : Monoid + Neg<Output=Self> { }
impl<T: Monoid + Neg<Output=Self>> Abelian for T { }


pub use self::present::Present;
mod present {

    /// A zero-sized difference that indicates the presence of a record.
    ///
    /// This difference type has no negation, and present records cannot be retracted.
    /// Addition and multiplication maintain presence, and zero does not inhabit the type.
    ///
    /// The primary feature of this type is that it has zero size, which reduces the overhead
    /// of differential dataflow's representations for settings where collections either do
    /// not change, or for which records are only added (for example, derived facts in Datalog).
    #[derive(Abomonation, Copy, Ord, PartialOrd, Eq, PartialEq, Debug, Clone, Serialize, Deserialize, Hash)]
    pub struct Present;

    impl<'a> std::ops::AddAssign<&'a Self> for Present {
        fn add_assign(&mut self, _rhs: &'a Self) { }
    }

    impl<T> std::ops::Mul<T> for Present {
        type Output = T;
        fn mul(self, rhs: T) -> T {
            rhs
        }
    }

    impl super::Semigroup for Present {
        fn is_zero(&self) -> bool { false }
    }
}

pub use self::pair::DiffPair;
mod pair {

    use std::ops::{AddAssign, Neg, Mul};
    use super::{Semigroup, Monoid};

    /// The difference defined by a pair of difference elements.
    ///
    /// This type is essentially a "pair", though in Rust the tuple types do not derive the numeric
    /// traits we require, and so we need to emulate the types ourselves. In the interest of ergonomics,
    /// we may eventually replace the numeric traits with our own, so that we can implement them for
    /// tuples and allow users to ignore details like these.
    #[derive(Abomonation, Copy, Ord, PartialOrd, Eq, PartialEq, Debug, Clone, Serialize, Deserialize)]
    pub struct DiffPair<R1, R2> {
        /// The first element in the pair.
        pub element1: R1,
        /// The second element in the pair.
        pub element2: R2,
    }

    impl<R1, R2> DiffPair<R1, R2> {
        /// Creates a new Diff pair from two elements.
        #[inline] pub fn new(elt1: R1, elt2: R2) -> Self {
            DiffPair {
                element1: elt1,
                element2: elt2,
            }
        }
    }

    impl<R1: Semigroup, R2: Semigroup> Semigroup for DiffPair<R1, R2> {
        #[inline] fn is_zero(&self) -> bool {
            self.element1.is_zero() && self.element2.is_zero()
        }
    }

    impl<'a, R1: AddAssign<&'a R1>, R2: AddAssign<&'a R2>> AddAssign<&'a DiffPair<R1, R2>> for DiffPair<R1, R2> {
        #[inline] fn add_assign(&mut self, rhs: &'a Self) {
            self.element1 += &rhs.element1;
            self.element2 += &rhs.element2;
        }
    }

    impl<R1: Neg, R2: Neg> Neg for DiffPair<R1, R2> {
        type Output = DiffPair<<R1 as Neg>::Output, <R2 as Neg>::Output>;
        #[inline] fn neg(self) -> Self::Output {
            DiffPair {
                element1: -self.element1,
                element2: -self.element2,
            }
        }
    }

    impl<T: Copy, R1: Mul<T>, R2: Mul<T>> Mul<T> for DiffPair<R1,R2> {
        type Output = DiffPair<<R1 as Mul<T>>::Output, <R2 as Mul<T>>::Output>;
        fn mul(self, other: T) -> Self::Output {
            DiffPair::new(
                self.element1 * other,
                self.element2 * other,
            )
        }
    }

    impl<R1: Monoid, R2: Monoid> Monoid for DiffPair<R1, R2> {
        fn zero() -> Self {
            Self {
                element1: R1::zero(),
                element2: R2::zero(),
            }
        }
    }

    // // TODO: This currently causes rustc to trip a recursion limit, because who knows why.
    // impl<R1: Diff, R2: Diff> Mul<DiffPair<R1,R2>> for isize
    // where isize: Mul<R1>, isize: Mul<R2>, <isize as Mul<R1>>::Output: Diff, <isize as Mul<R2>>::Output: Diff {
    //     type Output = DiffPair<<isize as Mul<R1>>::Output, <isize as Mul<R2>>::Output>;
    //     fn mul(self, other: DiffPair<R1,R2>) -> Self::Output {
    //         DiffPair::new(
    //             self * other.element1,
    //             self * other.element2,
    //         )
    //     }
    // }
}

pub use self::vector::DiffVector;
mod vector {

    use std::ops::{AddAssign, Neg, Mul};
    use super::{Semigroup, Monoid};

    /// A variable number of accumulable updates.
    #[derive(Abomonation, Ord, PartialOrd, Eq, PartialEq, Debug, Clone, Serialize, Deserialize)]
    pub struct DiffVector<R> {
        buffer: Vec<R>,
    }

    impl<R> DiffVector<R> {
        /// Create new DiffVector from Vec
        #[inline(always)]
        pub fn new(vec: Vec<R>) -> DiffVector<R> {
            DiffVector { buffer: vec }
        }
    }

    impl<R> IntoIterator for DiffVector<R> {
        type Item = R;
        type IntoIter = ::std::vec::IntoIter<R>;
        fn into_iter(self) -> Self::IntoIter {
            self.buffer.into_iter()
        }
    }

    impl<R> std::ops::Deref for DiffVector<R> {
        type Target = [R];
        fn deref(&self) -> &Self::Target {
            &self.buffer[..]
        }
    }

    impl<R> std::ops::DerefMut for DiffVector<R> {
        fn deref_mut(&mut self) -> &mut Self::Target {
            &mut self.buffer[..]
        }
    }

    impl<R: Semigroup> Semigroup for DiffVector<R> {
        #[inline] fn is_zero(&self) -> bool {
            self.buffer.iter().all(|x| x.is_zero())
        }
    }

    impl<'a, R: AddAssign<&'a R>+Clone> AddAssign<&'a DiffVector<R>> for DiffVector<R> {
        #[inline]
        fn add_assign(&mut self, rhs: &'a Self) {

            // Ensure sufficient length to receive addition.
            while self.buffer.len() < rhs.buffer.len() {
                let element = &rhs.buffer[self.buffer.len()];
                self.buffer.push(element.clone());
            }

            // As other is not longer, apply updates without tests.
            for (index, update) in rhs.buffer.iter().enumerate() {
                self.buffer[index] += update;
            }
        }
    }

    impl<R: Neg<Output=R>+Clone> Neg for DiffVector<R> {
        type Output = DiffVector<<R as Neg>::Output>;
        #[inline]
        fn neg(mut self) -> Self::Output {
            for update in self.buffer.iter_mut() {
                *update = -update.clone();
            }
            self
        }
    }

    impl<T: Copy, R: Mul<T>> Mul<T> for DiffVector<R> {
        type Output = DiffVector<<R as Mul<T>>::Output>;
        fn mul(self, other: T) -> Self::Output {
            let buffer =
            self.buffer
                .into_iter()
                .map(|x| x * other)
                .collect();

            DiffVector { buffer }
        }
    }

    impl<R: Semigroup> Monoid for DiffVector<R> {
        fn zero() -> Self {
            Self { buffer: Vec::new() }
        }
    }
}