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//! Definition of linear combinations.

use curve25519_dalek::scalar::Scalar;
use std::iter::FromIterator;
use std::ops::{Add, Mul, Neg, Sub};

/// Represents a variable in a constraint system.
#[derive(Copy, Clone, Debug)]
pub enum Variable {
/// Represents an external input specified by a commitment.
Committed(usize),
/// Represents the left input of a multiplication gate.
MultiplierLeft(usize),
/// Represents the right input of a multiplication gate.
MultiplierRight(usize),
/// Represents the output of a multiplication gate.
MultiplierOutput(usize),
/// Represents the constant 1.
One(),
}

impl From<Variable> for LinearCombination {
fn from(v: Variable) -> LinearCombination {
LinearCombination {
terms: vec![(v, Scalar::one())],
}
}
}

impl<S: Into<Scalar>> From<S> for LinearCombination {
fn from(s: S) -> LinearCombination {
LinearCombination {
terms: vec![(Variable::One(), s.into())],
}
}
}

// Arithmetic on variables produces linear combinations

impl Neg for Variable {
type Output = LinearCombination;

fn neg(self) -> Self::Output {
-LinearCombination::from(self)
}
}

impl<L: Into<LinearCombination>> Add<L> for Variable {
type Output = LinearCombination;

fn add(self, other: L) -> Self::Output {
LinearCombination::from(self) + other.into()
}
}

impl<L: Into<LinearCombination>> Sub<L> for Variable {
type Output = LinearCombination;

fn sub(self, other: L) -> Self::Output {
LinearCombination::from(self) - other.into()
}
}

impl<S: Into<Scalar>> Mul<S> for Variable {
type Output = LinearCombination;

fn mul(self, other: S) -> Self::Output {
LinearCombination {
terms: vec![(self, other.into())],
}
}
}

// Arithmetic on scalars with variables produces linear combinations

impl Add<Variable> for Scalar {
type Output = LinearCombination;

fn add(self, other: Variable) -> Self::Output {
LinearCombination {
terms: vec![(Variable::One(), self), (other, Scalar::one())],
}
}
}

impl Sub<Variable> for Scalar {
type Output = LinearCombination;

fn sub(self, other: Variable) -> Self::Output {
LinearCombination {
terms: vec![(Variable::One(), self), (other, -Scalar::one())],
}
}
}

impl Mul<Variable> for Scalar {
type Output = LinearCombination;

fn mul(self, other: Variable) -> Self::Output {
LinearCombination {
terms: vec![(other, self)],
}
}
}

/// Represents a linear combination of
/// [Variables](::r1cs::Variable).  Each term is represented by a
/// (Variable, Scalar) pair.
#[derive(Clone, Debug)]
pub struct LinearCombination {
pub(super) terms: Vec<(Variable, Scalar)>,
}

impl Default for LinearCombination {
fn default() -> Self {
LinearCombination { terms: Vec::new() }
}
}

impl FromIterator<(Variable, Scalar)> for LinearCombination {
fn from_iter<T>(iter: T) -> Self
where
T: IntoIterator<Item = (Variable, Scalar)>,
{
LinearCombination {
terms: iter.into_iter().collect(),
}
}
}

impl<'a> FromIterator<&'a (Variable, Scalar)> for LinearCombination {
fn from_iter<T>(iter: T) -> Self
where
T: IntoIterator<Item = &'a (Variable, Scalar)>,
{
LinearCombination {
terms: iter.into_iter().cloned().collect(),
}
}
}

// Arithmetic on linear combinations

impl<L: Into<LinearCombination>> Add<L> for LinearCombination {
type Output = Self;

fn add(mut self, rhs: L) -> Self::Output {
self.terms.extend(rhs.into().terms.iter().cloned());
LinearCombination { terms: self.terms }
}
}

impl<L: Into<LinearCombination>> Sub<L> for LinearCombination {
type Output = Self;

fn sub(mut self, rhs: L) -> Self::Output {
self.terms
.extend(rhs.into().terms.iter().map(|(var, coeff)| (*var, -coeff)));
LinearCombination { terms: self.terms }
}
}

impl Mul<LinearCombination> for Scalar {
type Output = LinearCombination;

fn mul(self, other: LinearCombination) -> Self::Output {
let out_terms = other
.terms
.into_iter()
.map(|(var, scalar)| (var, scalar * self))
.collect();
LinearCombination { terms: out_terms }
}
}

impl Neg for LinearCombination {
type Output = Self;

fn neg(mut self) -> Self::Output {
for (_, s) in self.terms.iter_mut() {
*s = -*s
}
self
}
}

impl<S: Into<Scalar>> Mul<S> for LinearCombination {
type Output = Self;

fn mul(mut self, other: S) -> Self::Output {
let other = other.into();
for (_, s) in self.terms.iter_mut() {
*s *= other
}
self
}
}