#![feature(i128_type)]

#![cfg_attr(test, feature(test))]
#[cfg(test)]
extern crate test;

extern crate rand;
extern crate byteorder;

#[cfg(test)]
pub mod tests;

pub mod bls12_381;

#[cfg(feature = "unstable-wnaf")]
pub mod wnaf;

use std::fmt;

/// An "engine" is a collection of types (fields, elliptic curve groups, etc.)
/// with well-defined relationships. In particular, the G1/G2 curve groups are
/// of prime order `r`, and are equipped with a bilinear pairing function.
pub trait Engine {
    /// This is the scalar field of the G1/G2 groups.
    type Fr: PrimeField;

    /// The projective representation of an element in G1.
    type G1: CurveProjective<Base=Self::Fq, Scalar=Self::Fr, Affine=Self::G1Affine> + From<Self::G1Affine>;

    /// The affine representation of an element in G1.
    type G1Affine: CurveAffine<Base=Self::Fq, Scalar=Self::Fr, Projective=Self::G1> + From<Self::G1>;

    /// The projective representation of an element in G2.
    type G2: CurveProjective<Base=Self::Fqe, Scalar=Self::Fr, Affine=Self::G2Affine> + From<Self::G2Affine>;

    /// The affine representation of an element in G2.
    type G2Affine: CurveAffine<Base=Self::Fqe, Scalar=Self::Fr, Projective=Self::G2> + From<Self::G2>;

    /// The base field that hosts G1.
    type Fq: PrimeField + SqrtField;

    /// The extension field that hosts G2.
    type Fqe: SqrtField;

    /// The extension field that hosts the target group of the pairing.
    type Fqk: Field;

    /// Perform a miller loop with some number of (G1, G2) pairs.
    fn miller_loop<'a, I>(i: I) -> Self::Fqk
        where I: IntoIterator<Item=&'a (
                                    &'a <Self::G1Affine as CurveAffine>::Prepared,
                                    &'a <Self::G2Affine as CurveAffine>::Prepared
                               )>;

    /// Perform final exponentiation of the result of a miller loop.
    fn final_exponentiation(&Self::Fqk) -> Option<Self::Fqk>;

    /// Performs a complete pairing operation `(p, q)`.
    fn pairing<G1, G2>(p: G1, q: G2) -> Self::Fqk
        where G1: Into<Self::G1Affine>,
              G2: Into<Self::G2Affine>
    {
        Self::final_exponentiation(&Self::miller_loop(
            [(
                &(p.into().prepare()),
                &(q.into().prepare())
            )].into_iter()
        )).unwrap()
    }
}

/// Projective representation of an elliptic curve point guaranteed to be
/// in the correct prime order subgroup.
pub trait CurveProjective: PartialEq +
                           Eq +
                           Sized +
                           Copy +
                           Clone +
                           Send +
                           Sync +
                           fmt::Debug +
                           rand::Rand +
                           'static
{
    type Scalar: PrimeField;
    type Base: SqrtField;
    type Affine: CurveAffine<Projective=Self, Scalar=Self::Scalar>;

    /// Returns the additive identity.
    fn zero() -> Self;

    /// Returns a fixed generator of unknown exponent.
    fn one() -> Self;

    /// Determines if this point is the point at infinity.
    fn is_zero(&self) -> bool;

    /// Normalizes a slice of projective elements so that
    /// conversion to affine is cheap.
    fn batch_normalization(v: &mut [Self]);

    /// Checks if the point is already "normalized" so that
    /// cheap affine conversion is possible.
    fn is_normalized(&self) -> bool;

    /// Doubles this element.
    fn double(&mut self);

    /// Adds another element to this element.
    fn add_assign(&mut self, other: &Self);

    /// Subtracts another element from this element.
    fn sub_assign(&mut self, other: &Self) {
        let mut tmp = *other;
        tmp.negate();
        self.add_assign(&tmp);
    }

    /// Adds an affine element to this element.
    fn add_assign_mixed(&mut self, other: &Self::Affine);

    /// Negates this element.
    fn negate(&mut self);

    /// Performs scalar multiplication of this element.
    fn mul_assign<S: Into<<Self::Scalar as PrimeField>::Repr>>(&mut self, other: S);

    /// Converts this element into its affine representation.
    fn into_affine(&self) -> Self::Affine;

    /// Recommends a wNAF window table size given a scalar. Returns `None` if normal
    /// scalar multiplication is encouraged. If `Some` is returned, it will be between
    /// 2 and 22, inclusive.
    fn recommended_wnaf_for_scalar(scalar: <Self::Scalar as PrimeField>::Repr) -> Option<usize>;

    /// Recommends a wNAF window size given the number of scalars you intend to multiply
    /// a base by. Always returns a number between 2 and 22, inclusive.
    fn recommended_wnaf_for_num_scalars(num_scalars: usize) -> usize;
}

/// Affine representation of an elliptic curve point guaranteed to be
/// in the correct prime order subgroup.
pub trait CurveAffine: Copy +
                       Clone +
                       Sized +
                       Send +
                       Sync +
                       fmt::Debug +
                       PartialEq +
                       Eq +
                       'static
{
    type Scalar: PrimeField;
    type Base: SqrtField;
    type Projective: CurveProjective<Affine=Self, Scalar=Self::Scalar>;
    type Prepared: Clone + Send + Sync + 'static;
    type Uncompressed: EncodedPoint<Affine=Self>;
    type Compressed: EncodedPoint<Affine=Self>;

    /// Returns the additive identity.
    fn zero() -> Self;

    /// Returns a fixed generator of unknown exponent.
    fn one() -> Self;

    /// Determines if this point represents the point at infinity; the
    /// additive identity.
    fn is_zero(&self) -> bool;

    /// Determines if this point is on the curve and in the correct subgroup.
    fn is_valid(&self) -> bool;

    /// Negates this element.
    fn negate(&mut self);

    /// Performs scalar multiplication of this element with mixed addition.
    fn mul<S: Into<<Self::Scalar as PrimeField>::Repr>>(&self, other: S) -> Self::Projective;

    /// Prepares this element for pairing purposes.
    fn prepare(&self) -> Self::Prepared;

    /// Converts this element into its affine representation.
    fn into_projective(&self) -> Self::Projective;

    /// Converts this element into its compressed encoding, so long as it's not
    /// the point at infinity.
    fn into_compressed(&self) -> Result<Self::Compressed, ()> {
        <Self::Compressed as EncodedPoint>::from_affine(*self)
    }

    /// Converts this element into its uncompressed encoding, so long as it's not
    /// the point at infinity.
    fn into_uncompressed(&self) -> Result<Self::Uncompressed, ()> {
        <Self::Uncompressed as EncodedPoint>::from_affine(*self)
    }
}

/// An encoded elliptic curve point, which should essentially wrap a `[u8; N]`.
pub trait EncodedPoint: Sized +
                        Send +
                        Sync +
                        AsRef<[u8]> +
                        AsMut<[u8]> +
                        'static
{
    type Affine: CurveAffine;

    /// Creates an empty representation.
    fn empty() -> Self;

    /// Returns the number of bytes consumed by this representation.
    fn size() -> usize;

    /// Converts an `EncodedPoint` into a `CurveAffine` element,
    /// if the point is valid.
    fn into_affine(&self) -> Result<Self::Affine, ()> {
        let affine = self.into_affine_unchecked()?;

        if affine.is_valid() {
            Ok(affine)
        } else {
            Err(())
        }
    }

    /// Converts an `EncodedPoint` into a `CurveAffine` element,
    /// without checking if it's a valid point. Caller must be careful
    /// when using this, as misuse can violate API invariants.
    fn into_affine_unchecked(&self) -> Result<Self::Affine, ()>;

    /// Creates an `EncodedPoint` from an affine point, as long as the
    /// point is not the point at infinity.
    fn from_affine(affine: Self::Affine) -> Result<Self, ()>;
}

/// This trait represents an element of a field.
pub trait Field: Sized +
                 Eq +
                 Copy +
                 Clone +
                 Send +
                 Sync +
                 fmt::Debug +
                 'static +
                 rand::Rand
{
    /// Returns the zero element of the field, the additive identity.
    fn zero() -> Self;

    /// Returns the one element of the field, the multiplicative identity.
    fn one() -> Self;

    /// Returns true iff this element is zero.
    fn is_zero(&self) -> bool;

    /// Squares this element.
    fn square(&mut self);

    /// Doubles this element.
    fn double(&mut self);

    /// Negates this element.
    fn negate(&mut self);

    /// Adds another element to this element.
    fn add_assign(&mut self, other: &Self);

    /// Subtracts another element from this element.
    fn sub_assign(&mut self, other: &Self);

    /// Multiplies another element by this element.
    fn mul_assign(&mut self, other: &Self);

    /// Computes the multiplicative inverse of this element, if nonzero.
    fn inverse(&self) -> Option<Self>;

    /// Exponentiates this element by a power of the base prime modulus via
    /// the Frobenius automorphism.
    fn frobenius_map(&mut self, power: usize);

    /// Exponentiates this element by a number represented with `u64` limbs,
    /// least significant digit first.
    fn pow<S: AsRef<[u64]>>(&self, exp: S) -> Self
    {
        let mut res = Self::one();

        let mut found_one = false;

        for i in BitIterator::new(exp) {
            if found_one {
                res.square();
            } else {
                found_one = i;
            }

            if i {
                res.mul_assign(self);
            }
        }

        res
    }
}

/// This trait represents an element of a field that has a square root operation described for it.
pub trait SqrtField: Field
{
    /// Returns the square root of the field element, if it is
    /// quadratic residue.
    fn sqrt(&self) -> Option<Self>;
}

/// This trait represents a wrapper around a biginteger which can encode any element of a particular
/// prime field. It is a smart wrapper around a sequence of `u64` limbs, least-significant digit
/// first.
pub trait PrimeFieldRepr: Sized +
                          Copy +
                          Clone +
                          Eq +
                          Ord +
                          Send +
                          Sync +
                          fmt::Debug +
                          'static +
                          rand::Rand +
                          AsRef<[u64]> +
                          From<u64>
{
    /// Subtract another reprensetation from this one, returning the borrow bit.
    fn sub_noborrow(&mut self, other: &Self) -> bool;

    /// Add another representation to this one, returning the carry bit.
    fn add_nocarry(&mut self, other: &Self) -> bool;

    /// Compute the number of bits needed to encode this number.
    fn num_bits(&self) -> u32;

    /// Returns true iff this number is zero.
    fn is_zero(&self) -> bool;

    /// Returns true iff this number is odd.
    fn is_odd(&self) -> bool;

    /// Returns true iff this number is even.
    fn is_even(&self) -> bool;

    /// Performs a rightwise bitshift of this number, effectively dividing
    /// it by 2.
    fn div2(&mut self);

    /// Performs a rightwise bitshift of this number by some amount.
    fn divn(&mut self, amt: usize);

    /// Performs a leftwise bitshift of this number, effectively multiplying
    /// it by 2. Overflow is ignored.
    fn mul2(&mut self);
}

/// This represents an element of a prime field.
pub trait PrimeField: Field
{
    /// The prime field can be converted back and forth into this biginteger
    /// representation.
    type Repr: PrimeFieldRepr + From<Self>;

    /// Convert this prime field element into a biginteger representation.
    fn from_repr(Self::Repr) -> Result<Self, ()>;

    /// Convert a biginteger reprensentation into a prime field element, if
    /// the number is an element of the field.
    fn into_repr(&self) -> Self::Repr;

    /// Returns the field characteristic; the modulus.
    fn char() -> Self::Repr;

    /// Returns how many bits are needed to represent an element of this
    /// field.
    fn num_bits() -> u32;

    /// Returns how many bits of information can be reliably stored in the
    /// field element.
    fn capacity() -> u32;

    /// Returns the multiplicative generator of `char()` - 1 order. This element
    /// must also be quadratic nonresidue.
    fn multiplicative_generator() -> Self;

    /// Returns s such that 2^s * t = `char()` - 1 with t odd.
    fn s() -> usize;

    /// Returns the 2^s root of unity computed by exponentiating the `multiplicative_generator()`
    /// by t.
    fn root_of_unity() -> Self;
}

pub struct BitIterator<E> {
    t: E,
    n: usize
}

impl<E: AsRef<[u64]>> BitIterator<E> {
    pub fn new(t: E) -> Self {
        let n = t.as_ref().len() * 64;

        BitIterator {
            t: t,
            n: n
        }
    }
}

impl<E: AsRef<[u64]>> Iterator for BitIterator<E> {
    type Item = bool;

    fn next(&mut self) -> Option<bool> {
        if self.n == 0 {
            None
        } else {
            self.n -= 1;
            let part = self.n / 64;
            let bit = self.n - (64 * part);

            Some(self.t.as_ref()[part] & (1 << bit) > 0)
        }
    }
}

#[test]
fn test_bit_iterator() {
    let mut a = BitIterator::new([0xa953d79b83f6ab59, 0x6dea2059e200bd39]);
    let expected = "01101101111010100010000001011001111000100000000010111101001110011010100101010011110101111001101110000011111101101010101101011001";

    for e in expected.chars() {
        assert!(a.next().unwrap() == (e == '1'));
    }

    assert!(a.next().is_none());

    let expected = "1010010101111110101010000101101011101000011101110101001000011001100100100011011010001011011011010001011011101100110100111011010010110001000011110100110001100110011101101000101100011100100100100100001010011101010111110011101011000011101000111011011101011001";

    let mut a = BitIterator::new([0x429d5f3ac3a3b759, 0xb10f4c66768b1c92, 0x92368b6d16ecd3b4, 0xa57ea85ae8775219]);

    for e in expected.chars() {
        assert!(a.next().unwrap() == (e == '1'));
    }

    assert!(a.next().is_none());
}

/// Calculate a - b - borrow, returning the result and modifying
/// the borrow value.
#[inline(always)]
pub(crate) fn sbb(a: u64, b: u64, borrow: &mut u64) -> u64 {
    let tmp = (1u128 << 64) + (a as u128) - (b as u128) - (*borrow as u128);

    *borrow = if tmp >> 64 == 0 { 1 } else { 0 };

    tmp as u64
}

/// Calculate a + b + carry, returning the sum and modifying the
/// carry value.
#[inline(always)]
pub(crate) fn adc(a: u64, b: u64, carry: &mut u64) -> u64 {
    let tmp = (a as u128) + (b as u128) + (*carry as u128);

    *carry = (tmp >> 64) as u64;

    tmp as u64
}

/// Calculate a + (b * c) + carry, returning the least significant digit
/// and setting carry to the most significant digit.
#[inline(always)]
pub(crate) fn mac_with_carry(a: u64, b: u64, c: u64, carry: &mut u64) -> u64 {
    let tmp = (a as u128) + (b as u128) * (c as u128) + (*carry as u128);

    *carry = (tmp >> 64) as u64;

    tmp as u64
}