use crate::modulus::{ScalarOperations, VectorOperations};
use crate::modulus::prime::Prime;
use crate::modulus::ReduceOnce;
use crate::modulus::montgomery::Montgomery;
use crate::modulus::barrett::Barrett;
use crate::modulus::REDUCEMOD;
use crate::{apply_v, apply_vv, apply_vvv, apply_sv, apply_svv, apply_vvsv, apply_vsv};
use itertools::izip;

impl ScalarOperations<u64> for Prime<u64>{

    /// Applies a modular reduction on x based on REDUCE:
    /// - LAZY: no modular reduction.
    /// - ONCE: subtracts q if x >= q.
    /// - TWO: subtracts 2q if x >= 2q.
    /// - FOUR: subtracts 4q if x >= 4q.
    /// - BARRETT: maps x to x mod q using Barrett reduction.
    /// - BARRETTLAZY: maps x to x mod q using Barrett reduction with values in [0, 2q-1].
    #[inline(always)]
    fn sa_reduce_into_sa<const REDUCE:REDUCEMOD>(&self, a: &mut u64){
        self.montgomery.reduce_assign::<REDUCE>(a);
    }

    #[inline(always)]
    fn sa_add_sb_into_sc<const REDUCE:REDUCEMOD>(&self, a: &u64, b: &u64, c: &mut u64){
        *c = a.wrapping_add(*b);
        self.sa_reduce_into_sa::<REDUCE>(c);
    }

    #[inline(always)]
    fn sa_add_sb_into_sb<const REDUCE:REDUCEMOD>(&self, a: &u64, b: &mut u64){
        *b = a.wrapping_add(*b);
        self.sa_reduce_into_sa::<REDUCE>(b);
    }

    #[inline(always)]
    fn sa_sub_sb_into_sc<const REDUCE:REDUCEMOD>(&self, a: &u64, b: &u64, c: &mut u64){
        *c = a.wrapping_add(self.q.wrapping_sub(*b)).reduce_once(self.q);
    }

    #[inline(always)]
    fn sa_sub_sb_into_sb<const REDUCE:REDUCEMOD>(&self, a: &u64, b: &mut u64){
        *b = a.wrapping_add(self.q.wrapping_sub(*b)).reduce_once(self.q);
    }

    #[inline(always)]
    fn sa_neg_into_sa<const REDUCE:REDUCEMOD>(&self, a: &mut u64){
        *a = self.q.wrapping_sub(*a);
        self.sa_reduce_into_sa::<REDUCE>(a)
    }

    #[inline(always)]
    fn sa_neg_into_sb<const REDUCE:REDUCEMOD>(&self, a: &u64, b: &mut u64){
        *b = self.q.wrapping_sub(*a);
        self.sa_reduce_into_sa::<REDUCE>(b)
    }

    #[inline(always)]
    fn sa_prep_mont_into_sb<const REDUCE:REDUCEMOD>(&self, a: &u64, b: &mut Montgomery<u64>){
        self.montgomery.prepare_assign::<REDUCE>(*a, b);
    }

    #[inline(always)]
    fn sa_mont_mul_sb_into_sc<const REDUCE:REDUCEMOD>(&self, a: &Montgomery<u64>, b:&u64, c: &mut u64){
        *c = self.montgomery.mul_external::<REDUCE>(*a, *b);
    }

    #[inline(always)]
    fn sa_mont_mul_sb_into_sb<const REDUCE:REDUCEMOD>(&self, a:&Montgomery<u64>, b:&mut u64){
        self.montgomery.mul_external_assign::<REDUCE>(*a, b);
    }

    #[inline(always)]
    fn sa_barrett_mul_sb_into_sc<const REDUCE:REDUCEMOD>(&self, a: &Barrett<u64>, b:&u64, c: &mut u64){
        *c = self.barrett.mul_external::<REDUCE>(*a, *b);
    }

    #[inline(always)]
    fn sa_barrett_mul_sb_into_sb<const REDUCE:REDUCEMOD>(&self, a:&Barrett<u64>, b:&mut u64){
        self.barrett.mul_external_assign::<REDUCE>(*a, b);
    }

    #[inline(always)]
    fn sa_sub_sb_mul_sc_into_sd<const REDUCE:REDUCEMOD>(&self, a: &u64, b: &u64, c: &Barrett<u64>, d: &mut u64){
        *d = self.two_q.wrapping_sub(*b).wrapping_add(*a);
        self.barrett.mul_external_assign::<REDUCE>(*c, d);
    }

    #[inline(always)]
    fn sa_sub_sb_mul_sc_into_sb<const REDUCE:REDUCEMOD>(&self, a: &u64, c: &Barrett<u64>, b: &mut u64){
        *b = self.two_q.wrapping_sub(*b).wrapping_add(*a);
        self.barrett.mul_external_assign::<REDUCE>(*c, b);
    }
}

impl VectorOperations<u64> for Prime<u64>{

    /// Applies a modular reduction on x based on REDUCE:
    /// - LAZY: no modular reduction.
    /// - ONCE: subtracts q if x >= q.
    /// - TWO: subtracts 2q if x >= 2q.
    /// - FOUR: subtracts 4q if x >= 4q.
    /// - BARRETT: maps x to x mod q using Barrett reduction.
    /// - BARRETTLAZY: maps x to x mod q using Barrett reduction with values in [0, 2q-1].
    #[inline(always)]
    fn va_reduce_into_va<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &mut [u64]){
        apply_v!(self, Self::sa_reduce_into_sa::<REDUCE>, a, CHUNK);
    }

    #[inline(always)]
    fn va_add_vb_into_vc<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[u64], b:&[u64], c:&mut [u64]){
        apply_vvv!(self, Self::sa_add_sb_into_sc::<REDUCE>, a, b, c, CHUNK);
    }

    #[inline(always)]
    fn va_add_vb_into_vb<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[u64], b:&mut [u64]){
        apply_vv!(self, Self::sa_add_sb_into_sb::<REDUCE>, a, b, CHUNK);
    }

    #[inline(always)]
    fn va_add_sb_into_vc<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[u64], b:&u64, c:&mut [u64]){
        apply_vsv!(self, Self::sa_add_sb_into_sc::<REDUCE>, a, b, c, CHUNK);
    }

    #[inline(always)]
    fn sa_add_vb_into_vb<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a:&u64, b:&mut [u64]){
        apply_sv!(self, Self::sa_add_sb_into_sb::<REDUCE>, a, b, CHUNK);
    }

    #[inline(always)]
    fn va_sub_vb_into_vc<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[u64], b:&[u64], c:&mut [u64]){
        apply_vvv!(self, Self::sa_sub_sb_into_sc::<REDUCE>, a, b, c, CHUNK);
    }
    
    #[inline(always)]
    fn va_sub_vb_into_vb<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[u64], b:&mut [u64]){
        apply_vv!(self, Self::sa_sub_sb_into_sb::<REDUCE>, a, b, CHUNK);
    }

    #[inline(always)]
    fn va_neg_into_va<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &mut [u64]){
        apply_v!(self, Self::sa_neg_into_sa::<REDUCE>, a, CHUNK);
    }

    #[inline(always)]
    fn va_neg_into_vb<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[u64], b: &mut [u64]){
        apply_vv!(self, Self::sa_neg_into_sb::<REDUCE>, a, b, CHUNK);
    }

    #[inline(always)]
    fn va_prep_mont_into_vb<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[u64], b: &mut [Montgomery<u64>]){
        apply_vv!(self, Self::sa_prep_mont_into_sb::<REDUCE>, a, b, CHUNK);
    }

    #[inline(always)]
    fn va_mont_mul_vb_into_vc<const CHUNK:usize,const REDUCE:REDUCEMOD>(&self, a:& [Montgomery<u64>], b:&[u64], c: &mut [u64]){
        apply_vvv!(self, Self::sa_mont_mul_sb_into_sc::<REDUCE>, a, b, c, CHUNK);
    }

    #[inline(always)]
    fn va_mont_mul_vb_into_vb<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a:& [Montgomery<u64>], b:&mut [u64]){
        apply_vv!(self, Self::sa_mont_mul_sb_into_sb::<REDUCE>, a, b, CHUNK);
    }

    #[inline(always)]
    fn sa_barrett_mul_vb_into_vc<const CHUNK:usize,const REDUCE:REDUCEMOD>(&self, a:& Barrett<u64>, b:&[u64], c: &mut [u64]){
        apply_svv!(self, Self::sa_barrett_mul_sb_into_sc::<REDUCE>, a, b, c, CHUNK);
    }

    #[inline(always)]
    fn sa_barrett_mul_vb_into_vb<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a:& Barrett<u64>, b:&mut [u64]){
        apply_sv!(self, Self::sa_barrett_mul_sb_into_sb::<REDUCE>, a, b, CHUNK);
    }

    fn va_sub_vb_mul_sc_into_vd<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[u64], b: &[u64], c: &Barrett<u64>, d: &mut [u64]){
        apply_vvsv!(self, Self::sa_sub_sb_mul_sc_into_sd::<REDUCE>, a, b, c, d, CHUNK);
    }

    fn va_sub_vb_mul_sc_into_vb<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[u64], b: &Barrett<u64>, c: &mut [u64]){
        apply_vsv!(self, Self::sa_sub_sb_mul_sc_into_sb::<REDUCE>, a, b, c, CHUNK);
    }
}