package common

// An element of our base ring R which are polynomials over Z_q modulo
// the equation Xᴺ = -1, where q=2²³ - 2¹³ + 1 and N=256.
//
// Coefficients aren't always reduced.  See Normalize().
type Poly [N]uint32

// Reduces each of the coefficients to <2q.
func (p *Poly) reduceLe2QGeneric() {
	for i := uint(0); i < N; i++ {
		p[i] = ReduceLe2Q(p[i])
	}
}

// Reduce each of the coefficients to <q.
func (p *Poly) normalizeGeneric() {
	for i := uint(0); i < N; i++ {
		p[i] = modQ(p[i])
	}
}

// Normalize the coefficients in this polynomial assuming they are already
// bounded by 2q.
func (p *Poly) normalizeAssumingLe2QGeneric() {
	for i := 0; i < N; i++ {
		p[i] = le2qModQ(p[i])
	}
}

// Sets p to a + b.  Does not normalize polynomials.
func (p *Poly) addGeneric(a, b *Poly) {
	for i := uint(0); i < N; i++ {
		p[i] = a[i] + b[i]
	}
}

// Sets p to a - b.
//
// Warning: assumes coefficients of b are less than 2q.
func (p *Poly) subGeneric(a, b *Poly) {
	for i := uint(0); i < N; i++ {
		p[i] = a[i] + (2*Q - b[i])
	}
}

// Checks whether the "supnorm" (see sec 2.1 of the spec) of p is equal
// or greater than the given bound.
//
// Requires the coefficients of p to be normalized.
func (p *Poly) exceedsGeneric(bound uint32) bool {
	// Note that we are allowed to leak which coefficients break the bound,
	// but not their sign.
	for i := 0; i < N; i++ {
		// The central. reps. of {0,       1, ..., (Q-1)/2,  (Q+1)/2, ..., Q-1}
		// are given by          {0,       1, ..., (Q-1)/2, -(Q-1)/2, ...,  -1}
		// so their norms are    {0,       1, ..., (Q-1)/2,  (Q-1)/2, ...,   1}.
		// We'll compute them in a different way though.

		// Sets x to             {(Q-1)/2, (Q-3)/2, ..., 0, -1, ..., -(Q-1)/2}
		x := int32((Q-1)/2) - int32(p[i])
		// Sets x to             {(Q-1)/2, (Q-3)/2, ..., 0, 0, ...,  (Q-3)/2}
		x ^= (x >> 31)
		// Sets x to             {0,       1, ...,  (Q-1)/2, (Q-1)/2, ..., 1}
		x = int32((Q-1)/2) - x
		if uint32(x) >= bound {
			return true
		}
	}
	return false
}

// Splits p into p1 and p0 such that [i]p1 * 2ᴰ + [i]p0 = [i]p
// with -2ᴰ⁻¹ < [i]p0 ≤ 2ᴰ⁻¹.  Returns p0 + Q and p1.
//
// Requires the coefficients of p to be normalized.
func (p *Poly) Power2Round(p0PlusQ, p1 *Poly) {
	for i := 0; i < N; i++ {
		p0PlusQ[i], p1[i] = power2round(p[i])
	}
}

// Sets p to the polynomial whose coefficients are the pointwise multiplication
// of those of a and b.  The coefficients of p are bounded by 2q.
//
// Assumes a and b are in Montgomery form and that the pointwise product
// of each coefficient is below 2³² q.
func (p *Poly) mulHatGeneric(a, b *Poly) {
	for i := 0; i < N; i++ {
		p[i] = montReduceLe2Q(uint64(a[i]) * uint64(b[i]))
	}
}

// Sets p to 2ᵈ q without reducing.
//
// So it requires the coefficients of p  to be less than 2³²⁻ᴰ.
func (p *Poly) mulBy2toDGeneric(q *Poly) {
	for i := 0; i < N; i++ {
		p[i] = q[i] << D
	}
}