package bn256

import (
	"math/big"
)

// useLattice switch if we use lattice and GLV to accelerate computing.
// In product version, it could be a const.
// const useLattice = true
var useLattice = true

var half = new(big.Int).Rsh(N, 1)

var curveLattice = &lattice{
	vectors: [][]*big.Int{
		{bigFromBase10("287113247090025866066532163502283840641"), bigFromBase10("13835058055293825813")},
		{bigFromBase10("13835058055293825813"), bigFromBase10("-287113247090025866052697105446990014828")},
	},
	inverse: []*big.Int{
		bigFromBase10("287113247090025866052697105446990014828"),
		bigFromBase10("13835058055293825813"),
	},
	det: bigFromBase16("B640000002A3A6F1D603AB4FF58EC74449F2934B18EA8BEEE56EE19CD69ECF25"),
}

var targetLattice = &lattice{
	vectors: [][]*big.Int{
		{bigFromBase10("6917529027646912907"), bigFromBase10("6917529027646912906"), bigFromBase10("6917529027646912906"), bigFromBase10("-13835058055293825812")},
		{bigFromBase10("13835058055293825813"), bigFromBase10("-6917529027646912906"), bigFromBase10("-6917529027646912907"), bigFromBase10("-6917529027646912906")},
		{bigFromBase10("13835058055293825812"), bigFromBase10("13835058055293825813"), bigFromBase10("13835058055293825813"), bigFromBase10("13835058055293825813")},
		{bigFromBase10("6917529027646912905"), bigFromBase10("27670116110587651626"), bigFromBase10("-13835058055293825811"), bigFromBase10("6917529027646912905")},
	},

	inverse: []*big.Int{
		bigFromBase10("95704415696675288700373269546839468391"),
		bigFromBase10("3972228441934428951444310461776851119314861197558173512586"),
		bigFromBase10("1986114220967214475722155230888425559660889363292910212746"),
		bigFromBase10("-95704415696675288686538211491545642578"),
	},

	det: new(big.Int).Set(N),
}

type lattice struct {
	vectors [][]*big.Int
	inverse []*big.Int
	det     *big.Int
}

// decompose takes a scalar mod Order as input and finds a short, positive decomposition of it wrt to the lattice basis.
// output: out[0] + lambda*out[1] = 0 mod n
// [lambda](x,y) = (eta*x, y), eta^3 = 1
// TODO out[0] and out[1] should > 0 or ?
func (l *lattice) decompose(k *big.Int) []*big.Int {
	n := len(l.inverse)

	// Calculate closest vector in lattice to <k,0,0,...> with Babai's rounding.
	c := make([]*big.Int, n)
	for i := 0; i < n; i++ {
		c[i] = new(big.Int).Mul(k, l.inverse[i])
		round(c[i], l.det)
	}

	// Transform vectors according to c and subtract <k,0,0,...>.
	out := make([]*big.Int, n)
	temp := new(big.Int)

	for i := 0; i < n; i++ {
		out[i] = new(big.Int)

		for j := 0; j < n; j++ {
			temp.Mul(c[j], l.vectors[j][i])
			out[i].Add(out[i], temp)
		}

		out[i].Neg(out[i])

		//TODO why add
		out[i].Add(out[i], l.vectors[0][i]).Add(out[i], l.vectors[0][i])
	}
	out[0].Add(out[0], k)

	return out
}

func (l *lattice) Precompute(add func(i, j uint)) {
	n := uint(len(l.vectors))
	total := uint(1) << uint(n)

	for i := uint(0); i < n; i++ {
		for j := uint(0); j < total; j++ {
			if (j>>i)&1 == 1 {
				add(i, j)
			}
		}
	}
}

func (l *lattice) Multi(scalar *big.Int) []uint8 {
	decomp := l.decompose(scalar)

	maxLen := 0
	for _, x := range decomp {
		if x.BitLen() > maxLen {
			maxLen = x.BitLen()
		}
	}

	out := make([]uint8, maxLen)
	for j, x := range decomp {
		for i := 0; i < maxLen; i++ {
			//out[i] += uint8(x.Bit(i)) << uint(j)
			out[i] += uint8(x.Abs(x).Bit(i)) << uint(j)
		}
	}

	return out
}

// round sets num to num/denom rounded to the nearest integer.
func round(num, denom *big.Int) {
	r := new(big.Int)
	num.DivMod(num, denom, r)

	if r.Cmp(half) == 1 {
		num.Add(num, big.NewInt(1))
	}
}