/*
Copyright © 2025 filifa

This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
package lib

import (
	"math/big"
)

func solveCRT(a1, n1, a2, n2 *big.Int) (*big.Int, *big.Int) {
	// use Bezout's identity to find m1, m2 such that m1*n1 + m2*n2 = 1
	m1 := new(big.Int)
	m2 := new(big.Int)
	tmp := new(big.Int)
	tmp.GCD(m1, m2, n1, n2)

	// x = a1*m2*n2 + a2*m1*n1
	x := new(big.Int).Set(a1)
	x.Mul(x, m2)
	x.Mul(x, n2)

	tmp.Set(a2)
	tmp.Mul(tmp, m1)
	tmp.Mul(tmp, n1)

	x.Add(x, tmp)

	N := new(big.Int).Set(n1)
	N.Mul(N, n2)

	x.Mod(x, N)

	return x, N
}

/*
Given a system of congruences - defined by slices of remainders and moduli such that x = remainders[i] (mod moduli[i]) for each index i - CRTSolution outputs a solution to the system.
*/
func CRTSolution(remainders, moduli []*big.Int) (*big.Int, *big.Int) {
	n1 := new(big.Int)
	a1 := new(big.Int)
	for i, n2 := range moduli {
		a2 := remainders[i]
		if i == 0 {
			a1.Set(a2)
			n1.Set(n2)
			continue
		}

		a1, n1 = solveCRT(a1, n1, a2, n2)
	}

	return a1, n1
}

/*
ArePairwiseCoprime returns true if each pair of values in the input slice are coprime.
*/
func ArePairwiseCoprime(moduli []*big.Int) bool {
	z := new(big.Int)
	for i, a := range moduli {
		for _, b := range moduli[i+1:] {
			z.GCD(nil, nil, a, b)
			if z.Cmp(big.NewInt(1)) != 0 {
				return false
			}
		}
	}

	return true
}