85 lines
1.9 KiB
Go
85 lines
1.9 KiB
Go
/*
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Copyright © 2025 filifa
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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package lib
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import (
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"math/big"
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)
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func solveCRT(a1, n1, a2, n2 *big.Int) (*big.Int, *big.Int) {
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// use Bezout's identity to find m1, m2 such that m1*n1 + m2*n2 = 1
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m1 := new(big.Int)
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m2 := new(big.Int)
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tmp := new(big.Int)
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tmp.GCD(m1, m2, n1, n2)
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// x = a1*m2*n2 + a2*m1*n1
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x := new(big.Int).Set(a1)
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x.Mul(x, m2)
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x.Mul(x, n2)
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tmp.Set(a2)
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tmp.Mul(tmp, m1)
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tmp.Mul(tmp, n1)
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x.Add(x, tmp)
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N := new(big.Int).Set(n1)
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N.Mul(N, n2)
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x.Mod(x, N)
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return x, N
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}
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/*
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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.
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*/
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func CRTSolution(remainders, moduli []*big.Int) (*big.Int, *big.Int) {
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n1 := new(big.Int)
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a1 := new(big.Int)
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for i, n2 := range moduli {
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a2 := remainders[i]
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if i == 0 {
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a1.Set(a2)
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n1.Set(n2)
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continue
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}
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a1, n1 = solveCRT(a1, n1, a2, n2)
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}
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return a1, n1
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}
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/*
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ArePairwiseCoprime returns true if each pair of values in the input slice are coprime.
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*/
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func ArePairwiseCoprime(moduli []*big.Int) bool {
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z := new(big.Int)
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for i, a := range moduli {
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for _, b := range moduli[i+1:] {
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z.GCD(nil, nil, a, b)
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if z.Cmp(big.NewInt(1)) != 0 {
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return false
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}
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}
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}
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return true
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}
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