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check if moduli are pairwise coprime

This commit is contained in:
filifa 2025-08-18 21:43:45 -04:00
parent 5c560ecb1e
commit 455e8b1777
1 changed files with 32 additions and 8 deletions
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40
cmd/crt.go
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@ -27,12 +27,14 @@ import (
var remainders []string
var moduli []string
func solveTwo(a1, n1, a2, n2 *big.Int) (*big.Int, *big.Int) {
func crtSolve(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)
@ -51,28 +53,50 @@ func solveTwo(a1, n1, a2, n2 *big.Int) (*big.Int, *big.Int) {
return x, N
}
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
}
func crt(cmd *cobra.Command, args []string) {
if len(remainders) != len(moduli) {
log.Fatal("number of remainders and moduli do not match")
}
// TODO: check for pairwise comprime
n1 := new(big.Int)
a1 := new(big.Int)
for i := range remainders {
n2, ok := new(big.Int).SetString(moduli[i], 10)
ns := make([]*big.Int, len(moduli))
for i := range moduli {
n, ok := new(big.Int).SetString(moduli[i], 10)
if !ok {
log.Fatal("invalid input " + moduli[i])
}
ns[i] = new(big.Int).Set(n)
}
// TODO: support non-pairwise coprime moduli
if !arePairwiseCoprime(ns) {
log.Fatalf("moduli %v are not pairwise coprime", moduli)
}
n1 := new(big.Int)
a1 := new(big.Int)
for i, n2 := range ns {
a2, ok := new(big.Int).SetString(remainders[i], 10)
if !ok {
log.Fatal("invalid input " + remainders[i])
}
if i != 0 {
x, N := solveTwo(a1, n1, a2, n2)
x, N := crtSolve(a1, n1, a2, n2)
n1.Set(N)
a1.Set(x)
} else {