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compute totient with trial division

This commit is contained in:
filifa 2025-08-20 23:53:22 -04:00
parent a948056382
commit 37f40b25b4
1 changed files with 25 additions and 6 deletions
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31
cmd/primitiveRoot.go
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@ -29,15 +29,34 @@ var modulus string
var tpf []string var tpf []string
func totient(n *big.Int) *big.Int { func totient(n *big.Int) *big.Int {
total := big.NewInt(0) N := new(big.Int).Set(n)
for a := big.NewInt(1); a.Cmp(n) == -1; a.Add(a, big.NewInt(1)) {
gcd := new(big.Int).GCD(nil, nil, a, n) phi := new(big.Int).Set(N)
if gcd.Cmp(big.NewInt(1)) == 0 {
total.Add(total, big.NewInt(1)) sqrtn := new(big.Int).Sqrt(N)
for i := big.NewInt(2); i.Cmp(sqrtn) != 1; i.Add(i, big.NewInt(1)) {
mod := new(big.Int).Mod(N, i)
if mod.Cmp(big.NewInt(0)) != 0 {
continue
}
// phi -= phi // i
tmp := new(big.Int).Div(phi, i)
phi.Sub(phi, tmp)
for mod.Cmp(big.NewInt(0)) == 0 {
N.Div(N, i)
mod.Mod(N, i)
} }
} }
return total if N.Cmp(big.NewInt(1)) == 1 {
// phi -= phi // N
tmp := new(big.Int).Div(phi, N)
phi.Sub(phi, tmp)
}
return phi
} }
func multiplicativeOrder(g *big.Int, modulus *big.Int) *big.Int { func multiplicativeOrder(g *big.Int, modulus *big.Int) *big.Int {