mp_limb_t n_primitive_root_prime(mp_limb_t p)
{
mp_limb_t a;
n_factor_t factors;
n_factor_init(&factors);
n_factor(&factors, p - 1, 1);
a = n_primitive_root_prime_prefactor(p, &factors);
return a;
}
void
acb_dirichlet_group_init(acb_dirichlet_group_t G, ulong q)
{
slong k;
n_factor_t fac;
G->q = q;
G->q_odd = q;
G->q_even = 1;
while (G->q_odd % 2 == 0)
{
G->q_odd /= 2;
G->q_even *= 2;
}
n_factor_init(&fac);
n_factor(&fac, G->q_odd, 1);
G->num = fac.num;
G->primes = flint_malloc(G->num * sizeof(ulong));
G->exponents = flint_malloc(G->num * sizeof(ulong));
G->generators = flint_malloc(G->num * sizeof(ulong));
G->PHI = flint_malloc(G->num * sizeof(ulong));
for (k = 0; k < G->num; k++)
{
G->primes[k] = fac.p[k];
G->exponents[k] = fac.exp[k];
}
G->phi_q_odd = 1;
for (k = 0; k < G->num; k++)
G->phi_q_odd *= (G->primes[k] - 1) * n_pow(G->primes[k], G->exponents[k]-1);
if (G->q_even == 1)
G->phi_q = G->phi_q_odd;
else
G->phi_q = G->phi_q_odd * (G->q_even / 2);
for (k = 0; k < G->num; k++)
{
ulong phi;
G->generators[k] = primitive_root_p_and_p2(G->primes[k]);
phi = n_pow(G->primes[k], G->exponents[k] - 1) * (G->primes[k] - 1);
G->PHI[k] = G->phi_q_odd / phi;
}
}
ulong
dlog_crt_init(dlog_crt_t t, ulong a, ulong mod, ulong n, ulong num)
{
int k;
n_factor_t fac;
ulong * M, * u;
ulong cost = 0;
n_factor_init(&fac);
n_factor(&fac, n, 1);
t->num = fac.num;
nmod_init(&t->mod,mod);
nmod_init(&t->n, n);
M = t->expo = flint_malloc(t->num * sizeof(ulong));
u = t->crt_coeffs = flint_malloc(t->num * sizeof(ulong));
t->pre = flint_malloc(t->num * sizeof(dlog_precomp_struct));
for (k = 0; k < t->num; k++)
{
ulong p, e, mk;
p = fac.p[k];
e = fac.exp[k];
if (0 && mod % p == 0)
{
flint_printf("dlog_crt_init: modulus must be prime to order.\n");
abort();
}
mk = n_pow(p, e);
M[k] = n / mk;
u[k] = nmod_mul(M[k], n_invmod(M[k] % mk, mk), t->n);
/* depends on the power */
#if 0
flint_printf("[sub-crt -- init for size %wu mod %wu]\n", mk, mod);
#endif
dlog_precomp_pe_init(t->pre + k, nmod_pow_ui(a, M[k], t->mod), mod, p, e, mk, num);
cost += t->pre[k].cost;
}
#if 0
if (cost > 500)
flint_printf("[crt init for size %wu mod %wu -> cost %wu]\n", n,mod,cost);
#endif
return cost;
}
void
dirichlet_group_init(dirichlet_group_t G, ulong q)
{
slong k;
ulong e2;
n_factor_t fac;
G->q = q;
nmod_init(&G->mod, q);
e2 = n_remove(&q, 2);
G->q_even = 1 << e2;
/* number of components at p=2 */
G->neven = (e2 >= 3) ? 2 : (e2 == 2) ? 1 : 0;
/* warning: only factor odd part */
n_factor_init(&fac);
n_factor(&fac, q, 1);
G->num = fac.num + G->neven;
G->P = flint_malloc(G->num * sizeof(dirichlet_prime_group_struct));
G->generators = flint_malloc(G->num * sizeof(ulong));
G->PHI = flint_malloc(G->num * sizeof(ulong));
/* even part */
if (G->neven >= 1)
dirichlet_prime_group_init(&G->P[0], 2, e2);
if (G->neven == 2)
dirichlet_prime_group_init(&G->P[1], 4, e2);
/* odd part */
G->rad_q = 1;
for (k = G->neven; k < G->num; k++)
{
ulong p, e;
p = fac.p[k - G->neven];
e = fac.exp[k - G->neven];
G->rad_q *= p;
dirichlet_prime_group_init(&G->P[k], p, e);
}
dirichlet_group_lift_generators(G);
}
slong Util::compute_multiplicative_order(ulong a, ulong modulus) {
n_factor_t factors;
n_factor_init(&factors);
ulong order = modulus - 1;
n_factor(&factors, order, 1);
slong temp = 1;
for (slong i = 0; i < factors.num; i++) {
while (temp == 1 && factors.exp[i] > 0) {
order /= factors.p[i];
factors.exp[i]--;
temp = n_powmod(a, order, modulus);
}
if (temp != 1) {
order *= factors.p[i];
temp = 1;
}
}
return order;
}
