/* assume m is invertible */
void
dirichlet_char_log(dirichlet_char_t x, const dirichlet_group_t G, ulong m)
{
slong k;
/* even part */
if (G->neven >= 1)
{
x->log[0] = (m % 4 == 3);
if (G->neven == 2)
{
ulong m2 = (x->log[0]) ? -m % G->q_even : m % G->q_even;
if (G->P[1].dlog == NULL)
x->log[1] = dlog_mod2e_1mod4(m2, G->P[1].e,
nmod_inv(5, G->P[1].pe), G->P[1].pe);
else
x->log[1] = dlog_precomp(G->P[1].dlog, m2);
}
}
/* odd part */
for (k = G->neven; k < G->num; k++)
{
dirichlet_prime_group_struct P = G->P[k];
if (P.dlog == NULL)
{
x->log[k] = dlog_once(m % P.pe.n, P.g, P.pe, P.phi.n);
}
else
{
x->log[k] = dlog_precomp(P.dlog, m % P.pe.n);
}
}
/* keep value m */
x->n = m;
}
ulong
dlog_once(ulong b, ulong a, const nmod_t mod, ulong n)
{
if (b == 1)
return 0;
if (n < 50)
{
slong k;
ulong ak = 1;
for (k = 0; k < n; k++)
{
if (ak == b)
return k;
ak = nmod_mul(ak, a, mod);
}
flint_printf("FAIL[dlog once]: log(%wu,%wu) mod %wu not found (size %wu)\n",
b, a, mod.n, n);
flint_abort();
return 0; /* dummy return because flint_abort() is not declared noreturn */
}
else
{
ulong l;
dlog_precomp_t pre;
dlog_precomp_n_init(pre, a, mod.n, n, 1);
l = dlog_precomp(pre, b);
dlog_precomp_clear(pre);
return l;
}
}
void
dlog_vec_trivial(ulong *v, ulong nv, ulong a, ulong va, const nmod_t mod, ulong na, const nmod_t order)
{
ulong k;
dlog_precomp_t pre;
dlog_precomp_n_init(pre, a, mod.n, na, 50);
for (k = 1; k < nv; k++)
if (n_gcd(k, mod.n) > 1)
v[k] = DLOG_NOT_FOUND;
else
v[k] = dlog_precomp(pre, k % mod.n);
dlog_precomp_clear(pre);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("dlog....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000; iter++)
{
dlog_table_t table;
dlog_bsgs_t bsgs;
dlog_crt_t crt;
dlog_precomp_t pre1, pre100;
ulong p, a, k;
nmod_t modp;
if (iter < 10)
p = n_nth_prime(iter + 2);
else
p = n_randprime(state, 15, 0);
nmod_init(&modp, p);
a = n_primitive_root_prime(p);
dlog_table_init(table, a, p);
dlog_bsgs_init(bsgs, a, p, p-1, dlog_bsgs_size(p, 1));
dlog_crt_init(crt, a, p, p-1, 10);
dlog_precomp_n_init(pre1, a, p, p-1, 1);
dlog_precomp_n_init(pre100, a, p, p-1, 100);
for (k = 1; k < 100 && k < p; k++)
{
ulong l0, l1, l2, l3, l4, l5;
l1 = dlog_table(table, k);
l2 = dlog_bsgs(bsgs, k);
l3 = dlog_crt(crt, k);
l4 = dlog_precomp(pre1, k);
l5 = dlog_precomp(pre100, k);
if (iter < 50 && k <= 7)
l0 = dlog_once(k, a, modp, p-1);
else
l0 = l1;
if (l0 != l1 || l1 != l2 || l1 != l3 || l1 != l4 || l1 != l5)
{
flint_printf("\n\nFAIL: log(%wu,%wu) mod %wu\n\n",k,a,p);
flint_printf("once: %wu\ntable: %wu\nbsgs: %wu\ncrt: %wu\nprecomp1: %wu\nprecomp100: %wu\n\n",
l0, l1, l2, l3, l4, l5);
abort();
}
}
dlog_table_clear(table);
dlog_bsgs_clear(bsgs);
dlog_crt_clear(crt);
dlog_precomp_clear(pre1);
dlog_precomp_clear(pre100);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
