int
n_is_probabprime_fibonacci(mp_limb_t n)
{
mp_limb_t m;
n_pair_t V;
if (FLINT_ABS((mp_limb_signed_t) n) <= 3UL)
{
if (n >= 2UL)
return 1;
return 0;
}
m = (n - n_jacobi(5L, n)) / 2; /* cannot overflow
as (5/n) = 0 for n = 2^64-1 */
if (FLINT_BIT_COUNT(n) <= FLINT_D_BITS)
{
double npre = n_precompute_inverse(n);
V = fchain_precomp(m, n, npre);
return (n_mulmod_precomp(n - 3UL, V.x, n, npre) ==
n_mulmod_precomp(2UL, V.y, n, npre));
}
else
{
mp_limb_t ninv = n_preinvert_limb(n);
V = fchain2_preinv(m, n, ninv);
return (n_mulmod2_preinv(n - 3UL, V.x, n, ninv) ==
n_mulmod2_preinv(2UL, V.y, n, ninv));
}
}
int main(int argc, char *argv[])
{
ulong r, s, p, prec, s_prec;
ulong i, m, lambda, char1, char2;
fmpz_poly_t eis, eta, eta_r;
fmpz_t p1, c1, c2, ss1, ss, pp, ppl, pplc;
// input r, s, and the precision desired
if (argc == 4) {
r = atol(argv[1]);
s = atol(argv[2]);
prec = atol(argv[3]);
prec = n_nextprime(prec, 1) - 1;
}
if (argc != 4) {
printf("usage: shimura_coeffs r s n\n");
return EXIT_FAILURE;
}
// Compute the weight of the form f_r_s
lambda = r / 2 + s;
//printf("%d\n", lambda);
// This is the necessary precision of the input
s_prec = (prec + r) * prec * r / 24;
//printf("Necessary precision: %d terms\n", s_prec);
// First compute eta
//printf("Computing eta\n");
fmpz_poly_init(eta);
eta_series(&eta, s_prec);
// Next compute eta^r
//printf("Computing eta^%d\n", r);
fmpz_poly_init(eta_r);
fmpz_poly_pow_trunc(eta_r, eta, r, s_prec);
fmpz_poly_clear(eta);
// Next compute E_s
//printf("Computing E_%d\n", s);
fmpz_poly_init(eis);
if(s != 0) {
eis_series(&eis, s, s_prec);
}
//printf("Computing coefficients\n");
// Instead of computing the product, we will compute each coefficient as
// needed. This is potentially slower, but saves memory.
//
fmpz_init(p1);
fmpz_init(c1);
fmpz_init(c2);
fmpz_init(ss);
fmpz_init(ss1);
// compute alpha(p^2*r)
p = 2;
m = r*p*p;
while(p <= prec) {
fmpz_set_ui(ss1, 0);
if(s != 0) {
for(i = r; i <= m; i += 24) {
if((m - i) % 24 == 0) {
fmpz_poly_get_coeff_fmpz(c1, eta_r, (i - r) / 24);
fmpz_poly_get_coeff_fmpz(c2, eis, (m - i) / 24);
fmpz_addmul(ss1, c1, c2);
}
}
}
else {
if((m - r) % 24 == 0)
fmpz_poly_get_coeff_fmpz(ss1, eta_r, (m - r) / 24);
}
/*
if(p == 199) {
fmpz_print(ss1);
printf("\n");
}
*/
// compute character X12(p)
char1 = n_jacobi(12, p);
// compute character ((-1)^(lambda) * n | p)
if(lambda % 2 == 0) {
char2 = n_jacobi(r, p);
}
else {
char2 = n_jacobi(-r, p);
}
// compute p^(lambda - 1)
fmpz_set_ui(pp, p);
fmpz_pow_ui(ppl, pp, lambda - 1);
fmpz_mul_si(pplc, ppl, char1*char2);
fmpz_add(ss, ss1, pplc);
printf("%d:\t", p);
fmpz_print(ss);
printf("\n");
p = n_nextprime(p, 1);
m = r*p*p;
}
fmpz_clear(p1);
fmpz_clear(c1);
fmpz_clear(c2);
fmpz_clear(ss);
fmpz_clear(ss1);
return EXIT_SUCCESS;
}
