int
f_1x2(arb_t max, const arb_t t, params_t * p, slong prec)
{
arb_mul(max, t, t, prec);
arb_add_si(max, max, 1, prec);
arb_inv(max, max, prec);
return 1;
}
void arb_from_interval(arb_t x, const fmpz_t c, const slong k, const slong prec)
{
/* we build the ball that gives exactly (c 2^k, (c+1) 2^k) */
/* center: (2c+1) 2^(k-1) */
/* radius: 2^(k-1) */
if (prec <= 0 || prec < fmpz_bits(c) + 2)
{
fprintf(stderr, "not enough precision");
abort();
}
arb_set_fmpz(x, c);
arb_mul_2exp_si(x, x, 1);
arb_add_si(x, x, 1, prec);
arb_mul_2exp_si(x, x, k-1);
arb_add_error_2exp_si(x, k-1);
}
slong renf_set_embeddings_fmpz_poly(renf * nf, fmpz_poly_t pol, slong lim, slong prec)
{
slong i, n, n_exact, n_interval;
fmpq_poly_t p2;
arb_t a;
fmpz * c;
slong * k;
n = fmpz_poly_num_real_roots_upper_bound(pol);
c = _fmpz_vec_init(n);
k = (slong *) flint_malloc(n * sizeof(slong));
fmpz_poly_isolate_real_roots(NULL, &n_exact, c, k, &n_interval, pol);
if (n_exact)
{
fprintf(stderr, "ERROR (fmpz_poly_real_embeddings): rational roots\n");
abort();
}
arb_init(a);
fmpq_poly_init(p2);
fmpz_one(fmpq_poly_denref(p2));
fmpq_poly_fit_length(p2, pol->length);
_fmpz_vec_set(p2->coeffs, pol->coeffs, pol->length);
p2->length = pol->length;
for (i = 0; i < FLINT_MIN(lim, n_interval); i++)
{
arb_set_fmpz(a, c + i);
arb_mul_2exp_si(a, a, 1);
arb_add_si(a, a, 1, prec);
mag_one(arb_radref(a));
arb_mul_2exp_si(a, a, k[i] - 1);
renf_init(nf + i, p2, a, prec);
}
arb_clear(a);
fmpq_poly_clear(p2);
_fmpz_vec_clear(c, n);
flint_free(k);
return n_interval;
}
void
arb_poly_add_si(arb_poly_t res, const arb_poly_t x, long y, long prec)
{
long len = x->length;
if (len == 0)
{
arb_poly_set_si(res, y);
}
else
{
arb_poly_fit_length(res, len);
arb_add_si(res->coeffs, x->coeffs, y, prec);
if (res != x)
_arb_vec_set(res->coeffs + 1, x->coeffs + 1, len - 1);
_arb_poly_set_length(res, len);
_arb_poly_normalise(res);
}
}
void arb_fib_fmpz(arb_t f, const fmpz_t n, slong prec)
{
arb_t t, u;
slong wp, sign, i;
if (fmpz_sgn(n) < 0)
{
fmpz_t m;
fmpz_init(m);
fmpz_neg(m, n);
arb_fib_fmpz(f, m, prec);
if (fmpz_is_even(m))
arb_neg(f, f);
fmpz_clear(m);
return;
}
if (fmpz_cmp_ui(n, 4) <= 0)
{
ulong x = fmpz_get_ui(n);
arb_set_ui(f, x - (x > 1));
return;
}
wp = ARF_PREC_ADD(prec, 3 * fmpz_bits(n));
arb_init(u);
arb_init(t);
arb_set_ui(f, UWORD(1));
arb_set_ui(u, UWORD(1));
sign = -1;
for (i = fmpz_flog_ui(n, UWORD(2)) - 1; i > 0; i--)
{
arb_mul(t, f, f, wp);
arb_add(f, f, u, wp);
arb_mul_2exp_si(f, f, -1);
arb_mul(f, f, f, wp);
arb_mul_2exp_si(f, f, 1);
arb_submul_ui(f, t, 3, wp);
arb_sub_si(f, f, 2 * sign, wp);
arb_mul_ui(u, t, 5, wp);
arb_add_si(u, u, 2 * sign, wp);
sign = 1;
if (fmpz_tstbit(n, i))
{
arb_set(t, f);
arb_add(f, f, u, wp);
arb_mul_2exp_si(f, f, -1);
arb_mul_2exp_si(t, t, 1);
arb_add(u, f, t, wp);
sign = -1;
}
}
if (fmpz_tstbit(n, 0))
{
arb_add(f, f, u, wp);
arb_mul_2exp_si(f, f, -1);
arb_mul(f, f, u, wp);
arb_sub_si(f, f, sign, prec);
}
else
{
arb_mul(f, f, u, prec);
}
arb_clear(u);
arb_clear(t);
}
