Esempi in C++ (Cpp) per acb_dirichlet_zeta_rs

Esempio n. 1

/* todo: use euler product for complex s, and check efficiency
   for large negative integers */
void
acb_dirichlet_zeta(acb_t res, const acb_t s, slong prec)
{
    acb_t a;
    double cutoff;

    if (acb_is_int(s) &&
        arf_cmpabs_2exp_si(arb_midref(acb_realref(s)), FLINT_BITS - 1) < 0)
    {
        acb_zeta_si(res, arf_get_si(arb_midref(acb_realref(s)), ARF_RND_DOWN), prec);
        return;
    }

    cutoff = 24.0 * prec * sqrt(prec);

    if (arf_cmpabs_d(arb_midref(acb_imagref(s)), cutoff) >= 0 &&
        arf_cmpabs_d(arb_midref(acb_realref(s)), 10 + prec * 0.1) <= 0)
    {
        acb_dirichlet_zeta_rs(res, s, 0, prec);
        return;
    }

    acb_init(a);
    acb_one(a);

    if (arf_sgn(arb_midref(acb_realref(s))) < 0)
    {
        acb_t t, u, v;
        slong wp = prec + 6;

        acb_init(t);
        acb_init(u);
        acb_init(v);

        acb_sub_ui(t, s, 1, wp);

        /* 2 * (2pi)^(s-1) */
        arb_const_pi(acb_realref(u), wp);
        acb_mul_2exp_si(u, u, 1);
        acb_pow(u, u, t, wp);
        acb_mul_2exp_si(u, u, 1);

        /* sin(pi*s/2) */
        acb_mul_2exp_si(v, s, -1);
        acb_sin_pi(v, v, wp);
        acb_mul(u, u, v, wp);

        /* gamma(1-s) zeta(1-s) */
        acb_neg(t, t);
        acb_gamma(v, t, wp);
        acb_mul(u, u, v, wp);
        acb_hurwitz_zeta(v, t, a, wp);
        acb_mul(res, u, v, prec);

        acb_clear(t);
        acb_clear(u);
        acb_clear(v);
    }
    else
    {
        acb_hurwitz_zeta(res, s, a, prec);
    }

    acb_clear(a);
}

Esempio n. 2

File: zeta_rs.c Progetto: fredrik-johansson/arb

void
acb_dirichlet_zeta_rs_mid(acb_t res, const acb_t s, slong K, slong prec)
{
    acb_t R1, R2, X, t;
    slong wp;

    if (arf_sgn(arb_midref(acb_imagref(s))) < 0)
    {
        acb_init(t);
        acb_conj(t, s);
        acb_dirichlet_zeta_rs(res, t, K, prec);
        acb_conj(res, res);
        acb_clear(t);
        return;
    }

    acb_init(R1);
    acb_init(R2);
    acb_init(X);
    acb_init(t);

    /* rs_r increases the precision internally */
    wp = prec;

    acb_dirichlet_zeta_rs_r(R1, s, K, wp);

    if (arb_is_exact(acb_realref(s)) &&
        (arf_cmp_2exp_si(arb_midref(acb_realref(s)), -1) == 0))
    {
        acb_conj(R2, R1);
    }
    else
    {
        /* conj(R(conj(1-s))) */
        arb_sub_ui(acb_realref(t), acb_realref(s), 1, 10 * wp);
        arb_neg(acb_realref(t), acb_realref(t));
        arb_set(acb_imagref(t), acb_imagref(s));
        acb_dirichlet_zeta_rs_r(R2, t, K, wp);
        acb_conj(R2, R2);
    }

    if (acb_is_finite(R1) && acb_is_finite(R2))
    {
        wp += 10 + arf_abs_bound_lt_2exp_si(arb_midref(acb_imagref(s)));
        wp = FLINT_MAX(wp, 10);

        /* X = pi^(s-1/2) gamma((1-s)/2) rgamma(s/2)
             = (2 pi)^s rgamma(s) / (2 cos(pi s / 2)) */
        acb_rgamma(X, s, wp);
        acb_const_pi(t, wp);
        acb_mul_2exp_si(t, t, 1);
        acb_pow(t, t, s, wp);
        acb_mul(X, X, t, wp);
        acb_mul_2exp_si(t, s, -1);
        acb_cos_pi(t, t, wp);
        acb_mul_2exp_si(t, t, 1);
        acb_div(X, X, t, wp);

        acb_mul(R2, R2, X, wp);
    }

    /* R1 + X * R2 */
    acb_add(res, R1, R2, prec);

    acb_clear(R1);
    acb_clear(R2);
    acb_clear(X);
    acb_clear(t);
}