C++ (Cpp) acb_modular_theta_const_sum_basecase Examples

Example #1

File: t-theta_const_sum_rs.c Project: argriffing/arb

int main()
{
    slong iter;
    flint_rand_t state;

    flint_printf("theta_const_sum_rs....");
    fflush(stdout);

    flint_randinit(state);

    for (iter = 0; iter < 5000 * arb_test_multiplier(); iter++)
    {
        acb_t q, t2a, t2b, t3a, t3b, t4a, t4b;
        slong prec1, prec2, N;

        acb_init(q);
        acb_init(t2a);
        acb_init(t2b);
        acb_init(t3a);
        acb_init(t3b);
        acb_init(t4a);
        acb_init(t4b);

        prec1 = 2 + n_randint(state, 1000);
        prec2 = 2 + n_randint(state, 1000);
        N = n_randint(state, 300);

        acb_randtest(q, state, prec1, 3);

        acb_randtest(t2a, state, prec1, 3);
        acb_randtest(t2b, state, prec1, 3);
        acb_randtest(t3a, state, prec1, 3);
        acb_randtest(t3b, state, prec1, 3);
        acb_randtest(t4a, state, prec1, 3);
        acb_randtest(t4b, state, prec1, 3);

        acb_modular_theta_const_sum_basecase(t2a, t3a, t4a, q, N, prec1);
        acb_modular_theta_const_sum_rs(t2b, t3b, t4b, q, N, prec2);

        if (!acb_overlaps(t2a, t2b) || !acb_overlaps(t3a, t3b) || !acb_overlaps(t4a, t4b))
        {
            flint_printf("FAIL (overlap)  iter = %wd\n", iter);
            flint_printf("N = %wd\n", N);
            flint_printf("q = "); acb_printd(q, 50); flint_printf("\n\n");
            flint_printf("t2a = "); acb_printd(t2a, 50); flint_printf("\n\n");
            flint_printf("t2b = "); acb_printd(t2b, 50); flint_printf("\n\n");
            flint_printf("t3a = "); acb_printd(t3a, 50); flint_printf("\n\n");
            flint_printf("t3b = "); acb_printd(t3b, 50); flint_printf("\n\n");
            flint_printf("t4a = "); acb_printd(t4a, 50); flint_printf("\n\n");
            flint_printf("t4b = "); acb_printd(t4b, 50); flint_printf("\n\n");
            abort();
        }

        acb_clear(q);
        acb_clear(t2a);
        acb_clear(t2b);
        acb_clear(t3a);
        acb_clear(t3b);
        acb_clear(t4a);
        acb_clear(t4b);
    }

    flint_randclear(state);
    flint_cleanup();
    flint_printf("PASS\n");
    return EXIT_SUCCESS;
}

Example #2

File: theta_const_sum.c Project: jdemeyer/arb

void
acb_modular_theta_const_sum(acb_t theta2, acb_t theta3, acb_t theta4,
    const acb_t q, long prec)
{
    mag_t qmag, err;
    double log2q_approx;
    int is_real, is_real_or_imag;
    long N;

    mag_init(qmag);
    mag_init(err);

    acb_get_mag(qmag, q);
    log2q_approx = mag_get_log2_d_approx(qmag);

    is_real = arb_is_zero(acb_imagref(q));
    is_real_or_imag = is_real || arb_is_zero(acb_realref(q));

    if (log2q_approx >= 0.0)
    {
        N = 1;
        mag_inf(err);
    }
    else
    {
        N = 0;

        while (0.05 * N * N < prec)
        {
            if (log2q_approx * ((N+2)*(N+2)/4) < -prec - 2)
                break;
            N++;
        }
        N = (N+2)*(N+2)/4;

        mag_geom_series(err, qmag, N);
        mag_mul_2exp_si(err, err, 1); /* each term is taken twice */

        if (mag_is_inf(err))
            N = 1;
    }

    if (N < 1800)
        acb_modular_theta_const_sum_basecase(theta2, theta3, theta4, q, N, prec);
    else
        acb_modular_theta_const_sum_rs(theta2, theta3, theta4, q, N, prec);

    if (is_real_or_imag)
        arb_add_error_mag(acb_realref(theta2), err);
    else
        acb_add_error_mag(theta2, err);

    if (is_real)
    {
        arb_add_error_mag(acb_realref(theta3), err);
        arb_add_error_mag(acb_realref(theta4), err);
    }
    else
    {
        acb_add_error_mag(theta3, err);
        acb_add_error_mag(theta4, err);
    }

    mag_clear(qmag);
    mag_clear(err);
}