Пример #1
0
int main()
{
    slong iter;
    flint_rand_t state;

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

    flint_randinit(state);

    for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
    {
        acb_t s, t, u;
        dirichlet_group_t G;
        dirichlet_char_t chi;
        ulong q, k;
        slong prec;

        acb_init(s);
        acb_init(t);
        acb_init(u);

        q = 1 + n_randint(state, 50);
        prec = 2 + n_randint(state, 100);
        k = n_randint(state, n_euler_phi(q));

        dirichlet_group_init(G, q);
        dirichlet_char_init(chi, G);
        dirichlet_char_index(chi, G, k);

        if (n_randint(state, 2))
            acb_set_si(s, n_randint(state, 50) - 25);
        else
            acb_randtest(s, state, 2 + n_randint(state, 200), 2);

        acb_dirichlet_l_hurwitz(t, s, NULL, G, chi, prec);
        acb_dirichlet_l(u, s, G, chi, prec);

        if (!acb_overlaps(t, u))
        {
            flint_printf("FAIL: overlap\n\n");
            flint_printf("iter = %ld  q = %lu  k = %lu  prec = %ld\n\n", iter, q, k, prec);
            flint_printf("s = "); acb_printn(s, 100, 0); flint_printf("\n\n");
            flint_printf("t = "); acb_printn(t, 100, 0); flint_printf("\n\n");
            flint_printf("u = "); acb_printn(u, 100, 0); flint_printf("\n\n");
            abort();
        }

        dirichlet_char_clear(chi);
        dirichlet_group_clear(G);
        acb_clear(s);
        acb_clear(t);
        acb_clear(u);
    }

    flint_randclear(state);
    flint_cleanup();
    flint_printf("PASS\n");
    return EXIT_SUCCESS;
}
Пример #2
0
void
acb_poly_set_coeff_si(acb_poly_t poly, slong n, slong x)
{
    acb_poly_fit_length(poly, n + 1);

    if (n + 1 > poly->length)
    {
        _acb_vec_zero(poly->coeffs + poly->length, n - poly->length);
        poly->length = n + 1;
    }

    acb_set_si(poly->coeffs + n, x);
    _acb_poly_normalise(poly);
}
Пример #3
0
Файл: erf.c Проект: isuruf/arb
void
acb_hypgeom_erf_asymp(acb_t res, const acb_t z, slong prec, slong prec2)
{
    acb_t a, t, u;

    acb_init(a);
    acb_init(t);
    acb_init(u);

    acb_one(a);
    acb_mul_2exp_si(a, a, -1);
    acb_mul(t, z, z, prec2);

    acb_hypgeom_u_asymp(u, a, a, t, -1, prec2);

    acb_neg(t, t);
    acb_exp(t, t, prec2);
    acb_mul(u, u, t, prec2);

    acb_const_pi(t, prec2);
    acb_sqrt(t, t, prec2);
    acb_mul(t, t, z, prec2);

    acb_div(u, u, t, prec2);

    /* branch cut term: -1 or 1 */
    if (arb_contains_zero(acb_realref(z)))
    {
        arb_zero(acb_imagref(t));
        arf_zero(arb_midref(acb_realref(t)));
        mag_one(arb_radref(acb_realref(t)));
    }
    else
    {
        acb_set_si(t, arf_sgn(arb_midref(acb_realref(z))));
    }

    acb_sub(t, t, u, prec);

    if (arb_is_zero(acb_imagref(z)))
        arb_zero(acb_imagref(t));
    else if (arb_is_zero(acb_realref(z)))
        arb_zero(acb_realref(t));

    acb_set(res, t);

    acb_clear(a);
    acb_clear(t);
    acb_clear(u);
}
Пример #4
0
void
acb_unit_root(acb_t res, ulong order, slong prec)
{
    switch (order)
    {
    case 1:
        acb_one(res);
        break;
    case 2:
        acb_set_si(res, -1);
        break;
    case 4:
        acb_onei(res);
        break;
    default:
        _acb_unit_root(res, order, prec);
        break;
    }
}
Пример #5
0
static void
phase(acb_t res, const arb_t re, const arb_t im)
{
    if (arb_is_nonnegative(re) || arb_is_negative(im))
    {
        acb_one(res);
    }
    else if (arb_is_negative(re) && arb_is_nonnegative(im))
    {
        acb_set_si(res, -3);
    }
    else
    {
        arb_zero(acb_imagref(res));
        /* -1 +/- 2 */
        arf_set_si(arb_midref(acb_realref(res)), -1);
        mag_one(arb_radref(acb_realref(res)));
        mag_mul_2exp_si(arb_radref(acb_realref(res)), arb_radref(acb_realref(res)), 1);
    }
}
Пример #6
0
int main(int argc, char *argv[])
{
    acb_t s, t, a, b;
    mag_t tol;
    slong prec, goal;
    slong N;
    ulong k;
    int integral, ifrom, ito;
    int i, twice, havegoal, havetol;
    acb_calc_integrate_opt_t options;

    ifrom = ito = -1;

    for (i = 1; i < argc; i++)
    {
        if (!strcmp(argv[i], "-i"))
        {
            if (!strcmp(argv[i+1], "all"))
            {
                ifrom = 0;
                ito = NUM_INTEGRALS - 1;
            }
            else
            {
                ifrom = ito = atol(argv[i+1]);
                if (ito < 0 || ito >= NUM_INTEGRALS)
                    flint_abort();
            }
        }
    }

    if (ifrom == -1)
    {
        flint_printf("Compute integrals using acb_calc_integrate.\n");
        flint_printf("Usage: integrals -i n [-prec p] [-tol eps] [-twice] [...]\n\n");
        flint_printf("-i n       - compute integral n (0 <= n <= %d), or \"-i all\"\n", NUM_INTEGRALS - 1);
        flint_printf("-prec p    - precision in bits (default p = 64)\n");
        flint_printf("-goal p    - approximate relative accuracy goal (default p)\n");
        flint_printf("-tol eps   - approximate absolute error goal (default 2^-p)\n");
        flint_printf("-twice     - run twice (to see overhead of computing nodes)\n");
        flint_printf("-heap      - use heap for subinterval queue\n");
        flint_printf("-verbose   - show information\n");
        flint_printf("-verbose2  - show more information\n");
        flint_printf("-deg n     - use quadrature degree up to n\n");
        flint_printf("-eval n    - limit number of function evaluations to n\n");
        flint_printf("-depth n   - limit subinterval queue size to n\n\n");
        flint_printf("Implemented integrals:\n");
        for (integral = 0; integral < NUM_INTEGRALS; integral++)
            flint_printf("I%d = %s\n", integral, descr[integral]);
        flint_printf("\n");
        return 1;
    }

    acb_calc_integrate_opt_init(options);

    prec = 64;
    twice = 0;
    goal = 0;
    havetol = havegoal = 0;

    acb_init(a);
    acb_init(b);
    acb_init(s);
    acb_init(t);
    mag_init(tol);

    for (i = 1; i < argc; i++)
    {
        if (!strcmp(argv[i], "-prec"))
        {
            prec = atol(argv[i+1]);
        }
        else if (!strcmp(argv[i], "-twice"))
        {
            twice = 1;
        }
        else if (!strcmp(argv[i], "-goal"))
        {
            goal = atol(argv[i+1]);
            if (goal < 0)
            {
                flint_printf("expected goal >= 0\n");
                return 1;
            }
            havegoal = 1;
        }
        else if (!strcmp(argv[i], "-tol"))
        {
            arb_t x;
            arb_init(x);
            arb_set_str(x, argv[i+1], 10);
            arb_get_mag(tol, x);
            arb_clear(x);
            havetol = 1;
        }
        else if (!strcmp(argv[i], "-deg"))
        {
            options->deg_limit = atol(argv[i+1]);
        }
        else if (!strcmp(argv[i], "-eval"))
        {
            options->eval_limit = atol(argv[i+1]);
        }
        else if (!strcmp(argv[i], "-depth"))
        {
            options->depth_limit = atol(argv[i+1]);
        }
        else if (!strcmp(argv[i], "-verbose"))
        {
            options->verbose = 1;
        }
        else if (!strcmp(argv[i], "-verbose2"))
        {
            options->verbose = 2;
        }
        else if (!strcmp(argv[i], "-heap"))
        {
            options->use_heap = 1;
        }
    }

    if (!havegoal)
        goal = prec;

    if (!havetol)
        mag_set_ui_2exp_si(tol, 1, -prec);

    for (integral = ifrom; integral <= ito; integral++)
    {
        flint_printf("I%d = %s ...\n", integral, descr[integral]);

        for (i = 0; i < 1 + twice; i++)
        {
            TIMEIT_ONCE_START
            switch (integral)
            {
            case 0:
                acb_set_d(a, 0);
                acb_set_d(b, 100);
                acb_calc_integrate(s, f_sin, NULL, a, b, goal, tol, options, prec);
                break;

            case 1:
                acb_set_d(a, 0);
                acb_set_d(b, 1);
                acb_calc_integrate(s, f_atanderiv, NULL, a, b, goal, tol, options, prec);
                acb_mul_2exp_si(s, s, 2);
                break;

            case 2:
                acb_set_d(a, 0);
                acb_one(b);
                acb_mul_2exp_si(b, b, goal);
                acb_calc_integrate(s, f_atanderiv, NULL, a, b, goal, tol, options, prec);
                arb_add_error_2exp_si(acb_realref(s), -goal);
                acb_mul_2exp_si(s, s, 1);
                break;

            case 3:
                acb_set_d(a, 0);
                acb_set_d(b, 1);
                acb_calc_integrate(s, f_circle, NULL, a, b, goal, tol, options, prec);
                acb_mul_2exp_si(s, s, 2);
                break;

            case 4:
                acb_set_d(a, 0);
                acb_set_d(b, 8);
                acb_calc_integrate(s, f_rump, NULL, a, b, goal, tol, options, prec);
                break;

            case 5:
                acb_set_d(a, 1);
                acb_set_d(b, 101);
                acb_calc_integrate(s, f_floor, NULL, a, b, goal, tol, options, prec);
                break;

            case 6:
                acb_set_d(a, 0);
                acb_set_d(b, 1);
                acb_calc_integrate(s, f_helfgott, NULL, a, b, goal, tol, options, prec);
                break;

            case 7:
                acb_zero(s);

                acb_set_d_d(a, -1.0, -1.0);
                acb_set_d_d(b, 2.0, -1.0);
                acb_calc_integrate(t, f_zeta, NULL, a, b, goal, tol, options, prec);
                acb_add(s, s, t, prec);

                acb_set_d_d(a, 2.0, -1.0);
                acb_set_d_d(b, 2.0, 1.0);
                acb_calc_integrate(t, f_zeta, NULL, a, b, goal, tol, options, prec);
                acb_add(s, s, t, prec);

                acb_set_d_d(a, 2.0, 1.0);
                acb_set_d_d(b, -1.0, 1.0);
                acb_calc_integrate(t, f_zeta, NULL, a, b, goal, tol, options, prec);
                acb_add(s, s, t, prec);

                acb_set_d_d(a, -1.0, 1.0);
                acb_set_d_d(b, -1.0, -1.0);
                acb_calc_integrate(t, f_zeta, NULL, a, b, goal, tol, options, prec);
                acb_add(s, s, t, prec);

                acb_const_pi(t, prec);
                acb_div(s, s, t, prec);
                acb_mul_2exp_si(s, s, -1);
                acb_div_onei(s, s);
                break;

            case 8:
                acb_set_d(a, 0);
                acb_set_d(b, 1);
                acb_calc_integrate(s, f_essing, NULL, a, b, goal, tol, options, prec);
                break;

            case 9:
                acb_set_d(a, 0);
                acb_set_d(b, 1);
                acb_calc_integrate(s, f_essing2, NULL, a, b, goal, tol, options, prec);
                break;

            case 10:
                acb_set_d(a, 0);
                acb_set_d(b, 10000);
                acb_calc_integrate(s, f_factorial1000, NULL, a, b, goal, tol, options, prec);
                break;

            case 11:
                acb_set_d_d(a, 1.0, 0.0);
                acb_set_d_d(b, 1.0, 1000.0);
                acb_calc_integrate(s, f_gamma, NULL, a, b, goal, tol, options, prec);
                break;

            case 12:
                acb_set_d(a, -10.0);
                acb_set_d(b, 10.0);
                acb_calc_integrate(s, f_sin_plus_small, NULL, a, b, goal, tol, options, prec);
                break;

            case 13:
                acb_set_d(a, -1020.0);
                acb_set_d(b, -1010.0);
                acb_calc_integrate(s, f_exp, NULL, a, b, goal, tol, options, prec);
                break;

            case 14:
                acb_set_d(a, 0);
                acb_set_d(b, ceil(sqrt(goal * 0.693147181) + 1.0));
                acb_calc_integrate(s, f_gaussian, NULL, a, b, goal, tol, options, prec);
                acb_mul(b, b, b, prec);
                acb_neg(b, b);
                acb_exp(b, b, prec);
                arb_add_error(acb_realref(s), acb_realref(b));
                break;

            case 15:
                acb_set_d(a, 0.0);
                acb_set_d(b, 1.0);
                acb_calc_integrate(s, f_spike, NULL, a, b, goal, tol, options, prec);
                break;

            case 16:
                acb_set_d(a, 0.0);
                acb_set_d(b, 8.0);
                acb_calc_integrate(s, f_monster, NULL, a, b, goal, tol, options, prec);
                break;

            case 17:
                acb_set_d(a, 0);
                acb_set_d(b, ceil(goal * 0.693147181 + 1.0));
                acb_calc_integrate(s, f_sech, NULL, a, b, goal, tol, options, prec);
                acb_neg(b, b);
                acb_exp(b, b, prec);
                acb_mul_2exp_si(b, b, 1);
                arb_add_error(acb_realref(s), acb_realref(b));
                break;

            case 18:
                acb_set_d(a, 0);
                acb_set_d(b, ceil(goal * 0.693147181 / 3.0 + 2.0));
                acb_calc_integrate(s, f_sech3, NULL, a, b, goal, tol, options, prec);
                acb_neg(b, b);
                acb_mul_ui(b, b, 3, prec);
                acb_exp(b, b, prec);
                acb_mul_2exp_si(b, b, 3);
                acb_div_ui(b, b, 3, prec);
                arb_add_error(acb_realref(s), acb_realref(b));
                break;

            case 19:
                if (goal < 0)
                    abort();
                /* error bound 2^-N (1+N) when truncated at 2^-N */
                N = goal + FLINT_BIT_COUNT(goal);
                acb_one(a);
                acb_mul_2exp_si(a, a, -N);
                acb_one(b);
                acb_calc_integrate(s, f_log_div1p, NULL, a, b, goal, tol, options, prec);
                acb_set_ui(b, N + 1);
                acb_mul_2exp_si(b, b, -N);
                arb_add_error(acb_realref(s), acb_realref(b));
                break;

           case 20:
                if (goal < 0)
                    abort();
                /* error bound (N+1) exp(-N) when truncated at N */
                N = goal + FLINT_BIT_COUNT(goal);
                acb_zero(a);
                acb_set_ui(b, N);
                acb_calc_integrate(s, f_log_div1p_transformed, NULL, a, b, goal, tol, options, prec);
                acb_neg(b, b);
                acb_exp(b, b, prec);
                acb_mul_ui(b, b, N + 1, prec);
                arb_add_error(acb_realref(s), acb_realref(b));
                break;

            case 21:

                acb_zero(s);

                N = 10;

                acb_set_d_d(a, 0.5, -0.5);
                acb_set_d_d(b, 0.5, 0.5);
                acb_calc_integrate(t, f_elliptic_p_laurent_n, &N, a, b, goal, tol, options, prec);
                acb_add(s, s, t, prec);

                acb_set_d_d(a, 0.5, 0.5);
                acb_set_d_d(b, -0.5, 0.5);
                acb_calc_integrate(t, f_elliptic_p_laurent_n, &N, a, b, goal, tol, options, prec);
                acb_add(s, s, t, prec);

                acb_set_d_d(a, -0.5, 0.5);
                acb_set_d_d(b, -0.5, -0.5);
                acb_calc_integrate(t, f_elliptic_p_laurent_n, &N, a, b, goal, tol, options, prec);
                acb_add(s, s, t, prec);

                acb_set_d_d(a, -0.5, -0.5);
                acb_set_d_d(b, 0.5, -0.5);
                acb_calc_integrate(t, f_elliptic_p_laurent_n, &N, a, b, goal, tol, options, prec);
                acb_add(s, s, t, prec);

                acb_const_pi(t, prec);
                acb_div(s, s, t, prec);
                acb_mul_2exp_si(s, s, -1);
                acb_div_onei(s, s);
                break;

            case 22:

                acb_zero(s);

                N = 1000;

                acb_set_d_d(a, 100.0, 0.0);
                acb_set_d_d(b, 100.0, N);
                acb_calc_integrate(t, f_zeta_frac, NULL, a, b, goal, tol, options, prec);
                acb_add(s, s, t, prec);

                acb_set_d_d(a, 100, N);
                acb_set_d_d(b, 0.5, N);
                acb_calc_integrate(t, f_zeta_frac, NULL, a, b, goal, tol, options, prec);
                acb_add(s, s, t, prec);

                acb_div_onei(s, s);
                arb_zero(acb_imagref(s));

                acb_set_ui(t, N);
                acb_dirichlet_hardy_theta(t, t, NULL, NULL, 1, prec);
                acb_add(s, s, t, prec);

                acb_const_pi(t, prec);
                acb_div(s, s, t, prec);
                acb_add_ui(s, s, 1, prec);
                break;

            case 23:
                acb_set_d(a, 0.0);
                acb_set_d(b, 1000.0);
                acb_calc_integrate(s, f_lambertw, NULL, a, b, goal, tol, options, prec);
                break;

            case 24:
                acb_set_d(a, 0.0);
                acb_const_pi(b, prec);
                acb_calc_integrate(s, f_max_sin_cos, NULL, a, b, goal, tol, options, prec);
                break;

            case 25:
                acb_set_si(a, -1);
                acb_set_si(b, 1);
                acb_calc_integrate(s, f_erf_bent, NULL, a, b, goal, tol, options, prec);
                break;

            case 26:
                acb_set_si(a, -10);
                acb_set_si(b, 10);
                acb_calc_integrate(s, f_airy_ai, NULL, a, b, goal, tol, options, prec);
                break;

            case 27:
                acb_set_si(a, 0);
                acb_set_si(b, 10);
                acb_calc_integrate(s, f_horror, NULL, a, b, goal, tol, options, prec);
                break;

            case 28:
                acb_set_d_d(a, -1, -1);
                acb_set_d_d(b, -1, 1);
                acb_calc_integrate(s, f_sqrt, NULL, a, b, goal, tol, options, prec);
                break;

            case 29:
                acb_set_d(a, 0);
                acb_set_d(b, ceil(sqrt(goal * 0.693147181) + 1.0));
                acb_calc_integrate(s, f_gaussian_twist, NULL, a, b, goal, tol, options, prec);
                acb_mul(b, b, b, prec);
                acb_neg(b, b);
                acb_exp(b, b, prec);
                arb_add_error(acb_realref(s), acb_realref(b));
                arb_add_error(acb_imagref(s), acb_realref(b));
                break;

            case 30:
                acb_set_d(a, 0);
                acb_set_d(b, ceil(goal * 0.693147181 + 1.0));
                acb_calc_integrate(s, f_exp_airy, NULL, a, b, goal, tol, options, prec);
                acb_neg(b, b);
                acb_exp(b, b, prec);
                acb_mul_2exp_si(b, b, 1);
                arb_add_error(acb_realref(s), acb_realref(b));
                break;

            case 31:
                acb_zero(a);
                acb_const_pi(b, prec);
                acb_calc_integrate(s, f_sin_cos_frac, NULL, a, b, goal, tol, options, prec);
                break;

            case 32:
                acb_zero(a);
                acb_set_ui(b, 3);
                acb_calc_integrate(s, f_sin_near_essing, NULL, a, b, goal, tol, options, prec);
                break;

            case 33:
                acb_zero(a);
                acb_zero(b);
                k = 3;
                scaled_bessel_select_N(acb_realref(b), k, prec);
                acb_calc_integrate(s, f_scaled_bessel, &k, a, b, goal, tol, options, prec);
                scaled_bessel_tail_bound(acb_realref(a), k, acb_realref(b), prec);
                arb_add_error(acb_realref(s), acb_realref(a));
                break;

            case 34:
                acb_zero(a);
                acb_zero(b);
                k = 15;
                scaled_bessel_select_N(acb_realref(b), k, prec);
                acb_calc_integrate(s, f_scaled_bessel, &k, a, b, goal, tol, options, prec);
                scaled_bessel_tail_bound(acb_realref(a), k, acb_realref(b), prec);
                arb_add_error(acb_realref(s), acb_realref(a));
                break;

            case 35:
                acb_set_d_d(a, -1, -1);
                acb_set_d_d(b, -1, 1);
                acb_calc_integrate(s, f_rsqrt, NULL, a, b, goal, tol, options, prec);
                break;

            default:
                abort();
            }

            TIMEIT_ONCE_STOP
        }
        flint_printf("I%d = ", integral);
        acb_printn(s, 3.333 * prec, 0);
        flint_printf("\n\n");
    }

    acb_clear(a);
    acb_clear(b);
    acb_clear(s);
    acb_clear(t);
    mag_clear(tol);

    flint_cleanup();
    return 0;
}
Пример #7
0
void
_acb_poly_rgamma_series(acb_ptr res, acb_srcptr h, slong hlen, slong len, slong prec)
{
    int reflect;
    slong i, rflen, r, n, wp;
    acb_ptr t, u, v;
    acb_struct f[2];

    hlen = FLINT_MIN(hlen, len);

    if (hlen == 1)
    {
        acb_rgamma(res, h, prec);
        _acb_vec_zero(res + 1, len - 1);
        return;
    }

    /* use real code for real input */
    if (_acb_vec_is_real(h, hlen))
    {
        arb_ptr tmp = _arb_vec_init(len);
        for (i = 0; i < hlen; i++)
            arb_set(tmp + i, acb_realref(h + i));
        _arb_poly_rgamma_series(tmp, tmp, hlen, len, prec);
        for (i = 0; i < len; i++)
            acb_set_arb(res + i, tmp + i);
        _arb_vec_clear(tmp, len);
        return;
    }

    wp = prec + FLINT_BIT_COUNT(prec);

    t = _acb_vec_init(len);
    u = _acb_vec_init(len);
    v = _acb_vec_init(len);
    acb_init(f);
    acb_init(f + 1);

    /* otherwise use Stirling series */
    acb_gamma_stirling_choose_param(&reflect, &r, &n, h, 1, 0, wp);

    /* rgamma(h) = (gamma(1-h+r) sin(pi h)) / (rf(1-h, r) * pi), h = h0 + t*/
    if (reflect)
    {
        /* u = gamma(r+1-h) */
        acb_sub_ui(f, h, r + 1, wp);
        acb_neg(f, f);
        _acb_poly_gamma_stirling_eval(t, f, n, len, wp);
        _acb_poly_exp_series(u, t, len, len, wp);
        for (i = 1; i < len; i += 2)
            acb_neg(u + i, u + i);

        /* v = sin(pi x) */
        acb_set(f, h);
        acb_one(f + 1);
        _acb_poly_sin_pi_series(v, f, 2, len, wp);

        _acb_poly_mullow(t, u, len, v, len, len, wp);

        /* rf(1-h,r) * pi */
        if (r == 0)
        {
            acb_const_pi(u, wp);
            _acb_vec_scalar_div(v, t, len, u, wp);
        }
        else
        {
            acb_sub_ui(f, h, 1, wp);
            acb_neg(f, f);
            acb_set_si(f + 1, -1);
            rflen = FLINT_MIN(len, r + 1);
            _acb_poly_rising_ui_series(v, f, FLINT_MIN(2, len), r, rflen, wp);
            acb_const_pi(u, wp);
            _acb_vec_scalar_mul(v, v, rflen, u, wp);

            /* divide by rising factorial */
            /* TODO: might better to use div_series, when it has a good basecase */
            _acb_poly_inv_series(u, v, rflen, len, wp);
            _acb_poly_mullow(v, t, len, u, len, len, wp);
        }
    }
    else
    {
        /* rgamma(h) = rgamma(h+r) rf(h,r) */
        if (r == 0)
        {
            acb_add_ui(f, h, r, wp);
            _acb_poly_gamma_stirling_eval(t, f, n, len, wp);
            _acb_vec_neg(t, t, len);
            _acb_poly_exp_series(v, t, len, len, wp);
        }
        else
        {
            acb_set(f, h);
            acb_one(f + 1);
            rflen = FLINT_MIN(len, r + 1);
            _acb_poly_rising_ui_series(t, f, FLINT_MIN(2, len), r, rflen, wp);

            acb_add_ui(f, h, r, wp);
            _acb_poly_gamma_stirling_eval(v, f, n, len, wp);
            _acb_vec_neg(v, v, len);
            _acb_poly_exp_series(u, v, len, len, wp);

            _acb_poly_mullow(v, u, len, t, rflen, len, wp);
        }
    }

    /* compose with nonconstant part */
    acb_zero(t);
    _acb_vec_set(t + 1, h + 1, hlen - 1);
    _acb_poly_compose_series(res, v, len, t, hlen, len, prec);

    acb_clear(f);
    acb_clear(f + 1);
    _acb_vec_clear(t, len);
    _acb_vec_clear(u, len);
    _acb_vec_clear(v, len);
}
Пример #8
0
Файл: t-2f1.c Проект: isuruf/arb
int main()
{
    slong iter;
    flint_rand_t state;

    flint_printf("2f1....");
    fflush(stdout);

    flint_randinit(state);

    for (iter = 0; iter < 3000; iter++)
    {
        acb_t a, b, c, z, w1, w2, t;
        slong prec1, prec2;
        int reg1, reg2, ebits;
        int alg1, alg2;

        acb_init(a);
        acb_init(b);
        acb_init(c);
        acb_init(z);
        acb_init(w1);
        acb_init(w2);
        acb_init(t);

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

        if (n_randint(state, 20) == 0)
            ebits = 30;
        else
            ebits = 5;

        switch (n_randint(state, 3))
        {
            case 0:
                acb_set_si(a, n_randint(state, 500));
                acb_set_si(b, n_randint(state, 500));
                acb_set_si(c, n_randint(state, 10));
                break;
            case 1:
                acb_set_si(a, n_randint(state, 200) - 100);
                acb_set_si(b, n_randint(state, 200) - 100);
                acb_set_si(c, n_randint(state, 200) - 100);
                break;
            default:
                acb_randtest_param(a, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits));
                acb_randtest_param(b, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits));
                acb_randtest_param(c, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits));
        }

        acb_randtest_param(z, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits));
        acb_randtest(w1, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits));
        acb_randtest(w2, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits));

        reg1 = n_randint(state, 2);
        reg2 = n_randint(state, 2);

        alg1 = n_randint(state, 10);
        alg2 = n_randint(state, 10);

        switch (alg1)
        {
            case 0:
                acb_hypgeom_2f1_direct(w1, a, b, c, z, reg1, prec1);
                break;
            case 1:
            case 2:
            case 3:
            case 4:
            case 5:
                acb_hypgeom_2f1_transform(w1, a, b, c, z, reg1, alg1, prec1);
                break;
            case 6:
                acb_hypgeom_2f1_corner(w1, a, b, c, z, reg1, prec1);
                break;
            default:
                acb_hypgeom_2f1(w1, a, b, c, z, reg1, prec1);
        }

        switch (alg2)
        {
            case 0:
                acb_hypgeom_2f1_direct(w2, a, b, c, z, reg2, prec2);
                break;
            case 1:
            case 2:
            case 3:
            case 4:
            case 5:
                acb_hypgeom_2f1_transform(w2, a, b, c, z, reg2, alg2, prec2);
                break;
            case 6:
                acb_hypgeom_2f1_corner(w2, a, b, c, z, reg2, prec2);
                break;
            default:
                acb_hypgeom_2f1(w2, a, b, c, z, reg2, prec2);
        }

        if (reg1 != reg2)
        {
            acb_rgamma(t, c, prec2);

            if (reg1)
                acb_mul(w2, w2, t, prec2);
            else
                acb_mul(w1, w1, t, prec2);
        }

        if (!acb_overlaps(w1, w2))
        {
            flint_printf("FAIL: consistency\n\n");
            flint_printf("iter = %wd, prec1 = %wd, prec2 = %wd\n\n", iter, prec1, prec2);
            flint_printf("alg1 = %d, alg2 = %d\n\n", alg1, alg2);
            flint_printf("reg1 = %d, reg2 = %d\n\n", reg1, reg2);
            flint_printf("a = "); acb_printd(a, 30); flint_printf("\n\n");
            flint_printf("b = "); acb_printd(b, 30); flint_printf("\n\n");
            flint_printf("c = "); acb_printd(c, 30); flint_printf("\n\n");
            flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n");
            flint_printf("w1 = "); acb_printd(w1, 30); flint_printf("\n\n");
            flint_printf("w2 = "); acb_printd(w2, 30); flint_printf("\n\n");
            abort();
        }

        acb_clear(a);
        acb_clear(b);
        acb_clear(c);
        acb_clear(z);
        acb_clear(w1);
        acb_clear(w2);
        acb_clear(t);
    }

    flint_randclear(state);
    flint_cleanup();
    flint_printf("PASS\n");
    return EXIT_SUCCESS;
}
Пример #9
0
int main(int argc, char *argv[])
{
    acb_t r, s, a, b;
    arf_t inr, outr;
    long digits, prec;

    if (argc < 2)
    {
        printf("integrals d\n");
        printf("compute integrals using d decimal digits of precision\n");
        return 1;
    }

    acb_init(r);
    acb_init(s);
    acb_init(a);
    acb_init(b);
    arf_init(inr);
    arf_init(outr);

    arb_calc_verbose = 0;

    digits = atol(argv[1]);
    prec = digits * 3.32193;
    printf("Digits: %ld\n", digits);

    printf("----------------------------------------------------------------\n");
    printf("Integral of sin(t) from 0 to 100.\n");
    arf_set_d(inr, 0.125);
    arf_set_d(outr, 1.0);
    TIMEIT_ONCE_START
    acb_set_si(a, 0);
    acb_set_si(b, 100);
    acb_calc_integrate_taylor(r, sinx, NULL, a, b, inr, outr, prec, 1.1 * prec);
    printf("RESULT:\n");
    acb_printd(r, digits); printf("\n");
    TIMEIT_ONCE_STOP

    printf("----------------------------------------------------------------\n");
    printf("Elliptic integral F(phi, m) = integral of 1/sqrt(1 - m*sin(t)^2)\n");
    printf("from 0 to phi, with phi = 6+6i, m = 1/2. Integration path\n");
    printf("0 -> 6 -> 6+6i.\n");
    arf_set_d(inr, 0.2);
    arf_set_d(outr, 0.5);
    TIMEIT_ONCE_START
    acb_set_si(a, 0);
    acb_set_si(b, 6);
    acb_calc_integrate_taylor(r, elliptic, NULL, a, b, inr, outr, prec, 1.1 * prec);
    acb_set_si(a, 6);
    arb_set_si(acb_realref(b), 6);
    arb_set_si(acb_imagref(b), 6);
    acb_calc_integrate_taylor(s, elliptic, NULL, a, b, inr, outr, prec, 1.1 * prec);
    acb_add(r, r, s, prec);
    printf("RESULT:\n");
    acb_printd(r, digits); printf("\n");
    TIMEIT_ONCE_STOP

    printf("----------------------------------------------------------------\n");
    printf("Bessel function J_n(z) = (1/pi) * integral of cos(t*n - z*sin(t))\n");
    printf("from 0 to pi. With n = 10, z = 20 + 10i.\n");
    arf_set_d(inr, 0.1);
    arf_set_d(outr, 0.5);
    TIMEIT_ONCE_START
    acb_set_si(a, 0);
    acb_const_pi(b, 3 * prec);
    acb_calc_integrate_taylor(r, bessel, NULL, a, b, inr, outr, prec, 3 * prec);
    acb_div(r, r, b, prec);
    printf("RESULT:\n");
    acb_printd(r, digits); printf("\n");
    TIMEIT_ONCE_STOP

    acb_clear(r);
    acb_clear(s);
    acb_clear(a);
    acb_clear(b);
    arf_clear(inr);
    arf_clear(outr);

    flint_cleanup();
    return 0;
}
Пример #10
0
int main()
{
    slong iter;
    flint_rand_t state;

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

    flint_randinit(state);

    for (iter = 0; iter < 1000; iter++)
    {
        acb_t n, a, b, n1, a1, b1, z, res1, res2, res3, s;
        slong prec;

        acb_init(n);
        acb_init(a);
        acb_init(b);
        acb_init(n1);
        acb_init(a1);
        acb_init(b1);
        acb_init(z);
        acb_init(res1);
        acb_init(res2);
        acb_init(res3);
        acb_init(s);

        prec = 2 + n_randint(state, 300);

        if (n_randint(state, 2))
        {
            acb_set_si(n, n_randint(state, 20) - 10);
            acb_set_si(a, n_randint(state, 20) - 10);
            acb_set_si(b, n_randint(state, 20) - 10);
        }
        else
        {
            acb_randtest_param(n, state, 1 + n_randint(state, 400), 10);
            acb_randtest_param(a, state, 1 + n_randint(state, 400), 10);
            acb_randtest_param(b, state, 1 + n_randint(state, 400), 10);
        }

        acb_randtest_param(z, state, 1 + n_randint(state, 400), 10);

        acb_sub_ui(n1, n, 1, prec);
        acb_sub_ui(a1, a, 1, prec);
        acb_sub_ui(b1, b, 1, prec);

        acb_hypgeom_jacobi_p(res1, n, a, b1, z, prec);
        acb_hypgeom_jacobi_p(res2, n, a1, b, z, 2 + n_randint(state, 300));
        acb_hypgeom_jacobi_p(res3, n1, a, b, z, 2 + n_randint(state, 300));

        acb_sub(s, res1, res2, prec);

        if (!acb_overlaps(s, res3))
        {
            flint_printf("FAIL: consistency\n\n");
            flint_printf("iter = %wd\n\n", iter);
            flint_printf("n = "); acb_printd(n, 30); flint_printf("\n\n");
            flint_printf("a = "); acb_printd(a, 30); flint_printf("\n\n");
            flint_printf("b = "); acb_printd(b, 30); flint_printf("\n\n");
            flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n");
            flint_printf("res1 = "); acb_printd(res1, 30); flint_printf("\n\n");
            flint_printf("res2 = "); acb_printd(res2, 30); flint_printf("\n\n");
            flint_printf("res3 = "); acb_printd(res3, 30); flint_printf("\n\n");
            flint_printf("s = "); acb_printd(s, 30); flint_printf("\n\n");
            abort();
        }

        acb_clear(n);
        acb_clear(a);
        acb_clear(b);
        acb_clear(n1);
        acb_clear(a1);
        acb_clear(b1);
        acb_clear(z);
        acb_clear(res1);
        acb_clear(res2);
        acb_clear(res3);
        acb_clear(s);
    }

    flint_randclear(state);
    flint_cleanup();
    flint_printf("PASS\n");
    return EXIT_SUCCESS;
}
Пример #11
0
int main()
{
    slong iter;
    flint_rand_t state;

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

    flint_randinit(state);

    for (iter = 0; iter < 2000 * arb_test_multiplier(); iter++)
    {
        acb_t n, m, n1, m1, z, res1, res2, res3, s;
        slong prec;

        acb_init(n);
        acb_init(m);
        acb_init(n1);
        acb_init(m1);
        acb_init(z);
        acb_init(res1);
        acb_init(res2);
        acb_init(res3);
        acb_init(s);

        prec = 2 + n_randint(state, 200);

        if (n_randint(state, 2))
        {
            acb_set_si(n, n_randint(state, 20) - 10);
            acb_set_si(m, n_randint(state, 20) - 10);
        }
        else
        {
            acb_randtest_param(n, state, 1 + n_randint(state, 400), 10);
            acb_randtest_param(m, state, 1 + n_randint(state, 400), 10);
        }

        acb_randtest_param(z, state, 1 + n_randint(state, 400), 10);

        acb_sub_ui(n1, n, 1, prec);
        acb_sub_ui(m1, m, 1, prec);

        acb_hypgeom_laguerre_l(res1, n, m, z, prec);
        acb_hypgeom_laguerre_l(res2, n1, m, z, 2 + n_randint(state, 200));
        acb_hypgeom_laguerre_l(res3, n, m1, z, 2 + n_randint(state, 200));

        acb_add(s, res2, res3, prec);

        if (acb_is_finite(res1) && acb_is_finite(s) && !acb_overlaps(res1, s))
        {
            flint_printf("FAIL: consistency\n\n");
            flint_printf("iter = %wd\n\n", iter);
            flint_printf("n = "); acb_printd(n, 30); flint_printf("\n\n");
            flint_printf("m = "); acb_printd(m, 30); flint_printf("\n\n");
            flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n");
            flint_printf("res1 = "); acb_printd(res1, 30); flint_printf("\n\n");
            flint_printf("res2 = "); acb_printd(res2, 30); flint_printf("\n\n");
            flint_printf("res3 = "); acb_printd(res3, 30); flint_printf("\n\n");
            flint_printf("s = "); acb_printd(s, 30); flint_printf("\n\n");
            abort();
        }

        acb_clear(n);
        acb_clear(m);
        acb_clear(n1);
        acb_clear(m1);
        acb_clear(z);
        acb_clear(res1);
        acb_clear(res2);
        acb_clear(res3);
        acb_clear(s);
    }

    flint_randclear(state);
    flint_cleanup();
    flint_printf("PASS\n");
    return EXIT_SUCCESS;
}
Пример #12
0
void
_acb_poly_zeta_cpx_reflect(acb_ptr t, const acb_t h, const acb_t a, int deflate, slong len, slong prec)
{
    /* use reflection formula */
    if (arf_sgn(arb_midref(acb_realref(h))) < 0 && acb_is_one(a))
    {
        /* zeta(s) = (2*pi)**s * sin(pi*s/2) / pi * gamma(1-s) * zeta(1-s) */
        acb_t pi, hcopy;
        acb_ptr f, s1, s2, s3, s4, u;
        slong i;

        acb_init(pi);
        acb_init(hcopy);
        f = _acb_vec_init(2);
        s1 = _acb_vec_init(len);
        s2 = _acb_vec_init(len);
        s3 = _acb_vec_init(len);
        s4 = _acb_vec_init(len);
        u = _acb_vec_init(len);
        acb_set(hcopy, h);

        acb_const_pi(pi, prec);

        /* s1 = (2*pi)**s */
        acb_mul_2exp_si(pi, pi, 1);
        _acb_poly_pow_cpx(s1, pi, h, len, prec);
        acb_mul_2exp_si(pi, pi, -1);

        /* s2 = sin(pi*s/2) / pi */
        acb_set(f, h);
        acb_one(f + 1);
        acb_mul_2exp_si(f, f, -1);
        acb_mul_2exp_si(f + 1, f + 1, -1);
        _acb_poly_sin_pi_series(s2, f, 2, len, prec);
        _acb_vec_scalar_div(s2, s2, len, pi, prec);

        /* s3 = gamma(1-s) */
        acb_sub_ui(f, hcopy, 1, prec);
        acb_neg(f, f);
        acb_set_si(f + 1, -1);
        _acb_poly_gamma_series(s3, f, 2, len, prec);

        /* s4 = zeta(1-s) */
        acb_sub_ui(f, hcopy, 1, prec);
        acb_neg(f, f);
        _acb_poly_zeta_cpx_series(s4, f, a, 0, len, prec);
        for (i = 1; i < len; i += 2)
            acb_neg(s4 + i, s4 + i);

        _acb_poly_mullow(u, s1, len, s2, len, len, prec);
        _acb_poly_mullow(s1, s3, len, s4, len, len, prec);
        _acb_poly_mullow(t, u, len, s1, len, len, prec);

        /* add 1/(1-(s+t)) = 1/(1-s) + t/(1-s)^2 + ... */
        if (deflate)
        {
            acb_sub_ui(u, hcopy, 1, prec);
            acb_neg(u, u);
            acb_inv(u, u, prec);
            for (i = 1; i < len; i++)
                acb_mul(u + i, u + i - 1, u, prec);
            _acb_vec_add(t, t, u, len, prec);
        }

        acb_clear(pi);
        acb_clear(hcopy);
        _acb_vec_clear(f, 2);
        _acb_vec_clear(s1, len);
        _acb_vec_clear(s2, len);
        _acb_vec_clear(s3, len);
        _acb_vec_clear(s4, len);
        _acb_vec_clear(u, len);
    }
    else
    {
        _acb_poly_zeta_cpx_series(t, h, a, deflate, len, prec);
    }
}
Пример #13
0
int main()
{
    long iter;
    flint_rand_t state;

    printf("legendre_q....");
    fflush(stdout);

    flint_randinit(state);

    for (iter = 0; iter < 1000; iter++)
    {
        acb_t n, m, z, res1, res2;
        long prec1, prec2, ebits;

        acb_init(n);
        acb_init(m);
        acb_init(z);
        acb_init(res1);
        acb_init(res2);

        prec1 = 2 + n_randint(state, 300);
        prec2 = 2 + n_randint(state, 300);
        ebits = 1 + n_randint(state, 10);

        if (n_randint(state, 2))
        {
            acb_set_si(m, n_randint(state, 20) - 10);
            acb_set_si(n, n_randint(state, 20) - 10);
        }
        else
        {
            acb_randtest_param(n, state, 1 + n_randint(state, 400), ebits);
            acb_randtest_param(m, state, 1 + n_randint(state, 400), ebits);
        }

        acb_randtest_param(z, state, 1 + n_randint(state, 400), ebits);

        _acb_hypgeom_legendre_q_single(res1, n, m, z, prec1);
        _acb_hypgeom_legendre_q_double(res2, n, m, z, prec2);

        if (!acb_overlaps(res1, res2))
        {
            printf("FAIL: consistency 1\n\n");
            printf("iter = %ld, prec1 = %ld, prec2 = %ld\n\n", iter, prec1, prec2);
            printf("m = "); acb_printd(m, 30); printf("\n\n");
            printf("n = "); acb_printd(n, 30); printf("\n\n");
            printf("z = "); acb_printd(z, 30); printf("\n\n");
            printf("res1 = "); acb_printd(res1, 30); printf("\n\n");
            printf("res2 = "); acb_printd(res2, 30); printf("\n\n");
            abort();
        }

        acb_clear(n);
        acb_clear(m);
        acb_clear(z);
        acb_clear(res1);
        acb_clear(res2);
    }

    for (iter = 0; iter < 2000; iter++)
    {
        acb_t n, m, z, res1, res2, t, u;
        long prec1, prec2, ebits;
        int type;

        acb_init(n);
        acb_init(m);
        acb_init(z);
        acb_init(res1);
        acb_init(res2);
        acb_init(t);
        acb_init(u);

        prec1 = 2 + n_randint(state, 300);
        prec2 = 2 + n_randint(state, 300);
        ebits = 1 + n_randint(state, 10);

        if (n_randint(state, 2))
        {
            acb_set_si(m, n_randint(state, 20) - 10);
            acb_set_si(n, n_randint(state, 20) - 10);
        }
        else
        {
            acb_randtest_param(n, state, 1 + n_randint(state, 400), ebits);
            acb_randtest_param(m, state, 1 + n_randint(state, 400), ebits);
        }

        acb_randtest_param(z, state, 1 + n_randint(state, 400), ebits);

        type = n_randint(state, 2);

        acb_hypgeom_legendre_q(res1, n, m, z, type, prec1);

        acb_neg(t, m);
        acb_hypgeom_legendre_p(res2, n, t, z, type, prec2);
        acb_add(u, m, n, prec2);
        acb_add_ui(u, u, 1, prec2);
        acb_gamma(u, u, prec2);
        acb_mul(res2, res2, u, prec2);
        acb_sub(u, n, m, prec2);
        acb_add_ui(u, u, 1, prec2);
        acb_rgamma(u, u, prec2);
        acb_mul(res2, res2, u, prec2);

        acb_hypgeom_legendre_p(t, n, m, z, type, prec2);

        if (type == 0)
        {
            acb_cos_pi(u, m, prec2);
            acb_mul(t, t, u, prec2);
        }
        acb_sub(res2, t, res2, prec2);

        if (type == 1)
        {
            acb_exp_pi_i(t, m, prec2);
            acb_mul(res2, res2, t, prec2);
        }

        acb_sin_pi(t, m, prec2);

        if (acb_contains_zero(t))
            acb_indeterminate(res2);
        else
            acb_div(res2, res2, t, prec2);

        acb_const_pi(t, prec2);
        acb_mul(res2, res2, t, prec2);
        acb_mul_2exp_si(res2, res2, -1);

        if (!acb_overlaps(res1, res2))
        {
            printf("FAIL: consistency 2\n\n");
            printf("iter = %ld, prec1 = %ld, prec2 = %ld\n\n", iter, prec1, prec2);
            printf("type = %d\n\n", type);
            printf("m = "); acb_printd(m, 30); printf("\n\n");
            printf("n = "); acb_printd(n, 30); printf("\n\n");
            printf("z = "); acb_printd(z, 30); printf("\n\n");
            printf("res1 = "); acb_printd(res1, 30); printf("\n\n");
            printf("res2 = "); acb_printd(res2, 30); printf("\n\n");
            abort();
        }

        acb_clear(n);
        acb_clear(m);
        acb_clear(z);
        acb_clear(res1);
        acb_clear(res2);
        acb_clear(t);
        acb_clear(u);
    }

    flint_randclear(state);
    flint_cleanup();
    printf("PASS\n");
    return EXIT_SUCCESS;
}
Пример #14
0
int main()
{
    slong iter;
    flint_rand_t state;

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

    flint_randinit(state);

    for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
    {
        acb_t a, s, b, c;
        slong prec1, prec2;

        prec1 = 2 + n_randint(state, 500);
        prec2 = prec1 + 30;

        acb_init(a);
        acb_init(s);
        acb_init(b);
        acb_init(c);

        if (iter < 200)
        {
            slong i = n_randint(state, 5);

            acb_set_si(s, -2 + i);
            acb_one(a);

            acb_randtest(c, state, 1 + n_randint(state, 500), 3);
            acb_add(s, s, c, prec2);
            acb_sub(s, s, c, prec2);

            acb_polygamma(b, s, a, prec1);
            acb_zero(c);
            arb_set_str(acb_realref(c), testdata[i], prec2);
        }
        else
        {
            acb_randtest(a, state, 1 + n_randint(state, 500), 3);
            acb_randtest(s, state, 1 + n_randint(state, 500), 3);

            acb_polygamma(b, s, a, prec1);

            acb_randtest(c, state, 1 + n_randint(state, 500), 3);
            acb_add(s, s, c, prec2);
            acb_sub(s, s, c, prec2);

            acb_polygamma(c, s, a, prec2);
        }

        if (!acb_overlaps(b, c))
        {
            flint_printf("FAIL: overlap\n\n");
            flint_printf("a = "); acb_print(a); flint_printf("\n\n");
            flint_printf("s = "); acb_print(s); flint_printf("\n\n");
            flint_printf("b = "); acb_print(b); flint_printf("\n\n");
            flint_printf("c = "); acb_print(c); flint_printf("\n\n");
            flint_abort();
        }

        acb_clear(a);
        acb_clear(s);
        acb_clear(b);
        acb_clear(c);
    }

    flint_randclear(state);
    flint_cleanup();
    flint_printf("PASS\n");
    return EXIT_SUCCESS;
}
Пример #15
0
void
acb_hypgeom_chebyshev_t(acb_t res, const acb_t n, const acb_t z, slong prec)
{
    acb_t t;

    if (acb_is_int(n) && 
        arf_cmpabs_2exp_si(arb_midref(acb_realref(n)), FLINT_BITS - 1) < 0)
    {
        slong k = arf_get_si(arb_midref(acb_realref(n)), ARF_RND_DOWN);
        acb_chebyshev_t_ui(res, FLINT_ABS(k), z, prec);
        return;
    }

    if (acb_is_zero(z))
    {
        acb_mul_2exp_si(res, n, -1);
        acb_cos_pi(res, res, prec);
        return;
    }

    if (acb_is_one(z))
    {
        acb_one(res);
        return;
    }

    acb_init(t);
    acb_set_si(t, -1);

    if (acb_equal(t, z))
    {
        acb_cos_pi(res, n, prec);
    }
    else
    {
        acb_sub_ui(t, z, 1, prec);

        if (arf_cmpabs_2exp_si(arb_midref(acb_realref(t)), -2 - prec / 10) < 0 &&
            arf_cmpabs_2exp_si(arb_midref(acb_imagref(t)), -2 - prec / 10) < 0)
        {
            acb_t a, c;

            acb_init(a);
            acb_init(c);

            acb_neg(a, n);
            acb_one(c);
            acb_mul_2exp_si(c, c, -1);
            acb_neg(t, t);
            acb_mul_2exp_si(t, t, -1);
            acb_hypgeom_2f1(res, a, n, c, t, 0, prec);

            acb_clear(a);
            acb_clear(c);
        }
        else if (arb_is_nonnegative(acb_realref(t)))
        {
            acb_acosh(t, z, prec);
            acb_mul(t, t, n, prec);
            acb_cosh(res, t, prec);
        }
        else
        {
            acb_acos(t, z, prec);
            acb_mul(t, t, n, prec);
            acb_cos(res, t, prec);
        }
    }

    acb_clear(t);
}
Пример #16
0
int main()
{
    slong iter;
    flint_rand_t state;

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

    flint_randinit(state);

    for (iter = 0; iter < 2000; iter++)
    {
        slong prec1, prec2;
        acb_poly_t f, g;
        acb_t c, d, e;

        prec1 = 2 + n_randint(state, 500);
        prec2 = 2 + n_randint(state, 500);

        acb_poly_init(f);
        acb_poly_init(g);

        acb_init(c);
        acb_init(d);
        acb_init(e);

        acb_poly_randtest(f, state, 1 + n_randint(state, 40), 1 + n_randint(state, 500), 10);
        acb_poly_randtest(g, state, 1 + n_randint(state, 20), 1 + n_randint(state, 500), 10);

        if (n_randint(state, 2))
            acb_set_si(c, n_randint(state, 5) - 2);
        else
            acb_randtest(c, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100));

        if (n_randint(state, 2))
            acb_set_si(d, n_randint(state, 5) - 2);
        else
            acb_randtest(d, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100));

        acb_add(e, c, d, prec1);

        /* check f(x+c)(x+d) = f(x+c+d) */
        acb_poly_taylor_shift_convolution(g, f, e, prec2);
        acb_poly_taylor_shift_convolution(f, f, c, prec1);
        acb_poly_taylor_shift_convolution(f, f, d, prec1);

        if (!acb_poly_overlaps(f, g))
        {
            flint_printf("FAIL\n\n");

            flint_printf("c = "); acb_printd(c, 15); flint_printf("\n\n");
            flint_printf("d = "); acb_printd(d, 15); flint_printf("\n\n");

            flint_printf("f = "); acb_poly_printd(f, 15); flint_printf("\n\n");
            flint_printf("g = "); acb_poly_printd(g, 15); flint_printf("\n\n");

            abort();
        }

        acb_poly_clear(f);
        acb_poly_clear(g);

        acb_clear(c);
        acb_clear(d);
        acb_clear(e);
    }

    flint_randclear(state);
    flint_cleanup();
    flint_printf("PASS\n");
    return EXIT_SUCCESS;
}
Пример #17
0
int main()
{
    slong iter;
    flint_rand_t state;

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

    flint_randinit(state);

    for (iter = 0; iter < 2000 * arb_test_multiplier(); iter++)
    {
        acb_t n, na, nb, m, z, res1, res2, res3, t, u;
        slong prec1, prec2, ebits;
        int type;

        acb_init(n);
        acb_init(na);
        acb_init(nb);
        acb_init(m);
        acb_init(z);
        acb_init(res1);
        acb_init(res2);
        acb_init(res3);
        acb_init(t);
        acb_init(u);

        prec1 = 2 + n_randint(state, 300);
        prec2 = 2 + n_randint(state, 300);
        ebits = 1 + n_randint(state, 10);

        if (n_randint(state, 2))
        {
            acb_set_si(m, n_randint(state, 20) - 10);
            acb_set_si(n, n_randint(state, 20) - 10);
        }
        else
        {
            acb_randtest_param(n, state, 1 + n_randint(state, 400), ebits);
            acb_randtest_param(m, state, 1 + n_randint(state, 400), ebits);
        }

        acb_randtest_param(z, state, 1 + n_randint(state, 400), ebits);

        acb_sub_ui(na, n, 1, prec2);
        acb_add_ui(nb, n, 1, prec2);

        type = n_randint(state, 2);

        acb_hypgeom_legendre_p(res1, n, m, z, type, prec1);
        acb_hypgeom_legendre_p(res2, na, m, z, type, prec2);
        acb_hypgeom_legendre_p(res3, nb, m, z, type, prec2);

        acb_add(t, n, m, prec2);
        acb_mul(t, t, res2, prec2);
        acb_sub(u, n, m, prec2);
        acb_add_ui(u, u, 1, prec2);
        acb_mul(u, u, res3, prec2);
        acb_add(t, t, u, prec2);

        acb_mul_2exp_si(u, n, 1);
        acb_add_ui(u, u, 1, prec2);
        acb_mul(u, u, z, prec2);
        acb_mul(u, u, res1, prec2);

        if (!acb_overlaps(t, u))
        {
            flint_printf("FAIL: consistency\n\n");
            flint_printf("iter = %wd, prec1 = %wd, prec2 = %wd\n\n", iter, prec1, prec2);
            flint_printf("type = %d\n\n", type);
            flint_printf("n = "); acb_printd(n, 30); flint_printf("\n\n");
            flint_printf("m = "); acb_printd(m, 30); flint_printf("\n\n");
            flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n");
            flint_printf("res1 = "); acb_printd(res1, 30); flint_printf("\n\n");
            flint_printf("res2 = "); acb_printd(res2, 30); flint_printf("\n\n");
            flint_printf("res3 = "); acb_printd(res3, 30); flint_printf("\n\n");
            flint_printf("t = "); acb_printd(t, 30); flint_printf("\n\n");
            flint_printf("u = "); acb_printd(u, 30); flint_printf("\n\n");
            abort();
        }

        acb_clear(n);
        acb_clear(na);
        acb_clear(nb);
        acb_clear(m);
        acb_clear(z);
        acb_clear(res1);
        acb_clear(res2);
        acb_clear(res3);
        acb_clear(t);
        acb_clear(u);
    }

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