コード例 #1
0
int main()
{
    slong iter;
    flint_rand_t state;

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

    flint_randinit(state);

    for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
    {
        slong m, n, bits1, bits2, bits3;
        acb_poly_t a, b, c, d;

        bits1 = 2 + n_randint(state, 100);
        bits2 = 2 + n_randint(state, 100);
        bits3 = 2 + n_randint(state, 100);

        m = 1 + n_randint(state, 30);
        n = 1 + n_randint(state, 30);

        acb_poly_init(a);
        acb_poly_init(b);
        acb_poly_init(c);
        acb_poly_init(d);

        acb_poly_randtest(a, state, m, bits1, 5);
        acb_poly_randtest(b, state, m, bits1, 5);

        /* check exp(a+b) = exp(a) exp(b) */
        acb_poly_exp_series_basecase(c, a, n, bits2);
        acb_poly_exp_series_basecase(d, b, n, bits2);
        acb_poly_mullow(c, c, d, n, bits2);

        acb_poly_add(d, a, b, bits3);
        acb_poly_exp_series_basecase(d, d, n, bits3);   /* also aliasing test */

        if (!acb_poly_overlaps(c, d))
        {
            flint_printf("FAIL\n\n");

            flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n");
            flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n");
            flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n");
            flint_printf("d = "); acb_poly_printd(d, 15); flint_printf("\n\n");
            abort();
        }

        acb_poly_clear(a);
        acb_poly_clear(b);
        acb_poly_clear(c);
        acb_poly_clear(d);
    }

    flint_randclear(state);
    flint_cleanup();
    flint_printf("PASS\n");
    return EXIT_SUCCESS;
}
コード例 #2
0
ファイル: t-evaluate2.c プロジェクト: isuruf/arb
int main()
{
    slong iter;
    flint_rand_t state;

    flint_printf("evaluate2....");
    fflush(stdout);

    flint_randinit(state);

    for (iter = 0; iter < 10000; iter++)
    {
        acb_poly_t f, g;
        acb_t x, y1, z1, y2, z2;

        acb_init(x);
        acb_init(y1);
        acb_init(z1);
        acb_init(y2);
        acb_init(z2);
        acb_poly_init(f);
        acb_poly_init(g);

        acb_randtest(x, state, 2 + n_randint(state, 1000), 5);
        acb_poly_randtest(f, state, 2 + n_randint(state, 100), 2 + n_randint(state, 1000), 5);
        acb_poly_derivative(g, f, 2 + n_randint(state, 1000));

        acb_poly_evaluate2(y1, z1, f, x, 2 + n_randint(state, 1000));

        acb_poly_evaluate_horner(y2, f, x, 2 + n_randint(state, 1000));
        acb_poly_evaluate_horner(z2, g, x, 2 + n_randint(state, 1000));

        if (!acb_overlaps(y1, y2) || !acb_overlaps(z1, z2))
        {
            flint_printf("FAIL\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");
            flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n");
            flint_printf("y1 = "); acb_printd(y1, 15); flint_printf("\n\n");
            flint_printf("z1 = "); acb_printd(z1, 15); flint_printf("\n\n");
            flint_printf("y2 = "); acb_printd(y2, 15); flint_printf("\n\n");
            flint_printf("z2 = "); acb_printd(z2, 15); flint_printf("\n\n");
            abort();
        }

        acb_poly_clear(f);
        acb_poly_clear(g);
        acb_clear(x);
        acb_clear(y1);
        acb_clear(z1);
        acb_clear(y2);
        acb_clear(z2);
    }

    flint_randclear(state);
    flint_cleanup();
    flint_printf("PASS\n");
    return EXIT_SUCCESS;
}
コード例 #3
0
void
acb_poly_binomial_transform(acb_poly_t b, const acb_poly_t a, slong len, slong prec)
{
    if (len == 0 || a->length == 0)
    {
        acb_poly_zero(b);
        return;
    }

    if (b == a)
    {
        acb_poly_t c;
        acb_poly_init2(c, len);
        _acb_poly_binomial_transform(c->coeffs, a->coeffs, a->length, len, prec);
        acb_poly_swap(b, c);
        acb_poly_clear(c);
    }
    else
    {
        acb_poly_fit_length(b, len);
        _acb_poly_binomial_transform(b->coeffs, a->coeffs, a->length, len, prec);
    }

    _acb_poly_set_length(b, len);
    _acb_poly_normalise(b);
}
コード例 #4
0
ファイル: sqrt_series.c プロジェクト: isuruf/arb
void
acb_poly_sqrt_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec)
{
    if (n == 0)
    {
        acb_poly_zero(g);
        return;
    }

    if (g == h)
    {
        acb_poly_t t;
        acb_poly_init(t);
        acb_poly_sqrt_series(t, h, n, prec);
        acb_poly_swap(g, t);
        acb_poly_clear(t);
        return;
    }

    acb_poly_fit_length(g, n);
    if (h->length == 0)
        _acb_vec_indeterminate(g->coeffs, n);
    else
        _acb_poly_sqrt_series(g->coeffs, h->coeffs, h->length, n, prec);
    _acb_poly_set_length(g, n);
    _acb_poly_normalise(g);
}
コード例 #5
0
ファイル: mul.c プロジェクト: isuruf/arb
void
acb_poly_mul(acb_poly_t res, const acb_poly_t poly1,
             const acb_poly_t poly2, slong prec)
{
    slong len_out;

    if ((poly1->length == 0) || (poly2->length == 0))
    {
        acb_poly_zero(res);
        return;
    }

    len_out = poly1->length + poly2->length - 1;

    if (res == poly1 || res == poly2)
    {
        acb_poly_t temp;
        acb_poly_init2(temp, len_out);
        _acb_poly_mul(temp->coeffs, poly1->coeffs, poly1->length,
                      poly2->coeffs, poly2->length, prec);
        acb_poly_swap(res, temp);
        acb_poly_clear(temp);
    }
    else
    {
        acb_poly_fit_length(res, len_out);
        _acb_poly_mul(res->coeffs, poly1->coeffs, poly1->length,
                      poly2->coeffs, poly2->length, prec);
    }

    _acb_poly_set_length(res, len_out);
    _acb_poly_normalise(res);
}
コード例 #6
0
ファイル: inv_series.c プロジェクト: fredrik-johansson/arb
void
acb_poly_inv_series(acb_poly_t Qinv, const acb_poly_t Q, slong n, slong prec)
{
    if (n == 0)
    {
        acb_poly_zero(Qinv);
        return;
    }

    if (Q->length == 0)
    {
        acb_poly_fit_length(Qinv, n);
        _acb_vec_indeterminate(Qinv->coeffs, n);
        _acb_poly_set_length(Qinv, n);
        return;
    }

    if (Qinv == Q)
    {
        acb_poly_t t;
        acb_poly_init(t);
        acb_poly_inv_series(t, Q, n, prec);
        acb_poly_swap(Qinv, t);
        acb_poly_clear(t);
        return;
    }

    acb_poly_fit_length(Qinv, n);
    _acb_poly_inv_series(Qinv->coeffs, Q->coeffs, Q->length, n, prec);
    _acb_poly_set_length(Qinv, n);
    _acb_poly_normalise(Qinv);
}
コード例 #7
0
void
acb_poly_revert_series_lagrange_fast(acb_poly_t Qinv,
                                    const acb_poly_t Q, slong n, slong prec)
{
    slong Qlen = Q->length;

    if (Qlen < 2 || !acb_is_zero(Q->coeffs)
                 || acb_contains_zero(Q->coeffs + 1))
    {
        flint_printf("Exception (acb_poly_revert_series_lagrange_fast). Input \n"
               "must have zero constant term and nonzero coefficient of x^1.\n");
        abort();
    }

    if (Qinv != Q)
    {
        acb_poly_fit_length(Qinv, n);
        _acb_poly_revert_series_lagrange_fast(Qinv->coeffs, Q->coeffs, Qlen, n, prec);
    }
    else
    {
        acb_poly_t t;
        acb_poly_init2(t, n);
        _acb_poly_revert_series_lagrange_fast(t->coeffs, Q->coeffs, Qlen, n, prec);
        acb_poly_swap(Qinv, t);
        acb_poly_clear(t);
    }

    _acb_poly_set_length(Qinv, n);
    _acb_poly_normalise(Qinv);
}
コード例 #8
0
ファイル: compose_series.c プロジェクト: argriffing/arb
void
acb_poly_compose_series(acb_poly_t res,
                    const acb_poly_t poly1,
                    const acb_poly_t poly2, slong n, slong prec)
{
    slong len1 = poly1->length;
    slong len2 = poly2->length;
    slong lenr;

    if (len2 != 0 && !acb_is_zero(poly2->coeffs))
    {
        flint_printf("exception: compose_series: inner "
                "polynomial must have zero constant term\n");
        abort();
    }

    if (len1 == 0 || n == 0)
    {
        acb_poly_zero(res);
        return;
    }

    if (len2 == 0 || len1 == 1)
    {
        acb_poly_set_acb(res, poly1->coeffs);
        return;
    }

    lenr = FLINT_MIN((len1 - 1) * (len2 - 1) + 1, n);
    len1 = FLINT_MIN(len1, lenr);
    len2 = FLINT_MIN(len2, lenr);

    if ((res != poly1) && (res != poly2))
    {
        acb_poly_fit_length(res, lenr);
        _acb_poly_compose_series(res->coeffs, poly1->coeffs, len1,
                                        poly2->coeffs, len2, lenr, prec);
        _acb_poly_set_length(res, lenr);
        _acb_poly_normalise(res);
    }
    else
    {
        acb_poly_t t;
        acb_poly_init2(t, lenr);
        _acb_poly_compose_series(t->coeffs, poly1->coeffs, len1,
                                        poly2->coeffs, len2, lenr, prec);
        _acb_poly_set_length(t, lenr);
        _acb_poly_normalise(t);
        acb_poly_swap(res, t);
        acb_poly_clear(t);
    }
}
コード例 #9
0
int
main(void)
{
    int i, j, result;
    flint_rand_t state;

    flint_printf("get/set_coeff_acb....");
    fflush(stdout);

    flint_randinit(state);

    for (i = 0; i < 100; i++)
    {
        acb_poly_t a;
        acb_t x1, x2;
        slong coeff, len;

        acb_poly_init(a);
        acb_init(x1);
        acb_init(x2);
        len = n_randint(state, 100) + 1;

        for (j = 0; j < 100; j++)
        {
            acb_randtest(x1, state, 2 + n_randint(state, 200), 10);
            coeff = n_randint(state, len);
            acb_poly_set_coeff_acb(a, coeff, x1);
            acb_poly_get_coeff_acb(x2, a, coeff);

            result = (acb_equal(x1, x2));
            if (!result)
            {
                flint_printf("FAIL:\n");
                flint_printf("x1 = "), acb_print(x1), flint_printf("\n");
                flint_printf("x2 = "), acb_print(x2), flint_printf("\n");
                flint_printf("coeff = %wd, length = %wd\n", coeff, len);
                flint_abort();
            }
        }

        acb_clear(x1);
        acb_clear(x2);
        acb_poly_clear(a);
    }

    flint_randclear(state);
    flint_cleanup();
    flint_printf("PASS\n");
    return 0;
}
コード例 #10
0
int main()
{
    slong iter;
    flint_rand_t state;

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

    flint_randinit(state);

    for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
    {
        acb_poly_t f;
        acb_t x, y1, y2;

        acb_init(x);
        acb_init(y1);
        acb_init(y2);
        acb_poly_init(f);

        acb_randtest(x, state, 2 + n_randint(state, 1000), 5);
        acb_poly_randtest(f, state, 2 + n_randint(state, 100), 2 + n_randint(state, 1000), 5);

        acb_poly_evaluate_rectangular(y1, f, x, 2 + n_randint(state, 1000));
        acb_poly_evaluate_horner(y2, f, x, 2 + n_randint(state, 1000));

        if (!acb_overlaps(y1, y2))
        {
            flint_printf("FAIL\n\n");
            flint_printf("f = "); acb_poly_printd(f, 15); flint_printf("\n\n");
            flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n");
            flint_printf("y1 = "); acb_printd(y1, 15); flint_printf("\n\n");
            flint_printf("y2 = "); acb_printd(y2, 15); flint_printf("\n\n");
            abort();
        }

        acb_poly_clear(f);
        acb_clear(x);
        acb_clear(y1);
        acb_clear(y2);
    }

    flint_randclear(state);
    flint_cleanup();
    flint_printf("PASS\n");
    return EXIT_SUCCESS;
}
コード例 #11
0
ファイル: 2f1_series_direct.c プロジェクト: isuruf/arb
void
acb_hypgeom_2f1_series_direct(acb_poly_t res,
    const acb_poly_t a, const acb_poly_t b,
    const acb_poly_t c, const acb_poly_t z, int regularized, slong len, slong prec)
{
    acb_poly_struct aa[4];

    aa[0] = *a;
    aa[1] = *b;
    aa[2] = *c;
    acb_poly_init(&aa[3]);
    acb_poly_one(&aa[3]);

    acb_hypgeom_pfq_series_direct(res, aa, 2, aa + 2, 2, z,
        regularized, -1, len, prec);

    acb_poly_clear(&aa[3]);
}
コード例 #12
0
ファイル: t-get_coeff_ptr.c プロジェクト: bluescarni/arb
int
main(void)
{
    int i, result;
    flint_rand_t state;

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

    flint_randinit(state);

    for (i = 0; i < 1000; i++)
    {
        acb_poly_t A;
        acb_t a;
        long n = n_randint(state, 100);

        acb_poly_init(A);
        acb_poly_randtest(A, state, n_randint(state, 100), 100, 10);
        acb_init(a);

        acb_poly_get_coeff_acb(a, A, n);

        result = n < acb_poly_length(A) ? 
                     acb_equal(a, acb_poly_get_coeff_ptr(A, n)) : 
                     acb_poly_get_coeff_ptr(A, n) == NULL;
        if (!result)
        {
            printf("FAIL:\n");
            printf("A = "), acb_poly_printd(A, 10), printf("\n\n");
            printf("a = "), acb_print(a), printf("\n\n");
            printf("n = %ld\n\n", n);
            abort();
        }

        acb_poly_clear(A);
        acb_clear(a);
    }

    flint_randclear(state);
    flint_cleanup();
    printf("PASS\n");
    return 0;
}
コード例 #13
0
void
acb_poly_pow_ui_trunc_binexp(acb_poly_t res,
    const acb_poly_t poly, ulong exp, long len, long prec)
{
    long flen, rlen;

    flen = poly->length;

    if (exp == 0 && len != 0)
    {
        acb_poly_one(res);
    }
    else if (flen == 0 || len == 0)
    {
        acb_poly_zero(res);
    }
    else
    {
        rlen = poly_pow_length(flen, exp, len);

        if (res != poly)
        {
            acb_poly_fit_length(res, rlen);
            _acb_poly_pow_ui_trunc_binexp(res->coeffs,
                poly->coeffs, flen, exp, rlen, prec);
            _acb_poly_set_length(res, rlen);
            _acb_poly_normalise(res);
        }
        else
        {
            acb_poly_t t;
            acb_poly_init2(t, rlen);
            _acb_poly_pow_ui_trunc_binexp(t->coeffs,
                poly->coeffs, flen, exp, rlen, prec);
            _acb_poly_set_length(t, rlen);
            _acb_poly_normalise(t);
            acb_poly_swap(res, t);
            acb_poly_clear(t);
        }
    }
}
コード例 #14
0
ファイル: pow_ui.c プロジェクト: isuruf/arb
void
acb_poly_pow_ui(acb_poly_t res,
    const acb_poly_t poly, ulong exp, slong prec)
{
    slong flen, rlen;

    flen = poly->length;

    if (exp == 0)
    {
        acb_poly_one(res);
    }
    else if (flen == 0)
    {
        acb_poly_zero(res);
    }
    else
    {
        rlen = exp * (flen - 1) + 1;

        if (res != poly)
        {
            acb_poly_fit_length(res, rlen);
            _acb_poly_pow_ui(res->coeffs,
                poly->coeffs, flen, exp, prec);
            _acb_poly_set_length(res, rlen);
            _acb_poly_normalise(res);
        }
        else
        {
            acb_poly_t t;
            acb_poly_init2(t, rlen);
            _acb_poly_pow_ui(t->coeffs,
                poly->coeffs, flen, exp, prec);
            _acb_poly_set_length(t, rlen);
            _acb_poly_normalise(t);
            acb_poly_swap(res, t);
            acb_poly_clear(t);
        }
    }
}
コード例 #15
0
ファイル: mullow.c プロジェクト: isuruf/arb
void
acb_poly_mullow(acb_poly_t res, const acb_poly_t poly1,
                                            const acb_poly_t poly2,
                                                slong n, slong prec)
{
    slong len1, len2;

    len1 = poly1->length;
    len2 = poly2->length;

    if (len1 == 0 || len2 == 0 || n == 0)
    {
        acb_poly_zero(res);
        return;
    }

    n = FLINT_MIN((len1 + len2 - 1), n);
    len1 = FLINT_MIN(len1, n);
    len2 = FLINT_MIN(len2, n);

    if (res == poly1 || res == poly2)
    {
        acb_poly_t t;
        acb_poly_init2(t, n);
        _acb_poly_mullow(t->coeffs, poly1->coeffs, len1,
                                poly2->coeffs, len2, n, prec);
        acb_poly_swap(res, t);
        acb_poly_clear(t);
    }
    else
    {
        acb_poly_fit_length(res, n);
        _acb_poly_mullow(res->coeffs, poly1->coeffs, len1,
                                poly2->coeffs, len2, n, prec);
    }

    _acb_poly_set_length(res, n);
    _acb_poly_normalise(res);
}
コード例 #16
0
ファイル: compose.c プロジェクト: argriffing/arb
void acb_poly_compose(acb_poly_t res,
              const acb_poly_t poly1, const acb_poly_t poly2, slong prec)
{
    const slong len1 = poly1->length;
    const slong len2 = poly2->length;
    
    if (len1 == 0)
    {
        acb_poly_zero(res);
    }
    else if (len1 == 1 || len2 == 0)
    {
        acb_poly_set_acb(res, poly1->coeffs);
    }
    else
    {
        const slong lenr = (len1 - 1) * (len2 - 1) + 1;
        
        if (res != poly1 && res != poly2)
        {
            acb_poly_fit_length(res, lenr);
            _acb_poly_compose(res->coeffs, poly1->coeffs, len1,
                                                   poly2->coeffs, len2, prec);
        }
        else
        {
            acb_poly_t t;
            acb_poly_init2(t, lenr);
            _acb_poly_compose(t->coeffs, poly1->coeffs, len1,
                                                 poly2->coeffs, len2, prec);
            acb_poly_swap(res, t);
            acb_poly_clear(t);
        }

        _acb_poly_set_length(res, lenr);
        _acb_poly_normalise(res);
    }
}
コード例 #17
0
ファイル: mullow_classical.c プロジェクト: isuruf/arb
void
acb_poly_mullow_classical(acb_poly_t res, const acb_poly_t poly1,
                                            const acb_poly_t poly2,
                                                slong n, slong prec)
{
    slong len_out;

    if (poly1->length == 0 || poly2->length == 0 || n == 0)
    {
        acb_poly_zero(res);
        return;
    }

    len_out = poly1->length + poly2->length - 1;
    if (n > len_out)
        n = len_out;

    if (res == poly1 || res == poly2)
    {
        acb_poly_t t;
        acb_poly_init2(t, n);
        _acb_poly_mullow_classical(t->coeffs, poly1->coeffs, poly1->length,
                                    poly2->coeffs, poly2->length, n, prec);
        acb_poly_swap(res, t);
        acb_poly_clear(t);
    }
    else
    {
        acb_poly_fit_length(res, n);
        _acb_poly_mullow_classical(res->coeffs, poly1->coeffs, poly1->length,
                                    poly2->coeffs, poly2->length, n, prec);
    }

    _acb_poly_set_length(res, n);
    _acb_poly_normalise(res);
}
コード例 #18
0
ファイル: bessel_k.c プロジェクト: isuruf/arb
void
acb_hypgeom_bessel_k_0f1(acb_t res, const acb_t nu, const acb_t z, slong prec)
{
    if (acb_is_int(nu))
    {
        acb_poly_t nux, zx, rx;

        acb_poly_init(nux);
        acb_poly_init(zx);
        acb_poly_init(rx);

        acb_poly_set_coeff_acb(nux, 0, nu);
        acb_poly_set_coeff_si(nux, 1, 1);
        acb_poly_set_acb(zx, z);

        acb_hypgeom_bessel_k_0f1_series(rx, nux, zx, 1, prec);

        acb_poly_get_coeff_acb(res, rx, 0);

        acb_poly_clear(nux);
        acb_poly_clear(zx);
        acb_poly_clear(rx);
    }
    else
    {
        acb_t t, u, v, w;
        acb_struct b[2];

        acb_init(t);
        acb_init(u);
        acb_init(v);
        acb_init(w);
        acb_init(b + 0);
        acb_init(b + 1);

        /* u = 0F1(1+nu), v = 0F1(1-nu) */
        acb_mul(t, z, z, prec);
        acb_mul_2exp_si(t, t, -2);
        acb_add_ui(b, nu, 1, prec);
        acb_one(b + 1);
        acb_hypgeom_pfq_direct(u, NULL, 0, b, 2, t, -1, prec);
        acb_sub_ui(b, nu, 1, prec);
        acb_neg(b, b);
        acb_hypgeom_pfq_direct(v, NULL, 0, b, 2, t, -1, prec);

        /* v = v * gamma(nu) / (z/2)^nu */
        acb_mul_2exp_si(t, z, -1);
        acb_pow(t, t, nu, prec);
        acb_gamma(w, nu, prec);
        acb_mul(v, v, w, prec);
        acb_div(v, v, t, prec);

        /* u = u * t * pi / (gamma(nu) * nu * sin(pi nu)) */
        acb_mul(u, u, t, prec);
        acb_const_pi(t, prec);
        acb_mul(u, u, t, prec);
        acb_sin_pi(t, nu, prec);
        acb_mul(t, t, w, prec);
        acb_mul(t, t, nu, prec);
        acb_div(u, u, t, prec);

        acb_sub(res, v, u, prec);
        acb_mul_2exp_si(res, res, -1);

        acb_clear(t);
        acb_clear(u);
        acb_clear(v);
        acb_clear(w);
        acb_clear(b + 0);
        acb_clear(b + 1);
    }
}
コード例 #19
0
ファイル: t-compose.c プロジェクト: fredrik-johansson/arb
int main()
{
    slong iter;
    flint_rand_t state;

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

    flint_randinit(state);

    for (iter = 0; iter < 3000 * arb_test_multiplier(); iter++)
    {
        slong qbits1, qbits2, rbits1, rbits2, rbits3;
        fmpq_poly_t A, B, C;
        acb_poly_t a, b, c, d;

        qbits1 = 2 + n_randint(state, 200);
        qbits2 = 2 + n_randint(state, 200);
        rbits1 = 2 + n_randint(state, 200);
        rbits2 = 2 + n_randint(state, 200);
        rbits3 = 2 + n_randint(state, 200);

        fmpq_poly_init(A);
        fmpq_poly_init(B);
        fmpq_poly_init(C);

        acb_poly_init(a);
        acb_poly_init(b);
        acb_poly_init(c);
        acb_poly_init(d);

        fmpq_poly_randtest(A, state, 1 + n_randint(state, 20), qbits1);
        fmpq_poly_randtest(B, state, 1 + n_randint(state, 10), qbits2);
        fmpq_poly_compose(C, A, B);

        acb_poly_randtest(c, state, 1 + n_randint(state, 20), rbits1, 4);

        acb_poly_set_fmpq_poly(a, A, rbits1);
        acb_poly_set_fmpq_poly(b, B, rbits2);
        acb_poly_compose(c, a, b, rbits3);

        if (!acb_poly_contains_fmpq_poly(c, C))
        {
            flint_printf("FAIL\n\n");
            flint_printf("bits3 = %wd\n", rbits3);

            flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n");
            flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n");
            flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n");

            flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n");
            flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n");
            flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n");

            flint_abort();
        }

        acb_poly_set(d, a);
        acb_poly_compose(d, d, b, rbits3);
        if (!acb_poly_equal(d, c))
        {
            flint_printf("FAIL (aliasing 1)\n\n");
            flint_abort();
        }

        acb_poly_set(d, b);
        acb_poly_compose(d, a, d, rbits3);
        if (!acb_poly_equal(d, c))
        {
            flint_printf("FAIL (aliasing 2)\n\n");
            flint_abort();
        }

        fmpq_poly_clear(A);
        fmpq_poly_clear(B);
        fmpq_poly_clear(C);

        acb_poly_clear(a);
        acb_poly_clear(b);
        acb_poly_clear(c);
        acb_poly_clear(d);
    }

    flint_randclear(state);
    flint_cleanup();
    flint_printf("PASS\n");
    return EXIT_SUCCESS;
}
コード例 #20
0
int main()
{
    slong iter;
    flint_rand_t state;

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

    flint_randinit(state);

    /* compare with fmpq_poly */
    for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
    {
        slong qbits1, qbits2, rbits1, rbits2, rbits3, trunc;
        fmpq_poly_t A, B, C;
        acb_poly_t a, b, c, d;

        qbits1 = 2 + n_randint(state, 200);
        qbits2 = 2 + n_randint(state, 200);
        rbits1 = 2 + n_randint(state, 200);
        rbits2 = 2 + n_randint(state, 200);
        rbits3 = 2 + n_randint(state, 200);
        trunc = n_randint(state, 10);

        fmpq_poly_init(A);
        fmpq_poly_init(B);
        fmpq_poly_init(C);

        acb_poly_init(a);
        acb_poly_init(b);
        acb_poly_init(c);
        acb_poly_init(d);

        fmpq_poly_randtest(A, state, 1 + n_randint(state, 10), qbits1);
        fmpq_poly_randtest(B, state, 1 + n_randint(state, 10), qbits2);

        fmpq_poly_mullow(C, A, B, trunc);

        acb_poly_set_fmpq_poly(a, A, rbits1);
        acb_poly_set_fmpq_poly(b, B, rbits2);

        acb_poly_mullow_transpose(c, a, b, trunc, rbits3);

        if (!acb_poly_contains_fmpq_poly(c, C))
        {
            flint_printf("FAIL\n\n");
            flint_printf("bits3 = %wd\n", rbits3);
            flint_printf("trunc = %wd\n", trunc);

            flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n");
            flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n");
            flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n");

            flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n");
            flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n");
            flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n");

            abort();
        }

        acb_poly_set(d, a);
        acb_poly_mullow_transpose(d, d, b, trunc, rbits3);
        if (!acb_poly_equal(d, c))
        {
            flint_printf("FAIL (aliasing 1)\n\n");
            abort();
        }

        acb_poly_set(d, b);
        acb_poly_mullow_transpose(d, a, d, trunc, rbits3);
        if (!acb_poly_equal(d, c))
        {
            flint_printf("FAIL (aliasing 2)\n\n");
            abort();
        }

        /* test squaring */
        acb_poly_set(b, a);
        acb_poly_mullow_transpose(c, a, b, trunc, rbits3);
        acb_poly_mullow_transpose(d, a, a, trunc, rbits3);
        if (!acb_poly_overlaps(c, d))  /* not guaranteed to be identical */
        {
            flint_printf("FAIL (squaring)\n\n");

            flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n");
            flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n");
            flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n");

            abort();
        }

        acb_poly_mullow_transpose(a, a, a, trunc, rbits3);
        if (!acb_poly_equal(d, a))
        {
            flint_printf("FAIL (aliasing, squaring)\n\n");

            flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n");
            flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n");
            flint_printf("d = "); acb_poly_printd(d, 15); flint_printf("\n\n");

            abort();
        }

        fmpq_poly_clear(A);
        fmpq_poly_clear(B);
        fmpq_poly_clear(C);

        acb_poly_clear(a);
        acb_poly_clear(b);
        acb_poly_clear(c);
        acb_poly_clear(d);
    }

    /* compare with classical */
    for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
    {
        slong bits, trunc;
        acb_poly_t a, b, ab, ab2;

        bits = 2 + n_randint(state, 200);
        trunc = n_randint(state, 10);

        acb_poly_init(a);
        acb_poly_init(b);
        acb_poly_init(ab);
        acb_poly_init(ab2);

        acb_poly_randtest(a, state, 1 + n_randint(state, 10), bits, 5);
        acb_poly_randtest(b, state, 1 + n_randint(state, 10), bits, 5);

        acb_poly_mullow_classical(ab, a, b, trunc, bits);
        acb_poly_mullow_transpose(ab2, a, b, trunc, bits);

        if (!acb_poly_overlaps(ab, ab2))
        {
            flint_printf("FAIL\n\n");
            flint_printf("bits = %wd\n", bits);
            flint_printf("trunc = %wd\n", trunc);

            flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n");
            flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n");
            flint_printf("ab = "); acb_poly_printd(ab, 15); flint_printf("\n\n");
            flint_printf("ab2 = "); acb_poly_printd(ab2, 15); flint_printf("\n\n");

            abort();
        }

        acb_poly_clear(a);
        acb_poly_clear(b);
        acb_poly_clear(ab);
        acb_poly_clear(ab2);
    }

    flint_randclear(state);
    flint_cleanup();
    flint_printf("PASS\n");
    return EXIT_SUCCESS;
}
コード例 #21
0
ファイル: t-log_series.c プロジェクト: bluescarni/arb
int main()
{
    long iter;
    flint_rand_t state;

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

    flint_randinit(state);

    /* compare with fmpq_poly */
    for (iter = 0; iter < 10000; iter++)
    {
        long m, n, qbits, rbits1, rbits2;
        fmpq_poly_t A, B;
        acb_poly_t a, b;

        qbits = 2 + n_randint(state, 200);
        rbits1 = 2 + n_randint(state, 200);
        rbits2 = 2 + n_randint(state, 200);

        m = 1 + n_randint(state, 20);
        n = 1 + n_randint(state, 20);

        fmpq_poly_init(A);
        fmpq_poly_init(B);

        acb_poly_init(a);
        acb_poly_init(b);

        fmpq_poly_randtest_not_zero(A, state, m, qbits);
        fmpq_poly_set_coeff_ui(A, 0, 1UL);

        fmpq_poly_log_series(B, A, n);
        acb_poly_set_fmpq_poly(a, A, rbits1);
        acb_poly_randtest(b, state, 1 + n_randint(state, 20), rbits1, 5);
        acb_poly_log_series(b, a, n, rbits2);

        if (!acb_poly_contains_fmpq_poly(b, B))
        {
            printf("FAIL\n\n");
            printf("bits2 = %ld\n", rbits2);

            printf("A = "); fmpq_poly_print(A); printf("\n\n");
            printf("B = "); fmpq_poly_print(B); printf("\n\n");

            printf("a = "); acb_poly_printd(a, 15); printf("\n\n");
            printf("b = "); acb_poly_printd(b, 15); printf("\n\n");

            abort();
        }

        fmpq_poly_clear(A);
        fmpq_poly_clear(B);

        acb_poly_clear(a);
        acb_poly_clear(b);
    }

    /* test aliasing */
    for (iter = 0; iter < 10000; iter++)
    {
        long m, n, qbits, rbits1, rbits2;
        fmpq_poly_t A;
        acb_poly_t a, b;

        qbits = 2 + n_randint(state, 200);
        rbits1 = 2 + n_randint(state, 200);
        rbits2 = 2 + n_randint(state, 200);

        m = 1 + n_randint(state, 20);
        n = 1 + n_randint(state, 20);

        fmpq_poly_init(A);
        acb_poly_init(a);
        acb_poly_init(b);

        do {
            fmpq_poly_randtest_not_zero(A, state, m, qbits);
        } while (fmpz_sgn(A->coeffs + 0) <= 0);

        acb_poly_set_fmpq_poly(a, A, rbits1);

        acb_poly_log_series(b, a, n, rbits2);
        acb_poly_log_series(a, a, n, rbits2);

        if (!acb_poly_equal(a, b))
        {
            printf("FAIL\n\n");
            printf("bits2 = %ld\n", rbits2);

            printf("A = "); fmpq_poly_print(A); printf("\n\n");

            printf("a = "); acb_poly_printd(a, 15); printf("\n\n");
            printf("b = "); acb_poly_printd(b, 15); printf("\n\n");

            abort();
        }

        fmpq_poly_clear(A);
        acb_poly_clear(a);
        acb_poly_clear(b);
    }

    /* test that exp(log(f)) contains f */
    for (iter = 0; iter < 10000; iter++)
    {
        long m, n, qbits, rbits1, rbits2, rbits3;
        fmpq_poly_t A;
        acb_poly_t a, b, c;

        qbits = 2 + n_randint(state, 200);
        rbits1 = 2 + n_randint(state, 200);
        rbits2 = 2 + n_randint(state, 200);
        rbits3 = 2 + n_randint(state, 200);

        m = 1 + n_randint(state, 20);
        n = 1 + n_randint(state, 20);

        fmpq_poly_init(A);
        acb_poly_init(a);
        acb_poly_init(b);
        acb_poly_init(c);

        do {
            fmpq_poly_randtest_not_zero(A, state, m, qbits);
        } while (fmpz_sgn(A->coeffs + 0) <= 0);

        acb_poly_set_fmpq_poly(a, A, rbits1);

        acb_poly_randtest(b, state, 1 + n_randint(state, 20), rbits1, 5);
        acb_poly_log_series(b, a, n, rbits2);
        acb_poly_exp_series_basecase(c, b, n, rbits3);

        fmpq_poly_truncate(A, n);

        if (!acb_poly_contains_fmpq_poly(c, A))
        {
            printf("FAIL\n\n");
            printf("bits2 = %ld\n", rbits2);
            printf("bits3 = %ld\n", rbits3);

            printf("A = "); fmpq_poly_print(A); printf("\n\n");

            printf("a = "); acb_poly_printd(a, 15); printf("\n\n");
            printf("b = "); acb_poly_printd(b, 15); printf("\n\n");
            printf("c = "); acb_poly_printd(c, 15); printf("\n\n");

            abort();
        }

        fmpq_poly_clear(A);
        acb_poly_clear(a);
        acb_poly_clear(b);
        acb_poly_clear(c);
    }

    flint_randclear(state);
    flint_cleanup();
    printf("PASS\n");
    return EXIT_SUCCESS;
}
コード例 #22
0
int main()
{
    slong iter;
    flint_rand_t state;

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

    flint_randinit(state);

    /* compare with fmpz_poly */
    for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
    {
        slong zbits1, rbits1, rbits2, trunc;
        ulong e;
        fmpz_poly_t A, B;
        acb_poly_t a, b;

        zbits1 = 2 + n_randint(state, 100);
        rbits1 = 2 + n_randint(state, 200);
        rbits2 = 2 + n_randint(state, 200);
        e = n_randint(state, 50);
        trunc = n_randint(state, 40);

        fmpz_poly_init(A);
        fmpz_poly_init(B);

        acb_poly_init(a);
        acb_poly_init(b);

        fmpz_poly_randtest(A, state, 1 + n_randint(state, 10), zbits1);
        fmpz_poly_pow_trunc(B, A, e, trunc);

        acb_poly_set_fmpz_poly(a, A, rbits1);
        acb_poly_pow_ui_trunc_binexp(b, a, e, trunc, rbits2);

        if (!acb_poly_contains_fmpz_poly(b, B))
        {
            flint_printf("FAIL\n\n");
            flint_printf("bits2 = %wd\n", rbits2);
            flint_printf("e = %wu\n", e);
            flint_printf("trunc = %wd\n", trunc);

            flint_printf("A = "); fmpz_poly_print(A); flint_printf("\n\n");
            flint_printf("B = "); fmpz_poly_print(B); flint_printf("\n\n");

            flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n");
            flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n");

            abort();
        }

        acb_poly_pow_ui_trunc_binexp(a, a, e, trunc, rbits2);
        if (!acb_poly_equal(a, b))
        {
            flint_printf("FAIL (aliasing)\n\n");
            abort();
        }

        fmpz_poly_clear(A);
        fmpz_poly_clear(B);

        acb_poly_clear(a);
        acb_poly_clear(b);
    }

    flint_randclear(state);
    flint_cleanup();
    flint_printf("PASS\n");
    return EXIT_SUCCESS;
}
コード例 #23
0
int main()
{
    slong iter;
    flint_rand_t state;

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

    flint_randinit(state);

    for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
    {
        slong qbits1, rbits1, rbits2, n;
        fmpq_poly_t A, B;
        acb_poly_t a, b, c;

        qbits1 = 2 + n_randint(state, 200);
        rbits1 = 2 + n_randint(state, 200);
        rbits2 = 2 + n_randint(state, 200);
        n = 2 + n_randint(state, 25);

        fmpq_poly_init(A);
        fmpq_poly_init(B);

        acb_poly_init(a);
        acb_poly_init(b);
        acb_poly_init(c);

        do {
            fmpq_poly_randtest(A, state, 1 + n_randint(state, 25), qbits1);
            fmpq_poly_set_coeff_ui(A, 0, 0);
        } while (A->length < 2 || fmpz_is_zero(A->coeffs + 1));

        fmpq_poly_revert_series(B, A, n);

        acb_poly_set_fmpq_poly(a, A, rbits1);
        acb_poly_revert_series(b, a, n, rbits2);

        if (!acb_poly_contains_fmpq_poly(b, B))
        {
            flint_printf("FAIL\n\n");
            flint_printf("n = %wd, bits2 = %wd\n", n, rbits2);

            flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n");
            flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n");

            flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n");
            flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n");

            abort();
        }

        acb_poly_set(c, a);
        acb_poly_revert_series(c, c, n, rbits2);
        if (!acb_poly_equal(c, b))
        {
            flint_printf("FAIL (aliasing)\n\n");
            abort();
        }

        fmpq_poly_clear(A);
        fmpq_poly_clear(B);

        acb_poly_clear(a);
        acb_poly_clear(b);
        acb_poly_clear(c);
    }

    flint_randclear(state);
    flint_cleanup();
    flint_printf("PASS\n");
    return EXIT_SUCCESS;
}
コード例 #24
0
ファイル: t-cos_pi_series.c プロジェクト: argriffing/arb
int main()
{
    slong iter;
    flint_rand_t state;

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

    flint_randinit(state);

    for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
    {
        slong m, n1, n2, bits1, bits2, bits3;
        acb_poly_t S, A, B, C;
        acb_t pi;

        bits1 = 2 + n_randint(state, 200);
        bits2 = 2 + n_randint(state, 200);
        bits3 = 2 + n_randint(state, 200);

        m = 1 + n_randint(state, 30);
        n1 = 1 + n_randint(state, 30);
        n2 = 1 + n_randint(state, 30);

        acb_poly_init(S);
        acb_poly_init(A);
        acb_poly_init(B);
        acb_poly_init(C);
        acb_init(pi);

        acb_poly_randtest(S, state, m, bits1, 3);
        acb_poly_randtest(A, state, m, bits1, 3);
        acb_poly_randtest(B, state, m, bits1, 3);

        acb_poly_cos_pi_series(A, S, n1, bits2);

        acb_const_pi(pi, bits3);
        acb_poly_set_acb(B, pi);
        acb_poly_mul(B, S, B, bits3);
        acb_poly_cos_series(B, B, n2, bits3);

        acb_poly_set(C, A);
        acb_poly_truncate(C, FLINT_MIN(n1, n2));
        acb_poly_truncate(B, FLINT_MIN(n1, n2));

        if (!acb_poly_overlaps(B, C))
        {
            flint_printf("FAIL\n\n");
            flint_printf("S = "); acb_poly_printd(S, 15); flint_printf("\n\n");
            flint_printf("A = "); acb_poly_printd(A, 15); flint_printf("\n\n");
            flint_printf("B = "); acb_poly_printd(B, 15); flint_printf("\n\n");
            abort();
        }

        acb_poly_cos_pi_series(S, S, n1, bits2);

        if (!acb_poly_overlaps(A, S))
        {
            flint_printf("FAIL (aliasing)\n\n");
            abort();
        }

        acb_poly_clear(S);
        acb_poly_clear(A);
        acb_poly_clear(B);
        acb_poly_clear(C);
        acb_clear(pi);
    }

    flint_randclear(state);
    flint_cleanup();
    flint_printf("PASS\n");
    return EXIT_SUCCESS;
}
コード例 #25
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;
}
コード例 #26
0
/* F = 1 + U + U^2 + U^3 + ... = 1/(1-U)

   U = product of (1 + |A-B|/(|B[0] - |B[1:]|)
       product of (1 / (|B[0] - |B[1:]|))
       * |Z|
*/
void
acb_hypgeom_pfq_series_bound_factor(arb_poly_t F,
    const acb_poly_struct * a, long p,
    const acb_poly_struct * b, long q, 
    const acb_poly_t z,
    long n, long len, long prec)
{
    long i;

    arb_poly_t T, U, V;
    acb_poly_t BN, AB;

    /* not convergent */
    if (p > q)
    {
        arb_poly_fit_length(F, len);
        _arb_vec_indeterminate(F->coeffs, len);
        _arb_poly_set_length(F, len);
        return;
    }

    arb_poly_init(T);
    arb_poly_init(U);
    arb_poly_init(V);

    acb_poly_init(BN);
    acb_poly_init(AB);

    acb_poly_majorant(U, z, prec);

    for (i = 0; i < q; i++)
    {
        acb_poly_add_si(BN, b + i, n, prec);

        if (acb_poly_length(BN) != 0 &&
                arb_is_positive(acb_realref(BN->coeffs)))
        {
            if (i < p)
            {
                /* 1 + |a-b|/reciprocal_majorant(b + n) */
                acb_poly_sub(AB, a + i, b + i, prec);
                acb_poly_majorant(T, AB, prec);
                acb_poly_reciprocal_majorant(V, BN, prec);
                arb_poly_div_series(T, T, V, len, prec);
                arb_poly_add_si(T, T, 1, prec);
                arb_poly_mullow(U, U, T, len, prec);
            }
            else
            {
                acb_poly_reciprocal_majorant(T, BN, prec);
                arb_poly_div_series(U, U, T, len, prec);
            }
        }
        else
        {
            arb_poly_fit_length(U, len);
            _arb_vec_indeterminate(U->coeffs, len);
            _arb_poly_set_length(U,  len);
            break;
        }
    }

    /* F = 1/(1-U) */
    arb_poly_geometric_sum(F, U, len, prec);

    arb_poly_clear(T);
    arb_poly_clear(U);
    arb_poly_clear(V);

    acb_poly_clear(BN);
    acb_poly_clear(AB);
}
コード例 #27
0
void
acb_hypgeom_pfq_series_direct(acb_poly_t res,
    const acb_poly_struct * a, long p,
    const acb_poly_struct * b, long q,
    const acb_poly_t z, int regularized,
    long n, long len, long prec)
{
    acb_poly_t s, t, err;
    arb_poly_t C, T;
    long i;
    int is_real;

    /* default algorithm to choose number of terms */
    if (n < 0)
    {
        n = acb_hypgeom_pfq_series_choose_n(a, p, b, q, z, len, prec);
    }

    acb_poly_init(s);
    acb_poly_init(t);
    acb_poly_init(err);
    arb_poly_init(C);
    arb_poly_init(T);

    acb_hypgeom_pfq_series_sum_forward(s, t, a, p, b, q, z, regularized, n, len, prec);

    if (acb_poly_length(t) != 0)
    {
        is_real = acb_poly_is_real(z);
        for (i = 0; i < p; i++)
            is_real = is_real && acb_poly_is_real(a + i);
        for (i = 0; i < q; i++)
            is_real = is_real && acb_poly_is_real(b + i);

        acb_poly_majorant(T, t, MAG_BITS);
        acb_hypgeom_pfq_series_bound_factor(C, a, p, b, q, z, n, len, MAG_BITS);

        arb_poly_mullow(T, T, C, len, MAG_BITS);

        /* create polynomial of errors */
        acb_poly_fit_length(err, len);

        for (i = 0; i < FLINT_MIN(len, T->length); i++)
        {
            arb_add_error(acb_realref(err->coeffs + i), T->coeffs + i);
            if (!is_real)
                arb_add_error(acb_imagref(err->coeffs + i), T->coeffs + i);
        }

        _acb_poly_set_length(err, len);
        _acb_poly_normalise(err);

        acb_poly_add(s, s, err, prec);
    }

    acb_poly_set(res, s);

    acb_poly_clear(s);
    acb_poly_clear(t);
    acb_poly_clear(err);
    arb_poly_clear(C);
    arb_poly_clear(T);
}
コード例 #28
0
void
acb_hypgeom_pfq_series_sum_forward(acb_poly_t s, acb_poly_t t,
    const acb_poly_struct * a, long p,
    const acb_poly_struct * b, long q,
    const acb_poly_t z, int regularized,
    long n, long len, long prec)
{
    acb_poly_t u, v;
    acb_poly_t tmp;
    long k, i;

    acb_poly_init(u);
    acb_poly_init(v);
    acb_poly_init(tmp);

    if (!regularized)
    {
        acb_poly_zero(s);
        acb_poly_one(t);

        for (k = 0; k < n && acb_poly_length(t) != 0; k++)
        {
            acb_poly_add(s, s, t, prec);

            if (p > 0)
            {
                acb_poly_add_si(u, a, k, prec);

                for (i = 1; i < p; i++)
                {
                    acb_poly_add_si(v, a + i, k, prec);
                    acb_poly_mullow(u, u, v, len, prec);
                }

                acb_poly_mullow(t, t, u, len, prec);
            }

            if (q > 0)
            {
                acb_poly_add_si(u, b, k, prec);

                for (i = 1; i < q; i++)
                {
                    acb_poly_add_si(v, b + i, k, prec);
                    acb_poly_mullow(u, u, v, len, prec);
                }

                acb_poly_div_series(t, t, u, len, prec);
            }

            acb_poly_mullow(t, t, z, len, prec);
        }
    }
    else
    {
        acb_poly_zero(s);

        for (i = 0; i < q; i++)
        {
            if (i == 0)
            {
                acb_poly_rgamma_series(t, b + i, len, prec);
            }
            else
            {
                acb_poly_rgamma_series(u, b + i, len, prec);
                acb_poly_mullow(tmp, t, u, len, prec);
                acb_poly_swap(tmp, t);
            }
        }

        for (k = 0; k < n; k++)
        {
            acb_poly_add(s, s, t, prec);

            if (p > 0)
            {
                acb_poly_add_si(u, a, k, prec);

                for (i = 1; i < p; i++)
                {
                    acb_poly_add_si(v, a + i, k, prec);
                    acb_poly_mullow(tmp, u, v, len, prec);
                    acb_poly_swap(tmp, u);
                }

                acb_poly_mullow(tmp, t, u, len, prec);
                acb_poly_swap(tmp, t);
            }

            if (q > 0)
            {
                acb_poly_add_si(u, b, k, prec);

                for (i = 1; i < q; i++)
                {
                    acb_poly_add_si(v, b + i, k, prec);
                    acb_poly_mullow(tmp, u, v, len, prec);
                    acb_poly_swap(tmp, u);
                }

                if (acb_poly_length(u) > 0 && !acb_contains_zero(u->coeffs))
                {
                    acb_poly_div_series(tmp, t, u, len, prec);
                    acb_poly_mullow(t, tmp, z, len, prec);
                }
                else
                {
                    /* compute term from scratch */
                    acb_poly_one(t);

                    for (i = 0; i < p; i++)
                    {
                        acb_poly_rising_ui_series(v, a + i, k + 1, len, prec);
                        acb_poly_mullow(t, t, v, len, prec);
                    }

                    for (i = 0; i < q; i++)
                    {
                        acb_poly_add_si(v, b + i, k + 1, prec);
                        acb_poly_rgamma_series(v, v, len, prec);
                        acb_poly_mullow(t, t, v, len, prec);
                    }

                    acb_poly_pow_ui_trunc_binexp(v, z, k + 1, len, prec);
                    acb_poly_mullow(t, t, v, len, prec);
                }
            }
            else
            {
                acb_poly_mullow(tmp, t, z, len, prec);
                acb_poly_swap(tmp, t);
            }
        }
    }

    acb_poly_clear(u);
    acb_poly_clear(v);
    acb_poly_clear(tmp);
}
コード例 #29
0
int main()
{
    slong iter;
    flint_rand_t state;

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

    flint_randinit(state);

    for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
    {
        acb_poly_t ai, aip, bi, bip, ai2, aip2, bi2, bip2, z, w, t;
        acb_t c;
        slong n1, n2, prec1, prec2;
        unsigned int mask;

        acb_poly_init(ai); acb_poly_init(aip);
        acb_poly_init(bi); acb_poly_init(bip);
        acb_poly_init(ai2); acb_poly_init(aip2);
        acb_poly_init(bi2); acb_poly_init(bip2);
        acb_poly_init(z); acb_poly_init(w);
        acb_poly_init(t); acb_init(c);

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

        n1 = n_randint(state, 6);
        n2 = n_randint(state, 6);

        acb_poly_randtest(ai, state, 10, prec1, 10);
        acb_poly_randtest(aip, state, 10, prec1, 10);
        acb_poly_randtest(bi, state, 10, prec1, 10);
        acb_poly_randtest(bip, state, 10, prec1, 10);
        acb_poly_randtest(z, state, 1 + n_randint(state, 10), prec1, 10);

        acb_hypgeom_airy_series(ai, aip, bi, bip, z, n1, prec1);

        acb_poly_mullow(w, ai, bip, n1, prec1);
        acb_poly_mullow(t, bi, aip, n1, prec1);
        acb_poly_sub(w, w, t, prec1);

        acb_const_pi(c, prec1);
        acb_inv(c, c, prec1);
        acb_poly_set_acb(t, c);
        acb_poly_truncate(t, n1);

        if (!acb_poly_overlaps(w, t))
        {
            flint_printf("FAIL: wronskian\n\n");
            flint_printf("z = "); acb_poly_printd(z, 30); flint_printf("\n\n");
            flint_printf("ai = "); acb_poly_printd(ai, 30); flint_printf("\n\n");
            flint_printf("aip = "); acb_poly_printd(aip, 30); flint_printf("\n\n");
            flint_printf("bi = "); acb_poly_printd(bi, 30); flint_printf("\n\n");
            flint_printf("bip = "); acb_poly_printd(bip, 30); flint_printf("\n\n");
            flint_printf("w = "); acb_poly_printd(w, 30); flint_printf("\n\n");
            abort();
        }

        mask = n_randlimb(state);

        acb_hypgeom_airy_series((mask & 1) ? ai2 : NULL,
                                (mask & 2) ? aip2 : NULL,
                                (mask & 4) ? bi2 : NULL,
                                (mask & 8) ? bip2 : NULL, z, n2, prec2);

        acb_poly_truncate(ai, FLINT_MIN(n1, n2));
        acb_poly_truncate(aip, FLINT_MIN(n1, n2));
        acb_poly_truncate(bi, FLINT_MIN(n1, n2));
        acb_poly_truncate(bip, FLINT_MIN(n1, n2));
        acb_poly_truncate(ai2, FLINT_MIN(n1, n2));
        acb_poly_truncate(aip2, FLINT_MIN(n1, n2));
        acb_poly_truncate(bi2, FLINT_MIN(n1, n2));
        acb_poly_truncate(bip2, FLINT_MIN(n1, n2));

        if (((mask & 1) && (!acb_poly_overlaps(ai, ai2))) ||
            ((mask & 2) && (!acb_poly_overlaps(aip, aip2))) ||
            ((mask & 4) && (!acb_poly_overlaps(bi, bi2))) ||
            ((mask & 8) && (!acb_poly_overlaps(bip, bip2))))
        {
            flint_printf("FAIL: consistency (mask)\n\n");
            flint_printf("mask = %u\n\n", mask);
            flint_printf("len1 = %wd, len2 = %wd\n\n", n1, n2);
            flint_printf("z = "); acb_poly_printd(z, 30); flint_printf("\n\n");
            flint_printf("ai = "); acb_poly_printd(ai, 30); flint_printf("\n\n");
            flint_printf("ai2 = "); acb_poly_printd(ai2, 30); flint_printf("\n\n");
            flint_printf("aip = "); acb_poly_printd(aip, 30); flint_printf("\n\n");
            flint_printf("aip2 = "); acb_poly_printd(aip2, 30); flint_printf("\n\n");
            flint_printf("bi = "); acb_poly_printd(bi, 30); flint_printf("\n\n");
            flint_printf("bi2 = "); acb_poly_printd(bi2, 30); flint_printf("\n\n");
            flint_printf("bip = "); acb_poly_printd(bip, 30); flint_printf("\n\n");
            flint_printf("bip2 = "); acb_poly_printd(bip2, 30); flint_printf("\n\n");
            abort();
        }

        acb_poly_clear(ai); acb_poly_clear(aip);
        acb_poly_clear(bi); acb_poly_clear(bip);
        acb_poly_clear(ai2); acb_poly_clear(aip2);
        acb_poly_clear(bi2); acb_poly_clear(bip2);
        acb_poly_clear(z); acb_poly_clear(w);
        acb_poly_clear(t); acb_clear(c);
    }

    flint_randclear(state);
    flint_cleanup();
    flint_printf("PASS\n");
    return EXIT_SUCCESS;
}
コード例 #30
0
ファイル: bessel_k.c プロジェクト: isuruf/arb
void
acb_hypgeom_bessel_k_0f1_series(acb_poly_t res,
    const acb_poly_t nu, const acb_poly_t z,
    slong len, slong prec)
{
    acb_poly_t s, u, A, B;
    acb_poly_struct b[2];
    arb_t c;
    slong wlen;
    int singular;

    acb_poly_init(s);
    acb_poly_init(u);
    acb_poly_init(A);
    acb_poly_init(B);
    acb_poly_init(b + 0);
    acb_poly_init(b + 1);
    arb_init(c);

    singular = (nu->length == 0) || acb_is_int(nu->coeffs);
    wlen = len + (singular != 0);

    /* A = (z/2)^nu, B = 1/A */
    acb_poly_scalar_mul_2exp_si(A, z, -1);
    acb_poly_pow_series(A, A, nu, wlen, prec);
    acb_poly_inv_series(B, A, wlen, prec);

    acb_poly_mullow(u, z, z, wlen, prec);
    acb_poly_scalar_mul_2exp_si(u, u, -2);

    acb_poly_one(b + 1);
    acb_poly_add_si(b + 0, nu, 1, prec);
    acb_hypgeom_pfq_series_direct(s, NULL, 0, b, 2, u, 1, -1, wlen, prec);
    acb_poly_mullow(A, A, s, wlen, prec);

    acb_poly_add_si(b + 0, nu, -1, prec);
    acb_poly_neg(b + 0, b + 0);
    acb_hypgeom_pfq_series_direct(s, NULL, 0, b, 2, u, 1, -1, wlen, prec);
    acb_poly_mullow(B, B, s, wlen, prec);

    acb_poly_sub(A, B, A, prec);
    acb_poly_scalar_mul_2exp_si(A, A, -1);

    /* multiply by pi csc(pi nu) */
    acb_poly_sin_pi_series(B, nu, wlen, prec);

    if (singular)
    {
        acb_poly_shift_right(A, A, 1);
        acb_poly_shift_right(B, B, 1);
    }

    acb_poly_div_series(res, A, B, len, prec);

    arb_const_pi(c, prec);
    _acb_vec_scalar_mul_arb(res->coeffs, res->coeffs, res->length, c, prec);

    acb_poly_clear(s);
    acb_poly_clear(u);
    acb_poly_clear(A);
    acb_poly_clear(B);
    acb_poly_clear(b + 0);
    acb_poly_clear(b + 1);
    arb_clear(c);
}