Exemplo n.º 1
0
void
_acb_poly_compose_series_brent_kung(acb_ptr res,
    acb_srcptr poly1, long len1,
    acb_srcptr poly2, long len2, long n, long prec)
{
    acb_mat_t A, B, C;
    acb_ptr t, h;
    long i, m;

    if (n == 1)
    {
        acb_set(res, poly1);
        return;
    }

    m = n_sqrt(n) + 1;

    acb_mat_init(A, m, n);
    acb_mat_init(B, m, m);
    acb_mat_init(C, m, n);

    h = _acb_vec_init(n);
    t = _acb_vec_init(n);

    /* Set rows of B to the segments of poly1 */
    for (i = 0; i < len1 / m; i++)
        _acb_vec_set(B->rows[i], poly1 + i*m, m);
    _acb_vec_set(B->rows[i], poly1 + i*m, len1 % m);

    /* Set rows of A to powers of poly2 */
    acb_set_ui(A->rows[0] + 0, 1UL);
    _acb_vec_set(A->rows[1], poly2, len2);
    for (i = 2; i < m; i++)
        _acb_poly_mullow(A->rows[i], A->rows[(i + 1) / 2], n, A->rows[i / 2], n, n, prec);

    acb_mat_mul(C, B, A, prec);

    /* Evaluate block composition using the Horner scheme */
    _acb_vec_set(res, C->rows[m - 1], n);
    _acb_poly_mullow(h, A->rows[m - 1], n, poly2, len2, n, prec);

    for (i = m - 2; i >= 0; i--)
    {
        _acb_poly_mullow(t, res, n, h, n, n, prec);
        _acb_poly_add(res, t, n, C->rows[i], n, prec);
    }

    _acb_vec_clear(h, n);
    _acb_vec_clear(t, n);

    acb_mat_clear(A);
    acb_mat_clear(B);
    acb_mat_clear(C);
}
Exemplo n.º 2
0
void
acb_poly_add(acb_poly_t res, const acb_poly_t poly1,
              const acb_poly_t poly2, long prec)
{
    long max = FLINT_MAX(poly1->length, poly2->length);

    acb_poly_fit_length(res, max);

    _acb_poly_add(res->coeffs, poly1->coeffs, poly1->length, poly2->coeffs,
                   poly2->length, prec);

    _acb_poly_set_length(res, max);
    _acb_poly_normalise(res);
}
Exemplo n.º 3
0
void
acb_poly_add_series(acb_poly_t res, const acb_poly_t poly1,
              const acb_poly_t poly2, slong len, slong prec)
{
    slong len1, len2;

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

    len1 = FLINT_MIN(len1, len);
    len2 = FLINT_MIN(len2, len);
    len = FLINT_MAX(len1, len2);

    acb_poly_fit_length(res, len);
    _acb_poly_add(res->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, prec);
    _acb_poly_set_length(res, len);
    _acb_poly_normalise(res);
}
Exemplo n.º 4
0
void
_acb_poly_compose_series_horner(acb_ptr res, acb_srcptr poly1, slong len1,
                            acb_srcptr poly2, slong len2, slong n, slong prec)
{
    if (n == 1)
    {
        acb_set(res, poly1);
    }
    else
    {
        slong i = len1 - 1;
        slong lenr;

        acb_ptr t = _acb_vec_init(n);

        lenr = len2;
        _acb_vec_scalar_mul(res, poly2, len2, poly1 + i, prec);
        i--;
        acb_add(res, res, poly1 + i, prec);

        while (i > 0)
        {
            i--;
            if (lenr + len2 - 1 < n)
            {
                _acb_poly_mul(t, res, lenr, poly2, len2, prec);
                lenr = lenr + len2 - 1;
            }
            else
            {
                _acb_poly_mullow(t, res, lenr, poly2, len2, n, prec);
                lenr = n;
            }
            _acb_poly_add(res, t, lenr, poly1 + i, 1, prec);
        }

        _acb_vec_zero(res + lenr, n - lenr);
        _acb_vec_clear(t, n);
    }
}