flint-sys 0.9.0

Bindings to the FLINT C library
Documentation 
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/*
    Copyright (C) 2012, 2013 Fredrik Johansson

    This file is part of FLINT.

    FLINT is free software: you can redistribute it and/or modify it under
    the terms of the GNU Lesser General Public License (LGPL) as published
    by the Free Software Foundation; either version 3 of the License, or
    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
*/

#include "arb_poly.h"
#include "acb_poly.h"

static void
_acb_poly_rising_ui_series_bsplit(acb_ptr res,
    acb_srcptr f, slong flen, ulong a, ulong b,
        slong trunc, slong prec)
{
    flen = FLINT_MIN(flen, trunc);

    if (b - a == 1)
    {
        acb_add_ui(res, f, a, prec);
        _acb_vec_set(res + 1, f + 1, flen - 1);
    }
    else
    {
        acb_ptr L, R;
        slong len1, len2;

        slong m = a + (b - a) / 2;

        len1 = poly_pow_length(flen, m - a, trunc);
        len2 = poly_pow_length(flen, b - m, trunc);

        L = _acb_vec_init(len1 + len2);
        R = L + len1;

        _acb_poly_rising_ui_series_bsplit(L, f, flen, a, m, trunc, prec);
        _acb_poly_rising_ui_series_bsplit(R, f, flen, m, b, trunc, prec);

        _acb_poly_mullow(res, L, len1, R, len2,
            FLINT_MIN(trunc, len1 + len2 - 1), prec);

        _acb_vec_clear(L, len1 + len2);
    }
}

void
_acb_poly_rising_ui_series(acb_ptr res,
    acb_srcptr f, slong flen, ulong r,
        slong trunc, slong prec)
{
    if (trunc == 1 || flen == 1)
    {
        acb_rising_ui(res, f, r, prec);
        _acb_vec_zero(res + 1, trunc - 1);
    }
    else if (trunc == 2)
    {
        acb_rising2_ui(res, res + 1, f, r, prec);
        acb_mul(res + 1, res + 1, f + 1, prec);
    }
    else
    {
        _acb_poly_rising_ui_series_bsplit(res, f, flen, 0, r, trunc, prec);
    }
}

void
acb_poly_rising_ui_series(acb_poly_t res, const acb_poly_t f, ulong r, slong trunc, slong prec)
{
    slong len;

    if ((f->length == 0 && r != 0) || trunc == 0)
    {
        acb_poly_zero(res);
        return;
    }

    if (r == 0)
    {
        acb_poly_one(res);
        return;
    }

    len = poly_pow_length(f->length, r, trunc);

    if (f == res)
    {
        acb_poly_t tmp;
        acb_poly_init(tmp);
        acb_poly_rising_ui_series(tmp, f, r, len, prec);
        acb_poly_swap(tmp, res);
        acb_poly_clear(tmp);
    }
    else
    {
        acb_poly_fit_length(res, len);
        _acb_poly_rising_ui_series(res->coeffs, f->coeffs, f->length, r, len, prec);
        _acb_poly_set_length(res, len);
        _acb_poly_normalise(res);
    }
}