/*
    Copyright (C) 2013 Fredrik Johansson

    This file is part of Arb.

    Arb 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 2.1 of the License, or
    (at your option) any later version.  See <http://www.gnu.org/licenses/>.
*/

#include "arb_poly.h"

void
_arb_poly_newton_convergence_factor(arf_t convergence_factor,
    arb_srcptr poly, slong len,
    const arb_t convergence_interval, slong prec)
{
    arb_ptr deriv;
    arb_t t, u;

    arb_init(t);
    arb_init(u);
    deriv = _arb_vec_init(len - 1);

    _arb_poly_derivative(deriv, poly, len, prec);
    _arb_poly_evaluate(t, deriv, len - 1, convergence_interval, prec);

    _arb_poly_derivative(deriv, deriv, len - 1, prec);
    _arb_poly_evaluate(u, deriv, len - 2, convergence_interval, prec);

    arb_div(t, u, t, prec);
    arb_mul_2exp_si(t, t, -1);

    arb_get_abs_ubound_arf(convergence_factor, t, prec);

    _arb_vec_clear(deriv, len - 1);
    arb_clear(t);
    arb_clear(u);
}