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/*
Copyright (C) 2020 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 "fmpz_poly.h"
#include "arb_fmpz_poly.h"
#include "qqbar.h"
void
_qqbar_enclosure_raw(acb_t res, const fmpz_poly_t poly, const acb_t zin, slong prec)
{
slong d, orig_prec, step, acc;
fmpz_poly_t deriv;
acb_t z, zmid, t, u;
if (acb_rel_accuracy_bits(zin) >= prec - 3)
{
acb_set(res, zin);
return;
}
d = fmpz_poly_degree(poly);
if (d == 1)
{
arb_set_fmpz(acb_realref(res), poly->coeffs);
arb_div_fmpz(acb_realref(res), acb_realref(res), poly->coeffs + 1, prec);
arb_neg(acb_realref(res), acb_realref(res));
arb_zero(acb_imagref(res));
return;
}
orig_prec = prec;
acc = acb_rel_accuracy_bits(zin);
prec = FLINT_MAX(acc, 32) + 10;
fmpz_poly_init(deriv);
fmpz_poly_derivative(deriv, poly);
acb_init(z);
acb_init(zmid);
acb_init(t);
acb_init(u);
acb_set(z, zin);
for (step = 0; ; step++)
{
/*
printf("trying %ld, %ld\n", step, prec);
acb_printn(z, prec, ARB_STR_CONDENSE * 10);
printf("\n");
*/
if (step > 40 || prec > 1000000000)
{
flint_throw(FLINT_ERROR, "qqbar_enclosure_raw: root refinement not converging\n");
}
prec *= 2;
/* Interval Newton refinement */
acb_get_mid(zmid, z);
arb_fmpz_poly_evaluate_acb(t, poly, zmid, prec);
arb_fmpz_poly_evaluate_acb(u, deriv, z, prec);
acb_div(t, t, u, prec);
acb_sub(t, zmid, t, prec);
if (acb_contains(z, t) && acb_rel_accuracy_bits(t) >= 1.1 * orig_prec)
{
acb_set(res, t);
break;
}
if (acb_contains(z, t) && acb_rel_accuracy_bits(t) > 1.5 * acb_rel_accuracy_bits(z))
{
/* Use refined value for next iteration */
acb_set(z, t);
}
else
{
/* Newton refinement seems to be converging too slowly --
force a slow recomputation of all roots (this could be improved...) */
acb_ptr roots;
slong found, i;
/*
printf("recompute %ld %ld\n", d, prec);
*/
roots = _acb_vec_init(d);
/*
fmpz_poly_print(poly);
printf("\n");
*/
if (!fmpz_poly_is_squarefree(poly))
flint_throw(FLINT_ERROR, "(%s)\n", __func__);
arb_fmpz_poly_complex_roots(roots, poly, 0, 2 * prec);
/* Check for unique root */
found = -1;
for (i = 0; i < d && found != -2; i++)
{
if (acb_overlaps(roots + i, z))
{
if (found == -1)
found = i;
else
found = -2;
}
}
if (found >= 0)
acb_set(t, roots + found);
_acb_vec_clear(roots, d);
if (found >= 0 && acb_rel_accuracy_bits(t) >= 1.1 * orig_prec)
{
acb_set(res, t);
break;
}
if (found >= 0 && acb_rel_accuracy_bits(t) > 1.5 * acb_rel_accuracy_bits(z) + 1)
{
/* Use refined value for next iteration */
acb_set(z, t);
}
}
}
fmpz_poly_clear(deriv);
acb_clear(z);
acb_clear(zmid);
acb_clear(t);
acb_clear(u);
}
void
qqbar_enclosure_raw(acb_t res, const qqbar_t x, slong prec)
{
_qqbar_enclosure_raw(res, QQBAR_POLY(x), QQBAR_ENCLOSURE(x), prec);
}