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/*
Copyright (C) 2017 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_fmpz_poly.h"
#include "flint/profiler.h"
static int check_accuracy(acb_ptr vec, slong len, slong prec)
{
slong i;
for (i = 0; i < len; i++)
{
if (acb_rel_accuracy_bits(vec + i) < prec)
return 0;
}
return 1;
}
static int check_isolation(acb_srcptr roots, slong len)
{
slong i, j;
for (i = 0; i < len; i++)
{
if (arf_sgn(arb_midref(acb_imagref(roots + i))) >= 0)
{
for (j = i + 1; j < len; j++)
{
if (arf_sgn(arb_midref(acb_imagref(roots + j))) >= 0)
{
if (acb_overlaps(roots + i, roots + j))
return 0;
}
}
}
}
return 1;
}
void
arb_fmpz_poly_complex_roots(acb_ptr roots, const fmpz_poly_t poly, int flags, slong target_prec)
{
slong i, j, prec, deg, deg_deflated, isolated, maxiter, deflation;
slong initial_prec, num_real;
acb_poly_t cpoly, cpoly_deflated;
fmpz_poly_t poly_deflated;
acb_ptr roots_deflated;
int removed_zero;
if (fmpz_poly_degree(poly) < 1)
return;
initial_prec = 32;
fmpz_poly_init(poly_deflated);
acb_poly_init(cpoly);
acb_poly_init(cpoly_deflated);
/* try to write poly as poly_deflated(x^deflation), possibly multiplied by x */
removed_zero = fmpz_is_zero(poly->coeffs);
if (removed_zero)
fmpz_poly_shift_right(poly_deflated, poly, 1);
else
fmpz_poly_set(poly_deflated, poly);
deflation = arb_fmpz_poly_deflation(poly_deflated);
arb_fmpz_poly_deflate(poly_deflated, poly_deflated, deflation);
deg = fmpz_poly_degree(poly);
deg_deflated = fmpz_poly_degree(poly_deflated);
if (flags & ARB_FMPZ_POLY_ROOTS_VERBOSE)
{
flint_printf("searching for %wd roots, %wd deflated\n", deg, deg_deflated);
}
/* we only need deg_deflated entries, but the remainder will be useful
as scratch space */
roots_deflated = _acb_vec_init(deg);
for (prec = initial_prec; ; prec *= 2)
{
acb_poly_set_fmpz_poly(cpoly_deflated, poly_deflated, prec);
maxiter = FLINT_MIN(4 * deg_deflated + 64, prec);
if (flags & ARB_FMPZ_POLY_ROOTS_VERBOSE)
{
TIMEIT_ONCE_START
flint_printf("prec=%wd: ", prec);
isolated = acb_poly_find_roots(roots_deflated, cpoly_deflated,
prec == initial_prec ? NULL : roots_deflated, maxiter, prec);
flint_printf("%wd isolated roots | ", isolated);
TIMEIT_ONCE_STOP
}
else
{
isolated = acb_poly_find_roots(roots_deflated, cpoly_deflated,
prec == initial_prec ? NULL : roots_deflated, maxiter, prec);
}
if (isolated == deg_deflated)
{
if (!check_accuracy(roots_deflated, deg_deflated, target_prec))
continue;
if (deflation == 1)
{
_acb_vec_set(roots, roots_deflated, deg_deflated);
}
else /* compute all nth roots */
{
acb_t w, w2;
acb_init(w);
acb_init(w2);
acb_unit_root(w, deflation, prec);
acb_unit_root(w2, 2 * deflation, prec);
for (i = 0; i < deg_deflated; i++)
{
if (arf_sgn(arb_midref(acb_realref(roots_deflated + i))) > 0)
{
acb_root_ui(roots + i * deflation,
roots_deflated + i, deflation, prec);
}
else
{
acb_neg(roots + i * deflation, roots_deflated + i);
acb_root_ui(roots + i * deflation,
roots + i * deflation, deflation, prec);
acb_mul(roots + i * deflation,
roots + i * deflation, w2, prec);
}
for (j = 1; j < deflation; j++)
{
acb_mul(roots + i * deflation + j,
roots + i * deflation + j - 1, w, prec);
}
}
acb_clear(w);
acb_clear(w2);
}
/* by assumption that poly is squarefree, must be just one */
if (removed_zero)
acb_zero(roots + deg_deflated * deflation);
if (!check_accuracy(roots, deg, target_prec))
continue;
acb_poly_set_fmpz_poly(cpoly, poly, prec);
if (!acb_poly_validate_real_roots(roots, cpoly, prec))
continue;
for (i = 0; i < deg; i++)
{
if (arb_contains_zero(acb_imagref(roots + i)))
arb_zero(acb_imagref(roots + i));
}
if (!check_isolation(roots, deg))
{
/* extremely unlikely */
if (flags & ARB_FMPZ_POLY_ROOTS_VERBOSE)
flint_printf("isolation failure!\n");
continue;
}
if (flags & ARB_FMPZ_POLY_ROOTS_VERBOSE)
flint_printf("done!\n");
break;
}
}
_acb_vec_sort_pretty(roots, deg);
/* pair conjugates */
num_real = 0;
for (i = 0; i < deg; i++)
if (acb_is_real(roots + i))
num_real++;
if (deg != num_real)
{
for (i = num_real, j = 0; i < deg; i++)
{
if (arb_is_positive(acb_imagref(roots + i)))
{
acb_swap(roots_deflated + j, roots + i);
j++;
}
}
for (i = 0; i < (deg - num_real) / 2; i++)
{
acb_swap(roots + num_real + 2 * i, roots_deflated + i);
acb_conj(roots + num_real + 2 * i + 1, roots + num_real + 2 * i);
}
}
fmpz_poly_clear(poly_deflated);
acb_poly_clear(cpoly);
acb_poly_clear(cpoly_deflated);
_acb_vec_clear(roots_deflated, deg);
}
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