arb/arb_poly/newton_refine_root.c

77 lines
2.3 KiB
C

/*=============================================================================
This file is part of ARB.
ARB is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
ARB is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with ARB; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2013 Fredrik Johansson
******************************************************************************/
#include "arb_poly.h"
static __inline__ slong _arf_mag(const arf_t c)
{
slong m = arf_abs_bound_lt_2exp_si(c);
return FLINT_MAX(m, 0);
}
void
_arb_poly_newton_refine_root(arb_t r, arb_srcptr poly, slong len,
const arb_t start,
const arb_t convergence_interval,
const arf_t convergence_factor,
slong eval_extra_prec,
slong prec)
{
slong precs[FLINT_BITS];
slong i, iters, wp, padding, start_prec;
start_prec = arb_rel_accuracy_bits(start);
padding = 5 + _arf_mag(convergence_factor);
precs[0] = prec + padding;
iters = 1;
while ((iters < FLINT_BITS) && (precs[iters-1] + padding > 2*start_prec))
{
precs[iters] = (precs[iters-1] / 2) + padding;
iters++;
if (iters == FLINT_BITS)
{
flint_printf("newton_refine_root: initial value too imprecise\n");
abort();
}
}
arb_set(r, start);
for (i = iters - 1; i >= 0; i--)
{
wp = precs[i] + eval_extra_prec;
if (!_arb_poly_newton_step(r, poly, len, r, convergence_interval,
convergence_factor, wp))
{
flint_printf("warning: newton_refine_root: improvement failed\n");
break;
}
}
}