arb/arb_calc/refine_root_bisect.c
2019-02-12 09:22:08 +01:00

107 lines
2.5 KiB
C

/*
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_calc.h"
/* TODO: refactor/combine some of this code with isolate_roots.c */
int arb_calc_partition(arf_interval_t L, arf_interval_t R,
arb_calc_func_t func, void * param, const arf_interval_t block, slong prec)
{
arb_t t, m;
arf_t u;
int msign;
arb_init(t);
arb_init(m);
arf_init(u);
/* Compute the midpoint (TODO: try other points) */
arf_add(u, &block->a, &block->b, ARF_PREC_EXACT, ARF_RND_DOWN);
arf_mul_2exp_si(u, u, -1);
/* Evaluate and get sign at midpoint */
arb_set_arf(m, u);
func(t, m, param, 1, prec);
msign = arb_sgn_nonzero(t);
/* L, R = block, split at midpoint */
arf_set(&L->a, &block->a);
arf_set(&R->b, &block->b);
arf_set(&L->b, u);
arf_set(&R->a, u);
arb_clear(t);
arb_clear(m);
arf_clear(u);
return msign;
}
int arb_calc_refine_root_bisect(arf_interval_t r, arb_calc_func_t func,
void * param, const arf_interval_t start, slong iter, slong prec)
{
int asign, bsign, msign, result;
slong i;
arf_interval_t t, u;
arb_t m, v;
arf_interval_init(t);
arf_interval_init(u);
arb_init(m);
arb_init(v);
arb_set_arf(m, &start->a);
func(v, m, param, 1, prec);
asign = arb_sgn_nonzero(v);
arb_set_arf(m, &start->b);
func(v, m, param, 1, prec);
bsign = arb_sgn_nonzero(v);
/* must have proper sign changes */
if (asign == 0 || bsign == 0 || asign == bsign)
{
result = ARB_CALC_IMPRECISE_INPUT;
}
else
{
arf_interval_set(r, start);
result = ARB_CALC_SUCCESS;
for (i = 0; i < iter; i++)
{
msign = arb_calc_partition(t, u, func, param, r, prec);
/* the algorithm fails if the value at the midpoint cannot
be distinguished from zero */
if (msign == 0)
{
result = ARB_CALC_NO_CONVERGENCE;
break;
}
if (msign == asign)
arf_interval_swap(r, u);
else
arf_interval_swap(r, t);
}
}
arf_interval_clear(t);
arf_interval_clear(u);
arb_clear(m);
arb_clear(v);
return result;
}