mirror of
https://github.com/vale981/arb
synced 2025-03-04 17:01:40 -05:00
107 lines
2.5 KiB
C
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;
|
|
}
|
|
|