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https://github.com/vale981/arb
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77 lines
2.1 KiB
C
77 lines
2.1 KiB
C
/*=============================================================================
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This file is part of ARB.
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ARB is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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ARB is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with ARB; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2013 Fredrik Johansson
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******************************************************************************/
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#include "arb_calc.h"
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int arb_calc_newton_step(arb_t xnew, arb_calc_func_t func,
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void * param, const arb_t x, const arb_t conv_region,
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const arf_t conv_factor, slong prec)
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{
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mag_t err, v;
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arb_t t;
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arb_struct u[2];
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int result;
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mag_init(err);
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mag_init(v);
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arb_init(t);
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arb_init(u + 0);
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arb_init(u + 1);
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mag_mul(err, arb_radref(x), arb_radref(x));
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arf_get_mag(v, conv_factor);
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mag_mul(err, err, v);
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arf_set(arb_midref(t), arb_midref(x));
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mag_zero(arb_radref(t));
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func(u, t, param, 2, prec);
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arb_div(u, u, u + 1, prec);
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arb_sub(u, t, u, prec);
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mag_add(arb_radref(u), arb_radref(u), err);
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if (arb_contains(conv_region, u) &&
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(mag_cmp(arb_radref(u), arb_radref(x)) < 0))
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{
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arb_swap(xnew, u);
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result = ARB_CALC_SUCCESS;
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}
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else
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{
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arb_set(xnew, x);
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result = ARB_CALC_NO_CONVERGENCE;
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}
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arb_clear(t);
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arb_clear(u);
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arb_clear(u + 1);
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mag_clear(err);
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mag_clear(v);
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return result;
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}
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