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https://github.com/vale981/arb
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75 lines
2.3 KiB
C
75 lines
2.3 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) 2012, 2013 Fredrik Johansson
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******************************************************************************/
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#include "fmprb.h"
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void
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fmprb_root(fmprb_t z, const fmprb_t x, ulong k, long prec)
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{
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long r;
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if (fmprb_contains_negative(x))
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{
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fmpr_nan(fmprb_midref(z));
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fmpr_pos_inf(fmprb_radref(z));
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return;
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}
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if (fmprb_is_exact(x))
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{
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r = fmpr_root(fmprb_midref(z), fmprb_midref(x), k, prec, FMPR_RND_DOWN);
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fmpr_set_error_result(fmprb_radref(z), fmprb_midref(z), r);
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}
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else
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{
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fmpr_t t, u, err;
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fmpr_init(t);
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fmpr_init(u);
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fmpr_init(err);
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/* lower point */
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fmpr_sub(err, fmprb_midref(x), fmprb_radref(x), FMPRB_RAD_PREC, FMPR_RND_DOWN);
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/* derivative x^(1/k) / (x k) at lower point */
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fmpr_root(t, err, k, FMPRB_RAD_PREC, FMPR_RND_UP);
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fmpr_mul_ui(u, err, k, FMPRB_RAD_PREC, FMPR_RND_DOWN);
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fmpr_div(t, t, u, FMPRB_RAD_PREC, FMPR_RND_UP);
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/* multiplied by distance */
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fmpr_mul(err, t, fmprb_radref(x), FMPRB_RAD_PREC, FMPR_RND_UP);
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r = fmpr_root(fmprb_midref(z), fmprb_midref(x), k, prec, FMPR_RND_DOWN);
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fmpr_add_error_result(fmprb_radref(z), err, fmprb_midref(z), r,
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FMPRB_RAD_PREC, FMPR_RND_UP);
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fmpr_clear(t);
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fmpr_clear(u);
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fmpr_clear(err);
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}
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fmprb_adjust(z);
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}
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