mirror of
https://github.com/vale981/arb
synced 2025-03-06 01:41:39 -05:00
119 lines
3 KiB
C
119 lines
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 Fredrik Johansson
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******************************************************************************/
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#include "fmpcb_poly.h"
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static void
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_interpolate_newton(fmpcb_ptr ys, fmpcb_srcptr xs, long n, long prec)
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{
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fmpcb_t p, q, t;
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long i, j;
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fmpcb_init(p);
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fmpcb_init(q);
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fmpcb_init(t);
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for (i = 1; i < n; i++)
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{
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fmpcb_set(t, ys + i - 1);
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for (j = i; j < n; j++)
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{
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fmpcb_sub(p, ys + j, t, prec);
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fmpcb_sub(q, xs + j, xs + j - i, prec);
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fmpcb_set(t, ys + j);
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fmpcb_div(ys + j, p, q, prec);
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}
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}
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fmpcb_clear(p);
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fmpcb_clear(q);
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fmpcb_clear(t);
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}
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static void
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_newton_to_monomial(fmpcb_ptr ys, fmpcb_srcptr xs, long n, long prec)
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{
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fmpcb_t t, u;
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long i, j;
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fmpcb_init(t);
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fmpcb_init(u);
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for (i = n - 2; i >= 0; i--)
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{
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fmpcb_set(t, ys + i);
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fmpcb_set(ys + i, ys + i + 1);
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for (j = i + 1; j < n - 1; j++)
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{
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fmpcb_mul(u, ys + j, xs + i, prec);
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fmpcb_sub(ys + j, ys + j + 1, u, prec);
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}
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fmpcb_mul(u, ys + n - 1, xs + i, prec);
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fmpcb_sub(ys + n - 1, t, u, prec);
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}
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_fmpcb_poly_reverse(ys, ys, n, n);
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fmpcb_clear(t);
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fmpcb_clear(u);
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}
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void
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_fmpcb_poly_interpolate_newton(fmpcb_ptr poly, fmpcb_srcptr xs,
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fmpcb_srcptr ys, long n, long prec)
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{
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if (n == 1)
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{
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fmpcb_set(poly, ys);
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}
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else
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{
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_fmpcb_vec_set(poly, ys, n);
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_interpolate_newton(poly, xs, n, prec);
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while (n > 0 && fmpcb_is_zero(poly + n - 1)) n--;
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_newton_to_monomial(poly, xs, n, prec);
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}
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}
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void
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fmpcb_poly_interpolate_newton(fmpcb_poly_t poly,
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fmpcb_srcptr xs, fmpcb_srcptr ys, long n, long prec)
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{
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if (n == 0)
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{
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fmpcb_poly_zero(poly);
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}
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else
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{
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fmpcb_poly_fit_length(poly, n);
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_fmpcb_poly_set_length(poly, n);
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_fmpcb_poly_interpolate_newton(poly->coeffs,
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xs, ys, n, prec);
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_fmpcb_poly_normalise(poly);
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}
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}
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