mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
127 lines
3 KiB
C
127 lines
3 KiB
C
/*
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Copyright (C) 2012 Fredrik Johansson
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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 it under
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the terms of the GNU Lesser General Public License (LGPL) as published
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by the Free Software Foundation; either version 2.1 of the License, or
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(at your option) any later version. See <http://www.gnu.org/licenses/>.
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*/
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#include "acb_poly.h"
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void
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_acb_poly_interpolation_weights(acb_ptr w,
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acb_ptr * tree, slong len, slong prec)
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{
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acb_ptr tmp;
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slong i, n, height;
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if (len == 0)
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return;
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if (len == 1)
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{
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acb_one(w);
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return;
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}
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tmp = _acb_vec_init(len + 1);
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height = FLINT_CLOG2(len);
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n = WORD(1) << (height - 1);
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_acb_poly_mul_monic(tmp, tree[height-1], n + 1,
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tree[height-1] + (n + 1), (len - n + 1), prec);
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_acb_poly_derivative(tmp, tmp, len + 1, prec);
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_acb_poly_evaluate_vec_fast_precomp(w, tmp, len, tree, len, prec);
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for (i = 0; i < len; i++)
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acb_inv(w + i, w + i, prec);
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_acb_vec_clear(tmp, len + 1);
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}
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void
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_acb_poly_interpolate_fast_precomp(acb_ptr poly,
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acb_srcptr ys, acb_ptr * tree, acb_srcptr weights,
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slong len, slong prec)
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{
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acb_ptr t, u, pa, pb;
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slong i, pow, left;
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if (len == 0)
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return;
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t = _acb_vec_init(len);
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u = _acb_vec_init(len);
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for (i = 0; i < len; i++)
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acb_mul(poly + i, weights + i, ys + i, prec);
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for (i = 0; i < FLINT_CLOG2(len); i++)
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{
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pow = (WORD(1) << i);
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pa = tree[i];
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pb = poly;
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left = len;
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while (left >= 2 * pow)
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{
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_acb_poly_mul(t, pa, pow + 1, pb + pow, pow, prec);
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_acb_poly_mul(u, pa + pow + 1, pow + 1, pb, pow, prec);
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_acb_vec_add(pb, t, u, 2 * pow, prec);
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left -= 2 * pow;
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pa += 2 * pow + 2;
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pb += 2 * pow;
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}
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if (left > pow)
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{
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_acb_poly_mul(t, pa, pow + 1, pb + pow, left - pow, prec);
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_acb_poly_mul(u, pb, pow, pa + pow + 1, left - pow + 1, prec);
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_acb_vec_add(pb, t, u, left, prec);
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}
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}
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_acb_vec_clear(t, len);
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_acb_vec_clear(u, len);
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}
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void
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_acb_poly_interpolate_fast(acb_ptr poly,
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acb_srcptr xs, acb_srcptr ys, slong len, slong prec)
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{
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acb_ptr * tree;
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acb_ptr w;
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tree = _acb_poly_tree_alloc(len);
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_acb_poly_tree_build(tree, xs, len, prec);
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w = _acb_vec_init(len);
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_acb_poly_interpolation_weights(w, tree, len, prec);
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_acb_poly_interpolate_fast_precomp(poly, ys, tree, w, len, prec);
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_acb_vec_clear(w, len);
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_acb_poly_tree_free(tree, len);
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}
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void
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acb_poly_interpolate_fast(acb_poly_t poly,
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acb_srcptr xs, acb_srcptr ys, slong n, slong prec)
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{
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if (n == 0)
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{
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acb_poly_zero(poly);
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}
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else
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{
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acb_poly_fit_length(poly, n);
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_acb_poly_set_length(poly, n);
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_acb_poly_interpolate_fast(poly->coeffs, xs, ys, n, prec);
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_acb_poly_normalise(poly);
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}
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}
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