mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
97 lines
2 KiB
C
97 lines
2 KiB
C
/*
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Copyright (C) 2016 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 "arb_poly.h"
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void
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_arb_poly_taylor_shift_convolution(arb_ptr p, const arb_t c, slong len, slong prec)
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{
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slong i, n = len - 1;
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arb_t f, d;
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arb_ptr t, u;
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if (arb_is_zero(c) || len <= 1)
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return;
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t = _arb_vec_init(len);
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u = _arb_vec_init(len);
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arb_init(f);
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arb_init(d);
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arb_one(f);
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for (i = 2; i <= n; i++)
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{
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arb_mul_ui(f, f, i, prec);
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arb_mul(p + i, p + i, f, prec);
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}
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_arb_poly_reverse(p, p, len, len);
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arb_one(t + n);
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for (i = n; i > 0; i--)
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arb_mul_ui(t + i - 1, t + i, i, prec);
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if (arb_equal_si(c, -1))
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{
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for (i = 1; i <= n; i += 2)
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arb_neg(t + i, t + i);
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}
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else if (!arb_is_one(c))
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{
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arb_set(d, c);
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for (i = 1; i <= n; i++)
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{
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arb_mul(t + i, t + i, d, prec);
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arb_mul(d, d, c, prec);
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}
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}
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_arb_poly_mullow(u, p, len, t, len, len, prec);
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arb_mul(f, f, f, prec);
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if (arb_bits(f) > 0.25 * prec)
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{
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arb_inv(f, f, prec);
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}
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else
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{
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for (i = 0; i <= n; i++)
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arb_div(u + i, u + i, f, prec);
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arb_one(f);
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}
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for (i = n; i >= 0; i--)
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{
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arb_mul(p + i, u + n - i, f, prec);
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arb_mul_ui(f, f, (i == 0) ? 1 : i, prec);
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}
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_arb_vec_clear(t, len);
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_arb_vec_clear(u, len);
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arb_clear(f);
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arb_clear(d);
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}
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void
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arb_poly_taylor_shift_convolution(arb_poly_t g, const arb_poly_t f,
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const arb_t c, slong prec)
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{
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if (f != g)
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arb_poly_set_round(g, f, prec);
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_arb_poly_taylor_shift_convolution(g->coeffs, c, g->length, prec);
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}
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