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/*
Copyright (C) 2013 Fredrik Johansson
This file is part of Arb.
Arb is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include <math.h>
#include "arb_poly.h"
void
_arb_poly_binomial_transform_convolution(arb_ptr b, arb_srcptr a, slong alen, slong len, slong prec)
{
slong i;
arb_ptr c, d;
alen = FLINT_MIN(alen, len);
c = _arb_vec_init(alen);
d = _arb_vec_init(len);
_arb_poly_borel_transform(c, a, alen, prec);
for (i = 1; i < alen; i += 2)
arb_neg(c + i, c + i);
arb_one(d);
for (i = 1; i < len; i++)
arb_div_ui(d + i, d + i - 1, i, prec);
_arb_poly_mullow(b, d, len, c, alen, len, prec);
_arb_poly_inv_borel_transform(b, b, len, prec);
_arb_vec_clear(c, alen);
_arb_vec_clear(d, len);
}
void
arb_poly_binomial_transform_convolution(arb_poly_t b, const arb_poly_t a, slong len, slong prec)
{
if (len == 0 || a->length == 0)
{
arb_poly_zero(b);
return;
}
if (b == a)
{
arb_poly_t c;
arb_poly_init2(c, len);
_arb_poly_binomial_transform_convolution(c->coeffs, a->coeffs, a->length, len, prec);
arb_poly_swap(b, c);
arb_poly_clear(c);
}
else
{
arb_poly_fit_length(b, len);
_arb_poly_binomial_transform_convolution(b->coeffs, a->coeffs, a->length, len, prec);
}
_arb_poly_set_length(b, len);
_arb_poly_normalise(b);
}
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