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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 "arb_poly.h"
void
_arb_poly_evaluate_rectangular(arb_t y, arb_srcptr poly,
slong len, const arb_t x, slong prec)
{
slong i, m, r;
arb_ptr xs;
arb_t s, t, c;
if (len < 3)
{
if (len == 0)
{
arb_zero(y);
}
else if (len == 1)
{
arb_set_round(y, poly + 0, prec);
}
else if (len == 2)
{
arb_mul(y, x, poly + 1, prec);
arb_add(y, y, poly + 0, prec);
}
return;
}
m = n_sqrt(len) + 1;
r = (len + m - 1) / m;
xs = _arb_vec_init(m + 1);
arb_init(s);
arb_init(t);
arb_init(c);
_arb_vec_set_powers(xs, x, m + 1, prec);
arb_dot(y, poly + (r - 1) * m, 0, xs + 1, 1,
poly + (r - 1) * m + 1, 1, len - (r - 1) * m - 1, prec);
for (i = r - 2; i >= 0; i--)
{
arb_dot(s, poly + i * m, 0, xs + 1, 1,
poly + i * m + 1, 1, m - 1, prec);
arb_mul(y, y, xs + m, prec);
arb_add(y, y, s, prec);
}
_arb_vec_clear(xs, m + 1);
arb_clear(s);
arb_clear(t);
arb_clear(c);
}
void
arb_poly_evaluate_rectangular(arb_t res, const arb_poly_t f, const arb_t a, slong prec)
{
_arb_poly_evaluate_rectangular(res, f->coeffs, f->length, a, prec);
}
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