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/*
Copyright (C) 2012 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_compose_series_horner(arb_ptr res, arb_srcptr poly1, slong len1,
arb_srcptr poly2, slong len2, slong n, slong prec)
{
if (n == 1)
{
arb_set(res, poly1);
}
else
{
slong i = len1 - 1;
slong lenr;
arb_ptr t = _arb_vec_init(n);
lenr = len2;
_arb_vec_scalar_mul(res, poly2, len2, poly1 + i, prec);
i--;
arb_add(res, res, poly1 + i, prec);
while (i > 0)
{
i--;
if (lenr + len2 - 1 < n)
{
_arb_poly_mul(t, res, lenr, poly2, len2, prec);
lenr = lenr + len2 - 1;
}
else
{
_arb_poly_mullow(t, res, lenr, poly2, len2, n, prec);
lenr = n;
}
_arb_poly_add(res, t, lenr, poly1 + i, 1, prec);
}
_arb_vec_zero(res + lenr, n - lenr);
_arb_vec_clear(t, n);
}
}
void
arb_poly_compose_series_horner(arb_poly_t res,
const arb_poly_t poly1,
const arb_poly_t poly2, slong n, slong prec)
{
slong len1 = poly1->length;
slong len2 = poly2->length;
slong lenr;
if (len2 != 0 && !arb_is_zero(poly2->coeffs))
{
flint_printf("exception: compose_series: inner "
"polynomial must have zero constant term\n");
flint_abort();
}
if (len1 == 0 || n == 0)
{
arb_poly_zero(res);
return;
}
if (len2 == 0 || len1 == 1)
{
arb_poly_set_arb(res, poly1->coeffs);
return;
}
lenr = FLINT_MIN((len1 - 1) * (len2 - 1) + 1, n);
len1 = FLINT_MIN(len1, lenr);
len2 = FLINT_MIN(len2, lenr);
if ((res != poly1) && (res != poly2))
{
arb_poly_fit_length(res, lenr);
_arb_poly_compose_series_horner(res->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, lenr, prec);
_arb_poly_set_length(res, lenr);
_arb_poly_normalise(res);
}
else
{
arb_poly_t t;
arb_poly_init2(t, lenr);
_arb_poly_compose_series_horner(t->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, lenr, prec);
_arb_poly_set_length(t, lenr);
_arb_poly_normalise(t);
arb_poly_swap(res, t);
arb_poly_clear(t);
}
}
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