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/*
Copyright (C) 2010 William Hart
Copyright (C) 2012 Sebastian Pancratz
Copyright (C) 2012, 2016 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 "acb_poly.h"
/* compose by poly2 = a*x^n + c, no aliasing; n >= 1 */
void
_acb_poly_compose_axnc(acb_ptr res, acb_srcptr poly1, slong len1,
const acb_t c, const acb_t a, slong n, slong prec)
{
slong i;
_acb_vec_set_round(res, poly1, len1, prec);
/* shift by c (c = 0 case will be fast) */
_acb_poly_taylor_shift(res, c, len1, prec);
/* multiply by powers of a */
if (!acb_is_one(a))
{
if (acb_equal_si(a, -1))
{
for (i = 1; i < len1; i += 2)
acb_neg(res + i, res + i);
}
else if (len1 == 2)
{
acb_mul(res + 1, res + 1, a, prec);
}
else
{
acb_t t;
acb_init(t);
acb_set(t, a);
for (i = 1; i < len1; i++)
{
acb_mul(res + i, res + i, t, prec);
if (i + 1 < len1)
acb_mul(t, t, a, prec);
}
acb_clear(t);
}
}
/* stretch */
for (i = len1 - 1; i >= 1 && n > 1; i--)
{
acb_swap(res + i * n, res + i);
_acb_vec_zero(res + (i - 1) * n + 1, n - 1);
}
}
void
_acb_poly_compose(acb_ptr res,
acb_srcptr poly1, slong len1,
acb_srcptr poly2, slong len2, slong prec)
{
if (len1 == 1)
{
acb_set_round(res, poly1, prec);
}
else if (len2 == 1)
{
_acb_poly_evaluate(res, poly1, len1, poly2, prec);
}
else if (_acb_vec_is_zero(poly2 + 1, len2 - 2))
{
_acb_poly_compose_axnc(res, poly1, len1, poly2, poly2 + len2 - 1, len2 - 1, prec);
}
else if (len1 <= 7)
{
_acb_poly_compose_horner(res, poly1, len1, poly2, len2, prec);
}
else
{
_acb_poly_compose_divconquer(res, poly1, len1, poly2, len2, prec);
}
}
void acb_poly_compose(acb_poly_t res,
const acb_poly_t poly1, const acb_poly_t poly2, slong prec)
{
const slong len1 = poly1->length;
const slong len2 = poly2->length;
if (len1 == 0)
{
acb_poly_zero(res);
}
else if (len1 == 1 || len2 == 0)
{
acb_poly_set_acb(res, poly1->coeffs);
}
else
{
const slong lenr = (len1 - 1) * (len2 - 1) + 1;
if (res != poly1 && res != poly2)
{
acb_poly_fit_length(res, lenr);
_acb_poly_compose(res->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, prec);
}
else
{
acb_poly_t t;
acb_poly_init2(t, lenr);
_acb_poly_compose(t->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, prec);
acb_poly_swap(res, t);
acb_poly_clear(t);
}
_acb_poly_set_length(res, lenr);
_acb_poly_normalise(res);
}
}
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