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/*
Copyright (C) 2010 William Hart
Copyright (C) 2012 Sebastian Pancratz
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 "acb_poly.h"
void
_acb_poly_compose_divconquer(acb_ptr res, acb_srcptr poly1, slong len1,
acb_srcptr poly2, slong len2, slong prec)
{
slong i, j, k, n;
slong *hlen, alloc, powlen;
acb_ptr v, pow, temp;
acb_ptr * h;
if (len1 == 1)
{
acb_set(res, poly1);
return;
}
if (len2 == 1)
{
_acb_poly_evaluate(res, poly1, len1, poly2, prec);
return;
}
if (len1 == 2)
{
_acb_poly_compose_horner(res, poly1, len1, poly2, len2, prec);
return;
}
/* Initialisation */
hlen = (slong *) flint_malloc(((len1 + 1) / 2) * sizeof(slong));
for (k = 1; (2 << k) < len1; k++) ;
hlen[0] = hlen[1] = ((1 << k) - 1) * (len2 - 1) + 1;
for (i = k - 1; i > 0; i--)
{
slong hi = (len1 + (1 << i) - 1) / (1 << i);
for (n = (hi + 1) / 2; n < hi; n++)
hlen[n] = ((1 << i) - 1) * (len2 - 1) + 1;
}
powlen = (1 << k) * (len2 - 1) + 1;
alloc = 0;
for (i = 0; i < (len1 + 1) / 2; i++)
alloc += hlen[i];
v = _acb_vec_init(alloc + 2 * powlen);
h = (acb_ptr *) flint_malloc(((len1 + 1) / 2) * sizeof(acb_ptr));
h[0] = v;
for (i = 0; i < (len1 - 1) / 2; i++)
{
h[i + 1] = h[i] + hlen[i];
hlen[i] = 0;
}
hlen[(len1 - 1) / 2] = 0;
pow = v + alloc;
temp = pow + powlen;
/* Let's start the actual work */
for (i = 0, j = 0; i < len1 / 2; i++, j += 2)
{
if (!acb_is_zero(poly1 + j + 1))
{
_acb_vec_scalar_mul(h[i], poly2, len2, poly1 + j + 1, prec);
acb_add(h[i], h[i], poly1 + j, prec);
hlen[i] = len2;
}
else if (!acb_is_zero(poly1 + j))
{
acb_set(h[i], poly1 + j);
hlen[i] = 1;
}
}
if ((len1 & WORD(1)))
{
if (!acb_is_zero(poly1 + j))
{
acb_set(h[i], poly1 + j);
hlen[i] = 1;
}
}
_acb_poly_mul(pow, poly2, len2, poly2, len2, prec);
powlen = 2 * len2 - 1;
for (n = (len1 + 1) / 2; n > 2; n = (n + 1) / 2)
{
if (hlen[1] > 0)
{
slong templen = powlen + hlen[1] - 1;
_acb_poly_mul(temp, pow, powlen, h[1], hlen[1], prec);
_acb_poly_add(h[0], temp, templen, h[0], hlen[0], prec);
hlen[0] = FLINT_MAX(hlen[0], templen);
}
for (i = 1; i < n / 2; i++)
{
if (hlen[2*i + 1] > 0)
{
_acb_poly_mul(h[i], pow, powlen, h[2*i + 1], hlen[2*i + 1], prec);
hlen[i] = hlen[2*i + 1] + powlen - 1;
} else
hlen[i] = 0;
_acb_poly_add(h[i], h[i], hlen[i], h[2*i], hlen[2*i], prec);
hlen[i] = FLINT_MAX(hlen[i], hlen[2*i]);
}
if ((n & WORD(1)))
{
_acb_vec_set(h[i], h[2*i], hlen[2*i]);
hlen[i] = hlen[2*i];
}
_acb_poly_mul(temp, pow, powlen, pow, powlen, prec);
powlen += powlen - 1;
{
acb_ptr t = pow;
pow = temp;
temp = t;
}
}
_acb_poly_mul(res, pow, powlen, h[1], hlen[1], prec);
_acb_vec_add(res, res, h[0], hlen[0], prec);
_acb_vec_clear(v, alloc + 2 * powlen);
flint_free(h);
flint_free(hlen);
}
void
acb_poly_compose_divconquer(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_divconquer(res->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, prec);
}
else
{
acb_poly_t t;
acb_poly_init2(t, lenr);
_acb_poly_compose_divconquer(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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