/*=============================================================================
This file is part of FLINT.
FLINT is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
FLINT is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with FLINT; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2010 Sebastian Pancratz
Copyright (C) 2011 Fredrik Johansson
******************************************************************************/
#include <gmp.h>
#include "flint.h"
#include "fmpz.h"
#include "fmpz_vec.h"
#include "fmpz_poly.h"
#include "fmpq_poly.h"
#include "fmpq.h"
#include "fmpq_mat.h"
#include "ulong_extras.h"
static void
_fmpq_mat_get_row(fmpz * rnum, fmpz_t den, fmpq_mat_t A, slong i)
{
slong j;
fmpz_t t;
fmpz_init(t);
fmpz_one(den);
for (j = 0; j < fmpq_mat_ncols(A); j++)
fmpz_lcm(den, den, fmpq_mat_entry_den(A, i, j));
for (j = 0; j < fmpq_mat_ncols(A); j++)
{
fmpz_divexact(t, den, fmpq_mat_entry_den(A, i, j));
fmpz_mul(rnum + j, fmpq_mat_entry_num(A, i, j), t);
}
fmpz_clear(t);
}
void
_fmpq_poly_compose_series_brent_kung(fmpz * res, fmpz_t den, const fmpz * poly1,
const fmpz_t den1, slong len1, const fmpz * poly2,
const fmpz_t den2, slong len2, slong n)
{
fmpq_mat_t A, B, C;
fmpz_t tden, uden, hden;
fmpz *t, *u, *h, *swap;
slong i, j, m;
if (fmpz_is_one(den2))
{
_fmpz_poly_compose_series(res, poly1, len1, poly2, len2, n);
fmpz_set(den, den1);
_fmpq_poly_canonicalise(res, den, n);
return;
}
if (n == 1)
{
fmpz_set(res, poly1);
fmpz_set(den, den1);
_fmpq_poly_canonicalise(res, den, 1);
return;
}
m = n_sqrt(n) + 1;
fmpq_mat_init(A, m, n);
fmpq_mat_init(B, m, m);
fmpq_mat_init(C, m, n);
fmpz_init(tden);
fmpz_init(uden);
fmpz_init(hden);
h = _fmpz_vec_init(n);
t = _fmpz_vec_init(n);
u = _fmpz_vec_init(n);
/* Set rows of B to the segments of poly1 */
for (i = 0; i < len1; i++)
{
fmpz_set(fmpq_mat_entry_num(B, i / m, i % m), poly1 + i);
fmpz_set(fmpq_mat_entry_den(B, i / m, i % m), den1);
fmpq_canonicalise(fmpq_mat_entry(B, i / m, i % m));
}
/* Set rows of A to powers of poly2 */
fmpq_set_si(fmpq_mat_entry(A, 0, 0), WORD(1), WORD(1));
for (i = 0; i < len2; i++)
{
fmpz_set(fmpq_mat_entry_num(A, 1, i), poly2 + i);
fmpz_set(fmpq_mat_entry_den(A, 1, i), den2);
fmpq_canonicalise(fmpq_mat_entry(A, 1, i));
}
_fmpz_vec_set(h, poly2, len2);
fmpz_set(hden, den2);
for (i = 2; i < m; i++)
{
_fmpq_poly_mullow(t, tden, h, hden, n, poly2, den2, len2, n);
_fmpq_poly_canonicalise(t, tden, n);
for (j = 0; j < n; j++)
{
fmpz_set(fmpq_mat_entry_num(A, i, j), t + j);
fmpz_set(fmpq_mat_entry_den(A, i, j), tden);
fmpq_canonicalise(fmpq_mat_entry(A, i, j));
}
swap = t; t = h; h = swap;
fmpz_swap(hden, tden);
}
/* Compute h = poly2 ^ m */
_fmpq_poly_mullow(t, tden, h, hden, n, poly2, den2, len2, n);
_fmpq_poly_canonicalise(t, tden, n);
swap = t; t = h; h = swap;
fmpz_swap(hden, tden);
/* Matrix multiply */
fmpq_mat_mul(C, B, A);
fmpq_mat_clear(A);
fmpq_mat_clear(B);
/* Evaluate block composition using the Horner scheme */
_fmpq_mat_get_row(res, den, C, m - 1);
for (i = m - 2; i >= 0; i--)
{
_fmpq_poly_mullow(t, tden, res, den, n, h, hden, n, n);
/* we could canonicalise t here, but it does not seem to make
much of a difference */
_fmpq_mat_get_row(u, uden, C, i);
_fmpq_poly_add(res, den, t, tden, n, u, uden, n);
}
_fmpq_poly_canonicalise(res, den, n);
fmpq_mat_clear(C);
_fmpz_vec_clear(t, n);
_fmpz_vec_clear(u, n);
_fmpz_vec_clear(h, n);
fmpz_clear(tden);
fmpz_clear(uden);
fmpz_clear(hden);
}
void
fmpq_poly_compose_series_brent_kung(fmpq_poly_t res,
const fmpq_poly_t poly1, const fmpq_poly_t poly2, slong n)
{
slong len1 = poly1->length;
slong len2 = poly2->length;
slong lenr;
if (len2 != 0 && !fmpz_is_zero(poly2->coeffs))
{
flint_printf("Exception (fmpq_poly_compose_series_brent_kung). \n"
"Inner polynomial must have zero constant term.\n");
abort();
}
if (len1 == 0 || n == 0)
{
fmpq_poly_zero(res);
return;
}
if (len2 == 0 || len1 == 1)
{
fmpq_poly_fit_length(res, 1);
fmpz_set(res->coeffs, poly1->coeffs);
fmpz_set(res->den, poly1->den);
{
fmpz_t d;
fmpz_init(d);
fmpz_gcd(d, res->coeffs, res->den);
if (!fmpz_is_one(d))
{
fmpz_divexact(res->coeffs, res->coeffs, d);
fmpz_divexact(res->den, res->den, d);
}
fmpz_clear(d);
}
_fmpq_poly_set_length(res, 1);
_fmpq_poly_normalise(res);
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))
{
fmpq_poly_fit_length(res, lenr);
_fmpq_poly_compose_series_brent_kung(res->coeffs, res->den,
poly1->coeffs, poly1->den, len1,
poly2->coeffs, poly2->den, len2, lenr);
_fmpq_poly_set_length(res, lenr);
_fmpq_poly_normalise(res);
}
else
{
fmpq_poly_t t;
fmpq_poly_init2(t, lenr);
_fmpq_poly_compose_series_brent_kung(t->coeffs, t->den,
poly1->coeffs, poly1->den, len1,
poly2->coeffs, poly2->den, len2, lenr);
_fmpq_poly_set_length(t, lenr);
_fmpq_poly_normalise(t);
fmpq_poly_swap(res, t);
fmpq_poly_clear(t);
}
}