/*
Copyright (C) 2011 Fredrik Johansson
This file is part of FLINT.
FLINT 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 .
*/
#include
#include "flint.h"
#include "fmpz.h"
#include "fmpz_poly.h"
#include "fmpz_mat.h"
#include "ulong_extras.h"
void
_fmpz_poly_compose_series_brent_kung(fmpz * res, const fmpz * poly1, slong len1,
const fmpz * poly2, slong len2, slong n)
{
fmpz_mat_t A, B, C;
fmpz *t, *h;
slong i, m;
if (n == 1)
{
fmpz_set(res, poly1);
return;
}
m = n_sqrt(n) + 1;
fmpz_mat_init(A, m, n);
fmpz_mat_init(B, m, m);
fmpz_mat_init(C, m, n);
h = _fmpz_vec_init(n);
t = _fmpz_vec_init(n);
/* Set rows of B to the segments of poly1 */
for (i = 0; i < len1 / m; i++)
_fmpz_vec_set(B->rows[i], poly1 + i*m, m);
_fmpz_vec_set(B->rows[i], poly1 + i*m, len1 % m);
/* Set rows of A to powers of poly2 */
fmpz_one(A->rows[0]);
_fmpz_vec_set(A->rows[1], poly2, len2);
for (i = 2; i < m; i++)
_fmpz_poly_mullow(A->rows[i], A->rows[i-1], n, poly2, len2, n);
fmpz_mat_mul(C, B, A);
/* Evaluate block composition using the Horner scheme */
_fmpz_vec_set(res, C->rows[m - 1], n);
_fmpz_poly_mullow(h, A->rows[m - 1], n, poly2, len2, n);
for (i = m - 2; i >= 0; i--)
{
_fmpz_poly_mullow(t, res, n, h, n, n);
_fmpz_poly_add(res, t, n, C->rows[i], n);
}
_fmpz_vec_clear(h, n);
_fmpz_vec_clear(t, n);
fmpz_mat_clear(A);
fmpz_mat_clear(B);
fmpz_mat_clear(C);
}
void
fmpz_poly_compose_series_brent_kung(fmpz_poly_t res,
const fmpz_poly_t poly1, const fmpz_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 (fmpz_poly_compose_series_brent_kung). Inner \n"
"polynomial must have zero constant term.\n");
flint_abort();
}
if (len1 == 0 || n == 0)
{
fmpz_poly_zero(res);
return;
}
if (len2 == 0 || len1 == 1)
{
fmpz_poly_set_fmpz(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))
{
fmpz_poly_fit_length(res, lenr);
_fmpz_poly_compose_series_brent_kung(res->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, lenr);
_fmpz_poly_set_length(res, lenr);
_fmpz_poly_normalise(res);
}
else
{
fmpz_poly_t t;
fmpz_poly_init2(t, lenr);
_fmpz_poly_compose_series_brent_kung(t->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, lenr);
_fmpz_poly_set_length(t, lenr);
_fmpz_poly_normalise(t);
fmpz_poly_swap(res, t);
fmpz_poly_clear(t);
}
}