pow.c

/*=============================================================================

    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) 2011 Fredrik Johansson

******************************************************************************/

#include "flint.h"
#include "nmod_poly.h"
#include "nmod_poly_mat.h"

void
nmod_poly_mat_pow(nmod_poly_mat_t B, const nmod_poly_mat_t A, ulong exp)
{
    slong d = nmod_poly_mat_nrows(A);

    if (exp == 0 || d == 0)
    {
        nmod_poly_mat_one(B);
    }
    else if (exp == 1)
    {
        nmod_poly_mat_set(B, A);
    }
    else if (exp == 2)
    {
        nmod_poly_mat_sqr(B, A);
    }
    else if (d == 1)
    {
        nmod_poly_pow(nmod_poly_mat_entry(B, 0, 0),
                        nmod_poly_mat_entry(A, 0, 0), exp);
    }
    else
    {
        nmod_poly_mat_t T, U;
        slong i;

        nmod_poly_mat_init_set(T, A);
        nmod_poly_mat_init(U, d, d, nmod_poly_mat_modulus(A));

        for (i = ((slong) FLINT_BIT_COUNT(exp)) - 2; i >= 0; i--)
        {
            nmod_poly_mat_sqr(U, T);

            if (exp & (WORD(1) << i))
                nmod_poly_mat_mul(T, U, A);
            else
                nmod_poly_mat_swap(T, U);
        }

        nmod_poly_mat_swap(B, T);
        nmod_poly_mat_clear(T);
        nmod_poly_mat_clear(U);
    }
}