flint-sys 0.9.0

/*
    Copyright (C) 2010 Sebastian Pancratz
    Copyright (C) 2010, 2020 William Hart
    Copyright (C) 2011 Fredrik Johansson
    Copyright (C) 2013 Martin Lee

    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 3 of the License, or
    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
*/

#include "long_extras.h"
#include "mpn_extras.h"
#include "nmod_vec.h"
#include "nmod_poly.h"
#include "fmpz.h"

void
_nmod_poly_powmod_x_fmpz_preinv (nn_ptr res, fmpz_t e, nn_srcptr f, slong lenf,
                                      nn_srcptr finv, slong lenfinv, nmod_t mod)
{
    nn_ptr T, Q;
    slong lenT, lenQ, window;
    slong i, l, c;

    lenT = 2*lenf - 3;
    lenQ = FLINT_MAX(lenT - lenf + 1, 1);

    T = _nmod_vec_init(lenT + lenQ);
    Q = T + lenT;

    flint_mpn_zero (res, lenf - 1);
    res[0] = 1;

    l = z_sizeinbase (lenf - 1, 2) - 2;
    window = (WORD(1) << l);
    c = l;
    i = fmpz_sizeinbase(e, 2) - 2;

    if (i <= l)
    {
        window = (WORD(1) << i);
        c = i;
        l = i;
    }

    if (c == 0)
    {
        _nmod_poly_shift_left(T, res, lenf - 1, window);

        _nmod_poly_divrem_newton_n_preinv(Q, res, T, lenf - 1 + window, f,
                                                     lenf, finv, lenfinv, mod);

        c = l + 1;
        window = 0;
    }

    for (; i >= 0; i--)
    {
        _nmod_poly_mul(T, res, lenf - 1, res, lenf - 1, mod);

        _nmod_poly_divrem_newton_n_preinv(Q, res, T, 2*lenf - 3, f,
                                                     lenf, finv, lenfinv, mod);

        c--;

        if (fmpz_tstbit(e, i))
        {
            if (window == 0 && i <= l - 1)
                c = i;

            if (c >= 0)
              window = window | (WORD(1) << c);
        } else if (window == 0)
            c = l + 1;

        if (c == 0)
        {
            _nmod_poly_shift_left(T, res, lenf - 1, window);

            _nmod_poly_divrem_newton_n_preinv(Q, res, T, lenf - 1 + window, f,
                                                     lenf, finv, lenfinv, mod);

            c = l + 1;
            window = 0;
        }
    }

    _nmod_vec_clear(T);
}


void
nmod_poly_powmod_x_fmpz_preinv(nmod_poly_t res, fmpz_t e, const nmod_poly_t f,
                                                        const nmod_poly_t finv)
{
    slong lenf = f->length;
    slong trunc = lenf - 1;
    nmod_poly_t tmp;

    if (lenf == 0)
    {
        flint_throw(FLINT_ERROR, "Exception (nmod_poly_powmod_x_fmpz_preinv). Divide by zero.\n");
    }

    if (lenf == 1)
    {
        nmod_poly_zero(res);
        return;
    }

    if (lenf == 2)
    {
        nmod_poly_t r, poly;

        nmod_poly_init_mod(tmp, res->mod);
        nmod_poly_init_mod(r, res->mod);
        nmod_poly_init2_preinv(poly, res->mod.n, res->mod.ninv, 2);

        nmod_poly_set_coeff_ui(poly, 1, 1);

        nmod_poly_divrem(tmp, r, poly, f);

        nmod_poly_powmod_fmpz_binexp_preinv(res, r, e, f, finv);

        nmod_poly_clear(tmp);
        nmod_poly_clear(r);
        nmod_poly_clear(poly);

        return;
    }

    if (fmpz_cmp_ui(e, 2) <= 0)
    {
        if (fmpz_is_zero(e))
        {
            nmod_poly_fit_length(res, 1);

            res->coeffs[0] = 1;
            res->length = 1;
        } else if (fmpz_is_one(e))
        {
            nmod_poly_t r;

            nmod_poly_init2_preinv(r, res->mod.n, res->mod.ninv, 2);
            nmod_poly_set_coeff_ui(r, 1, 1);

            nmod_poly_init_preinv(tmp, res->mod.n, res->mod.ninv);

            nmod_poly_divrem (tmp, res, r, f);

            nmod_poly_clear(tmp);
            nmod_poly_clear(r);
        }
        else
        {
            nmod_poly_init2_preinv(tmp, res->mod.n, res->mod.ninv, 3);
            nmod_poly_set_coeff_ui(tmp, 1, 1);

            nmod_poly_mulmod(res, tmp, tmp, f);

            nmod_poly_clear(tmp);
        }
        return;
    }

    if (res == f || res == finv)
    {
        nmod_poly_init2(tmp, res->mod.n, trunc);

        _nmod_poly_powmod_x_fmpz_preinv(tmp->coeffs, e, f->coeffs, lenf,
                                           finv->coeffs, finv->length, f->mod);

        nmod_poly_swap(res, tmp);
        nmod_poly_clear(tmp);
    }
    else
    {
        nmod_poly_fit_length(res, trunc);

        _nmod_poly_powmod_x_fmpz_preinv(res->coeffs, e, f->coeffs, lenf,
                                           finv->coeffs, finv->length, f->mod);
    }

    res->length = trunc;
    _nmod_poly_normalise(res);
}

void
_nmod_poly_powmod_x_ui_preinv(nn_ptr res, ulong e, nn_srcptr f, slong lenf,
                                     nn_srcptr finv, slong lenfinv, nmod_t mod)
{
    nn_ptr T, Q;
    slong lenT, lenQ, window;
    int i, l, c;

    lenT = 2 * lenf - 3;
    lenQ = FLINT_MAX(lenT - lenf + 1, 1);

    T = _nmod_vec_init(lenT + lenQ);
    Q = T + lenT;

    flint_mpn_zero(res, lenf - 1);
    res[0] = 1;

    l = (int) z_sizeinbase(lenf - 1, 2) - 2;
    window = (WORD(1) << l);
    c = l;
    i = (int) FLINT_BIT_COUNT(e) - 2;

    if (i <= l)
    {
      window = (WORD(1) << i);
      c = i;
      l = i;
    }

    if (c == 0)
    {
        _nmod_poly_shift_left(T, res, lenf - 1, window);
        _nmod_poly_divrem_newton_n_preinv(Q, res, T, lenf - 1 + window, f,
                                                     lenf, finv, lenfinv, mod);
        c = l + 1;
        window = 0;
    }

    for ( ; i >= 0; i--)
    {
        _nmod_poly_mul(T, res, lenf - 1, res, lenf - 1, mod);
        _nmod_poly_divrem_newton_n_preinv(Q, res, T, 2*lenf - 3, f,
                                                     lenf, finv, lenfinv, mod);

        c--;

        if (e & (UWORD(1) << i))
        {
            if (window == 0 && i <= l - 1)
                c = i;

            if ( c >= 0)
              window = window | (WORD(1) << c);
        } else if (window == 0)
            c = l + 1;

        if (c == 0)
        {
            _nmod_poly_shift_left(T, res, lenf - 1, window);
            _nmod_poly_divrem_newton_n_preinv(Q, res, T, lenf - 1 + window,
                                                  f, lenf, finv, lenfinv, mod);

            c = l + 1;
            window = 0;
        }
    }

    _nmod_vec_clear(T);
}


void
nmod_poly_powmod_x_ui_preinv(nmod_poly_t res, ulong e, const nmod_poly_t f,
                             const nmod_poly_t finv)
{
    slong lenf = f->length;
    slong trunc = lenf - 1;
    nmod_poly_t tmp;

    if (lenf == 0)
    {
        flint_throw(FLINT_ERROR, "Exception (nmod_poly_powmod_x_ui_preinv). Divide by zero.\n");
    }

    if (lenf == 1)
    {
        nmod_poly_zero(res);
        return;
    }

    if (lenf == 2)
    {
        nmod_poly_t r, poly;

        nmod_poly_init_mod(tmp, res->mod);
        nmod_poly_init_mod(r, res->mod);
        nmod_poly_init2_preinv(poly, res->mod.n, res->mod.ninv, 2);

        nmod_poly_set_coeff_ui (poly, 1, 1);

        nmod_poly_divrem(tmp, r, poly, f);

        nmod_poly_powmod_ui_binexp_preinv(res, r, e, f, finv);

        nmod_poly_clear(tmp);
        nmod_poly_clear(r);
        nmod_poly_clear(poly);

        return;
    }

    if (e <= 2)
    {
        if (e == 0)
        {
            nmod_poly_fit_length(res, 1);

            res->coeffs[0] = 1;
            res->length = 1;
        }
        else if (e == 1)
        {
            nmod_poly_t r;

            nmod_poly_init2_preinv(r, res->mod.n, res->mod.ninv, 2);
            nmod_poly_set_coeff_ui(r, 1, 1);

            nmod_poly_init_mod(tmp, res->mod);

            nmod_poly_divrem(tmp, res, r, f);

            nmod_poly_clear(tmp);
            nmod_poly_clear(r);
        }
        else
        {
            nmod_poly_init2_preinv(tmp, res->mod.n, res->mod.ninv, 3);

            nmod_poly_set_coeff_ui(tmp, 1, 1);

            nmod_poly_mulmod(res, tmp, tmp, f);

            nmod_poly_clear(tmp);
        }
        return;
    }

    if (res == f || res == finv)
    {
        nmod_poly_init2(tmp, res->mod.n, trunc);

        _nmod_poly_powmod_x_ui_preinv(tmp->coeffs, e, f->coeffs, lenf,
                                           finv->coeffs, finv->length, f->mod);

               nmod_poly_swap(res, tmp);
        nmod_poly_clear(tmp);
    }
    else
    {
        nmod_poly_fit_length(res, trunc);

        _nmod_poly_powmod_x_ui_preinv(res->coeffs, e, f->coeffs, lenf,
                                           finv->coeffs, finv->length, f->mod);
    }

    res->length = trunc;
    _nmod_poly_normalise(res);
}