flint-sys 0.9.0

/*
    Copyright (C) 2010 Sebastian Pancratz
    Copyright (C) 2010 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 "ulong_extras.h"
#include "mpn_extras.h"
#include "nmod_vec.h"
#include "nmod_poly.h"
#include "fmpz.h"

void
_nmod_poly_powmod_fmpz_binexp_preinv (nn_ptr res, nn_srcptr poly, fmpz_t e,
            nn_srcptr f, slong lenf, nn_srcptr finv, slong lenfinv, nmod_t mod)
{
    nn_ptr T, Q;
    slong lenT, lenQ;
    slong i, bits;

    if (lenf == 2)
    {
        /* n = ndivg * g. Compute (poly[0]%ndivg)^e mod ndivg and use CRT */
        if (fmpz_abs_fits_ui(e))
        {
           ulong e_ui = fmpz_get_ui(e);

           res[0] = n_powmod2_ui_preinv(poly[0], e_ui, mod.n, mod.ninv);
        } else
        {
           fmpz_t p0, nf;

           fmpz_init_set_ui(p0, poly[0]);
           fmpz_init_set_ui(nf, mod.n);

           fmpz_powm(p0, p0, e, nf);
           res[0] = fmpz_get_ui(p0);

           fmpz_clear(p0);
           fmpz_clear(nf);
        }

        return;
    }

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

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

    _nmod_vec_set(res, poly, lenf - 1);

    bits = fmpz_sizeinbase(e, 2);
    for (i = bits - 2; 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);

        if (fmpz_tstbit(e, i))
        {
            _nmod_poly_mul(T, res, lenf - 1, poly, lenf - 1, mod);

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

    _nmod_vec_clear(T);
}

void
nmod_poly_powmod_fmpz_binexp_preinv(nmod_poly_t res, const nmod_poly_t poly,
                         fmpz_t e, const nmod_poly_t f, const nmod_poly_t finv)
{
    nn_ptr p;
    slong len = poly->length;
    slong lenf = f->length;
    slong trunc = lenf - 1;
    int pcopy = 0;

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

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

    if (len >= lenf)
    {
        nmod_poly_t t, r;

        nmod_poly_init_mod(t, res->mod);
        nmod_poly_init_mod(r, res->mod);

        nmod_poly_divrem(t, r, poly, f);

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

        nmod_poly_clear(t);
        nmod_poly_clear(r);

        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_set(res, poly);
        else
            nmod_poly_mulmod_preinv(res, poly, poly, f, finv);

        return;
    }

    if (len == 0)
    {
        nmod_poly_zero(res);
        return;
    }

    if (len < trunc)
    {
        p = _nmod_vec_init(trunc);

        flint_mpn_copyi(p, poly->coeffs, len);
        flint_mpn_zero(p + len, trunc - len);

        pcopy = 1;
    } else
        p = poly->coeffs;

    if ((res == poly && !pcopy) || res == f || res == finv)
    {
        nmod_poly_t t;

        nmod_poly_init2(t, poly->mod.n, trunc);

        _nmod_poly_powmod_fmpz_binexp_preinv(t->coeffs,
                 p, e, f->coeffs, lenf, finv->coeffs, finv->length, poly->mod);

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

        _nmod_poly_powmod_fmpz_binexp_preinv(res->coeffs,
                 p, e, f->coeffs, lenf, finv->coeffs, finv->length, poly->mod);
    }

    if (pcopy)
        _nmod_vec_clear(p);

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

void
_nmod_poly_powmod_ui_binexp_preinv(nn_ptr res, nn_srcptr poly, ulong e,
                    nn_srcptr f, slong lenf, nn_srcptr finv, slong lenfinv, nmod_t mod)
{
    nn_ptr T, Q;
    slong lenT, lenQ, i;

    if (lenf == 2)
    {
        res[0] = n_powmod2_ui_preinv(poly[0], e, mod.n, mod.ninv);
        return;
    }

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

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

    _nmod_vec_set(res, poly, lenf - 1);

    for (i = FLINT_BIT_COUNT(e) - 2; 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);

        if (e & (UWORD(1) << i))
        {
            _nmod_poly_mul(T, res, lenf - 1, poly, lenf - 1, mod);
            _nmod_poly_divrem_newton_n_preinv(Q, res, T, 2*lenf - 3, f,
                                                     lenf, finv, lenfinv, mod);
        }
    }

    _nmod_vec_clear(T);
}

void
nmod_poly_powmod_ui_binexp_preinv(nmod_poly_t res, const nmod_poly_t poly,
                          ulong e, const nmod_poly_t f, const nmod_poly_t finv)
{
    nn_ptr p;
    slong len = poly->length;
    slong lenf = f->length;
    slong trunc = lenf - 1;
    int pcopy = 0;

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

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

    if (len >= lenf)
    {
        nmod_poly_t t, r;

        nmod_poly_init_mod(t, res->mod);
        nmod_poly_init_mod(r, res->mod);

        nmod_poly_divrem(t, r, poly, f);

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

        nmod_poly_clear(t);
        nmod_poly_clear(r);
        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_set(res, poly);
        else
            nmod_poly_mulmod_preinv(res, poly, poly, f, finv);

        return;
    }

    if (len == 0)
    {
        nmod_poly_zero(res);
        return;
    }

    if (len < trunc)
    {
        p = _nmod_vec_init(trunc);

        flint_mpn_copyi(p, poly->coeffs, len);
        flint_mpn_zero(p + len, trunc - len);

        pcopy = 1;
    } else
        p = poly->coeffs;

    if ((res == poly && !pcopy) || res == f || res == finv)
    {
        nmod_poly_t t;

        nmod_poly_init2(t, poly->mod.n, trunc);

        _nmod_poly_powmod_ui_binexp_preinv(t->coeffs,
                 p, e, f->coeffs, lenf, finv->coeffs, finv->length, poly->mod);

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

        _nmod_poly_powmod_ui_binexp_preinv(res->coeffs,
                 p, e, f->coeffs, lenf, finv->coeffs, finv->length, poly->mod);
    }

    if (pcopy)
        _nmod_vec_clear(p);

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