Exemple #1
0
void _nmod_poly_div_newton(mp_ptr Q, mp_srcptr A, slong lenA, 
                                     mp_srcptr B, slong lenB, nmod_t mod)
{
    const slong lenQ = lenA - lenB + 1;
    mp_ptr Arev, Brev;

    Arev = _nmod_vec_init(2 * lenQ);
    Brev = Arev + lenQ;

    _nmod_poly_reverse(Arev, A + (lenA - lenQ), lenQ, lenQ);

    if (lenB >= lenQ)
    {
        _nmod_poly_reverse(Brev, B + (lenB - lenQ), lenQ, lenQ);
    }
    else
    {
        _nmod_poly_reverse(Brev, B, lenB, lenB);
        flint_mpn_zero(Brev + lenB, lenQ - lenB);
    }

    _nmod_poly_div_series(Q, Arev, Brev, lenQ, mod);

    _nmod_poly_reverse(Q, Q, lenQ, lenQ);

    _nmod_vec_clear(Arev);
}
Exemple #2
0
void nmod_poly_reverse(nmod_poly_t output, const nmod_poly_t input, long m)
{
    nmod_poly_fit_length(output, m);
     
    _nmod_poly_reverse(output->coeffs, input->coeffs, input->length, m);

    output->length = m;
    _nmod_poly_normalise(output);
}
Exemple #3
0
void
_nmod_poly_taylor_shift_convolution(mp_ptr p, mp_limb_t c, slong len, nmod_t mod)
{
    slong i, n = len - 1;
    mp_limb_t f, d;
    mp_ptr t, u;

    if (c == 0 || len <= 1)
        return;

    t = _nmod_vec_init(len);
    u = _nmod_vec_init(len);

    f = 1;
    for (i = 2; i <= n; i++)
    {
        f = n_mulmod2_preinv(f, i, mod.n, mod.ninv);
        p[i] = n_mulmod2_preinv(p[i], f, mod.n, mod.ninv);
    }

    _nmod_poly_reverse(p, p, len, len);

    t[n] = 1;
    for (i = n; i > 0; i--)
        t[i - 1] = n_mulmod2_preinv(t[i], i, mod.n, mod.ninv);

    if (c == mod.n - 1)
    {
        for (i = 1; i <= n; i += 2)
            t[i] = nmod_neg(t[i], mod);
    }
    else if (c != 1)
    {
        d = c;

        for (i = 1; i <= n; i++)
        {
            t[i] = n_mulmod2_preinv(t[i], d, mod.n, mod.ninv);
            d = n_mulmod2_preinv(d, c, mod.n, mod.ninv);
        }
    }

    _nmod_poly_mullow(u, p, len, t, len, len, mod);

    f = n_mulmod2_preinv(f, f, mod.n, mod.ninv);
    f = n_invmod(f, mod.n);

    for (i = n; i >= 0; i--)
    {
        p[i] = n_mulmod2_preinv(u[n - i], f, mod.n, mod.ninv);
        f = n_mulmod2_preinv(f, (i == 0) ? 1 : i, mod.n, mod.ninv);
    }

    _nmod_vec_clear(t);
    _nmod_vec_clear(u);
}
Exemple #4
0
void
_nmod_poly_inv_series_basecase(mp_ptr Qinv,
                               mp_srcptr Q, long n, nmod_t mod)
{
    mp_ptr X2n, Qrev;

    X2n = _nmod_vec_init(2*n);
    Qrev = X2n + n;

    _nmod_poly_reverse(Qrev, Q, n, n);

    X2n[n - 1] = 1;
    mpn_zero(X2n, n - 1);
    X2n -= (n - 1);

    _nmod_poly_div_divconquer(Qinv, X2n, 2*n - 1, Qrev, n, mod);

    _nmod_poly_reverse(Qinv, Qinv, n, n);

    _nmod_vec_free(X2n + n - 1);
}