Esempio n. 1
0
void
_arb_poly_inv_series(arb_ptr Qinv,
    arb_srcptr Q, slong Qlen, slong len, slong prec)
{
    arb_inv(Qinv, Q, prec);

    if (Qlen == 1)
    {
        _arb_vec_zero(Qinv + 1, len - 1);
    }
    else if (len == 2)
    {
        arb_div(Qinv + 1, Qinv, Q, prec);
        arb_mul(Qinv + 1, Qinv + 1, Q + 1, prec);
        arb_neg(Qinv + 1, Qinv + 1);
    }
    else
    {
        slong Qnlen, Wlen, W2len;
        arb_ptr W;

        W = _arb_vec_init(len);

        NEWTON_INIT(1, len)
        NEWTON_LOOP(m, n)

        Qnlen = FLINT_MIN(Qlen, n);
        Wlen = FLINT_MIN(Qnlen + m - 1, n);
        W2len = Wlen - m;
        MULLOW(W, Q, Qnlen, Qinv, m, Wlen, prec);
        MULLOW(Qinv + m, Qinv, m, W + m, W2len, n - m, prec);
        _arb_vec_neg(Qinv + m, Qinv + m, n - m);

        NEWTON_END_LOOP
        NEWTON_END

        _arb_vec_clear(W, len);
    }
}
Esempio n. 2
0
void
_arb_poly_inv_series(arb_ptr Qinv,
    arb_srcptr Q, slong Qlen, slong len, slong prec)
{
    Qlen = FLINT_MIN(Qlen, len);

    arb_inv(Qinv, Q, prec);

    if (Qlen == 1)
    {
        _arb_vec_zero(Qinv + 1, len - 1);
    }
    else if (len == 2)
    {
        arb_mul(Qinv + 1, Qinv, Qinv, prec);
        arb_mul(Qinv + 1, Qinv + 1, Q + 1, prec);
        arb_neg(Qinv + 1, Qinv + 1);
    }
    else
    {
        slong i, j, blen;

        /* The basecase algorithm is faster for much larger Qlen or len than
           this, but unfortunately also much less numerically stable. */
        if (Qlen == 2 || len <= 8)
            blen = len;
        else
            blen = FLINT_MIN(len, 4);

        for (i = 1; i < blen; i++)
        {
            arb_mul(Qinv + i, Q + 1, Qinv + i - 1, prec);

            for (j = 2; j < FLINT_MIN(i + 1, Qlen); j++)
                arb_addmul(Qinv + i, Q + j, Qinv + i - j, prec);

            if (!arb_is_one(Qinv))
                arb_mul(Qinv + i, Qinv + i, Qinv, prec);

            arb_neg(Qinv + i, Qinv + i);
        }

        if (len > blen)
        {
            slong Qnlen, Wlen, W2len;
            arb_ptr W;

            W = _arb_vec_init(len);

            NEWTON_INIT(blen, len)
            NEWTON_LOOP(m, n)

            Qnlen = FLINT_MIN(Qlen, n);
            Wlen = FLINT_MIN(Qnlen + m - 1, n);
            W2len = Wlen - m;
            MULLOW(W, Q, Qnlen, Qinv, m, Wlen, prec);
            MULLOW(Qinv + m, Qinv, m, W + m, W2len, n - m, prec);
            _arb_vec_neg(Qinv + m, Qinv + m, n - m);

            NEWTON_END_LOOP
            NEWTON_END

            _arb_vec_clear(W, len);
        }
    }
}