flint-sys 0.9.0

/*
    Copyright (C) 2012 Sebastian Pancratz

    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 "longlong.h"
#include "qadic.h"

/*
    Discussion on the choice of the norm algorithm.

    When the logarithm function does not converge for x,
    the only choice is the resultant method.

    However, when the logarithm function converges, we
    can choose between the analytic method and the resultant
    method.  Roughly speaking, we postulate that the analytic
    method has runtime A (log N)^2 mu(p,d,N), where mu(p,d,N)
    is (d log d) M(N log p).  The resultant method has runtime
    B d^4 M(N log p).  Experimentally, we find that A/B is
    somewhere around 4.

    TODO:  Repeat the experiments with p=2, which is an
    important special case.
 */

void _qadic_norm(fmpz_t rop, const fmpz *op, slong len,
                 const fmpz *a, const slong *j, slong lena,
                 const fmpz_t p, slong N)
{
    const slong d = j[lena - 1];

    if (len == 1)
    {
        fmpz_t pN;

        fmpz_init(pN);
        fmpz_pow_ui(pN, p, N);
        fmpz_powm_ui(rop, op + 0, d, pN);
        fmpz_clear(pN);
    }
    else
    {
        fmpz *y;
        slong w;

        y = _fmpz_vec_init(len);

        /* (y,len) := 1 - (op,len) */
        _fmpz_vec_neg(y, op, len);
        fmpz_add_ui(y + 0, y + 0, 1);

        w = _fmpz_vec_ord_p(y, len, p);

        if (w >= 2 || (*p != WORD(2) && w >= 1))
        {
            if ((slong) (4 * FLINT_FLOG2(N) * FLINT_FLOG2(N) * FLINT_FLOG2(d)) < d*d*d)
            {
                _qadic_norm_analytic(rop, y, w, len, a, j, lena, p, N);
            }
            else
            {
                _qadic_norm_resultant(rop, op, len, a, j, lena, p, N);
            }
        }
        else
        {
            _qadic_norm_resultant(rop, op, len, a, j, lena, p, N);
        }

        _fmpz_vec_clear(y, len);
    }
}

void qadic_norm(padic_t rop, const qadic_t op, const qadic_ctx_t ctx)
{
    const slong N  = padic_prec(rop);
    const slong d  = qadic_ctx_degree(ctx);
    const fmpz *p = (&ctx->pctx)->p;

    /* N(p^v u) = p^{dv} N(u) */

    if (qadic_is_zero(op) || d * op->val >= N)
    {
        padic_zero(rop);
    }
    else
    {
        _qadic_norm(padic_unit(rop), op->coeffs, op->length,
                    ctx->a, ctx->j, ctx->len, p, N - d * op->val);
        padic_val(rop) = d * op->val;
    }
}