flint-sys 0.9.0

/*
    Copyright (C) 2007, 2008 William Hart
    Copyright (C) 2011 Sebastian Pancratz
    Copyright (C) 2023 Fredrik Johansson

    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 "mpn_extras.h"
#include "nmod.h"
#include "nmod_vec.h"
#include "nmod_poly.h"
#include "gr_poly.h"

/* todo: when highly unbalanced, do initial division in input representation */
static ulong
_nmod_poly_resultant_euclidean_redc_fast(nn_srcptr poly1, slong len1,
                               nn_srcptr poly2, slong len2, nmod_t mod)
{
    gr_ctx_t ctx;
    ulong res, R;
    gr_ctx_init_nmod_redc_fast(ctx, mod.n);
    GR_MUST_SUCCEED(_gr_poly_resultant_euclidean(&res, poly1, len1, poly2, len2, ctx));

    /* Undo scaling factor from casting poly1 and poly2 to Montgomery representation */
    R = _nmod_redc_fast_2_pow_ui(FLINT_BITS * (len1 + len2 - 2), GR_NMOD_REDC_CTX(ctx));
    res = nmod_redc_fast_mul(res, R, GR_NMOD_REDC_CTX(ctx));

    res = nmod_redc_get_nmod(res, GR_NMOD_REDC_CTX(ctx));

    return res;
}

ulong
_nmod_poly_resultant(nn_srcptr poly1, slong len1,
                               nn_srcptr poly2, slong len2, nmod_t mod)
{
    if (poly1 == poly2)
    {
        return 0;
    }
    else if (len2 == 1)
    {
        return nmod_pow_ui(poly2[0], len1 - 1, mod);
    }
    else
    {
        ulong res;
        gr_ctx_t ctx;
        _gr_ctx_init_nmod(ctx, &mod);

        if (_gr_poly_resultant_small(&res, poly1, len1, poly2, len2, ctx) != GR_SUCCESS)
        {
            if (len2 < nmod_poly_gcd_hgcd_cutoff(mod))
            {
                if (NMOD_POLY_GCD_EUCLIDEAN_USE_REDC_FAST(len2, mod) && len1 < 8 * len2)
                    return _nmod_poly_resultant_euclidean_redc_fast(poly1, len1, poly2, len2, mod);
                else
                    return _nmod_poly_resultant_euclidean(poly1, len1, poly2, len2, mod);
            }
            else
            {
                return _nmod_poly_resultant_hgcd(poly1, len1, poly2, len2, mod);
            }
        }

        return res;
    }
}

ulong
nmod_poly_resultant(const nmod_poly_t f, const nmod_poly_t g)
{
    const slong len1 = f->length;
    const slong len2 = g->length;
    ulong r;

    if (len1 == 0 || len2 == 0)
    {
        r = 0;
    }
    else
    {
        if (len1 >= len2)
        {
            r = _nmod_poly_resultant(f->coeffs, len1, g->coeffs, len2, f->mod);
        }
        else
        {
            r = _nmod_poly_resultant(g->coeffs, len2, f->coeffs, len1, f->mod);
            if (((len1 | len2) & WORD(1)) == WORD(0))
                r = nmod_neg(r, f->mod);
        }
    }

    return r;
}

ulong
_nmod_poly_resultant_euclidean(nn_srcptr poly1, slong len1,
                               nn_srcptr poly2, slong len2, nmod_t mod)
{
    if (poly1 == poly2)
    {
        return 0;
    }
    else if (len2 == 1)
    {
        if (len1 == 1)
        {
            return 1;
        }
        else if (len1 == 2)
        {
            return poly2[0];
        }
        else
        {
            return nmod_pow_ui(poly2[0], len1 - 1, mod);
        }
    }
    else  /* len1 >= len2 >= 2 */
    {
        ulong res = 1;

        nn_ptr u, v, r, t, w;
        slong l0, l1, l2;
        ulong lc;

        w = _nmod_vec_init(3 * len1);
        u = w;
        v = w + len1;
        r = v + len1;

        _nmod_vec_set(u, poly1, len1);
        _nmod_vec_set(v, poly2, len2);
        l1 = len1;
        l2 = len2;

        do
        {
            l0 = l1;
            l1 = l2;
            lc = v[l1 - 1];

            _nmod_poly_rem(r, u, l0, v, l1, mod);
            l2 = l1 - 1;
            MPN_NORM(r, l2);
            {
                t = u;
                u = v;
                v = r;
                r = t;
            }

            if (l2 >= 1)
            {
                lc  = nmod_pow_ui(lc, l0 - l2, mod);
                res = nmod_mul(res, lc, mod);

                if (((l0 | l1) & 1) == 0)
                {
                    res = nmod_neg(res, mod);
                }
            }
            else
            {
                if (l1 == 1)
                {
                    lc  = nmod_pow_ui(lc, l0 - 1, mod);
                    res = nmod_mul(res, lc, mod);
                }
                else
                {
                    res = 0;
                }
            }
        }
        while (l2 > 0);

        _nmod_vec_clear(w);

        return res;
    }
}

ulong
nmod_poly_resultant_euclidean(const nmod_poly_t f, const nmod_poly_t g)
{
    const slong len1 = f->length;
    const slong len2 = g->length;
    ulong r;

    if (len1 == 0 || len2 == 0)
    {
        r = 0;
    }
    else
    {
        if (len1 >= len2)
        {
            r = _nmod_poly_resultant_euclidean(f->coeffs, len1,
                                               g->coeffs, len2, f->mod);
        }
        else
        {
            r = _nmod_poly_resultant_euclidean(g->coeffs, len2,
                                               f->coeffs, len1, f->mod);

            if (((len1 | len2) & WORD(1)) == WORD(0))
                r = nmod_neg(r, f->mod);
        }
    }

    return r;
}

ulong
_nmod_poly_resultant_hgcd(nn_srcptr poly1, slong len1,
                               nn_srcptr poly2, slong len2, nmod_t mod)
{
    gr_ctx_t ctx;
    slong inner_cutoff = nmod_poly_hgcd_iter_recursive_cutoff(mod);
    slong outer_cutoff = nmod_poly_hgcd_outer_cutoff(mod);
    ulong res;
    _gr_ctx_init_nmod(ctx, &mod);
    GR_MUST_SUCCEED(_gr_poly_resultant_hgcd(&res, poly1, len1, poly2, len2, inner_cutoff, outer_cutoff, ctx));
    return res;
}

ulong
nmod_poly_resultant_hgcd(const nmod_poly_t f, const nmod_poly_t g)
{
    const slong len1 = f->length;
    const slong len2 = g->length;
    ulong r;

    if (len1 == 0 || len2 == 0)
    {
        r = 0;
    }
    else
    {
        if (len1 >= len2)
        {
            r = _nmod_poly_resultant_hgcd(f->coeffs, len1, g->coeffs, len2, f->mod);
        }
        else
        {
            r = _nmod_poly_resultant_hgcd(g->coeffs, len2, f->coeffs, len1, f->mod);
            if (((len1 | len2) & WORD(1)) == WORD(0))
                r = nmod_neg(r, f->mod);
        }
    }

    return r;
}