flint-sys 0.9.0

Bindings to the FLINT C library
Documentation 
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/*
    Copyright (C) 2010 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 "fmpz.h"
#include "fmpz_vec.h"
#include "fmpz_poly.h"

void
_fmpz_poly_gcd(fmpz * res, const fmpz * poly1, slong len1,
               const fmpz * poly2, slong len2)
{
    FLINT_ASSERT(len2 >= 1);
    FLINT_ASSERT(len1 >= len2);

    /* remove powers of x */
    {
        slong val1 = 0, val2 = 0, d, rlen;

        while (val1 < len1 - 1 && fmpz_is_zero(poly1 + val1))
            val1++;
        while (val2 < len2 - 1 && fmpz_is_zero(poly2 + val2))
            val2++;

        if (val1 != 0 || val2 != 0)
        {
            d = FLINT_MIN(val1, val2);
            rlen = FLINT_MIN(len1 - val1, len2 - val2);

            if (len1 - val1 >= len2 - val2)
                _fmpz_poly_gcd(res + d, poly1 + val1, len1 - val1, poly2 + val2, len2 - val2);
            else
                _fmpz_poly_gcd(res + d, poly2 + val2, len2 - val2, poly1 + val1, len1 - val1);

            _fmpz_vec_zero(res, d);
            _fmpz_vec_zero(res + d + rlen, len2 - rlen - d);
            return;
        }
    }

    if (len1 < 6)
    {
        _fmpz_poly_gcd_subresultant(res, poly1, len1, poly2, len2);
    }
    else
    {
        slong b1, b2;

        b1 = _fmpz_vec_max_bits(poly1, len1);
        b2 = _fmpz_vec_max_bits(poly2, len2);
        b1 = FLINT_ABS(b1);
        b2 = FLINT_ABS(b2);

        if (b1 + b2 < 2 * FLINT_BITS)
        {
            if (_fmpz_poly_gcd_heuristic(res, poly1, len1, poly2, len2))
                return;
        }

        _fmpz_poly_gcd_modular(res, poly1, len1, poly2, len2);
    }
}

void
fmpz_poly_gcd(fmpz_poly_t res, const fmpz_poly_t poly1,
              const fmpz_poly_t poly2)
{
    if (poly1->length < poly2->length)
    {
        fmpz_poly_gcd(res, poly2, poly1);
    }
    else /* len1 >= len2 >= 0 */
    {
        const slong len1 = poly1->length;
        const slong len2 = poly2->length;

        if (len1 == 0) /* len1 = len2 = 0 */
        {
            fmpz_poly_zero(res);
        }
        else if (len2 == 0) /* len1 > len2 = 0 */
        {
            if (fmpz_sgn(poly1->coeffs + (len1 - 1)) > 0)
                fmpz_poly_set(res, poly1);
            else
                fmpz_poly_neg(res, poly1);
        }
        else /* len1 >= len2 >= 1 */
        {
            /* all current gcd functions automatically handle aliasing */

            fmpz_poly_fit_length(res, len2);

            _fmpz_poly_gcd(res->coeffs, poly1->coeffs, len1,
                                    poly2->coeffs, len2);

            _fmpz_poly_set_length(res, len2);
            _fmpz_poly_normalise(res);
        }
    }
}