flint-sys 0.9.0

/*
    Copyright (C) 2008, 2009 William Hart
    Copyright (C) 2010 Sebastian Pancratz
    Copyright (C) 2012 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 "fmpz.h"
#include "fmpz_vec.h"
#include "fmpz_poly.h"

static int
__fmpz_poly_divrem_divconquer(fmpz * Q, fmpz * R,
                              const fmpz * A, slong lenA,
                              const fmpz * B, slong lenB, int exact)
{
    if (lenA < 2 * lenB - 1)
    {
        /*
           Convert unbalanced division into a 2 n1 - 1 by n1 division
         */

        const slong n1 = lenA - lenB + 1;
        const slong n2 = lenB - n1;

        const fmpz * p1 = A + n2;
        const fmpz * d1 = B + n2;
        const fmpz * d2 = B;

        fmpz * W = _fmpz_vec_init((2 * n1 - 1) + lenB - 1);

        fmpz * d1q1 = R + n2;
        fmpz * d2q1 = W + (2 * n1 - 1);

        if (!_fmpz_poly_divrem_divconquer_recursive(Q, d1q1, W, p1, d1, n1, exact))
        {
            _fmpz_vec_clear(W, (2 * n1 - 1) + lenB - 1);
            return 0;
        }

        /*
           Compute d2q1 = Q d2, of length lenB - 1
         */

        if (n1 >= n2)
            _fmpz_poly_mul(d2q1, Q, n1, d2, n2);
        else
            _fmpz_poly_mul(d2q1, d2, n2, Q, n1);

        /*
           Compute BQ = d1q1 * x^n1 + d2q1, of length lenB - 1;
           then compute R = A - BQ
         */

        _fmpz_vec_swap(R, d2q1, n2);
        _fmpz_vec_add(R + n2, R + n2, d2q1 + n2, n1 - 1);
        _fmpz_vec_sub(R, A, R, lenA);

        _fmpz_vec_clear(W, (2 * n1 - 1) + lenB - 1);
    }
    else  /* lenA = 2 * lenB - 1 */
    {
        fmpz * W = _fmpz_vec_init(lenA);

        if (!_fmpz_poly_divrem_divconquer_recursive(Q, R, W, A, B, lenB, exact))
        {
            _fmpz_vec_clear(W, lenA);
            return 0;
        }

        _fmpz_vec_sub(R, A, R, lenA);

        _fmpz_vec_clear(W, lenA);
    }

    return 1;
}

int _fmpz_poly_divrem_divconquer(fmpz *Q, fmpz *R,
                                  const fmpz *A, slong lenA,
                                  const fmpz *B, slong lenB, int exact)
{
    if (lenA <= 2 * lenB - 1)
    {
        if (!__fmpz_poly_divrem_divconquer(Q, R, A, lenA, B, lenB, exact))
            return 0;
    }
    else  /* lenA > 2 * lenB - 1 */
    {
        slong shift, n = 2 * lenB - 1;
        fmpz *QB, *W;

        _fmpz_vec_set(R, A, lenA);
        W = _fmpz_vec_init(2 * n);
        QB = W + n;

        while (lenA >= n)
        {
            shift = lenA - n;
            if (!_fmpz_poly_divrem_divconquer_recursive(Q + shift, QB,
                W, R + shift, B, lenB, exact))
            {
                _fmpz_vec_clear(W, 2 * n);
                return 0;
            }
            _fmpz_vec_sub(R + shift, R + shift, QB, n);
            lenA -= lenB;
        }

        if (lenA >= lenB)
        {
            if (!__fmpz_poly_divrem_divconquer(Q, W, R, lenA, B, lenB, exact))
            {
                _fmpz_vec_clear(W, 2 * n);
                return 0;
            }
            _fmpz_vec_swap(W, R, lenA);
        }

        _fmpz_vec_clear(W, 2 * n);
    }

    return 1;
}

void
fmpz_poly_divrem_divconquer(fmpz_poly_t Q, fmpz_poly_t R,
                            const fmpz_poly_t A, const fmpz_poly_t B)
{
    const slong lenA = A->length;
    const slong lenB = B->length;
    fmpz_poly_t tQ, tR;
    fmpz *q, *r;

    if (lenB == 0)
    {
        flint_throw(FLINT_DIVZERO, "Exception (fmpz_poly_divrem_divconquer). Division by zero.\n");
    }

    if (lenA < lenB)
    {
        fmpz_poly_set(R, A);
        fmpz_poly_zero(Q);
        return;
    }

    if (Q == A || Q == B)
    {
        fmpz_poly_init2(tQ, lenA - lenB + 1);
        q = tQ->coeffs;
    }
    else
    {
        fmpz_poly_fit_length(Q, lenA - lenB + 1);
        q = Q->coeffs;
    }

    if (R == A || R == B)
    {
        fmpz_poly_init2(tR, lenA);
        r = tR->coeffs;
    }
    else
    {
        fmpz_poly_fit_length(R, lenA);
        r = R->coeffs;
    }

    _fmpz_poly_divrem_divconquer(q, r, A->coeffs, lenA, B->coeffs, lenB, 0);

    if (Q == A || Q == B)
    {
        _fmpz_poly_set_length(tQ, lenA - lenB + 1);
        fmpz_poly_swap(tQ, Q);
        fmpz_poly_clear(tQ);
    }
    else
        _fmpz_poly_set_length(Q, lenA - lenB + 1);

    if (R == A || R == B)
    {
        _fmpz_poly_set_length(tR, lenA);
        fmpz_poly_swap(tR, R);
        fmpz_poly_clear(tR);
    }
    else
        _fmpz_poly_set_length(R, lenA);

    _fmpz_poly_normalise(Q);
    _fmpz_poly_normalise(R);
}