flint-sys 0.9.0

/*
    Copyright (C) 2011 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 "fmpq.h"

void
_fmpq_sub(fmpz_t rnum, fmpz_t rden, const fmpz_t p, const fmpz_t q,
            const fmpz_t r, const fmpz_t s)
{
    fmpz_t g, a, b, t, u;

    if (!COEFF_IS_MPZ(*p) && !COEFF_IS_MPZ(*q) && !COEFF_IS_MPZ(*r) && !COEFF_IS_MPZ(*s))
    {
        _fmpq_add_small(rnum, rden, *p, *q, -(*r), *s);
        return;
    }

    /* Same denominator */
    if (fmpz_equal(q, s))
    {
        fmpz_sub(rnum, p, r);

        /* Both are integers */
        if (fmpz_is_one(q))
        {
            fmpz_set(rden, q);
        }
        else
        {
            fmpz_init(g);
            fmpz_gcd(g, rnum, q);

            if (fmpz_is_one(g))
            {
                fmpz_set(rden, q);
            }
            else
            {
                fmpz_divexact(rnum, rnum, g);
                fmpz_divexact(rden, q, g);
            }
            fmpz_clear(g);
        }
        return;
    }

    /* p/q is an integer */
    if (fmpz_is_one(q))
    {
        fmpz_init(t);
        fmpz_mul(t, p, s);
        fmpz_sub(rnum, t, r);
        fmpz_set(rden, s);
        fmpz_clear(t);
        return;
    }

    /* r/s is an integer */
    if (fmpz_is_one(s))
    {
        fmpz_init(t);
        fmpz_mul(t, r, q);
        fmpz_sub(rnum, p, t);
        fmpz_set(rden, q);
        fmpz_clear(t);
        return;
    }

    fmpz_init(g);
    fmpz_gcd(g, q, s);

    if (fmpz_is_one(g))
    {
        fmpz_init(t);
        fmpz_init(u);

        fmpz_mul(t, p, s);
        fmpz_mul(u, q, r);
        fmpz_sub(rnum, t, u);
        fmpz_mul(rden, q, s);

        fmpz_clear(t);
        fmpz_clear(u);
    }
    else
    {
        fmpz_init(a);
        fmpz_init(b);
        fmpz_init(t);
        fmpz_init(u);

        fmpz_divexact(a, q, g);
        fmpz_divexact(b, s, g);

        fmpz_mul(t, p, b);
        fmpz_mul(u, r, a);
        fmpz_sub(rnum, t, u);

        fmpz_gcd(t, rnum, g);

        if (fmpz_is_one(t))
        {
            fmpz_mul(rden, q, b);
        }
        else
        {
            fmpz_divexact(rnum, rnum, t);
            fmpz_divexact(g, q, t);
            fmpz_mul(rden, g, b);
        }

        fmpz_clear(a);
        fmpz_clear(b);
        fmpz_clear(t);
        fmpz_clear(u);
    }

    fmpz_clear(g);
}

void fmpq_sub(fmpq_t res, const fmpq_t op1, const fmpq_t op2)
{
    _fmpq_sub(fmpq_numref(res), fmpq_denref(res),
              fmpq_numref(op1), fmpq_denref(op1),
              fmpq_numref(op2), fmpq_denref(op2));
}

void
_fmpq_sub_fmpz(fmpz_t rnum, fmpz_t rden, const fmpz_t p, const fmpz_t q,
            const fmpz_t r)
{
    fmpz_t u;

    if (!COEFF_IS_MPZ(*p) && !COEFF_IS_MPZ(*q) && !COEFF_IS_MPZ(*r))
    {
        _fmpq_add_small(rnum, rden, *p, *q, -(*r), 1);
        return;
    }

    /* both are integers */
    if (fmpz_is_one(q))
    {
        fmpz_sub(rnum, p, r);
        fmpz_set(rden, q);
                return;
    }

    /*
    We want to compute p/q - r/1 where the inputs are already
    in canonical form.

    Note (p - q*r, q) is in canonical form.

    */

    fmpz_init(u);

    fmpz_mul(u, q, r);
    fmpz_sub(rnum, p, u);
    fmpz_set(rden, q);

    fmpz_clear(u);
}

void fmpq_sub_fmpz(fmpq_t res, const fmpq_t op1, const fmpz_t c)
{
    _fmpq_sub_fmpz(fmpq_numref(res), fmpq_denref(res),
              fmpq_numref(op1), fmpq_denref(op1), c);
}

void
_fmpq_sub_si(fmpz_t rnum, fmpz_t rden, const fmpz_t p, const fmpz_t q,
            slong r)
{
    fmpz_t u;

    if (!COEFF_IS_MPZ(*p) && !COEFF_IS_MPZ(*q) && r >= COEFF_MIN && r <= COEFF_MAX)
    {
        _fmpq_add_small(rnum, rden, *p, *q, -r, 1);
        return;
    }

    /* both are integers */
    if (fmpz_is_one(q))
    {
        if (r >= 0)
           fmpz_sub_ui(rnum, p, r);
        else
           fmpz_add_ui(rnum, p, -r);

        fmpz_set(rden, q);
        return;
    }

    /*
    We want to compute p/q - r/1 where the inputs are already
    in canonical form.

    Note (p - q*r, q) is in canonical form.

    */

    fmpz_init(u);

    fmpz_mul_si(u, q, r);
    fmpz_sub(rnum, p, u);
    fmpz_set(rden, q);

    fmpz_clear(u);
}

void fmpq_sub_si(fmpq_t res, const fmpq_t op1, slong c)
{
    _fmpq_sub_si(fmpq_numref(res), fmpq_denref(res),
              fmpq_numref(op1), fmpq_denref(op1), c);
}

void
_fmpq_sub_ui(fmpz_t rnum, fmpz_t rden, const fmpz_t p, const fmpz_t q,
            ulong r)
{
    fmpz_t u;

    if (!COEFF_IS_MPZ(*p) && !COEFF_IS_MPZ(*q) && r <= COEFF_MAX)
    {
        _fmpq_add_small(rnum, rden, *p, *q, -(slong) r, 1);
        return;
    }

    /* both are integers */
    if (fmpz_is_one(q))
    {
        fmpz_sub_ui(rnum, p, r);
        fmpz_set(rden, q);
        return;
    }

    /*
    We want to compute p/q - r/1 where the inputs are already
    in canonical form.

    Note (p - q*r, q) is in canonical form.

    */

    fmpz_init(u);

    fmpz_mul_ui(u, q, r);
    fmpz_sub(rnum, p, u);
    fmpz_set(rden, q);

    fmpz_clear(u);
}

void fmpq_sub_ui(fmpq_t res, const fmpq_t op1, ulong c)
{
    _fmpq_sub_ui(fmpq_numref(res), fmpq_denref(res),
              fmpq_numref(op1), fmpq_denref(op1), c);
}