flint-sys 0.9.0

/*
    Copyright (C) 2011 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 "test_helpers.h"
#include "fmpq_poly.h"

TEST_FUNCTION_START(fmpq_poly_xgcd, state)
{
    int cflags = 0, i, result;

    /* Generic case, where a and b are coprime *******************************/

    /* Verify d == s a + t b */
    for (i = 0; i < 100 * flint_test_multiplier(); i++)
    {
        fmpq_poly_t a, b, d, e, f, s, t;

        fmpq_poly_init(a);
        fmpq_poly_init(b);
        fmpq_poly_init(d);
        fmpq_poly_init(e);
        fmpq_poly_init(f);
        fmpq_poly_init(s);
        fmpq_poly_init(t);
        fmpq_poly_randtest(a, state, n_randint(state, 60), 80);
        fmpq_poly_randtest(b, state, n_randint(state, 60), 80);

        fmpq_poly_xgcd(d, s, t, a, b);
        fmpq_poly_mul(e, s, a);
        fmpq_poly_mul(f, t, b);
        fmpq_poly_add(e, e, f);

        cflags |= fmpq_poly_is_canonical(d) ? 0 : 1;
        cflags |= fmpq_poly_is_canonical(s) ? 0 : 2;
        cflags |= fmpq_poly_is_canonical(t) ? 0 : 4;
        result = (fmpq_poly_equal(d, e) && !cflags);
        if (!result)
        {
            flint_printf("FAIL (correctness #1):\n");
            fmpq_poly_debug(a), flint_printf("\n\n");
            fmpq_poly_debug(b), flint_printf("\n\n");
            fmpq_poly_debug(d), flint_printf("\n\n");
            fmpq_poly_debug(s), flint_printf("\n\n");
            fmpq_poly_debug(t), flint_printf("\n\n");
            flint_printf("cflags = %d\n\n", cflags);
            fflush(stdout);
            flint_abort();
        }

        fmpq_poly_clear(a);
        fmpq_poly_clear(b);
        fmpq_poly_clear(d);
        fmpq_poly_clear(e);
        fmpq_poly_clear(f);
        fmpq_poly_clear(s);
        fmpq_poly_clear(t);
    }

    /* Verify consistency with GCD */
    for (i = 0; i < 100 * flint_test_multiplier(); i++)
    {
        fmpq_poly_t a, b, d, s, t;

        fmpq_poly_init(a);
        fmpq_poly_init(b);
        fmpq_poly_init(d);
        fmpq_poly_init(s);
        fmpq_poly_init(t);
        fmpq_poly_randtest(a, state, n_randint(state, 60), 80);
        fmpq_poly_randtest(b, state, n_randint(state, 60), 80);

        fmpq_poly_xgcd(d, s, t, a, b);
        fmpq_poly_gcd(a, a, b);

        cflags |= fmpq_poly_is_canonical(d) ? 0 : 1;
        cflags |= fmpq_poly_is_canonical(s) ? 0 : 2;
        cflags |= fmpq_poly_is_canonical(t) ? 0 : 4;
        result = (fmpq_poly_equal(d, a) && !cflags);
        if (!result)
        {
            flint_printf("FAIL (GCD #1):\n");
            fmpq_poly_debug(a), flint_printf("\n\n");
            fmpq_poly_debug(b), flint_printf("\n\n");
            fmpq_poly_debug(d), flint_printf("\n\n");
            fmpq_poly_debug(s), flint_printf("\n\n");
            fmpq_poly_debug(t), flint_printf("\n\n");
            flint_printf("cflags = %d\n\n", cflags);
            fflush(stdout);
            flint_abort();
        }

        fmpq_poly_clear(a);
        fmpq_poly_clear(b);
        fmpq_poly_clear(d);
        fmpq_poly_clear(s);
        fmpq_poly_clear(t);
    }

    /* Generic case when a, b are most likely co-prime ***********************/

    /* Verify d == s a + t b */
    for (i = 0; i < 100 * flint_test_multiplier(); i++)
    {
        fmpq_poly_t a, b, d, s, t, z;

        fmpq_poly_init(a);
        fmpq_poly_init(b);
        fmpq_poly_init(d);
        fmpq_poly_init(s);
        fmpq_poly_init(t);
        fmpq_poly_init(z);
        fmpq_poly_randtest(a, state, n_randint(state, 60), 80);
        fmpq_poly_randtest(b, state, n_randint(state, 60), 80);
        fmpq_poly_randtest(z, state, n_randint(state, 20), 20);
        fmpq_poly_mul(a, a, z);
        fmpq_poly_mul(b, b, z);

        fmpq_poly_xgcd(d, s, t, a, b);
        fmpq_poly_mul(a, s, a);
        fmpq_poly_mul(b, t, b);
        fmpq_poly_add(a, a, b);

        cflags |= fmpq_poly_is_canonical(d) ? 0 : 1;
        cflags |= fmpq_poly_is_canonical(s) ? 0 : 2;
        cflags |= fmpq_poly_is_canonical(t) ? 0 : 4;
        result = (fmpq_poly_equal(d, a) && !cflags);
        if (!result)
        {
            flint_printf("FAIL (correctness #2):\n");
            fmpq_poly_debug(a), flint_printf("\n\n");
            fmpq_poly_debug(b), flint_printf("\n\n");
            fmpq_poly_debug(d), flint_printf("\n\n");
            fmpq_poly_debug(s), flint_printf("\n\n");
            fmpq_poly_debug(t), flint_printf("\n\n");
            flint_printf("cflags = %d\n\n", cflags);
            fflush(stdout);
            flint_abort();
        }

        fmpq_poly_clear(a);
        fmpq_poly_clear(b);
        fmpq_poly_clear(d);
        fmpq_poly_clear(s);
        fmpq_poly_clear(t);
        fmpq_poly_clear(z);
    }

    /* Verify consistency with GCD */
    for (i = 0; i < 100 * flint_test_multiplier(); i++)
    {
        fmpq_poly_t a, b, d, s, t, z;

        fmpq_poly_init(a);
        fmpq_poly_init(b);
        fmpq_poly_init(d);
        fmpq_poly_init(s);
        fmpq_poly_init(t);
        fmpq_poly_init(z);
        fmpq_poly_randtest(a, state, n_randint(state, 60), 80);
        fmpq_poly_randtest(b, state, n_randint(state, 60), 80);
        fmpq_poly_randtest(z, state, n_randint(state, 20), 20);
        fmpq_poly_mul(a, a, z);
        fmpq_poly_mul(b, b, z);

        fmpq_poly_xgcd(d, s, t, a, b);
        fmpq_poly_gcd(a, a, b);

        cflags |= fmpq_poly_is_canonical(d) ? 0 : 1;
        cflags |= fmpq_poly_is_canonical(s) ? 0 : 2;
        cflags |= fmpq_poly_is_canonical(t) ? 0 : 4;
        result = (fmpq_poly_equal(d, a) && !cflags);
        if (!result)
        {
            flint_printf("FAIL (GCD #2):\n");
            fmpq_poly_debug(a), flint_printf("\n\n");
            fmpq_poly_debug(b), flint_printf("\n\n");
            fmpq_poly_debug(d), flint_printf("\n\n");
            fmpq_poly_debug(s), flint_printf("\n\n");
            fmpq_poly_debug(t), flint_printf("\n\n");
            flint_printf("cflags = %d\n\n", cflags);
            fflush(stdout);
            flint_abort();
        }

        fmpq_poly_clear(a);
        fmpq_poly_clear(b);
        fmpq_poly_clear(d);
        fmpq_poly_clear(s);
        fmpq_poly_clear(t);
        fmpq_poly_clear(z);
    }

    /* regression test, see #1014 */
    {
        fmpq_poly_t a, b, d, s, t, z, z1;

        fmpq_poly_init(a);
        fmpq_poly_init(b);
        fmpq_poly_init(d);
        fmpq_poly_init(s);
        fmpq_poly_init(t);
        fmpq_poly_init(z);
        fmpq_poly_init(z1);

         fmpq_poly_one(a);
         fmpq_poly_one(b);
         fmpq_poly_shift_left(a, a, 400);
         fmpq_poly_shift_left(b, b, 400);
         fmpq_poly_sub_si(a, a, 1);
         fmpq_poly_add_si(b, b, 1);

        fmpq_poly_xgcd(d, s, t, a, b);
        fmpq_poly_mul(z, s, a);
        fmpq_poly_mul(z1, t, b);
        fmpq_poly_add(z, z, z1);

        if (!fmpq_poly_equal(z, d))
        {
            flint_printf("FAIL:\n");
            flint_printf("a: "); fmpq_poly_print_pretty(a, "x"), flint_printf("\n\n");
            flint_printf("b: "); fmpq_poly_print_pretty(b, "x"), flint_printf("\n\n");
            flint_printf("d: "); fmpq_poly_print_pretty(d, "x"), flint_printf("\n\n");
            flint_printf("s: "); fmpq_poly_print_pretty(s, "x"), flint_printf("\n\n");
            flint_printf("t: "); fmpq_poly_print_pretty(t, "x"), flint_printf("\n\n");
            fflush(stdout);
            flint_abort();
        }

        fmpq_poly_clear(a);
        fmpq_poly_clear(b);
        fmpq_poly_clear(d);
        fmpq_poly_clear(s);
        fmpq_poly_clear(t);
        fmpq_poly_clear(z);
        fmpq_poly_clear(z1);
    }

    TEST_FUNCTION_END(state);
}