flint-sys 0.9.0

Bindings to the FLINT C library
Documentation 
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/*
    Copyright (C) 2010 William Hart
    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 "test_helpers.h"
#include "ulong_extras.h"
#include "nmod_poly.h"

TEST_FUNCTION_START(nmod_poly_atanh_series, state)
{
    int i, result = 1;

    /* Check 2*atanh(A) = atanh(2*A/(1+A^2)) */
    for (i = 0; i < 100 * flint_test_multiplier(); i++)
    {
        nmod_poly_t A, B, atanhA, atanhB;
        slong n;
        ulong mod;

        mod = n_randtest_prime(state, 0);
        n = 1 + n_randtest(state) % 100;
        n = FLINT_MIN(n, mod);

        nmod_poly_init(A, mod);
        nmod_poly_init(B, mod);
        nmod_poly_init(atanhA, mod);
        nmod_poly_init(atanhB, mod);

        nmod_poly_randtest(A, state, n_randint(state, 100));
        nmod_poly_set_coeff_ui(A, 0, UWORD(0));

        nmod_poly_mullow(B, A, A, n);
        nmod_poly_set_coeff_ui(B, 0, UWORD(1));
        nmod_poly_div_series(B, A, B, n);
        nmod_poly_add(B, B, B);

        nmod_poly_atanh_series(atanhA, A, n);
        nmod_poly_atanh_series(atanhB, B, n);
        nmod_poly_add(atanhA, atanhA, atanhA);

        result = nmod_poly_equal(atanhA, atanhB);

        if (!result)
        {
            flint_printf("FAIL:\n");
            flint_printf("n = %wd, mod = %wu\n", n, mod);
            flint_printf("A: "); nmod_poly_print(A), flint_printf("\n\n");
            flint_printf("B: "); nmod_poly_print(B), flint_printf("\n\n");
            flint_printf("2*atanh(A): "); nmod_poly_print(atanhA), flint_printf("\n\n");
            flint_printf("atanh(B): "); nmod_poly_print(atanhB), flint_printf("\n\n");
            fflush(stdout);
            flint_abort();
        }

        nmod_poly_clear(A);
        nmod_poly_clear(B);
        nmod_poly_clear(atanhA);
        nmod_poly_clear(atanhB);
    }

    /* Check aliasing */
    for (i = 0; i < 100 * flint_test_multiplier(); i++)
    {
        nmod_poly_t A, B;
        slong n;
        ulong mod;
        mod = n_randtest_prime(state, 0);
        n = n_randtest(state) % 50;
        n = FLINT_MIN(n, mod);

        nmod_poly_init(A, mod);
        nmod_poly_init(B, mod);
        nmod_poly_randtest(A, state, n_randint(state, 50));
        nmod_poly_set_coeff_ui(A, 0, UWORD(0));

        nmod_poly_atanh_series(B, A, n);
        nmod_poly_atanh_series(A, A, n);

        result = nmod_poly_equal(A, B);
        if (!result)
        {
            flint_printf("FAIL:\n");
            nmod_poly_print(A), flint_printf("\n\n");
            nmod_poly_print(B), flint_printf("\n\n");
            fflush(stdout);
            flint_abort();
        }

        nmod_poly_clear(A);
        nmod_poly_clear(B);
    }

    TEST_FUNCTION_END(state);
}