arb/acb/test/t-chebyshev_t_ui.c

/*
    Copyright (C) 2014 Fredrik Johansson

    This file is part of Arb.

    Arb 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 2.1 of the License, or
    (at your option) any later version.  See <http://www.gnu.org/licenses/>.
*/

#include "acb.h"

int main()
{
    slong iter;
    flint_rand_t state;

    flint_printf("chebyshev_t_ui....");
    fflush(stdout);

    flint_randinit(state);

    for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
    {
        acb_t a, b, c, d;
        ulong n;
        slong prec;

        n = n_randtest(state);
        prec = 2 + n_randint(state, 300);

        acb_init(a);
        acb_init(b);
        acb_init(c);
        acb_init(d);

        acb_randtest(a, state, 1 + n_randint(state, 300), 5);
        acb_randtest(c, state, 1 + n_randint(state, 300), 5);

        acb_cos(b, a, prec);
        acb_chebyshev_t_ui(c, n, b, prec);

        acb_mul_ui(d, a, n, prec);
        acb_cos(d, d, prec);

        if (!acb_overlaps(c, d))
        {
            flint_printf("FAIL: c = T_n(cos(a)) = d = cos(n*a)\n\n");
            flint_printf("n = %wu\n\n", n);
            flint_printf("a = "); acb_print(a); flint_printf("\n\n");
            flint_printf("b = "); acb_print(b); flint_printf("\n\n");
            flint_printf("d = "); acb_print(c); flint_printf("\n\n");
            abort();
        }

        acb_chebyshev_t_ui(b, n, b, prec);

        if (!acb_equal(b, c))
        {
            flint_printf("FAIL: aliasing\n\n");
            flint_printf("n = %wu\n\n", n);
            flint_printf("b = "); acb_print(b); flint_printf("\n\n");
            flint_printf("c = "); acb_print(c); flint_printf("\n\n");
            abort();
        }

        acb_randtest(a, state, 1 + n_randint(state, 300), 5);
        acb_randtest(b, state, 1 + n_randint(state, 300), 5);
        acb_randtest(c, state, 1 + n_randint(state, 300), 5);

        acb_chebyshev_t2_ui(b, c, n, a, prec);
        acb_chebyshev_t_ui(d, n, a, prec);

        if (!acb_overlaps(b, d))
        {
            flint_printf("FAIL: T_n\n\n");
            flint_printf("n = %wu\n\n", n);
            flint_printf("a = "); acb_print(a); flint_printf("\n\n");
            flint_printf("b = "); acb_print(b); flint_printf("\n\n");
            flint_printf("c = "); acb_print(c); flint_printf("\n\n");
            flint_printf("b = "); acb_print(b); flint_printf("\n\n");
            abort();
        }

        if (n == 0)
            acb_set(d, a);
        else
            acb_chebyshev_t_ui(d, n - 1, a, prec);

        if (!acb_overlaps(c, d))
        {
            flint_printf("FAIL: T_{n-1}\n\n");
            flint_printf("n = %wu\n\n", n);
            flint_printf("a = "); acb_print(a); flint_printf("\n\n");
            flint_printf("b = "); acb_print(b); flint_printf("\n\n");
            flint_printf("c = "); acb_print(c); flint_printf("\n\n");
            flint_printf("b = "); acb_print(b); flint_printf("\n\n");
            abort();
        }

        acb_clear(a);
        acb_clear(b);
        acb_clear(c);
        acb_clear(d);
    }

    flint_randclear(state);
    flint_cleanup();
    flint_printf("PASS\n");
    return EXIT_SUCCESS;
}