flint-sys 0.9.0

Bindings to the FLINT C library
Documentation 
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/*
    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 "test_helpers.h"
#include <mpfr.h>
#include "fmpq.h"
#include "arb.h"

TEST_FUNCTION_START(arb_cos, state)
{
    slong iter;

    for (iter = 0; iter < 100000 * 0.1 * flint_test_multiplier(); iter++)
    {
        arb_t a, b;
        fmpq_t q;
        mpfr_t t;
        slong prec0, prec;

        prec0 = 400;
        if (iter % 100 == 0)
            prec0 = 8000;

        prec = 2 + n_randint(state, prec0);

        arb_init(a);
        arb_init(b);
        fmpq_init(q);
        mpfr_init2(t, prec0 + 100);

        arb_randtest(a, state, 1 + n_randint(state, prec0), 6);
        arb_randtest(b, state, 1 + n_randint(state, prec0), 6);
        arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, prec0));

        fmpq_get_mpfr(t, q, MPFR_RNDN);
        mpfr_cos(t, t, MPFR_RNDN);

        arb_cos(b, a, prec);

        if (!arb_contains_mpfr(b, t))
        {
            flint_printf("FAIL: containment\n\n");
            flint_printf("a = "); arb_print(a); flint_printf("\n\n");
            flint_printf("b = "); arb_print(b); flint_printf("\n\n");
            flint_abort();
        }

        arb_cos(a, a, prec);

        if (!arb_equal(a, b))
        {
            flint_printf("FAIL: aliasing\n\n");
            flint_abort();
        }

        arb_clear(a);
        arb_clear(b);
        fmpq_clear(q);
        mpfr_clear(t);
    }

    /* check large arguments */
    for (iter = 0; iter < 100000 * 0.1 * flint_test_multiplier(); iter++)
    {
        arb_t a, b, c, d;
        slong prec0, prec1, prec2;

        if (iter % 10 == 0)
            prec0 = 10000;
        else
            prec0 = 1000;

        prec1 = 2 + n_randint(state, prec0);
        prec2 = 2 + n_randint(state, prec0);

        arb_init(a);
        arb_init(b);
        arb_init(c);
        arb_init(d);

        arb_randtest_special(a, state, 1 + n_randint(state, prec0), prec0);
        arb_randtest_special(b, state, 1 + n_randint(state, prec0), 100);
        arb_randtest_special(c, state, 1 + n_randint(state, prec0), 100);
        arb_randtest_special(d, state, 1 + n_randint(state, prec0), 100);

        arb_cos(b, a, prec1);
        arb_cos(c, a, prec2);

        if (!arb_overlaps(b, c))
        {
            flint_printf("FAIL: overlap\n\n");
            flint_printf("a = "); arb_print(a); flint_printf("\n\n");
            flint_printf("b = "); arb_print(b); flint_printf("\n\n");
            flint_printf("c = "); arb_print(c); flint_printf("\n\n");
            flint_abort();
        }

        /* check cos(2a) = 2cos(a)^2-1 */
        arb_mul_2exp_si(c, a, 1);
        arb_cos(c, c, prec1);

        arb_mul(b, b, b, prec1);
        arb_mul_2exp_si(b, b, 1);
        arb_sub_ui(b, b, 1, prec1);

        if (!arb_overlaps(b, c))
        {
            flint_printf("FAIL: functional equation\n\n");
            flint_printf("a = "); arb_print(a); flint_printf("\n\n");
            flint_printf("b = "); arb_print(b); flint_printf("\n\n");
            flint_printf("c = "); arb_print(c); flint_printf("\n\n");
            flint_abort();
        }

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

    TEST_FUNCTION_END(state);
}