flint-sys 0.9.0

/*
    Copyright (C) 2012-2017 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_atan, state)
{
    slong iter;

    /* Compare with MPFR */
    for (iter = 0; iter < 10000 * 0.1 * flint_test_multiplier(); iter++)
    {
        arb_t a, b;
        fmpq_t q;
        mpfr_t t;
        slong prec = 2 + n_randint(state, 200);

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

        arb_randtest(a, state, 1 + n_randint(state, 200), 3);
        arb_randtest(b, state, 1 + n_randint(state, 200), 3);
        arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200));

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

        arb_atan(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_atan(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 < 10000 * 0.1 * flint_test_multiplier(); iter++)
    {
        arb_t a, b, c, d;
        slong prec1, prec2;

        prec1 = 2 + n_randint(state, 1000);
        prec2 = prec1 + 30;

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

        arb_randtest_precise(a, state, 1 + n_randint(state, 1000), 100);

        arb_atan(b, a, prec1);
        arb_atan(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 tan(atan(x)) = x */
        arb_sin_cos(c, d, b, prec1);
        arb_div(c, c, d, prec1);

        if (!arb_contains(c, a))
        {
            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_printf("d = "); arb_print(d); flint_printf("\n\n");
            flint_abort();
        }

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

    /* Compare with MPFR, higher precision. */
    for (iter = 0; iter < 200 * 0.1 * flint_test_multiplier(); iter++)
    {
        arb_t a, b;
        fmpq_t q;
        mpfr_t t;
        slong prec = 2 + n_randint(state, 5000);

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

        arb_randtest(a, state, 1 + n_randint(state, 5000), 8);
        arb_randtest(b, state, 1 + n_randint(state, 5000), 8);
        arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200));

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

        arb_atan(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("a = "); arb_printd(a, 50); flint_printf("\n\n");
            flint_printf("a = "); arb_print(a); flint_printf("\n\n");
            flint_printf("b = "); arb_printd(b, 50); flint_printf("\n\n");
            flint_abort();
        }

        arb_atan(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);
    }

    /* Higher precision + large arguments. */
    for (iter = 0; iter < 2000 * 0.1 * flint_test_multiplier(); iter++)
    {
        arb_t a, b, c, d;
        slong prec1, prec2;

        prec1 = 2 + n_randint(state, 5000);
        prec2 = prec1 + 30;

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

        arb_randtest_precise(a, state, 1 + n_randint(state, 5000), 100);

        arb_atan(b, a, prec1);
        arb_atan(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 tan(atan(x)) = x */
        arb_sin_cos(c, d, b, prec1);
        arb_div(c, c, d, prec1);

        if (!arb_contains(c, a))
        {
            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_printf("d = "); arb_print(d); flint_printf("\n\n");
            flint_abort();
        }

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

    /* Check wide arguments. */
    for (iter = 0; iter < 100000 * 0.1 * flint_test_multiplier(); iter++)
    {
        arb_t a, b, c, d;

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

        arb_randtest_precise(a, state, 1 + n_randint(state, 1000), 100);
        arb_randtest_precise(b, state, 1 + n_randint(state, 1000), 100);
        if (n_randint(state, 2))
            arb_add(a, a, b, 2 + n_randint(state, 1000));
        arb_union(d, a, b, 2 + n_randint(state, 1000));

        arb_atan(a, a, 2 + n_randint(state, 2000));
        arb_atan(b, b, 2 + n_randint(state, 2000));
        arb_atan(c, d, 2 + n_randint(state, 2000));

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