static void
bound_K(arb_t C, const arb_t AN, const arb_t B, const arb_t T, slong wp)
{
if (arb_is_zero(B) || arb_is_zero(T))
{
arb_one(C);
}
else
{
arb_div(C, B, AN, wp);
/* TODO: atan is dumb, should also bound by pi/2 */
arb_atan(C, C, wp);
arb_mul(C, C, T, wp);
if (arb_is_nonpositive(C))
arb_one(C);
else
arb_exp(C, C, wp);
}
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("atan....");
fflush(stdout);
flint_randinit(state);
/* Compare with MPFR */
for (iter = 0; iter < 10000 * arb_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 * arb_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 * arb_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 * arb_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 * arb_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);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
