void
acb_cot(acb_t r, const acb_t z, slong prec)
{
if (arb_is_zero(acb_imagref(z)))
{
arb_cot(acb_realref(r), acb_realref(z), prec);
arb_zero(acb_imagref(r));
}
else if (arb_is_zero(acb_realref(z)))
{
arb_coth(acb_imagref(r), acb_imagref(z), prec);
arb_neg(acb_imagref(r), acb_imagref(r));
arb_zero(acb_realref(r));
}
else
{
acb_t t;
acb_init(t);
if (arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), 0) < 0)
{
acb_sin_cos(r, t, z, prec + 4);
acb_div(r, t, r, prec);
}
else
{
acb_mul_2exp_si(t, z, 1);
if (arf_sgn(arb_midref(acb_imagref(z))) > 0)
{
acb_mul_onei(t, t);
acb_exp(t, t, prec + 4);
acb_sub_ui(r, t, 1, prec + 4);
acb_div(r, t, r, prec + 4);
acb_mul_2exp_si(r, r, 1);
acb_sub_ui(r, r, 1, prec);
acb_mul_onei(r, r);
}
else
{
acb_div_onei(t, t);
acb_exp(t, t, prec + 4);
acb_sub_ui(r, t, 1, prec + 4);
acb_div(r, t, r, prec + 4);
acb_mul_2exp_si(r, r, 1);
acb_sub_ui(r, r, 1, prec);
acb_div_onei(r, r);
}
}
acb_clear(t);
}
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("coth....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
arb_t x, y, a, b, c, d;
slong prec1, prec2;
prec1 = 2 + n_randint(state, 1000);
prec2 = prec1 + 30;
arb_init(x);
arb_init(y);
arb_init(a);
arb_init(b);
arb_init(c);
arb_init(d);
arb_randtest_precise(x, state, 1 + n_randint(state, 1000), 100);
arb_randtest_precise(y, state, 1 + n_randint(state, 1000), 100);
arb_coth(a, x, prec1);
arb_coth(b, x, prec2);
/* check consistency */
if (!arb_overlaps(a, b))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("x = "); arb_print(x); flint_printf("\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
abort();
}
/* check coth(x+y) = (1 + coth(x) coth(y)) / (coth(x) + coth(y)) */
arb_add(b, x, y, prec1);
arb_coth(b, b, prec1);
arb_coth(c, y, prec1);
arb_add(d, a, c, prec1);
arb_mul(c, a, c, prec1);
arb_add_ui(c, c, 1, prec1);
arb_div(d, c, d, prec1);
if (!arb_overlaps(b, d))
{
flint_printf("FAIL: functional equation\n\n");
flint_printf("x = "); arb_print(x); flint_printf("\n\n");
flint_printf("y = "); arb_print(y); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
flint_printf("d = "); arb_print(d); flint_printf("\n\n");
abort();
}
arb_coth(x, x, prec1);
if (!arb_overlaps(a, x))
{
flint_printf("FAIL: aliasing\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("x = "); arb_print(x); flint_printf("\n\n");
abort();
}
arb_clear(x);
arb_clear(y);
arb_clear(a);
arb_clear(b);
arb_clear(c);
arb_clear(d);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}