void
arb_hypgeom_fresnel(arb_t res1, arb_t res2, const arb_t z, int normalized, slong prec)
{
if (!arb_is_finite(z))
{
if (res1 != NULL) arb_indeterminate(res1);
if (res2 != NULL) arb_indeterminate(res2);
}
else
{
acb_t t, u;
acb_init(t);
acb_init(u);
arb_set(acb_realref(t), z);
acb_hypgeom_fresnel(res1 ? t : NULL, res2 ? u : NULL, t, normalized, prec);
if (res1 != NULL) arb_swap(res1, acb_realref(t));
if (res2 != NULL) arb_swap(res2, acb_realref(u));
acb_clear(t);
acb_clear(u);
}
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("fresnel....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
acb_t z, z2, s, c, u, v;
slong prec1, prec2;
int normalized;
prec1 = 2 + n_randint(state, 500);
prec2 = 2 + n_randint(state, 500);
acb_init(z);
acb_init(z2);
acb_init(s);
acb_init(c);
acb_init(u);
acb_init(v);
acb_randtest_special(z, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100));
acb_randtest_special(s, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100));
acb_randtest_special(c, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100));
normalized = n_randint(state, 2);
/* test S(z) + i C(z) = sqrt(pi/2) (1+i)/2 erf((1+i)/sqrt(2) z) */
/* u = rhs */
acb_onei(u);
acb_sqrt(u, u, prec1);
acb_mul(u, u, z, prec1);
acb_hypgeom_erf(u, u, prec1);
acb_mul_onei(v, u);
acb_add(u, u, v, prec1);
acb_mul_2exp_si(u, u, -1);
acb_const_pi(v, prec1);
acb_mul_2exp_si(v, v, -1);
acb_sqrt(v, v, prec1);
acb_mul(u, u, v, prec1);
if (normalized)
{
acb_const_pi(v, prec2);
acb_mul_2exp_si(v, v, -1);
acb_sqrt(v, v, prec2);
acb_div(z2, z, v, prec2);
}
else
{
acb_set(z2, z);
}
switch (n_randint(state, 4))
{
case 0:
acb_hypgeom_fresnel(s, c, z2, normalized, prec2);
break;
case 1:
acb_hypgeom_fresnel(s, NULL, z2, normalized, prec2);
acb_hypgeom_fresnel(NULL, c, z2, normalized, prec2);
break;
case 2:
acb_set(s, z2);
acb_hypgeom_fresnel(s, c, s, normalized, prec2);
break;
case 3:
acb_set(c, z2);
acb_hypgeom_fresnel(s, c, c, normalized, prec2);
break;
default:
acb_hypgeom_fresnel(s, c, z2, normalized, prec2);
}
if (normalized)
{
acb_mul(s, s, v, prec2);
acb_mul(c, c, v, prec2);
}
acb_mul_onei(v, c);
acb_add(v, v, s, prec2);
if (!acb_overlaps(u, v))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n");
flint_printf("s = "); acb_printd(s, 30); flint_printf("\n\n");
flint_printf("c = "); acb_printd(c, 30); flint_printf("\n\n");
flint_printf("u = "); acb_printd(u, 30); flint_printf("\n\n");
flint_printf("v = "); acb_printd(v, 30); flint_printf("\n\n");
abort();
}
acb_clear(z);
acb_clear(z2);
acb_clear(s);
acb_clear(c);
acb_clear(u);
acb_clear(v);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
