int main()
{
long iter;
flint_rand_t state;
printf("eta....");
fflush(stdout);
flint_randinit(state);
/* Test functional equation */
for (iter = 0; iter < 10000; iter++)
{
acb_t tau1, tau2, z1, z2, z3, t;
fmpq_t arg;
long e0, prec0, prec1, prec2;
psl2z_t g;
psl2z_init(g);
fmpq_init(arg);
acb_init(tau1);
acb_init(tau2);
acb_init(z1);
acb_init(z2);
acb_init(z3);
acb_init(t);
e0 = 1 + n_randint(state, 200);
prec0 = 2 + n_randint(state, 2000);
prec1 = 2 + n_randint(state, 2000);
prec2 = 2 + n_randint(state, 2000);
acb_randtest(tau1, state, prec0, e0);
acb_randtest(tau2, state, prec0, e0);
acb_randtest(z1, state, prec0, e0);
acb_randtest(z2, state, prec0, e0);
psl2z_randtest(g, state, 1 + n_randint(state, 200));
acb_modular_transform(tau2, g, tau1, prec0);
acb_modular_eta(z1, tau1, prec1);
acb_modular_eta(z2, tau2, prec2);
/* apply transformation */
fmpq_set_si(arg, acb_modular_epsilon_arg(g), 12);
arb_sin_cos_pi_fmpq(acb_imagref(t), acb_realref(t), arg, prec1);
acb_mul(z3, z1, t, prec1);
acb_mul_fmpz(t, tau1, &g->c, prec1);
acb_add_fmpz(t, t, &g->d, prec1);
acb_sqrt(t, t, prec1);
acb_mul(z3, z3, t, prec1);
if (!acb_overlaps(z3, z2))
{
printf("FAIL (overlap)\n");
printf("tau1 = "); acb_printd(tau1, 15); printf("\n\n");
printf("tau2 = "); acb_printd(tau2, 15); printf("\n\n");
printf("g = "); psl2z_print(g); printf("\n\n");
printf("z1 = "); acb_printd(z1, 15); printf("\n\n");
printf("z2 = "); acb_printd(z2, 15); printf("\n\n");
printf("z3 = "); acb_printd(z3, 15); printf("\n\n");
abort();
}
acb_modular_eta(tau1, tau1, prec2);
if (!acb_overlaps(z1, tau1))
{
printf("FAIL (aliasing)\n");
printf("tau1 = "); acb_print(tau1); printf("\n\n");
printf("tau2 = "); acb_print(tau2); printf("\n\n");
printf("z1 = "); acb_print(z1); printf("\n\n");
printf("z2 = "); acb_print(z2); printf("\n\n");
abort();
}
acb_clear(tau1);
acb_clear(tau2);
acb_clear(z1);
acb_clear(z2);
acb_clear(z3);
acb_clear(t);
psl2z_clear(g);
fmpq_clear(arg);
}
/* Test special values */
for (iter = 0; iter < 100; iter++)
{
acb_t tau, z;
arb_t t, u;
long prec;
acb_init(tau);
acb_init(z);
arb_init(t);
arb_init(u);
prec = 2 + n_randint(state, 2000);
acb_randtest(z, state, prec, 10);
acb_onei(tau);
acb_modular_eta(z, tau, prec);
arb_one(t);
arb_mul_2exp_si(t, t, -2);
arb_gamma(t, t, prec);
arb_const_pi(u, prec);
arb_root(u, u, 4, prec);
arb_pow_ui(u, u, 3, prec);
arb_div(t, t, u, prec);
arb_mul_2exp_si(t, t, -1);
if (!arb_overlaps(acb_realref(z), t) ||
!arb_contains_zero(acb_imagref(z)))
{
printf("FAIL (value 1)\n");
printf("tau = "); acb_print(tau); printf("\n\n");
printf("z = "); acb_print(z); printf("\n\n");
abort();
}
acb_clear(tau);
acb_clear(z);
arb_clear(t);
arb_clear(u);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("gamma_fmpq....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
arb_t r, s;
fmpq_t q;
slong accuracy, prec, pp, qq;
prec = 2 + n_randint(state, 1 << n_randint(state, 12));
prec += 20;
arb_init(r);
arb_init(s);
fmpq_init(q);
pp = -100 + n_randint(state, 10000);
qq = 1 + n_randint(state, 20);
fmpq_set_si(q, pp, qq);
arb_gamma_fmpq(r, q, prec);
arb_set_fmpq(s, q, prec);
arb_gamma(s, s, prec);
if (!arb_overlaps(r, s))
{
flint_printf("FAIL: containment\n\n");
flint_printf("prec = %wd\n", prec);
flint_printf("q = "); fmpq_print(q); flint_printf("\n\n");
flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n");
flint_printf("s = "); arb_printd(s, prec / 3.33); flint_printf("\n\n");
abort();
}
if (!(fmpz_is_one(fmpq_denref(q)) && fmpz_sgn(fmpq_numref(q)) <= 0)
&& FLINT_ABS(pp / qq) < 10)
{
accuracy = arb_rel_accuracy_bits(r);
if (accuracy < prec - 6)
{
flint_printf("FAIL: poor accuracy\n\n");
flint_printf("prec = %wd\n", prec);
flint_printf("q = "); fmpq_print(q); flint_printf("\n\n");
flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n");
abort();
}
}
arb_clear(r);
arb_clear(s);
fmpq_clear(q);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("central_bin_ui....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
arb_t b1, b2, t;
ulong n;
slong prec1, prec2, acc1;
n = n_randtest(state);
prec1 = 2 + n_randint(state, 1000);
prec2 = prec1 + 30;
arb_init(b1);
arb_init(b2);
arb_init(t);
arb_hypgeom_central_bin_ui(b1, n, prec1);
arb_set_ui(t, n);
arb_add_ui(t, t, n, prec2);
arb_add_ui(t, t, 1, prec2);
arb_gamma(t, t, prec2);
arb_set_ui(b2, n);
arb_add_ui(b2, b2, 1, prec2);
arb_rgamma(b2, b2, prec2);
arb_mul(b2, b2, b2, prec2);
arb_mul(b2, b2, t, prec2);
if (!arb_overlaps(b1, b2))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("n = %wu\n\n", n);
flint_printf("b1 = "); arb_printn(b1, 50, 0); flint_printf("\n\n");
flint_printf("b2 = "); arb_printn(b2, 50, 0); flint_printf("\n\n");
flint_abort();
}
acc1 = arb_rel_accuracy_bits(b1);
if (acc1 < prec1 - 2)
{
flint_printf("FAIL: poor accuracy\n\n");
flint_printf("prec1 = %wd, acc1 = %wd\n", prec1, acc1);
flint_printf("b1 = "); arb_printn(b1, prec1 / 3.33, 0); flint_printf("\n\n");
flint_printf("b2 = "); arb_printn(b2, prec2 / 3.33, 0); flint_printf("\n\n");
flint_abort();
}
arb_clear(b1);
arb_clear(b2);
arb_clear(t);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
