int main()
{
slong iter;
flint_rand_t state;
flint_printf("root_ui....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
acb_t a, b, c;
ulong k;
slong prec;
prec = 2 + n_randint(state, 1000);
k = n_randtest_not_zero(state);
acb_init(a);
acb_init(b);
acb_init(c);
acb_randtest(a, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_randtest(b, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_root_ui(b, a, k, prec);
acb_pow_ui(c, b, k, prec);
if (!acb_contains(c, a))
{
flint_printf("FAIL: containment\n\n");
flint_printf("k = %wu\n", k);
flint_printf("a = "); acb_print(a); flint_printf("\n\n");
flint_printf("b = "); acb_print(b); flint_printf("\n\n");
flint_printf("c = "); acb_print(c); flint_printf("\n\n");
flint_abort();
}
acb_root_ui(a, a, k, prec);
if (!acb_equal(a, b))
{
flint_printf("FAIL: aliasing\n\n");
flint_abort();
}
acb_clear(a);
acb_clear(b);
acb_clear(c);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("roots....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
acb_t x, y, z;
acb_dirichlet_roots_t roots;
ulong n, k;
slong prec;
slong iter2;
n = 1 + n_randint(state, 1000);
prec = 2 + n_randint(state, 200);
acb_init(x);
acb_init(y);
acb_init(z);
acb_dirichlet_roots_init(roots, n, n_randtest(state), prec);
acb_unit_root(y, n, prec);
for (iter2 = 0; iter2 <= FLINT_MIN(n, 20); iter2++)
{
k = n_randint(state, 2 * n);
acb_dirichlet_root(x, roots, k, prec);
acb_pow_ui(z, y, k, prec);
if (!acb_overlaps(x, z))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("iter = %wd n = %wu k = %wu prec = %wd\n\n", iter, n, k, prec);
flint_printf("x = "); acb_printn(x, 30, 0); flint_printf("\n\n");
flint_printf("z = "); acb_printn(z, 30, 0); flint_printf("\n\n");
flint_abort();
}
}
acb_dirichlet_roots_clear(roots);
acb_clear(x);
acb_clear(y);
acb_clear(z);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
void
acb_modular_delta(acb_t z, const acb_t tau, long prec)
{
psl2z_t g;
arf_t one_minus_eps;
acb_t tau_prime, t1, t2, t3, t4, q;
psl2z_init(g);
arf_init(one_minus_eps);
acb_init(tau_prime);
acb_init(t1);
acb_init(t2);
acb_init(t3);
acb_init(t4);
acb_init(q);
arf_set_ui_2exp_si(one_minus_eps, 63, -6);
acb_modular_fundamental_domain_approx(tau_prime, g, tau,
one_minus_eps, prec);
acb_exp_pi_i(q, tau_prime, prec);
acb_modular_theta_const_sum(t2, t3, t4, q, prec);
/* (t2 t3 t4) ^ 8 * q^2 */
acb_mul(t1, t2, t3, prec);
acb_mul(t1, t1, t4, prec);
acb_mul(t1, t1, t1, prec);
acb_mul(t1, t1, t1, prec);
acb_mul(t1, t1, q, prec);
acb_mul(t1, t1, t1, prec);
acb_mul_2exp_si(t1, t1, -8);
if (!fmpz_is_zero(&g->c))
{
acb_mul_fmpz(t2, tau, &g->c, prec);
acb_add_fmpz(t2, t2, &g->d, prec);
acb_pow_ui(t2, t2, 12, prec);
acb_div(t1, t1, t2, prec);
}
acb_set(z, t1);
psl2z_clear(g);
arf_clear(one_minus_eps);
acb_clear(tau_prime);
acb_clear(t1);
acb_clear(t2);
acb_clear(t3);
acb_clear(t4);
acb_clear(q);
}
void
acb_mat_pow_ui(acb_mat_t B, const acb_mat_t A, ulong exp, long prec)
{
long d = acb_mat_nrows(A);
if (exp <= 2 || d <= 1)
{
if (exp == 0 || d == 0)
{
acb_mat_one(B);
}
else if (d == 1)
{
acb_pow_ui(acb_mat_entry(B, 0, 0),
acb_mat_entry(A, 0, 0), exp, prec);
}
else if (exp == 1)
{
acb_mat_set(B, A);
}
else if (exp == 2)
{
acb_mat_mul(B, A, A, prec); /* todo: sqr */
}
}
else
{
acb_mat_t T, U;
long i;
acb_mat_init(T, d, d);
acb_mat_set(T, A);
acb_mat_init(U, d, d);
for (i = ((long) FLINT_BIT_COUNT(exp)) - 2; i >= 0; i--)
{
acb_mat_mul(U, T, T, prec); /* todo: sqr */
if (exp & (1L << i))
acb_mat_mul(T, U, A, prec);
else
acb_mat_swap(T, U);
}
acb_mat_swap(B, T);
acb_mat_clear(T);
acb_mat_clear(U);
}
}
/* f(z) = exp(-z) (I_0(z/k))^k, from Bruno Salvy */
int
f_scaled_bessel(acb_ptr res, const acb_t z, void * param, slong order, slong prec)
{
acb_t nu;
ulong k = ((ulong *) param)[0];
acb_init(nu);
acb_div_ui(res, z, k, prec);
acb_hypgeom_bessel_i_scaled(res, nu, res, prec);
acb_pow_ui(res, res, k, prec);
acb_clear(nu);
return 0;
}
/* f(z) = sech(10(x-0.2))^2 + sech(100(x-0.4))^4 + sech(1000(x-0.6))^6 */
int
f_spike(acb_ptr res, const acb_t z, void * param, slong order, slong prec)
{
acb_t a, b, c;
if (order > 1)
flint_abort(); /* Would be needed for Taylor method. */
acb_init(a);
acb_init(b);
acb_init(c);
acb_mul_ui(a, z, 10, prec);
acb_sub_ui(a, a, 2, prec);
acb_sech(a, a, prec);
acb_pow_ui(a, a, 2, prec);
acb_mul_ui(b, z, 100, prec);
acb_sub_ui(b, b, 40, prec);
acb_sech(b, b, prec);
acb_pow_ui(b, b, 4, prec);
acb_mul_ui(c, z, 1000, prec);
acb_sub_ui(c, c, 600, prec);
acb_sech(c, c, prec);
acb_pow_ui(c, c, 6, prec);
acb_add(res, a, b, prec);
acb_add(res, res, c, prec);
acb_clear(a);
acb_clear(b);
acb_clear(c);
return 0;
}
/* f(z) = exp(-z) z^1000 */
int
f_factorial1000(acb_ptr res, const acb_t z, void * param, slong order, slong prec)
{
acb_t t;
if (order > 1)
flint_abort(); /* Would be needed for Taylor method. */
acb_init(t);
acb_pow_ui(t, z, 1000, prec);
acb_neg(res, z);
acb_exp(res, res, prec);
acb_mul(res, res, t, prec);
acb_clear(t);
return 0;
}
void
integrals_edge_factors_gc(acb_ptr res, const acb_t cab, const acb_t ba2, sec_t c, slong prec)
{
slong i;
acb_t cj, ci;
acb_init(cj);
acb_init(ci);
/* polynomial shift */
acb_vec_polynomial_shift(res, cab, c.g, prec);
/* constants cj, j = 1 */
/* c_1 = (1-zeta^-1) ba2^(-d/2) (-I)^i
* = 2 / ba2^(d/2) */
acb_pow_ui(cj, ba2, c.d / 2, prec);
if (c.d % 2)
{
acb_t t;
acb_init(t);
acb_sqrt(t, ba2, prec);
acb_mul(cj, cj, t, prec);
acb_clear(t);
}
acb_inv(cj, cj, prec);
acb_mul_2exp_si(cj, cj, 1);
_acb_vec_scalar_mul(res, res, c.g, cj, prec);
/* constant ci = -I * ba2*/
acb_one(ci);
for (i = 1; i < c.g; i++)
{
acb_mul(ci, ci, ba2, prec);
acb_div_onei(ci, ci);
acb_mul(res + i, res + i, ci, prec);
}
acb_clear(ci);
acb_clear(cj);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("eisenstein....");
fflush(stdout);
flint_randinit(state);
/* Test functional equation */
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
acb_t tau1, tau2, t;
acb_ptr r1, r2;
slong e0, prec0, prec1, prec2, len1, len2, i;
psl2z_t g;
psl2z_init(g);
acb_init(tau1);
acb_init(tau2);
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);
len1 = n_randint(state, 20);
len2 = n_randint(state, 20);
r1 = _acb_vec_init(len1);
r2 = _acb_vec_init(len2);
acb_randtest(tau1, state, prec0, e0);
acb_randtest(tau2, state, prec0, e0);
psl2z_randtest(g, state, 1 + n_randint(state, 200));
acb_modular_transform(tau2, g, tau1, prec0);
acb_modular_eisenstein(r1, tau1, len1, prec1);
acb_modular_eisenstein(r2, tau2, len2, prec2);
for (i = 0; i < FLINT_MIN(len1, len2); i++)
{
acb_mul_fmpz(t, tau1, &g->c, prec1);
acb_add_fmpz(t, t, &g->d, prec1);
acb_pow_ui(t, t, 2 * i + 4, prec1);
acb_mul(t, t, r1 + i, prec1);
if (!acb_overlaps(t, r2 + i))
{
flint_printf("FAIL (overlap)\n");
flint_printf("tau1 = "); acb_printd(tau1, 15); flint_printf("\n\n");
flint_printf("tau2 = "); acb_printd(tau2, 15); flint_printf("\n\n");
flint_printf("g = "); psl2z_print(g); flint_printf("\n\n");
flint_printf("r1 = "); acb_printd(r1 + i, 15); flint_printf("\n\n");
flint_printf("r2 = "); acb_printd(r2 + i, 15); flint_printf("\n\n");
flint_printf("t = "); acb_printd(t, 15); flint_printf("\n\n");
flint_abort();
}
}
acb_clear(tau1);
acb_clear(tau2);
acb_clear(t);
_acb_vec_clear(r1, len1);
_acb_vec_clear(r2, len2);
psl2z_clear(g);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
long iter;
flint_rand_t state;
printf("lambda....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000; iter++)
{
acb_t tau1, tau2, z1, z2, z3, t;
long e0, prec0, prec1, prec2, step;
acb_init(tau1);
acb_init(tau2);
acb_init(z1);
acb_init(z2);
acb_init(z3);
acb_init(t);
e0 = 1 + n_randint(state, 100);
prec0 = 2 + n_randint(state, 1000);
prec1 = 2 + n_randint(state, 1000);
prec2 = 2 + n_randint(state, 1000);
acb_randtest(tau1, state, prec0, e0);
acb_randtest(tau2, state, prec0, e0);
acb_randtest(z1, state, prec0, e0);
acb_randtest(z2, state, prec0, e0);
acb_set(tau2, tau1);
step = n_randint(state, 10);
/* Test invariance */
while (step --> 0)
{
if (n_randint(state, 2))
{
acb_add_ui(tau2, tau2, 2, prec0);
}
else
{
acb_mul_si(z1, tau2, -2, prec0);
acb_add_ui(z1, z1, 1, prec0);
acb_div(tau2, tau2, z1, prec0);
}
}
acb_modular_lambda(z1, tau1, prec1);
acb_modular_lambda(z2, tau2, prec2);
/* Compare with eta */
acb_mul_2exp_si(tau1, tau1, -1);
acb_modular_eta(z3, tau1, prec2);
acb_mul_2exp_si(tau1, tau1, 2);
acb_modular_eta(t, tau1, prec2);
acb_mul(t, t, t, prec2);
acb_mul(z3, z3, t, prec2);
acb_mul_2exp_si(tau1, tau1, -1);
acb_modular_eta(t, tau1, prec2);
acb_pow_ui(t, t, 3, prec2);
acb_div(z3, z3, t, prec2);
acb_pow_ui(z3, z3, 8, prec2);
acb_mul_2exp_si(z3, z3, 4);
if (!acb_overlaps(z1, z2) || !acb_overlaps(z1, z3))
{
printf("FAIL (overlap)\n");
printf("tau1 = "); acb_printd(tau1, 15); printf("\n\n");
printf("tau2 = "); acb_printd(tau2, 15); 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_lambda(tau1, tau1, prec2);
if (!acb_overlaps(z1, tau1))
{
printf("FAIL (aliasing)\n");
printf("tau1 = "); acb_printd(tau1, 15); printf("\n\n");
printf("tau2 = "); acb_printd(tau2, 15); printf("\n\n");
printf("z1 = "); acb_printd(z1, 15); printf("\n\n");
printf("z2 = "); acb_printd(z2, 15); printf("\n\n");
abort();
}
acb_clear(tau1);
acb_clear(tau2);
acb_clear(z1);
acb_clear(z2);
acb_clear(z3);
acb_clear(t);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
void
acb_hypgeom_m(acb_t res, const acb_t a, const acb_t b, const acb_t z, int regularized, long prec)
{
long m = LONG_MAX;
long n = LONG_MAX;
if (acb_is_int(a) &&
arf_cmpabs_2exp_si(arb_midref(acb_realref(a)), 30) < 0)
{
m = arf_get_si(arb_midref(acb_realref(a)), ARF_RND_DOWN);
}
if (acb_is_int(b) &&
arf_cmpabs_2exp_si(arb_midref(acb_realref(b)), 30) < 0)
{
n = arf_get_si(arb_midref(acb_realref(b)), ARF_RND_DOWN);
}
/* terminating */
if (m <= 0 && m < n && m > -10 * prec && (n > 0 || !regularized))
{
acb_hypgeom_m_1f1(res, a, b, z, regularized, prec);
return;
}
/* large */
if (acb_hypgeom_u_use_asymp(z, prec))
{
acb_hypgeom_m_asymp(res, a, b, z, regularized, prec);
return;
}
/* remove singularity */
if (n <= 0 && n > -10 * prec && regularized)
{
acb_t c, d, t, u;
acb_init(c);
acb_init(d);
acb_init(t);
acb_init(u);
acb_sub(c, a, b, prec);
acb_add_ui(c, c, 1, prec);
acb_neg(d, b);
acb_add_ui(d, d, 2, prec);
acb_hypgeom_m_1f1(t, c, d, z, 0, prec);
acb_pow_ui(u, z, 1 - n, prec);
acb_mul(t, t, u, prec);
acb_rising_ui(u, a, 1 - n, prec);
acb_mul(t, t, u, prec);
arb_fac_ui(acb_realref(u), 1 - n, prec);
acb_div_arb(res, t, acb_realref(u), prec);
acb_clear(c);
acb_clear(d);
acb_clear(t);
acb_clear(u);
}
else
{
acb_hypgeom_m_1f1(res, a, b, z, regularized, prec);
}
}
void
_acb_hypgeom_m_1f1(acb_t res, const acb_t a, const acb_t b, const acb_t z,
int regularized, slong prec, slong gamma_prec, int kummer)
{
if (regularized)
{
/* Remove singularity */
if (acb_is_int(b) && arb_is_nonpositive(acb_realref(b)) &&
arf_cmpabs_2exp_si(arb_midref(acb_realref(b)), 30) < 0)
{
acb_t c, d, t, u;
slong n;
n = arf_get_si(arb_midref(acb_realref(b)), ARF_RND_DOWN);
acb_init(c);
acb_init(d);
acb_init(t);
acb_init(u);
acb_sub(c, a, b, prec);
acb_add_ui(c, c, 1, prec);
acb_neg(d, b);
acb_add_ui(d, d, 2, prec);
_acb_hypgeom_m_1f1(t, c, d, z, 0, prec, gamma_prec, kummer);
acb_pow_ui(u, z, 1 - n, prec);
acb_mul(t, t, u, prec);
acb_rising_ui(u, a, 1 - n, prec);
acb_mul(t, t, u, prec);
arb_fac_ui(acb_realref(u), 1 - n, prec);
acb_div_arb(res, t, acb_realref(u), prec);
acb_clear(c);
acb_clear(d);
acb_clear(t);
acb_clear(u);
}
else
{
acb_t t;
acb_init(t);
acb_rgamma(t, b, gamma_prec);
_acb_hypgeom_m_1f1(res, a, b, z, 0, prec, gamma_prec, kummer);
acb_mul(res, res, t, prec);
acb_clear(t);
}
return;
}
/* Kummer's transformation */
if (kummer)
{
acb_t u, v;
acb_init(u);
acb_init(v);
acb_sub(u, b, a, prec);
acb_neg(v, z);
_acb_hypgeom_m_1f1(u, u, b, v, regularized, prec, gamma_prec, 0);
acb_exp(v, z, prec);
acb_mul(res, u, v, prec);
acb_clear(u);
acb_clear(v);
return;
}
if (acb_is_one(a))
{
acb_hypgeom_pfq_direct(res, NULL, 0, b, 1, z, -1, prec);
}
else
{
acb_struct c[3];
c[0] = *a;
c[1] = *b;
acb_init(c + 2);
acb_one(c + 2);
acb_hypgeom_pfq_direct(res, c, 1, c + 1, 2, z, -1, prec);
acb_clear(c + 2);
}
}
void
_acb_poly_pow_ui_trunc_binexp(acb_ptr res,
acb_srcptr f, long flen, ulong exp, long len, long prec)
{
acb_ptr v, R, S, T;
long rlen;
ulong bit;
if (exp <= 1)
{
if (exp == 0)
acb_one(res);
else if (exp == 1)
_acb_vec_set_round(res, f, len, prec);
return;
}
/* (f * x^r)^m = x^(rm) * f^m */
while (flen > 1 && acb_is_zero(f))
{
if (((ulong) len) > exp)
{
_acb_vec_zero(res, exp);
len -= exp;
res += exp;
}
else
{
_acb_vec_zero(res, len);
return;
}
f++;
flen--;
}
if (exp == 2)
{
_acb_poly_mullow(res, f, flen, f, flen, len, prec);
return;
}
if (flen == 1)
{
acb_pow_ui(res, f, exp, prec);
return;
}
v = _acb_vec_init(len);
bit = 1UL << (FLINT_BIT_COUNT(exp) - 2);
if (n_zerobits(exp) % 2)
{
R = res;
S = v;
}
else
{
R = v;
S = res;
}
MUL(R, rlen, f, flen, f, flen, len, prec);
if (bit & exp)
{
MUL(S, rlen, R, rlen, f, flen, len, prec);
T = R;
R = S;
S = T;
}
while (bit >>= 1)
{
if (bit & exp)
{
MUL(S, rlen, R, rlen, R, rlen, len, prec);
MUL(R, rlen, S, rlen, f, flen, len, prec);
}
else
{
MUL(S, rlen, R, rlen, R, rlen, len, prec);
T = R;
R = S;
S = T;
}
}
_acb_vec_clear(v, len);
}
void
acb_elliptic_p_jet(acb_ptr r, const acb_t z, const acb_t tau, slong len, slong prec)
{
acb_t t01, t02, t03, t04;
acb_ptr tz1, tz2, tz3, tz4;
acb_t t;
int real;
slong k;
if (len < 1)
return;
if (len == 1)
{
acb_elliptic_p(r, z, tau, prec);
return;
}
real = acb_is_real(z) && arb_is_int_2exp_si(acb_realref(tau), -1) &&
arb_is_positive(acb_imagref(tau));
acb_init(t);
acb_init(t01);
acb_init(t02);
acb_init(t03);
acb_init(t04);
tz1 = _acb_vec_init(len);
tz2 = _acb_vec_init(len);
tz3 = _acb_vec_init(len);
tz4 = _acb_vec_init(len);
acb_modular_theta_jet(tz1, tz2, tz3, tz4, z, tau, len, prec);
/* [theta_4(z) / theta_1(z)]^2 */
_acb_poly_div_series(tz2, tz4, len, tz1, len, len, prec);
_acb_poly_mullow(tz1, tz2, len, tz2, len, len, prec);
acb_zero(t);
acb_modular_theta(t01, t02, t03, t04, t, tau, prec);
/* [theta_2(0) * theta_3(0)] ^2 */
acb_mul(t, t02, t03, prec);
acb_mul(t, t, t, prec);
_acb_vec_scalar_mul(tz1, tz1, len, t, prec);
/* - [theta_2(0)^4 + theta_3(0)^4] / 3 */
acb_pow_ui(t02, t02, 4, prec);
acb_pow_ui(t03, t03, 4, prec);
acb_add(t, t02, t03, prec);
acb_div_ui(t, t, 3, prec);
acb_sub(tz1, tz1, t, prec);
/* times pi^2 */
acb_const_pi(t, prec);
acb_mul(t, t, t, prec);
_acb_vec_scalar_mul(r, tz1, len, t, prec);
if (real)
{
for (k = 0; k < len; k++)
arb_zero(acb_imagref(r + k));
}
acb_clear(t);
acb_clear(t01);
acb_clear(t02);
acb_clear(t03);
acb_clear(t04);
_acb_vec_clear(tz1, len);
_acb_vec_clear(tz2, len);
_acb_vec_clear(tz3, len);
_acb_vec_clear(tz4, len);
}
int main()
{
long iter;
flint_rand_t state;
printf("det....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000; iter++)
{
fmpq_mat_t Q;
fmpq_t Qdet;
acb_mat_t A;
acb_t Adet, imagunit;
long n, qbits, prec;
int imaginary;
n = n_randint(state, 8);
qbits = 1 + n_randint(state, 100);
prec = 2 + n_randint(state, 200);
imaginary = n_randint(state, 2);
fmpq_mat_init(Q, n, n);
fmpq_init(Qdet);
acb_mat_init(A, n, n);
acb_init(Adet);
acb_init(imagunit);
fmpq_mat_randtest(Q, state, qbits);
fmpq_mat_det(Qdet, Q);
acb_mat_set_fmpq_mat(A, Q, prec);
if (imaginary)
{
acb_onei(imagunit);
acb_mat_scalar_mul_acb(A, A, imagunit, prec);
}
acb_mat_det(Adet, A, prec);
if (imaginary)
{
acb_onei(imagunit);
acb_inv(imagunit, imagunit, prec);
acb_pow_ui(imagunit, imagunit, n, prec);
acb_mul(Adet, Adet, imagunit, prec);
}
if (!acb_contains_fmpq(Adet, Qdet))
{
printf("FAIL (containment, iter = %ld)\n", iter);
printf("n = %ld, prec = %ld\n", n, prec);
printf("\n");
printf("Q = \n"); fmpq_mat_print(Q); printf("\n\n");
printf("Qdet = \n"); fmpq_print(Qdet); printf("\n\n");
printf("A = \n"); acb_mat_printd(A, 15); printf("\n\n");
printf("Adet = \n"); acb_printd(Adet, 15); printf("\n\n");
printf("Adet = \n"); acb_print(Adet); printf("\n\n");
abort();
}
fmpq_mat_clear(Q);
fmpq_clear(Qdet);
acb_mat_clear(A);
acb_clear(Adet);
acb_clear(imagunit);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
long iter;
flint_rand_t state;
printf("delta....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000; iter++)
{
acb_t tau, z1, z2;
long e0, prec0, prec1, prec2;
acb_init(tau);
acb_init(z1);
acb_init(z2);
e0 = 1 + n_randint(state, 10);
prec0 = 2 + n_randint(state, 1000);
prec1 = 2 + n_randint(state, 1000);
prec2 = 2 + n_randint(state, 1000);
acb_randtest(tau, state, prec0, e0);
acb_randtest(z1, state, prec0, e0);
acb_randtest(z2, state, prec0, e0);
/* compare with eta */
acb_modular_delta(z1, tau, prec1);
acb_modular_eta(z2, tau, prec2);
acb_pow_ui(z2, z2, 24, prec2);
if (!acb_overlaps(z1, z2))
{
printf("FAIL (overlap)\n");
printf("tau = "); acb_printd(tau, 15); printf("\n\n");
printf("z1 = "); acb_printd(z1, 15); printf("\n\n");
printf("z2 = "); acb_printd(z2, 15); printf("\n\n");
abort();
}
acb_modular_delta(tau, tau, prec1);
if (!acb_overlaps(z1, tau))
{
printf("FAIL (aliasing)\n");
printf("tau = "); acb_printd(tau, 15); printf("\n\n");
printf("z1 = "); acb_printd(z1, 15); printf("\n\n");
printf("z2 = "); acb_printd(z2, 15); printf("\n\n");
abort();
}
acb_clear(tau);
acb_clear(z1);
acb_clear(z2);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
