int main()
{
printf("seq_set_fmpq_pow....");
fflush(stdout);
{
long i;
fmpq_t t, u;
fmpz_holonomic_t op;
fmpq_t c, initial;
fmpz_holonomic_init(op);
fmpq_init(t);
fmpq_init(u);
fmpq_init(c);
fmpq_init(initial);
fmpq_set_si(c, -7, 3);
fmpz_holonomic_seq_set_fmpq_pow(op, c);
fmpq_set_si(initial, -2, 1);
for (i = 0; i < 20; i++)
{
fmpz_holonomic_get_nth_fmpq(t, op, initial, 0, i);
fmpz_pow_ui(fmpq_numref(u), fmpq_numref(c), i);
fmpz_pow_ui(fmpq_denref(u), fmpq_denref(c), i);
fmpz_mul_si(fmpq_numref(u), fmpq_numref(u), -2);
if (!fmpq_equal(t, u))
{
printf("FAIL\n");
printf("i = %ld, t = ", i); fmpq_print(t);
printf(" u = "); fmpq_print(u);
printf("\n");
abort();
}
}
fmpq_clear(c);
fmpq_clear(t);
fmpq_clear(u);
fmpq_clear(initial);
fmpz_holonomic_clear(op);
}
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
void
bernoulli_cache_compute(long n)
{
if (bernoulli_cache_num < n)
{
long i, new_num;
bernoulli_rev_t iter;
if (bernoulli_cache_num == 0)
{
flint_register_cleanup_function(bernoulli_cleanup);
}
new_num = FLINT_MAX(bernoulli_cache_num + 128, n);
bernoulli_cache = flint_realloc(bernoulli_cache, new_num * sizeof(fmpq));
for (i = bernoulli_cache_num; i < new_num; i++)
fmpq_init(bernoulli_cache + i);
i = new_num - 1;
i -= (i % 2);
bernoulli_rev_init(iter, i);
for ( ; i >= bernoulli_cache_num; i -= 2)
{
bernoulli_rev_next(fmpq_numref(bernoulli_cache + i),
fmpq_denref(bernoulli_cache + i), iter);
}
bernoulli_rev_clear(iter);
if (new_num > 1)
fmpq_set_si(bernoulli_cache + 1, -1, 2);
bernoulli_cache_num = new_num;
}
}
static void
_acb_unit_root(acb_t res, ulong order, slong prec)
{
fmpq_t t;
fmpq_init(t);
fmpq_set_si(t, 2, order);
arb_sin_cos_pi_fmpq(acb_imagref(res), acb_realref(res), t, prec);
fmpq_clear(t);
}
int main()
{
long iter;
flint_rand_t state;
printf("series_fmpq_hypgeom....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 250; iter++)
{
fmprb_ptr u, v;
fmpq_t a;
ulong p, q;
long i, len, prec1, prec2;
len = 1 + n_randint(state, 10);
prec1 = 2 + n_randint(state, 1000);
prec2 = prec1 + 30;
u = _fmprb_vec_init(len);
v = _fmprb_vec_init(len);
fmpq_init(a);
q = 1 + n_randint(state, 20);
p = q - n_randint(state, q);
fmpq_set_si(a, p, q);
gamma_series_fmpq_hypgeom(u, a, len, prec1);
gamma_series_fmpq_hypgeom(v, a, len, prec2);
for (i = 0; i < len; i++)
{
if (!fmprb_overlaps(u + i, v + i))
{
printf("FAIL: overlap\n\n");
printf("p = %lu, q = %lu, len = %ld, i = %ld\n\n", p, q, len, i);
printf("u = "); fmprb_printd(u + i, prec1 / 3.33); printf("\n\n");
printf("v = "); fmprb_printd(v + i, prec2 / 3.33); printf("\n\n");
abort();
}
}
fmpq_clear(a);
_fmprb_vec_clear(u, len);
_fmprb_vec_clear(v, len);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
int
main(void)
{
int i;
FLINT_TEST_INIT(state);
flint_printf("set_si....");
fflush(stdout);
for (i = 0; i < 10000; i++)
{
fmpq_t x, y;
fmpz_t p, q;
slong P, Q;
fmpq_init(x);
fmpq_init(y);
fmpz_init(p);
fmpz_init(q);
P = z_randtest(state);
Q = n_randtest_not_zero(state);
fmpz_set_si(p, P);
fmpz_set_ui(q, Q);
fmpq_set_fmpz_frac(x, p, q);
fmpq_set_si(y, P, Q);
if (!fmpq_is_canonical(y) || !fmpq_equal(x, y))
{
flint_printf("FAIL");
flint_printf("p: "); fmpz_print(p); flint_printf("\n");
flint_printf("q: "); fmpz_print(q); flint_printf("\n");
flint_printf("x: "); fmpq_print(x); flint_printf("\n");
flint_printf("y: "); fmpq_print(y); flint_printf("\n");
abort();
}
fmpq_clear(x);
fmpq_clear(y);
fmpz_clear(p);
fmpz_clear(q);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
void
_acb_poly_roots_initial_values(acb_ptr roots, slong deg, slong prec)
{
slong i;
fmpq_t q;
fmpq_init(q);
fmpq_set_si(q, 4, 10);
arb_set_fmpq(acb_realref(roots + 0), q, prec);
mag_zero(arb_radref(acb_realref(roots + 0)));
fmpq_set_si(q, 9, 10);
arb_set_fmpq(acb_imagref(roots + 0), q, prec);
mag_zero(arb_radref(acb_imagref(roots + 0)));
fmpq_clear(q);
for (i = 1; i < deg; i++)
{
acb_mul(roots + i, roots + i - 1, roots + 0, prec);
mag_zero(arb_radref(acb_realref(roots + i)));
mag_zero(arb_radref(acb_imagref(roots + i)));
}
}
void
acb_dirichlet_pairing(acb_t res, const dirichlet_group_t G, ulong m, ulong n, slong prec)
{
ulong expo;
expo = dirichlet_pairing(G, m, n);
if (expo == DIRICHLET_CHI_NULL)
acb_zero(res);
else
{
fmpq_t t;
fmpq_init(t);
fmpq_set_si(t, 2 * expo, G->expo);
arb_sin_cos_pi_fmpq(acb_imagref(res), acb_realref(res), t, prec);
fmpq_clear(t);
}
}
void _dgsl_rot_mp_sqrt_sigma_2(fmpq_poly_t rop, const fmpz_poly_t g, const mpfr_t sigma,
const int r, const long n, const mpfr_prec_t prec, const oz_flag_t flags) {
fmpq_poly_zero(rop);
fmpq_t r_q2;
fmpq_init(r_q2);
fmpq_set_si(r_q2, r, 1);
fmpq_mul(r_q2, r_q2, r_q2);
fmpq_neg(r_q2, r_q2);
fmpq_poly_set_coeff_fmpq(rop, 0, r_q2);
fmpq_clear(r_q2);
fmpq_poly_t g_q; fmpq_poly_init(g_q);
fmpq_poly_set_fmpz_poly(g_q, g);
fmpq_poly_t ng; fmpq_poly_init(ng);
fmpq_poly_oz_invert_approx(ng, g_q, n, prec, flags);
fmpq_poly_t ngt;
fmpq_poly_init(ngt);
fmpq_poly_oz_conjugate(ngt, ng, n);
fmpq_poly_t nggt;
fmpq_poly_init(nggt);
fmpq_poly_oz_mul(nggt, ng, ngt, n);
/**
We compute sqrt(g^-T · g^-1) to use it as the starting point for
convergence on sqrt(σ^2 · g^-T · g^-1 - r^2) below. We can compute the
former with less precision than the latter
*/
mpfr_t norm;
mpfr_init2(norm, prec);
fmpz_poly_eucl_norm_mpfr(norm, g, MPFR_RNDN);
double p = mpfr_get_d(norm, MPFR_RNDN);
/**
|g^-1| ~= 1/|g|
|g^-T| ~= |g^-1|
|g^-1·g^-T| ~= sqrt(n)·|g^-T|·|g^-1|
*/
fmpq_poly_t sqrt_start; fmpq_poly_init(sqrt_start);
p = log2(n) + 4*log2(p);
int fail = -1;
while (fail) {
p = 2*p;
if (fail<0)
fail = fmpq_poly_oz_sqrt_approx_db(sqrt_start, nggt, n, p, prec/2, flags, NULL);
else
fail = fmpq_poly_oz_sqrt_approx_db(sqrt_start, nggt, n, p, prec/2, flags, sqrt_start);
if(fail)
fprintf(stderr, "FAILED for precision %7.1f with code (%d), doubling precision.\n", p, fail);
}
fmpq_t sigma2;
fmpq_init(sigma2);
fmpq_set_mpfr(sigma2, sigma, MPFR_RNDN);
fmpq_poly_scalar_mul_fmpq(sqrt_start, sqrt_start, sigma2);
fmpq_mul(sigma2, sigma2, sigma2);
fmpq_poly_scalar_mul_fmpq(nggt, nggt, sigma2);
fmpq_clear(sigma2);
fmpq_poly_add(rop, rop, nggt);
p = p + 2*log2(mpfr_get_d(sigma, MPFR_RNDN));
fmpq_poly_oz_sqrt_approx_babylonian(rop, rop, n, p, prec, flags, sqrt_start);
mpfr_clear(norm);
fmpq_poly_clear(g_q);
fmpq_poly_clear(ng);
fmpq_poly_clear(ngt);
fmpq_poly_clear(nggt);
fmpq_poly_clear(sqrt_start);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("rising_ui_rs....");
fflush(stdout);
flint_randinit(state);
/* compare with fmpq */
for (iter = 0; iter < 1000; iter++)
{
arb_t a, b;
fmpq_t x, y, z;
ulong n, step;
slong i;
arb_init(a);
arb_init(b);
fmpq_init(x);
fmpq_init(y);
fmpq_init(z);
arb_randtest(a, state, 1 + n_randint(state, 1000), 10);
arb_randtest(b, state, 1 + n_randint(state, 1000), 10);
n = n_randint(state, 80);
arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 10));
step = n_randint(state, 20);
arb_rising_ui_rs(b, a, n, step, 2 + n_randint(state, 1000));
fmpq_one(y);
for (i = 0; i < n; i++)
{
fmpq_set_si(z, i, 1);
fmpq_add(z, x, z);
fmpq_mul(y, y, z);
}
if (!arb_contains_fmpq(b, y))
{
flint_printf("FAIL: containment\n\n");
flint_printf("n = %wu\n", n);
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("x = "); fmpq_print(x); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
flint_printf("y = "); fmpq_print(y); flint_printf("\n\n");
abort();
}
arb_clear(a);
arb_clear(b);
fmpq_clear(x);
fmpq_clear(y);
fmpq_clear(z);
}
/* aliasing of y and x */
for (iter = 0; iter < 500; iter++)
{
arb_t x, y;
ulong n, step;
slong prec;
arb_init(x);
arb_init(y);
arb_randtest(x, state, 1 + n_randint(state, 200), 10);
arb_randtest(y, state, 1 + n_randint(state, 200), 10);
n = n_randint(state, 100);
prec = 2 + n_randint(state, 1000);
step = n_randint(state, 20);
arb_rising_ui_rs(y, x, n, step, prec);
arb_rising_ui_rs(x, x, n, step, prec);
if (!arb_equal(x, y))
{
flint_printf("FAIL: aliasing\n\n");
flint_printf("x = "); arb_print(x); flint_printf("\n\n");
flint_printf("y = "); arb_print(y); flint_printf("\n\n");
flint_printf("n = %wu\n", n);
abort();
}
arb_clear(x);
arb_clear(y);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
void test_field2(flint_rand_t state)
{
/* test in QQ[3^(1/4)] */
renf_t nf;
renf_elem_t a;
fmpq_t d, k;
fmpq_poly_t p;
fmpq_init(d);
fmpq_poly_init(p);
fmpq_set_si(d, 3, 1);
renf_init_nth_root_fmpq(nf, d, 4, 10 + n_randint(state, 10));
fmpq_clear(d);
fmpq_init(k);
renf_elem_init(a, nf);
/* test rationals */
/* --> 3^(1/4) */
fmpq_poly_set_coeff_si(p, 1, 1);
renf_elem_set_fmpq_poly(a, p, nf);
check_ceil(a, nf, 2, "3^(1/4)");
/* --> 3^(1/4) - p_34 / q_34 */
/* ceil = 1 */
fmpz_set_str(fmpq_numref(k), "3871793620206447926", 10);
fmpz_set_str(fmpq_denref(k), "2941926960111028069", 10);
fmpq_neg(k, k);
fmpq_poly_set_coeff_fmpq(p, 0, k);
renf_elem_set_fmpq_poly(a, p, nf);
check_ceil(a, nf, 1, "3^(1/4)");
/* --> 3^(1/4) - p_35 / q_35 */
/* ceil = 0 */
fmpz_set_str(fmpq_numref(k), "4393442218385055959", 10);
fmpz_set_str(fmpq_denref(k), "3338294180377262795", 10);
fmpq_neg(k, k);
fmpq_poly_set_coeff_fmpq(p, 0, k);
renf_elem_set_fmpq_poly(a, p, nf);
check_ceil(a, nf, 0, "3^(1/4)");
/* --> 3^(1/4) - p_200 / q_200 */
fmpz_set_str(fmpq_numref(k), "51566086581654990699052199424489069476470199719930170996263916596162993841059250500042162091", 10);
fmpz_set_str(fmpq_denref(k), "39181752754141206003124111890355840072199542360218864430892618765033598468868752146602163065", 10);
fmpq_neg(k, k);
fmpq_poly_set_coeff_fmpq(p, 0, k);
renf_elem_set_fmpq_poly(a, p, nf);
check_ceil(a, nf, 1, "3^(1/4)");
/* --> 3^(1/4) - p_201 / q_201 */
fmpz_set_str(fmpq_numref(k), "80796322887694335717970676356641716096406222234122724217891106756946083353628876437327250032", 10);
fmpz_set_str(fmpq_denref(k), "61391929399498685496270115285641595325756438975454257165479021482386018841773493669624721869", 10);
fmpq_neg(k, k);
fmpq_poly_set_coeff_fmpq(p, 0, k);
renf_elem_set_fmpq_poly(a, p, nf);
check_ceil(a, nf, 0, "3^(1/4)");
/* */
fmpz_set_str(fmpq_numref(k), "13231942875843754343234", 10);
fmpz_set_str(fmpq_denref(k), "14321431341231112121", 10);
fmpq_poly_set_coeff_fmpq(p, 3, k);
fmpz_set_str(fmpq_numref(k), "148589873455543948591", 10);
fmpz_set_str(fmpq_denref(k), "12332111221111", 10);
fmpq_neg(k, k);
fmpq_poly_set_coeff_fmpq(p, 2, k);
fmpz_set_str(fmpq_numref(k), "1233321469998711012392391", 10);
fmpz_set_str(fmpq_denref(k), "11814121556810191", 10);
fmpq_poly_set_coeff_fmpq(p, 1, k);
fmpz_set_str(fmpq_numref(k), "1249152314425433983202991363672458443993964487436329478959287771807457205881969983777233465754608376177969464841", 10);
fmpz_set_str(fmpq_denref(k), "10720278662399817731713810382544982753044312944075797382817281426908463944866446042500978893159281330135", 10);
fmpq_neg(k, k);
fmpq_poly_set_coeff_fmpq(p, 0, k);
renf_elem_set_fmpq_poly(a, p, nf);
check_ceil(a, nf, 231, "3^(1/4)");
renf_elem_clear(a, nf);
renf_clear(nf);
fmpq_clear(k);
fmpq_poly_clear(p);
}
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()
{
printf("get_series....");
fflush(stdout);
{
fmpq_t s;
fmpz_holonomic_t re, de, ans;
fmpq_init(s);
fmpz_holonomic_init(re);
fmpz_holonomic_init(de);
fmpz_holonomic_init(ans);
fmpz_holonomic_fit_length(ans, 4);
fmpq_set_si(s, -7, 3);
/* exp(x) */
fmpz_holonomic_fun_set_exp(de);
fmpz_holonomic_get_series(re, de);
fmpz_poly_set_si(ans->coeffs + 0, -1);
fmpz_poly_set_si2(ans->coeffs + 1, 1, 1);
_fmpz_holonomic_set_length(ans, 2);
check(re, ans, de);
/* sin/cos(x) */
fmpz_holonomic_fun_set_sin_cos(de);
fmpz_holonomic_get_series(re, de);
fmpz_poly_set_str(ans->coeffs + 0, "1 1");
fmpz_poly_set_str(ans->coeffs + 1, "0");
fmpz_poly_set_str(ans->coeffs + 2, "3 2 3 1");
_fmpz_holonomic_set_length(ans, 3);
check(re, ans, de);
/* log(x) */
fmpz_holonomic_fun_set_log(de);
fmpz_holonomic_get_series(re, de);
fmpz_poly_set_si(ans->coeffs + 0, 1);
_fmpz_holonomic_set_length(ans, 1);
check(re, ans, de);
/* log(s+x) */
fmpz_holonomic_shift_fmpq(de, de, s);
fmpz_holonomic_get_series(re, de);
fmpz_poly_set_str(ans->coeffs + 0, "2 0 -3");
fmpz_poly_set_str(ans->coeffs + 1, "2 7 7");
_fmpz_holonomic_set_length(ans, 2);
check(re, ans, de);
/* atan(x) */
fmpz_holonomic_fun_set_atan(de);
fmpz_holonomic_get_series(re, de);
fmpz_poly_set_str(ans->coeffs + 0, "2 0 1");
fmpz_poly_set_str(ans->coeffs + 1, "0");
fmpz_poly_set_str(ans->coeffs + 2, "2 2 1");
_fmpz_holonomic_set_length(ans, 3);
check(re, ans, de);
/* atan(s+x) */
fmpz_holonomic_shift_fmpq(de, de, s);
fmpz_holonomic_get_series(re, de);
fmpz_poly_set_str(ans->coeffs + 0, "2 0 9");
fmpz_poly_set_str(ans->coeffs + 1, "2 -42 -42");
fmpz_poly_set_str(ans->coeffs + 2, "2 116 58");
_fmpz_holonomic_set_length(ans, 3);
check(re, ans, de);
/* erf(x) */
fmpz_holonomic_fun_set_erf(de);
fmpz_holonomic_get_series(re, de);
fmpz_poly_set_str(ans->coeffs + 0, "2 0 2");
fmpz_poly_set_str(ans->coeffs + 1, "0");
fmpz_poly_set_str(ans->coeffs + 2, "3 2 3 1");
_fmpz_holonomic_set_length(ans, 3);
check(re, ans, de);
/* erf(s+x) */
fmpz_holonomic_shift_fmpq(de, de, s);
fmpz_holonomic_get_series(re, de);
fmpz_poly_set_str(ans->coeffs + 0, "2 0 6");
fmpz_poly_set_str(ans->coeffs + 1, "2 -14 -14");
fmpz_poly_set_str(ans->coeffs + 2, "3 6 9 3");
_fmpz_holonomic_set_length(ans, 3);
check(re, ans, de);
/* x^s */
fmpz_holonomic_fun_set_pow_fmpq(de, s);
fmpz_holonomic_get_series(re, de);
fmpz_poly_set_si(ans->coeffs + 0, 1);
_fmpz_holonomic_set_length(ans, 1);
check(re, ans, de);
/* (x+s)^s */
fmpz_holonomic_shift_fmpq(de, de, s);
fmpz_holonomic_normalise_content(de);
fmpz_holonomic_get_series(re, de);
fmpz_poly_set_str(ans->coeffs + 0, "2 -7 -3");
fmpz_poly_set_str(ans->coeffs + 1, "2 7 7");
_fmpz_holonomic_set_length(ans, 2);
check(re, ans, de);
/* x^n */
fmpz_holonomic_fun_set_pow_fmpz(de, fmpq_numref(s));
fmpz_holonomic_get_series(re, de);
fmpz_poly_set_si(ans->coeffs + 0, 1);
_fmpz_holonomic_set_length(ans, 1);
check(re, ans, de);
/* (x+s)^n */
fmpz_holonomic_shift_fmpq(de, de, s);
fmpz_holonomic_normalise_content(de);
fmpz_holonomic_get_series(re, de);
fmpz_poly_set_str(ans->coeffs + 0, "2 -21 -3");
fmpz_poly_set_str(ans->coeffs + 1, "2 7 7");
_fmpz_holonomic_set_length(ans, 2);
check(re, ans, de);
fmpz_holonomic_clear(re);
fmpz_holonomic_clear(de);
fmpz_holonomic_clear(ans);
fmpq_clear(s);
}
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
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;
}
void set_from_long(ElementType& result, long a) const {fmpq_set_si(&result, a, 1);}
void set_var(ElementType& result, int v) const {fmpq_set_si(&result,1,1);}
