int main()
{
slong iter;
flint_rand_t state;
flint_printf("evaluate2....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000; iter++)
{
acb_poly_t f, g;
acb_t x, y1, z1, y2, z2;
acb_init(x);
acb_init(y1);
acb_init(z1);
acb_init(y2);
acb_init(z2);
acb_poly_init(f);
acb_poly_init(g);
acb_randtest(x, state, 2 + n_randint(state, 1000), 5);
acb_poly_randtest(f, state, 2 + n_randint(state, 100), 2 + n_randint(state, 1000), 5);
acb_poly_derivative(g, f, 2 + n_randint(state, 1000));
acb_poly_evaluate2(y1, z1, f, x, 2 + n_randint(state, 1000));
acb_poly_evaluate_horner(y2, f, x, 2 + n_randint(state, 1000));
acb_poly_evaluate_horner(z2, g, x, 2 + n_randint(state, 1000));
if (!acb_overlaps(y1, y2) || !acb_overlaps(z1, z2))
{
flint_printf("FAIL\n\n");
flint_printf("f = "); acb_poly_printd(f, 15); flint_printf("\n\n");
flint_printf("g = "); acb_poly_printd(g, 15); flint_printf("\n\n");
flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n");
flint_printf("y1 = "); acb_printd(y1, 15); flint_printf("\n\n");
flint_printf("z1 = "); acb_printd(z1, 15); flint_printf("\n\n");
flint_printf("y2 = "); acb_printd(y2, 15); flint_printf("\n\n");
flint_printf("z2 = "); acb_printd(z2, 15); flint_printf("\n\n");
abort();
}
acb_poly_clear(f);
acb_poly_clear(g);
acb_clear(x);
acb_clear(y1);
acb_clear(z1);
acb_clear(y2);
acb_clear(z2);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("l....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
acb_t s, t, u;
dirichlet_group_t G;
dirichlet_char_t chi;
ulong q, k;
slong prec;
acb_init(s);
acb_init(t);
acb_init(u);
q = 1 + n_randint(state, 50);
prec = 2 + n_randint(state, 100);
k = n_randint(state, n_euler_phi(q));
dirichlet_group_init(G, q);
dirichlet_char_init(chi, G);
dirichlet_char_index(chi, G, k);
if (n_randint(state, 2))
acb_set_si(s, n_randint(state, 50) - 25);
else
acb_randtest(s, state, 2 + n_randint(state, 200), 2);
acb_dirichlet_l_hurwitz(t, s, NULL, G, chi, prec);
acb_dirichlet_l(u, s, G, chi, prec);
if (!acb_overlaps(t, u))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("iter = %ld q = %lu k = %lu prec = %ld\n\n", iter, q, k, prec);
flint_printf("s = "); acb_printn(s, 100, 0); flint_printf("\n\n");
flint_printf("t = "); acb_printn(t, 100, 0); flint_printf("\n\n");
flint_printf("u = "); acb_printn(u, 100, 0); flint_printf("\n\n");
abort();
}
dirichlet_char_clear(chi);
dirichlet_group_clear(G);
acb_clear(s);
acb_clear(t);
acb_clear(u);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
long iter;
flint_rand_t state;
printf("exp....");
fflush(stdout);
flint_randinit(state);
/* check exp(a+b) = exp(a)*exp(b) */
for (iter = 0; iter < 10000; iter++)
{
acb_t a, b, c, d, e;
long prec;
acb_init(a);
acb_init(b);
acb_init(c);
acb_init(d);
acb_init(e);
acb_randtest(a, state, 1 + n_randint(state, 200), 3);
acb_randtest(b, state, 1 + n_randint(state, 200), 3);
acb_randtest(c, state, 1 + n_randint(state, 200), 3);
prec = 2 + n_randint(state, 200);
acb_add(c, a, b, prec);
acb_exp(c, c, prec);
acb_exp(d, a, prec);
acb_exp(e, b, prec);
acb_mul(d, d, e, prec);
if (!acb_overlaps(c, d))
{
printf("FAIL: overlap\n\n");
printf("a = "); acb_print(a); printf("\n\n");
printf("b = "); acb_print(b); printf("\n\n");
printf("c = "); acb_print(c); printf("\n\n");
printf("d = "); acb_print(d); printf("\n\n");
abort();
}
acb_clear(a);
acb_clear(b);
acb_clear(c);
acb_clear(d);
acb_clear(e);
}
flint_randclear(state);
flint_cleanup();
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;
}
int main()
{
flint_printf("spherical_y....");
fflush(stdout);
{
slong i, n, m;
acb_t z, w, x, y;
acb_init(z);
acb_init(w);
acb_init(x);
acb_init(y);
i = 0;
arb_set_str(acb_realref(x), "0.2", 64);
arb_set_str(acb_imagref(x), "0.3", 64);
arb_set_str(acb_realref(y), "0.3", 64);
arb_set_str(acb_imagref(y), "0.4", 64);
for (n = -4; n <= 4; n++)
{
for (m = -4; m <= 4; m++)
{
acb_hypgeom_spherical_y(z, n, m, x, y, 64);
acb_set_d_d(w, testdata[2 * i], testdata[2 * i + 1]);
mag_set_d(arb_radref(acb_realref(w)), 1e-13);
mag_set_d(arb_radref(acb_imagref(w)), 1e-13);
if (!acb_overlaps(z, w))
{
flint_printf("FAIL: value\n\n");
flint_printf("n = %wd, m = %wd\n", n, m);
flint_printf("z = "); acb_printd(z, 20); flint_printf("\n\n");
flint_printf("w = "); acb_printd(w, 20); flint_printf("\n\n");
abort();
}
i++;
}
}
acb_clear(z);
acb_clear(w);
acb_clear(x);
acb_clear(y);
}
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int
_acb_poly_overlaps(acb_srcptr poly1, slong len1,
acb_srcptr poly2, slong len2)
{
slong i;
for (i = 0; i < len2; i++)
if (!acb_overlaps(poly1 + i, poly2 + i))
return 0;
for (i = len2; i < len1; i++)
if (!acb_contains_zero(poly1 + i))
return 0;
return 1;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("evaluate_rectangular....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
acb_poly_t f;
acb_t x, y1, y2;
acb_init(x);
acb_init(y1);
acb_init(y2);
acb_poly_init(f);
acb_randtest(x, state, 2 + n_randint(state, 1000), 5);
acb_poly_randtest(f, state, 2 + n_randint(state, 100), 2 + n_randint(state, 1000), 5);
acb_poly_evaluate_rectangular(y1, f, x, 2 + n_randint(state, 1000));
acb_poly_evaluate_horner(y2, f, x, 2 + n_randint(state, 1000));
if (!acb_overlaps(y1, y2))
{
flint_printf("FAIL\n\n");
flint_printf("f = "); acb_poly_printd(f, 15); flint_printf("\n\n");
flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n");
flint_printf("y1 = "); acb_printd(y1, 15); flint_printf("\n\n");
flint_printf("y2 = "); acb_printd(y2, 15); flint_printf("\n\n");
abort();
}
acb_poly_clear(f);
acb_clear(x);
acb_clear(y1);
acb_clear(y2);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("sinc....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
acb_t a, b, c, d;
acb_init(a);
acb_init(b);
acb_init(c);
acb_init(d);
acb_randtest(a, state, 1 + n_randint(state, 400), 2 + n_randint(state, 100));
acb_randtest(b, state, 1 + n_randint(state, 400), 2 + n_randint(state, 100));
acb_randtest(c, state, 1 + n_randint(state, 400), 2 + n_randint(state, 100));
acb_sinc(b, a, 2 + n_randint(state, 400));
acb_sin(c, a, 2 + n_randint(state, 400));
acb_mul(d, b, a, 2 + n_randint(state, 400));
/* check consistency */
if (!acb_overlaps(c, d))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("a = "); acb_printd(a, 30); flint_printf("\n\n");
flint_printf("b = "); acb_printd(b, 30); flint_printf("\n\n");
flint_printf("c = "); acb_printd(c, 30); flint_printf("\n\n");
flint_printf("d = "); acb_printd(d, 30); flint_printf("\n\n");
abort();
}
acb_set(c, a);
acb_sinc(c, c, 2 + n_randint(state, 400));
if (!acb_overlaps(b, c))
{
flint_printf("FAIL: aliasing\n\n");
flint_printf("a = "); acb_printd(a, 30); flint_printf("\n\n");
flint_printf("b = "); acb_printd(c, 30); flint_printf("\n\n");
flint_printf("c = "); acb_printd(c, 30); flint_printf("\n\n");
abort();
}
acb_clear(a);
acb_clear(b);
acb_clear(c);
acb_clear(d);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("asinh....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
acb_t x, a, b;
slong prec1, prec2;
prec1 = 2 + n_randint(state, 1000);
prec2 = prec1 + 30;
acb_init(x);
acb_init(a);
acb_init(b);
acb_randtest_special(x, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100));
acb_randtest_special(a, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100));
acb_randtest_special(b, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100));
acb_asinh(a, x, prec1);
acb_asinh(b, x, prec2);
/* check consistency */
if (!acb_overlaps(a, b))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n");
flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n");
flint_printf("b = "); acb_printd(b, 15); flint_printf("\n\n");
abort();
}
/* check sinh(asinh(x)) = x */
acb_sinh(b, b, prec1);
if (!acb_contains(b, x))
{
flint_printf("FAIL: functional equation\n\n");
flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n");
flint_printf("b = "); acb_printd(b, 15); flint_printf("\n\n");
abort();
}
acb_asinh(x, x, prec1);
if (!acb_overlaps(a, x))
{
flint_printf("FAIL: aliasing\n\n");
flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n");
flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n");
abort();
}
acb_clear(x);
acb_clear(a);
acb_clear(b);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
void
check_periods()
{
FILE * fp;
int ip, f, in, im;
int flag = 0;
flint_printf("periods...");
fflush(stdout);
fp = fopen("ref_periods.txt", "r");
if (fp == NULL)
abort();
for (ip = 0; ip < nm; ip++)
{
slong prec = vp[ip];
acb_t ref;
acb_init(ref);
for (f = 0; f < nf; f++)
{
for (in = 0; in < nn; in++)
{
fmpz_poly_t pol;
fmpz_poly_init(pol);
vf[f](pol, vn[in]);
for (im = 0; im < nm; im++)
{
slong c;
abel_jacobi_t aj;
abel_jacobi_init_poly(aj, vm[im], pol);
abel_jacobi_compute(aj, flag, prec);
/* check 4 entries of each matrix */
for (c = 0; c < nc; c++)
{
acb_ptr coeff;
acb_get_file(ref, fp, prec);
coeff = acb_mat_entry(aj->omega0, c % 2, c / 2);
if (!acb_overlaps(ref, coeff))
{
flint_printf("FAIL:\n\n");
flint_printf("pol = ");
fmpz_poly_print(pol);
flint_printf("\nn = %ld, m = %ld, prec = %ld\n", vn[in], vm[im], prec);
flint_printf("\nref = ");
acb_printd(ref, 20);
flint_printf("\nperiod = ");
acb_printd(coeff, 20);
flint_printf("\n\n");
abort();
}
}
abel_jacobi_clear(aj);
}
fmpz_poly_clear(pol);
}
}
acb_clear(ref);
}
fclose(fp);
flint_cleanup();
printf("PASS\n");
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("pfq_sum_rs....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
acb_ptr a, b;
acb_t z, s1, s2, t1, t2;
slong i, p, q, n, prec1, prec2;
p = n_randint(state, 5);
q = n_randint(state, 5);
n = n_randint(state, 300);
prec1 = 2 + n_randint(state, 500);
prec2 = 2 + n_randint(state, 500);
acb_init(z);
acb_init(s1);
acb_init(s2);
acb_init(t1);
acb_init(t2);
acb_randtest_special(z, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100));
acb_randtest_special(s1, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100));
acb_randtest_special(t1, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100));
acb_randtest_special(s2, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100));
acb_randtest_special(t2, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100));
a = _acb_vec_init(p);
b = _acb_vec_init(q);
for (i = 0; i < p; i++)
acb_randtest(a + i, state, 1 + n_randint(state, 100), 1 + n_randint(state, 10));
for (i = 0; i < q; i++)
acb_randtest(b + i, state, 1 + n_randint(state, 100), 1 + n_randint(state, 10));
acb_hypgeom_pfq_sum_forward(s1, t1, a, p, b, q, z, n, prec1);
acb_hypgeom_pfq_sum_rs(s2, t2, a, p, b, q, z, n, prec2);
if (!acb_overlaps(s1, s2) || !acb_overlaps(t1, t2))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("z = "); acb_print(a); flint_printf("\n\n");
flint_printf("s1 = "); acb_print(s1); flint_printf("\n\n");
flint_printf("s2 = "); acb_print(s2); flint_printf("\n\n");
flint_printf("t1 = "); acb_print(t1); flint_printf("\n\n");
flint_printf("t2 = "); acb_print(t2); flint_printf("\n\n");
flint_abort();
}
_acb_vec_clear(a, p);
_acb_vec_clear(b, q);
acb_clear(z);
acb_clear(s1);
acb_clear(s2);
acb_clear(t1);
acb_clear(t2);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("pow....");
fflush(stdout);
flint_randinit(state);
/* check large arguments */
for (iter = 0; iter < 20000 * arb_test_multiplier(); iter++)
{
acb_t a, b, c, d, e, f;
slong prec1, prec2;
prec1 = 2 + n_randint(state, 1000);
prec2 = prec1 + 30;
acb_init(a);
acb_init(b);
acb_init(c);
acb_init(d);
acb_init(e);
acb_init(f);
acb_randtest(a, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 200));
if (n_randint(state, 4) == 0)
arb_zero(acb_imagref(a));
acb_randtest(b, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 200));
if (n_randint(state, 4) == 0)
arb_zero(acb_imagref(b));
acb_pow(c, a, b, prec1);
acb_pow(d, a, b, prec2);
if (!acb_overlaps(c, d))
{
flint_printf("FAIL: overlap\n\n");
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_printf("d = "); acb_print(d); flint_printf("\n\n");
flint_abort();
}
acb_randtest(c, state, 1 + n_randint(state, 1000), 200);
/* check a^(b+c) = a^b*a^c */
acb_add(e, b, c, prec1);
acb_pow(d, a, e, prec1);
acb_pow(e, a, b, prec1);
acb_pow(f, a, c, prec1);
acb_mul(e, e, f, prec1);
if (!acb_overlaps(d, e))
{
flint_printf("FAIL: functional equation\n\n");
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_printf("d = "); acb_print(d); flint_printf("\n\n");
flint_printf("e = "); acb_print(e); flint_printf("\n\n");
flint_abort();
}
acb_pow(c, a, b, prec1);
acb_set(d, a);
acb_pow(d, d, b, prec2);
if (!acb_overlaps(c, d))
{
flint_printf("FAIL: aliasing 1\n\n");
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_printf("d = "); acb_print(d); flint_printf("\n\n");
flint_abort();
}
acb_set(d, b);
acb_pow(d, a, d, prec2);
if (!acb_overlaps(c, d))
{
flint_printf("FAIL: aliasing 2\n\n");
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_printf("d = "); acb_print(d); flint_printf("\n\n");
flint_abort();
}
acb_clear(a);
acb_clear(b);
acb_clear(c);
acb_clear(d);
acb_clear(e);
acb_clear(f);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("legendre_p....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 2000 * arb_test_multiplier(); iter++)
{
acb_t n, na, nb, m, z, res1, res2, res3, t, u;
slong prec1, prec2, ebits;
int type;
acb_init(n);
acb_init(na);
acb_init(nb);
acb_init(m);
acb_init(z);
acb_init(res1);
acb_init(res2);
acb_init(res3);
acb_init(t);
acb_init(u);
prec1 = 2 + n_randint(state, 300);
prec2 = 2 + n_randint(state, 300);
ebits = 1 + n_randint(state, 10);
if (n_randint(state, 2))
{
acb_set_si(m, n_randint(state, 20) - 10);
acb_set_si(n, n_randint(state, 20) - 10);
}
else
{
acb_randtest_param(n, state, 1 + n_randint(state, 400), ebits);
acb_randtest_param(m, state, 1 + n_randint(state, 400), ebits);
}
acb_randtest_param(z, state, 1 + n_randint(state, 400), ebits);
acb_sub_ui(na, n, 1, prec2);
acb_add_ui(nb, n, 1, prec2);
type = n_randint(state, 2);
acb_hypgeom_legendre_p(res1, n, m, z, type, prec1);
acb_hypgeom_legendre_p(res2, na, m, z, type, prec2);
acb_hypgeom_legendre_p(res3, nb, m, z, type, prec2);
acb_add(t, n, m, prec2);
acb_mul(t, t, res2, prec2);
acb_sub(u, n, m, prec2);
acb_add_ui(u, u, 1, prec2);
acb_mul(u, u, res3, prec2);
acb_add(t, t, u, prec2);
acb_mul_2exp_si(u, n, 1);
acb_add_ui(u, u, 1, prec2);
acb_mul(u, u, z, prec2);
acb_mul(u, u, res1, prec2);
if (!acb_overlaps(t, u))
{
flint_printf("FAIL: consistency\n\n");
flint_printf("iter = %wd, prec1 = %wd, prec2 = %wd\n\n", iter, prec1, prec2);
flint_printf("type = %d\n\n", type);
flint_printf("n = "); acb_printd(n, 30); flint_printf("\n\n");
flint_printf("m = "); acb_printd(m, 30); flint_printf("\n\n");
flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n");
flint_printf("res1 = "); acb_printd(res1, 30); flint_printf("\n\n");
flint_printf("res2 = "); acb_printd(res2, 30); flint_printf("\n\n");
flint_printf("res3 = "); acb_printd(res3, 30); flint_printf("\n\n");
flint_printf("t = "); acb_printd(t, 30); flint_printf("\n\n");
flint_printf("u = "); acb_printd(u, 30); flint_printf("\n\n");
abort();
}
acb_clear(n);
acb_clear(na);
acb_clear(nb);
acb_clear(m);
acb_clear(z);
acb_clear(res1);
acb_clear(res2);
acb_clear(res3);
acb_clear(t);
acb_clear(u);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("laguerre_l....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 2000 * arb_test_multiplier(); iter++)
{
acb_t n, m, n1, m1, z, res1, res2, res3, s;
slong prec;
acb_init(n);
acb_init(m);
acb_init(n1);
acb_init(m1);
acb_init(z);
acb_init(res1);
acb_init(res2);
acb_init(res3);
acb_init(s);
prec = 2 + n_randint(state, 200);
if (n_randint(state, 2))
{
acb_set_si(n, n_randint(state, 20) - 10);
acb_set_si(m, n_randint(state, 20) - 10);
}
else
{
acb_randtest_param(n, state, 1 + n_randint(state, 400), 10);
acb_randtest_param(m, state, 1 + n_randint(state, 400), 10);
}
acb_randtest_param(z, state, 1 + n_randint(state, 400), 10);
acb_sub_ui(n1, n, 1, prec);
acb_sub_ui(m1, m, 1, prec);
acb_hypgeom_laguerre_l(res1, n, m, z, prec);
acb_hypgeom_laguerre_l(res2, n1, m, z, 2 + n_randint(state, 200));
acb_hypgeom_laguerre_l(res3, n, m1, z, 2 + n_randint(state, 200));
acb_add(s, res2, res3, prec);
if (acb_is_finite(res1) && acb_is_finite(s) && !acb_overlaps(res1, s))
{
flint_printf("FAIL: consistency\n\n");
flint_printf("iter = %wd\n\n", iter);
flint_printf("n = "); acb_printd(n, 30); flint_printf("\n\n");
flint_printf("m = "); acb_printd(m, 30); flint_printf("\n\n");
flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n");
flint_printf("res1 = "); acb_printd(res1, 30); flint_printf("\n\n");
flint_printf("res2 = "); acb_printd(res2, 30); flint_printf("\n\n");
flint_printf("res3 = "); acb_printd(res3, 30); flint_printf("\n\n");
flint_printf("s = "); acb_printd(s, 30); flint_printf("\n\n");
abort();
}
acb_clear(n);
acb_clear(m);
acb_clear(n1);
acb_clear(m1);
acb_clear(z);
acb_clear(res1);
acb_clear(res2);
acb_clear(res3);
acb_clear(s);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
long iter;
flint_rand_t state;
printf("u....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 2000; iter++)
{
acb_t a0, a1, a2, b, z, w0, w1, w2, t, u;
long prec0, prec1, prec2;
acb_init(a0);
acb_init(a1);
acb_init(a2);
acb_init(b);
acb_init(z);
acb_init(w0);
acb_init(w1);
acb_init(w2);
acb_init(t);
acb_init(u);
prec0 = 2 + n_randint(state, 700);
prec1 = 2 + n_randint(state, 700);
prec2 = 2 + n_randint(state, 700);
acb_randtest_maybe_half_int(a0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_randtest_maybe_half_int(b, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_randtest(z, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_randtest(w0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_randtest(w1, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_randtest(w2, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_add_ui(a1, a0, 1, prec0);
acb_add_ui(a2, a0, 2, prec0);
switch (n_randint(state, 3))
{
case 0:
acb_hypgeom_u_asymp_proper(w0, a0, b, z, prec0);
break;
case 1:
acb_hypgeom_u_1f1(w0, a0, b, z, prec0);
break;
default:
acb_hypgeom_u(w0, a0, b, z, prec0);
}
switch (n_randint(state, 3))
{
case 0:
acb_hypgeom_u_asymp_proper(w1, a0, b, z, prec1);
break;
case 1:
acb_hypgeom_u_1f1(w1, a0, b, z, prec1);
break;
default:
acb_hypgeom_u(w1, a0, b, z, prec1);
}
if (!acb_overlaps(w0, w1))
{
printf("FAIL: consistency\n\n");
printf("a = "); acb_printd(a0, 30); printf("\n\n");
printf("b = "); acb_printd(b, 30); printf("\n\n");
printf("z = "); acb_printd(z, 30); printf("\n\n");
printf("w0 = "); acb_printd(w0, 30); printf("\n\n");
printf("w1 = "); acb_printd(w1, 30); printf("\n\n");
abort();
}
switch (n_randint(state, 3))
{
case 0:
acb_hypgeom_u_asymp_proper(w1, a1, b, z, prec1);
break;
case 1:
acb_hypgeom_u_1f1(w1, a1, b, z, prec1);
break;
default:
acb_hypgeom_u(w1, a1, b, z, prec1);
}
switch (n_randint(state, 3))
{
case 0:
acb_hypgeom_u_asymp_proper(w2, a2, b, z, prec2);
break;
case 1:
acb_hypgeom_u_1f1(w2, a2, b, z, prec2);
break;
default:
acb_hypgeom_u(w2, a2, b, z, prec2);
}
acb_set(t, w0);
acb_mul_2exp_si(u, a0, 1);
acb_sub(u, u, b, prec0);
acb_add(u, u, z, prec0);
acb_add_ui(u, u, 2, prec0);
acb_submul(t, w1, u, prec0);
acb_sub(u, a2, b, prec0);
acb_mul(u, u, a1, prec0);
acb_addmul(t, w2, u, prec0);
if (!acb_contains_zero(t))
{
printf("FAIL: contiguous relation\n\n");
printf("a = "); acb_printd(a0, 30); printf("\n\n");
printf("b = "); acb_printd(b, 30); printf("\n\n");
printf("z = "); acb_printd(z, 30); printf("\n\n");
printf("w0 = "); acb_printd(w0, 30); printf("\n\n");
printf("w1 = "); acb_printd(w1, 30); printf("\n\n");
printf("w2 = "); acb_printd(w2, 30); printf("\n\n");
printf("t = "); acb_printd(t, 30); printf("\n\n");
abort();
}
acb_clear(a0);
acb_clear(a1);
acb_clear(a2);
acb_clear(b);
acb_clear(z);
acb_clear(w0);
acb_clear(w1);
acb_clear(w2);
acb_clear(t);
acb_clear(u);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
long iter;
flint_rand_t state;
printf("rising_ui_rs....");
fflush(stdout);
flint_randinit(state);
/* check functional equation */
for (iter = 0; iter < 1000; iter++)
{
acb_t x, xn, y, z;
ulong n, m, step1, step2, step3;
acb_init(x);
acb_init(xn);
acb_init(y);
acb_init(z);
acb_randtest(x, state, 1 + n_randint(state, 4000), 10);
n = n_randint(state, 80);
m = n_randint(state, 40);
acb_add_ui(xn, x, n, 1 + n_randint(state, 4000));
step1 = n_randint(state, 20);
step2 = n_randint(state, 20);
step3 = n_randint(state, 20);
acb_rising_ui_rs(y, x, n, step1, 2 + n_randint(state, 4000));
acb_rising_ui_rs(z, xn, m, step2, 2 + n_randint(state, 4000));
acb_mul(y, y, z, 2 + n_randint(state, 4000));
acb_rising_ui_rs(z, x, n + m, step3, 2 + n_randint(state, 4000));
if (!acb_overlaps(y, z))
{
printf("FAIL: overlap\n\n");
printf("n = %lu\n", n);
printf("m = %lu\n", m);
printf("x = "); acb_print(x); printf("\n\n");
printf("xn = "); acb_print(xn); printf("\n\n");
printf("y = "); acb_print(y); printf("\n\n");
printf("z = "); acb_print(z); printf("\n\n");
abort();
}
acb_clear(x);
acb_clear(xn);
acb_clear(y);
acb_clear(z);
}
/* aliasing of y and x */
for (iter = 0; iter < 1000; iter++)
{
acb_t x, y;
ulong n;
long prec;
ulong step;
acb_init(x);
acb_init(y);
acb_randtest(x, state, 1 + n_randint(state, 200), 10);
acb_randtest(y, state, 1 + n_randint(state, 200), 10);
n = n_randint(state, 100);
step = n_randint(state, 20);
prec = 2 + n_randint(state, 4000);
acb_rising_ui_rs(y, x, n, step, prec);
acb_rising_ui_rs(x, x, n, step, prec);
if (!acb_equal(x, y))
{
printf("FAIL: aliasing\n\n");
printf("x = "); acb_print(x); printf("\n\n");
printf("y = "); acb_print(y); printf("\n\n");
printf("n = %lu\n", n);
abort();
}
acb_clear(x);
acb_clear(y);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("div....");
fflush(stdout);
flint_randinit(state);
/* test aliasing of c and a */
for (iter = 0; iter < 100000; iter++)
{
acb_t a, b, c;
slong prec;
acb_init(a);
acb_init(b);
acb_init(c);
acb_randtest(a, state, 1 + n_randint(state, 200), 10);
acb_randtest(b, state, 1 + n_randint(state, 200), 10);
acb_randtest(c, state, 1 + n_randint(state, 200), 10);
prec = 2 + n_randint(state, 200);
acb_div(c, a, b, prec);
acb_div(a, a, b, prec);
if (!acb_equal(a, c))
{
flint_printf("FAIL: aliasing c, a\n\n");
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");
abort();
}
acb_clear(a);
acb_clear(b);
acb_clear(c);
}
/* test aliasing of c and b */
for (iter = 0; iter < 100000; iter++)
{
acb_t a, b, c;
slong prec;
acb_init(a);
acb_init(b);
acb_init(c);
acb_randtest(a, state, 1 + n_randint(state, 200), 10);
acb_randtest(b, state, 1 + n_randint(state, 200), 10);
acb_randtest(c, state, 1 + n_randint(state, 200), 10);
prec = 2 + n_randint(state, 200);
acb_div(c, a, b, prec);
acb_div(b, a, b, prec);
if (!acb_equal(b, c))
{
flint_printf("FAIL: aliasing c, b\n\n");
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");
abort();
}
acb_clear(a);
acb_clear(b);
acb_clear(c);
}
/* test aliasing a, a */
for (iter = 0; iter < 100000; iter++)
{
acb_t a, b, c, d;
slong prec;
acb_init(a);
acb_init(b);
acb_init(c);
acb_init(d);
acb_randtest(a, state, 1 + n_randint(state, 200), 10);
acb_randtest(b, state, 1 + n_randint(state, 200), 10);
acb_randtest(c, state, 1 + n_randint(state, 200), 10);
prec = 2 + n_randint(state, 200);
acb_set(b, a);
acb_div(c, a, a, prec);
acb_div(d, a, b, prec);
if (!acb_overlaps(c, d))
{
flint_printf("FAIL: aliasing a, a\n\n");
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_printf("d = "); acb_print(d); flint_printf("\n\n");
abort();
}
acb_clear(a);
acb_clear(b);
acb_clear(c);
acb_clear(d);
}
/* test aliasing a, a, a */
for (iter = 0; iter < 100000; iter++)
{
acb_t a, b, c;
slong prec;
acb_init(a);
acb_init(b);
acb_init(c);
acb_randtest(a, state, 1 + n_randint(state, 200), 10);
acb_randtest(b, state, 1 + n_randint(state, 200), 10);
acb_randtest(c, state, 1 + n_randint(state, 200), 10);
prec = 2 + n_randint(state, 200);
acb_set(b, a);
acb_div(c, a, b, prec);
acb_div(a, a, a, prec);
if (!acb_overlaps(a, c))
{
flint_printf("FAIL: aliasing a, a, a\n\n");
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");
abort();
}
acb_clear(a);
acb_clear(b);
acb_clear(c);
}
/* test (a+b)/c = a/c + b/c */
for (iter = 0; iter < 100000; iter++)
{
acb_t a, b, c, d, e, f;
acb_init(a);
acb_init(b);
acb_init(c);
acb_init(d);
acb_init(e);
acb_init(f);
acb_randtest(a, state, 1 + n_randint(state, 200), 10);
acb_randtest(b, state, 1 + n_randint(state, 200), 10);
acb_randtest(c, state, 1 + n_randint(state, 200), 10);
acb_add(d, a, b, 2 + n_randint(state, 200));
acb_div(e, d, c, 2 + n_randint(state, 200));
acb_div(d, a, c, 2 + n_randint(state, 200));
acb_div(f, b, c, 2 + n_randint(state, 200));
acb_add(f, d, f, 2 + n_randint(state, 200));
if (!acb_overlaps(e, f))
{
flint_printf("FAIL: (a+b)/c = a/c + b/c\n\n");
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_printf("e = "); acb_print(e); flint_printf("\n\n");
flint_printf("f = "); acb_print(f); flint_printf("\n\n");
abort();
}
acb_clear(a);
acb_clear(b);
acb_clear(c);
acb_clear(d);
acb_clear(e);
acb_clear(f);
}
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;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("jacobi_p....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000; iter++)
{
acb_t n, a, b, n1, a1, b1, z, res1, res2, res3, s;
slong prec;
acb_init(n);
acb_init(a);
acb_init(b);
acb_init(n1);
acb_init(a1);
acb_init(b1);
acb_init(z);
acb_init(res1);
acb_init(res2);
acb_init(res3);
acb_init(s);
prec = 2 + n_randint(state, 300);
if (n_randint(state, 2))
{
acb_set_si(n, n_randint(state, 20) - 10);
acb_set_si(a, n_randint(state, 20) - 10);
acb_set_si(b, n_randint(state, 20) - 10);
}
else
{
acb_randtest_param(n, state, 1 + n_randint(state, 400), 10);
acb_randtest_param(a, state, 1 + n_randint(state, 400), 10);
acb_randtest_param(b, state, 1 + n_randint(state, 400), 10);
}
acb_randtest_param(z, state, 1 + n_randint(state, 400), 10);
acb_sub_ui(n1, n, 1, prec);
acb_sub_ui(a1, a, 1, prec);
acb_sub_ui(b1, b, 1, prec);
acb_hypgeom_jacobi_p(res1, n, a, b1, z, prec);
acb_hypgeom_jacobi_p(res2, n, a1, b, z, 2 + n_randint(state, 300));
acb_hypgeom_jacobi_p(res3, n1, a, b, z, 2 + n_randint(state, 300));
acb_sub(s, res1, res2, prec);
if (!acb_overlaps(s, res3))
{
flint_printf("FAIL: consistency\n\n");
flint_printf("iter = %wd\n\n", iter);
flint_printf("n = "); acb_printd(n, 30); flint_printf("\n\n");
flint_printf("a = "); acb_printd(a, 30); flint_printf("\n\n");
flint_printf("b = "); acb_printd(b, 30); flint_printf("\n\n");
flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n");
flint_printf("res1 = "); acb_printd(res1, 30); flint_printf("\n\n");
flint_printf("res2 = "); acb_printd(res2, 30); flint_printf("\n\n");
flint_printf("res3 = "); acb_printd(res3, 30); flint_printf("\n\n");
flint_printf("s = "); acb_printd(s, 30); flint_printf("\n\n");
abort();
}
acb_clear(n);
acb_clear(a);
acb_clear(b);
acb_clear(n1);
acb_clear(a1);
acb_clear(b1);
acb_clear(z);
acb_clear(res1);
acb_clear(res2);
acb_clear(res3);
acb_clear(s);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
slong
_acb_poly_validate_roots(acb_ptr roots,
acb_srcptr poly, slong len, slong prec)
{
slong i, j, deg;
slong isolated, nonisolated, total_isolated;
acb_ptr deriv;
acb_ptr tmp;
int *overlap;
deg = len - 1;
deriv = _acb_vec_init(deg);
overlap = flint_calloc(deg, sizeof(int));
tmp = flint_malloc(sizeof(acb_struct) * deg);
_acb_poly_derivative(deriv, poly, len, prec);
/* compute an inclusion interval for each point */
for (i = 0; i < deg; i++)
{
_acb_poly_root_inclusion(roots + i, roots + i,
poly, deriv, len, prec);
}
/* find which points do not overlap with any other points */
for (i = 0; i < deg; i++)
{
for (j = i + 1; j < deg; j++)
{
if (acb_overlaps(roots + i, roots + j))
{
overlap[i] = overlap[j] = 1;
}
}
}
/* count and move all isolated roots to the front of the array */
total_isolated = 0;
for (i = 0; i < deg; i++)
total_isolated += (overlap[i] == 0);
for (i = 0; i < deg; i++)
tmp[i] = roots[i];
isolated = 0;
nonisolated = 0;
for (i = 0; i < deg; i++)
{
if (overlap[i] == 0)
{
roots[isolated] = tmp[i];
isolated++;
}
else
{
roots[total_isolated + nonisolated] = tmp[i];
nonisolated++;
}
}
_acb_vec_clear(deriv, deg);
flint_free(tmp);
flint_free(overlap);
return isolated;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("rising2_ui....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000; iter++)
{
acb_t a, u, v, u2, v2;
fmpz *f;
acb_ptr g;
ulong n;
slong i, prec;
acb_init(a);
acb_init(u);
acb_init(v);
acb_init(u2);
acb_init(v2);
acb_randtest(a, state, 1 + n_randint(state, 4000), 10);
acb_randtest(u, state, 1 + n_randint(state, 4000), 10);
acb_randtest(v, state, 1 + n_randint(state, 4000), 10);
n = n_randint(state, 120);
f = _fmpz_vec_init(n + 1);
g = _acb_vec_init(n + 1);
prec = 2 + n_randint(state, 4000);
acb_rising2_ui(u, v, a, n, prec);
arith_stirling_number_1u_vec(f, n, n + 1);
for (i = 0; i <= n; i++)
acb_set_fmpz(g + i, f + i);
_acb_poly_evaluate(u2, g, n + 1, a, prec);
_acb_poly_derivative(g, g, n + 1, prec);
_acb_poly_evaluate(v2, g, n, a, prec);
if (!acb_overlaps(u, u2) || !acb_overlaps(v, v2))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("n = %wu\n", n);
flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n");
flint_printf("u = "); acb_printd(u, 15); flint_printf("\n\n");
flint_printf("u2 = "); acb_printd(u2, 15); flint_printf("\n\n");
flint_printf("v = "); acb_printd(v, 15); flint_printf("\n\n");
flint_printf("v2 = "); acb_printd(v2, 15); flint_printf("\n\n");
abort();
}
acb_set(u2, a);
acb_rising2_ui(u2, v, u2, n, prec);
if (!acb_equal(u2, u))
{
flint_printf("FAIL: aliasing 1\n\n");
flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n");
flint_printf("u = "); acb_printd(u, 15); flint_printf("\n\n");
flint_printf("u2 = "); acb_printd(u2, 15); flint_printf("\n\n");
flint_printf("n = %wu\n", n);
abort();
}
acb_set(v2, a);
acb_rising2_ui(u, v2, v2, n, prec);
if (!acb_equal(v2, v))
{
flint_printf("FAIL: aliasing 2\n\n");
flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n");
flint_printf("v = "); acb_printd(v, 15); flint_printf("\n\n");
flint_printf("v2 = "); acb_printd(v2, 15); flint_printf("\n\n");
flint_printf("n = %wu\n", n);
abort();
}
acb_clear(a);
acb_clear(u);
acb_clear(v);
acb_clear(u2);
acb_clear(v2);
_fmpz_vec_clear(f, n + 1);
_acb_vec_clear(g, n + 1);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("agm1....");
fflush(stdout);
flint_randinit(state);
/* check particular values against table */
{
acb_t z, t;
acb_ptr w1;
slong i, j, prec, cnj;
acb_init(z);
acb_init(t);
w1 = _acb_vec_init(NUM_DERIVS);
for (prec = 32; prec <= 512; prec *= 4)
{
for (i = 0; i < NUM_TESTS; i++)
{
for (cnj = 0; cnj < 2; cnj++)
{
if (cnj == 1 && agm_testdata[i][0] < 0 &&
agm_testdata[i][1] == 0)
continue;
acb_zero(z);
arf_set_d(arb_midref(acb_realref(z)), agm_testdata[i][0]);
arf_set_d(arb_midref(acb_imagref(z)), cnj ? -agm_testdata[i][1] : agm_testdata[i][1]);
acb_agm1_cpx(w1, z, NUM_DERIVS, prec);
for (j = 0; j < NUM_DERIVS; j++)
{
arf_set_d(arb_midref(acb_realref(t)), agm_testdata[i][2+2*j]);
mag_set_d(arb_radref(acb_realref(t)), fabs(agm_testdata[i][2+2*j]) * EPS);
arf_set_d(arb_midref(acb_imagref(t)), cnj ? -agm_testdata[i][2+2*j+1] : agm_testdata[i][2+2*j+1]);
mag_set_d(arb_radref(acb_imagref(t)), fabs(agm_testdata[i][2+2*j+1]) * EPS);
if (!acb_overlaps(w1 + j, t))
{
flint_printf("FAIL\n\n");
flint_printf("j = %wd\n\n", j);
flint_printf("z = "); acb_printd(z, 15); flint_printf("\n\n");
flint_printf("t = "); acb_printd(t, 15); flint_printf("\n\n");
flint_printf("w1 = "); acb_printd(w1 + j, 15); flint_printf("\n\n");
abort();
}
}
}
}
}
_acb_vec_clear(w1, NUM_DERIVS);
acb_clear(z);
acb_clear(t);
}
/* self-consistency test */
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
acb_ptr m1, m2;
acb_t z1, z2, t;
slong i, len1, len2, prec1, prec2;
len1 = n_randint(state, 10);
len2 = n_randint(state, 10);
prec1 = 2 + n_randint(state, 2000);
prec2 = 2 + n_randint(state, 2000);
m1 = _acb_vec_init(len1);
m2 = _acb_vec_init(len2);
acb_init(z1);
acb_init(z2);
acb_init(t);
acb_randtest(z1, state, prec1, 1 + n_randint(state, 100));
if (n_randint(state, 2))
{
acb_set(z2, z1);
}
else
{
acb_randtest(t, state, prec2, 1 + n_randint(state, 100));
acb_add(z2, z1, t, prec2);
acb_sub(z2, z2, t, prec2);
}
acb_agm1_cpx(m1, z1, len1, prec1);
acb_agm1_cpx(m2, z2, len2, prec2);
for (i = 0; i < FLINT_MIN(len1, len2); i++)
{
if (!acb_overlaps(m1 + i, m2 + i))
{
flint_printf("FAIL (overlap)\n\n");
flint_printf("iter = %wd, i = %wd, len1 = %wd, len2 = %wd, prec1 = %wd, prec2 = %wd\n\n",
iter, i, len1, len2, prec1, prec2);
flint_printf("z1 = "); acb_printd(z1, 30); flint_printf("\n\n");
flint_printf("z2 = "); acb_printd(z2, 30); flint_printf("\n\n");
flint_printf("m1 = "); acb_printd(m1, 30); flint_printf("\n\n");
flint_printf("m2 = "); acb_printd(m2, 30); flint_printf("\n\n");
abort();
}
}
_acb_vec_clear(m1, len1);
_acb_vec_clear(m2, len2);
acb_clear(z1);
acb_clear(z2);
acb_clear(t);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
long iter;
flint_rand_t state;
printf("bessel_j....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 2000; iter++)
{
acb_t nu0, nu1, nu2, z, w0, w1, w2, t, u;
long prec0, prec1, prec2;
acb_init(nu0);
acb_init(nu1);
acb_init(nu2);
acb_init(z);
acb_init(w0);
acb_init(w1);
acb_init(w2);
acb_init(t);
acb_init(u);
prec0 = 2 + n_randint(state, 1000);
prec1 = 2 + n_randint(state, 1000);
prec2 = 2 + n_randint(state, 1000);
acb_randtest_param(nu0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_randtest(z, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_randtest(w0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_randtest(w1, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_randtest(w2, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_sub_ui(nu1, nu0, 1, prec0);
acb_sub_ui(nu2, nu0, 2, prec0);
switch (n_randint(state, 3))
{
case 0:
acb_hypgeom_bessel_j_asymp(w0, nu0, z, prec0);
break;
case 1:
acb_hypgeom_bessel_j_0f1(w0, nu0, z, prec0);
break;
default:
acb_hypgeom_bessel_j(w0, nu0, z, prec0);
}
switch (n_randint(state, 3))
{
case 0:
acb_hypgeom_bessel_j_asymp(w1, nu0, z, prec1);
break;
case 1:
acb_hypgeom_bessel_j_0f1(w1, nu0, z, prec1);
break;
default:
acb_hypgeom_bessel_j(w1, nu0, z, prec1);
}
if (!acb_overlaps(w0, w1))
{
printf("FAIL: consistency\n\n");
printf("nu = "); acb_printd(nu0, 30); printf("\n\n");
printf("z = "); acb_printd(z, 30); printf("\n\n");
printf("w0 = "); acb_printd(w0, 30); printf("\n\n");
printf("w1 = "); acb_printd(w1, 30); printf("\n\n");
abort();
}
switch (n_randint(state, 3))
{
case 0:
acb_hypgeom_bessel_j_asymp(w1, nu1, z, prec1);
break;
case 1:
acb_hypgeom_bessel_j_0f1(w1, nu1, z, prec1);
break;
default:
acb_hypgeom_bessel_j(w1, nu1, z, prec1);
}
switch (n_randint(state, 3))
{
case 0:
acb_hypgeom_bessel_j_asymp(w2, nu2, z, prec2);
break;
case 1:
acb_hypgeom_bessel_j_0f1(w2, nu2, z, prec2);
break;
default:
acb_hypgeom_bessel_j(w2, nu2, z, prec2);
}
acb_mul(t, w1, nu1, prec0);
acb_mul_2exp_si(t, t, 1);
acb_submul(t, w2, z, prec0);
acb_submul(t, w0, z, prec0);
if (!acb_contains_zero(t))
{
printf("FAIL: contiguous relation\n\n");
printf("nu = "); acb_printd(nu0, 30); printf("\n\n");
printf("z = "); acb_printd(z, 30); printf("\n\n");
printf("w0 = "); acb_printd(w0, 30); printf("\n\n");
printf("w1 = "); acb_printd(w1, 30); printf("\n\n");
printf("w2 = "); acb_printd(w2, 30); printf("\n\n");
printf("t = "); acb_printd(t, 30); printf("\n\n");
abort();
}
acb_neg(t, nu0);
switch (n_randint(state, 3))
{
case 0:
acb_hypgeom_bessel_j_asymp(w2, t, z, prec2);
break;
case 1:
acb_hypgeom_bessel_j_0f1(w2, t, z, prec2);
break;
default:
acb_hypgeom_bessel_j(w2, t, z, prec2);
}
acb_mul(w1, w1, w2, prec2);
acb_neg(t, nu1);
switch (n_randint(state, 3))
{
case 0:
acb_hypgeom_bessel_j_asymp(w2, t, z, prec2);
break;
case 1:
acb_hypgeom_bessel_j_0f1(w2, t, z, prec2);
break;
default:
acb_hypgeom_bessel_j(w2, t, z, prec2);
}
acb_mul(w0, w0, w2, prec2);
acb_add(w0, w0, w1, prec2);
acb_sin_pi(t, nu0, prec2);
acb_const_pi(u, prec2);
acb_mul(u, u, z, prec2);
acb_div(t, t, u, prec2);
acb_mul_2exp_si(t, t, 1);
if (!acb_overlaps(w0, t))
{
printf("FAIL: wronskian\n\n");
printf("nu = "); acb_printd(nu0, 30); printf("\n\n");
printf("z = "); acb_printd(z, 30); printf("\n\n");
printf("w0 = "); acb_printd(w0, 30); printf("\n\n");
printf("t = "); acb_printd(t, 30); printf("\n\n");
abort();
}
acb_clear(nu0);
acb_clear(nu1);
acb_clear(nu2);
acb_clear(z);
acb_clear(w0);
acb_clear(w1);
acb_clear(w2);
acb_clear(t);
acb_clear(u);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("zeta_cpx_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
acb_t s, a;
acb_ptr z1, z2;
slong i, len, prec1, prec2;
int deflate;
acb_init(s);
acb_init(a);
if (n_randint(state, 2))
{
acb_randtest(s, state, 1 + n_randint(state, 300), 3);
}
else
{
arb_set_ui(acb_realref(s), 1);
arb_mul_2exp_si(acb_realref(s), acb_realref(s), -1);
arb_randtest(acb_imagref(s), state, 1 + n_randint(state, 300), 4);
}
switch (n_randint(state, 3))
{
case 0:
acb_randtest(a, state, 1 + n_randint(state, 300), 3);
break;
case 1:
arb_randtest(acb_realref(a), state, 1 + n_randint(state, 300), 3);
break;
case 2:
acb_one(a);
break;
}
prec1 = 2 + n_randint(state, 300);
prec2 = prec1 + 30;
len = 1 + n_randint(state, 20);
deflate = n_randint(state, 2);
z1 = _acb_vec_init(len);
z2 = _acb_vec_init(len);
_acb_poly_zeta_cpx_series(z1, s, a, deflate, len, prec1);
_acb_poly_zeta_cpx_series(z2, s, a, deflate, len, prec2);
for (i = 0; i < len; i++)
{
if (!acb_overlaps(z1 + i, z2 + i))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("iter = %wd\n", iter);
flint_printf("deflate = %d, len = %wd, i = %wd\n\n", deflate, len, i);
flint_printf("s = "); acb_printd(s, prec1 / 3.33); flint_printf("\n\n");
flint_printf("a = "); acb_printd(a, prec1 / 3.33); flint_printf("\n\n");
flint_printf("z1 = "); acb_printd(z1 + i, prec1 / 3.33); flint_printf("\n\n");
flint_printf("z2 = "); acb_printd(z2 + i, prec2 / 3.33); flint_printf("\n\n");
abort();
}
}
acb_clear(a);
acb_clear(s);
_acb_vec_clear(z1, len);
_acb_vec_clear(z2, len);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
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("gamma_upper....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 2000; iter++)
{
acb_t a0, a1, b, z, w0, w1, t, u;
long prec0, prec1;
int modified;
acb_init(a0);
acb_init(a1);
acb_init(b);
acb_init(z);
acb_init(w0);
acb_init(w1);
acb_init(t);
acb_init(u);
modified = n_randint(state, 2);
prec0 = 2 + n_randint(state, 1000);
prec1 = 2 + n_randint(state, 1000);
acb_randtest_maybe_half_int(a0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_randtest(z, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_randtest(w0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_randtest(w1, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_add_ui(a1, a0, 1, prec0);
switch (n_randint(state, 4))
{
case 0:
acb_hypgeom_gamma_upper_asymp(w0, a0, z, modified, prec0);
break;
case 1:
acb_hypgeom_gamma_upper_1f1a(w0, a0, z, modified, prec0);
break;
case 2:
acb_hypgeom_gamma_upper_1f1b(w0, a0, z, modified, prec0);
break;
default:
acb_hypgeom_gamma_upper(w0, a0, z, modified, prec0);
}
switch (n_randint(state, 4))
{
case 0:
acb_hypgeom_gamma_upper_asymp(w1, a0, z, modified, prec1);
break;
case 1:
acb_hypgeom_gamma_upper_1f1a(w1, a0, z, modified, prec1);
break;
case 2:
acb_hypgeom_gamma_upper_1f1b(w1, a0, z, modified, prec1);
break;
default:
acb_hypgeom_gamma_upper(w1, a0, z, modified, prec1);
}
if (!acb_overlaps(w0, w1))
{
printf("FAIL: consistency\n\n");
printf("nu = "); acb_printd(a0, 30); printf("\n\n");
printf("z = "); acb_printd(z, 30); printf("\n\n");
printf("w0 = "); acb_printd(w0, 30); printf("\n\n");
printf("w1 = "); acb_printd(w1, 30); printf("\n\n");
abort();
}
switch (n_randint(state, 4))
{
case 0:
acb_hypgeom_gamma_upper_asymp(w1, a1, z, modified, prec1);
break;
case 1:
acb_hypgeom_gamma_upper_1f1a(w1, a1, z, modified, prec1);
break;
case 2:
acb_hypgeom_gamma_upper_1f1b(w1, a1, z, modified, prec1);
break;
default:
acb_hypgeom_gamma_upper(w1, a1, z, modified, prec1);
}
/* a Gamma(a,z) + exp(-z) z^a = Gamma(a+1,z) */
if (modified)
acb_one(t);
else
acb_pow(t, z, a0, prec0);
acb_neg(u, z);
acb_exp(u, u, prec0);
acb_mul(t, t, u, prec0);
if (modified)
{
acb_mul(b, w1, z, prec0);
acb_addmul(t, a0, w0, prec0);
acb_sub(t, t, b, prec0);
}
else
{
acb_addmul(t, a0, w0, prec0);
acb_sub(t, t, w1, prec0);
}
if (!acb_contains_zero(t))
{
printf("FAIL: contiguous relation\n\n");
printf("nu = "); acb_printd(a0, 30); printf("\n\n");
printf("z = "); acb_printd(z, 30); printf("\n\n");
printf("w0 = "); acb_printd(w0, 30); printf("\n\n");
printf("w1 = "); acb_printd(w1, 30); printf("\n\n");
printf("t = "); acb_printd(t, 30); printf("\n\n");
abort();
}
acb_clear(a0);
acb_clear(a1);
acb_clear(b);
acb_clear(z);
acb_clear(w0);
acb_clear(w1);
acb_clear(t);
acb_clear(u);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("2f1....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 3000; iter++)
{
acb_t a, b, c, z, w1, w2, t;
slong prec1, prec2;
int reg1, reg2, ebits;
int alg1, alg2;
acb_init(a);
acb_init(b);
acb_init(c);
acb_init(z);
acb_init(w1);
acb_init(w2);
acb_init(t);
prec1 = 2 + n_randint(state, 300);
prec2 = 2 + n_randint(state, 300);
if (n_randint(state, 20) == 0)
ebits = 30;
else
ebits = 5;
switch (n_randint(state, 3))
{
case 0:
acb_set_si(a, n_randint(state, 500));
acb_set_si(b, n_randint(state, 500));
acb_set_si(c, n_randint(state, 10));
break;
case 1:
acb_set_si(a, n_randint(state, 200) - 100);
acb_set_si(b, n_randint(state, 200) - 100);
acb_set_si(c, n_randint(state, 200) - 100);
break;
default:
acb_randtest_param(a, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits));
acb_randtest_param(b, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits));
acb_randtest_param(c, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits));
}
acb_randtest_param(z, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits));
acb_randtest(w1, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits));
acb_randtest(w2, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits));
reg1 = n_randint(state, 2);
reg2 = n_randint(state, 2);
alg1 = n_randint(state, 10);
alg2 = n_randint(state, 10);
switch (alg1)
{
case 0:
acb_hypgeom_2f1_direct(w1, a, b, c, z, reg1, prec1);
break;
case 1:
case 2:
case 3:
case 4:
case 5:
acb_hypgeom_2f1_transform(w1, a, b, c, z, reg1, alg1, prec1);
break;
case 6:
acb_hypgeom_2f1_corner(w1, a, b, c, z, reg1, prec1);
break;
default:
acb_hypgeom_2f1(w1, a, b, c, z, reg1, prec1);
}
switch (alg2)
{
case 0:
acb_hypgeom_2f1_direct(w2, a, b, c, z, reg2, prec2);
break;
case 1:
case 2:
case 3:
case 4:
case 5:
acb_hypgeom_2f1_transform(w2, a, b, c, z, reg2, alg2, prec2);
break;
case 6:
acb_hypgeom_2f1_corner(w2, a, b, c, z, reg2, prec2);
break;
default:
acb_hypgeom_2f1(w2, a, b, c, z, reg2, prec2);
}
if (reg1 != reg2)
{
acb_rgamma(t, c, prec2);
if (reg1)
acb_mul(w2, w2, t, prec2);
else
acb_mul(w1, w1, t, prec2);
}
if (!acb_overlaps(w1, w2))
{
flint_printf("FAIL: consistency\n\n");
flint_printf("iter = %wd, prec1 = %wd, prec2 = %wd\n\n", iter, prec1, prec2);
flint_printf("alg1 = %d, alg2 = %d\n\n", alg1, alg2);
flint_printf("reg1 = %d, reg2 = %d\n\n", reg1, reg2);
flint_printf("a = "); acb_printd(a, 30); flint_printf("\n\n");
flint_printf("b = "); acb_printd(b, 30); flint_printf("\n\n");
flint_printf("c = "); acb_printd(c, 30); flint_printf("\n\n");
flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n");
flint_printf("w1 = "); acb_printd(w1, 30); flint_printf("\n\n");
flint_printf("w2 = "); acb_printd(w2, 30); flint_printf("\n\n");
abort();
}
acb_clear(a);
acb_clear(b);
acb_clear(c);
acb_clear(z);
acb_clear(w1);
acb_clear(w2);
acb_clear(t);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("fundamental_domain_approx....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
fmpq_t x, y;
psl2z_t g;
arf_t one_minus_eps, tol;
acb_t z, w, w2;
arb_t t;
slong prec;
fmpq_init(x);
fmpq_init(y);
psl2z_init(g);
acb_init(z);
acb_init(w);
acb_init(w2);
arf_init(one_minus_eps);
arf_init(tol);
arb_init(t);
/* pick an exact point in the upper half plane */
fmpq_randtest(x, state, 1 + n_randint(state, 500));
do {
fmpq_randtest(y, state, 1 + n_randint(state, 500));
} while (fmpz_sgn(fmpq_numref(y)) <= 0);
/* pick a tolerance */
arf_set_ui_2exp_si(tol, 1, -(slong) n_randint(state, 500));
/* now increase the precision until convergence */
for (prec = 32; ; prec *= 2)
{
if (prec > 16384)
{
flint_printf("FAIL (no convergence)\n");
flint_printf("x = "); fmpq_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpq_print(y); flint_printf("\n\n");
flint_printf("z = "); acb_printd(z, 50); flint_printf("\n\n");
flint_printf("w = "); acb_printd(w, 50); flint_printf("\n\n");
flint_printf("w2 = "); acb_printd(w2, 50); flint_printf("\n\n");
flint_printf("g = "); psl2z_print(g); flint_printf("\n\n");
abort();
}
arb_set_fmpq(acb_realref(z), x, prec);
arb_set_fmpq(acb_imagref(z), y, prec);
arf_set_ui_2exp_si(one_minus_eps, 1, -prec / 4);
arf_sub_ui(one_minus_eps, one_minus_eps, 1, prec, ARF_RND_DOWN);
arf_neg(one_minus_eps, one_minus_eps);
acb_modular_fundamental_domain_approx(w, g, z, one_minus_eps, prec);
acb_modular_transform(w2, g, z, prec);
if (!psl2z_is_correct(g) || !acb_overlaps(w, w2))
{
flint_printf("FAIL (incorrect transformation)\n");
flint_printf("x = "); fmpq_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpq_print(y); flint_printf("\n\n");
flint_printf("z = "); acb_printd(z, 50); flint_printf("\n\n");
flint_printf("w = "); acb_printd(w, 50); flint_printf("\n\n");
flint_printf("w2 = "); acb_printd(w2, 50); flint_printf("\n\n");
flint_printf("g = "); psl2z_print(g); flint_printf("\n\n");
abort();
}
/* success */
if (acb_modular_is_in_fundamental_domain(w, tol, prec))
break;
}
/* check that g^(-1) * w contains x+yi */
psl2z_inv(g, g);
acb_modular_transform(w2, g, w, 2 + n_randint(state, 1000));
if (!arb_contains_fmpq(acb_realref(w2), x) ||
!arb_contains_fmpq(acb_imagref(w2), y))
{
flint_printf("FAIL (inverse containment)\n");
flint_printf("x = "); fmpq_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpq_print(y); flint_printf("\n\n");
flint_printf("z = "); acb_printd(z, 50); flint_printf("\n\n");
flint_printf("w = "); acb_printd(w, 50); flint_printf("\n\n");
flint_printf("w2 = "); acb_printd(w2, 50); flint_printf("\n\n");
flint_printf("g = "); psl2z_print(g); flint_printf("\n\n");
abort();
}
fmpq_clear(x);
fmpq_clear(y);
psl2z_clear(g);
acb_clear(z);
acb_clear(w);
acb_clear(w2);
arf_clear(one_minus_eps);
arf_clear(tol);
arb_clear(t);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("si....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
acb_t z0, z1, w0, w1;
slong prec0, prec1;
acb_init(z0);
acb_init(z1);
acb_init(w0);
acb_init(w1);
prec0 = 2 + n_randint(state, 1000);
prec1 = 2 + n_randint(state, 1000);
acb_randtest(z0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_randtest(w0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_randtest(w1, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_set(z1, z0);
if (n_randint(state, 2))
{
acb_add(z1, z1, w0, prec0);
acb_sub(z1, z1, w0, prec0);
}
switch (n_randint(state, 3))
{
case 0:
acb_hypgeom_si_1f2(w0, z0, prec0);
break;
case 1:
acb_hypgeom_si_asymp(w0, z0, prec0);
break;
default:
acb_hypgeom_si(w0, z0, prec0);
}
switch (n_randint(state, 3))
{
case 0:
acb_hypgeom_si_1f2(w1, z1, prec1);
break;
case 1:
acb_hypgeom_si_asymp(w1, z1, prec1);
break;
default:
acb_hypgeom_si(w1, z1, prec1);
}
if (!acb_overlaps(w0, w1))
{
flint_printf("FAIL: consistency\n\n");
flint_printf("z0 = "); acb_printd(z0, 30); flint_printf("\n\n");
flint_printf("z1 = "); acb_printd(z1, 30); flint_printf("\n\n");
flint_printf("w0 = "); acb_printd(w0, 30); flint_printf("\n\n");
flint_printf("w1 = "); acb_printd(w1, 30); flint_printf("\n\n");
abort();
}
acb_clear(z0);
acb_clear(z1);
acb_clear(w0);
acb_clear(w1);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("theta_sum....");
fflush(stdout);
flint_randinit(state);
/* Very weak test, just testing the error bounds and not
that we compute the right functions */
for (iter = 0; iter < 10000; iter++)
{
acb_ptr t1a, t1b, t2a, t2b, t3a, t3b, t4a, t4b;
acb_t w, q;
int w_is_unit;
slong prec0, e0, prec1, prec2, len1, len2, i;
acb_init(w);
acb_init(q);
e0 = 1 + n_randint(state, 100);
prec0 = 2 + n_randint(state, 3000);
prec1 = 2 + n_randint(state, 3000);
prec2 = 2 + n_randint(state, 3000);
len1 = 1 + n_randint(state, 30);
len2 = 1 + n_randint(state, 30);
t1a = _acb_vec_init(len1);
t2a = _acb_vec_init(len1);
t3a = _acb_vec_init(len1);
t4a = _acb_vec_init(len1);
t1b = _acb_vec_init(len2);
t2b = _acb_vec_init(len2);
t3b = _acb_vec_init(len2);
t4b = _acb_vec_init(len2);
if (n_randint(state, 2))
{
arb_randtest(acb_realref(q), state, prec0, e0);
arb_zero(acb_imagref(q));
acb_exp_pi_i(w, q, prec0);
w_is_unit = n_randint(state, 2);
}
else
{
acb_randtest(w, state, prec0, e0);
w_is_unit = 0;
}
acb_randtest(q, state, prec0, e0);
for (i = 0; i < len1; i++)
{
acb_randtest(t1a + i, state, prec0, e0);
acb_randtest(t2a + i, state, prec0, e0);
acb_randtest(t3a + i, state, prec0, e0);
acb_randtest(t4a + i, state, prec0, e0);
}
for (i = 0; i < len2; i++)
{
acb_randtest(t1b + i, state, prec0, e0);
acb_randtest(t2b + i, state, prec0, e0);
acb_randtest(t3b + i, state, prec0, e0);
acb_randtest(t4b + i, state, prec0, e0);
}
acb_modular_theta_sum(t1a, t2a, t3a, t4a,
w, w_is_unit, q, len1, prec1);
acb_modular_theta_sum(t1b, t2b, t3b, t4b,
w, w_is_unit & n_randint(state, 2), q, len2, prec2);
for (i = 0; i < FLINT_MIN(len1, len2); i++)
{
if (!acb_overlaps(t1a + i, t1b + i)
|| !acb_overlaps(t2a + i, t2b + i)
|| !acb_overlaps(t3a + i, t3b + i)
|| !acb_overlaps(t4a + i, t4b + i))
{
flint_printf("FAIL (overlap) iter = %wd\n", iter);
flint_printf("len1 = %wd, len2 = %wd, prec1 = %wd, prec2 = %wd\n\n",
len1, len2, prec1, prec2);
flint_printf("i = %wd\n\n", i);
flint_printf("q = "); acb_printd(q, 50); flint_printf("\n\n");
flint_printf("w = "); acb_printd(w, 50); flint_printf("\n\n");
flint_printf("t1a = "); acb_printd(t1a + i, 50); flint_printf("\n\n");
flint_printf("t1b = "); acb_printd(t1b + i, 50); flint_printf("\n\n");
flint_printf("t2a = "); acb_printd(t2a + i, 50); flint_printf("\n\n");
flint_printf("t2b = "); acb_printd(t2b + i, 50); flint_printf("\n\n");
flint_printf("t3a = "); acb_printd(t3a + i, 50); flint_printf("\n\n");
flint_printf("t3b = "); acb_printd(t3b + i, 50); flint_printf("\n\n");
flint_printf("t4a = "); acb_printd(t4a + i, 50); flint_printf("\n\n");
flint_printf("t4b = "); acb_printd(t4b + i, 50); flint_printf("\n\n");
abort();
}
}
_acb_vec_clear(t1a, len1);
_acb_vec_clear(t2a, len1);
_acb_vec_clear(t3a, len1);
_acb_vec_clear(t4a, len1);
_acb_vec_clear(t1b, len2);
_acb_vec_clear(t2b, len2);
_acb_vec_clear(t3b, len2);
_acb_vec_clear(t4b, len2);
acb_clear(w);
acb_clear(q);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
