int main()
{
slong iter;
flint_rand_t state;
flint_printf("rsqrt....");
fflush(stdout);
flint_randinit(state);
/* check (a^(-1/2))^(-2) = a */
for (iter = 0; iter < 10000; 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, 2000), 10);
acb_randtest(b, state, 1 + n_randint(state, 2000), 10);
prec = 2 + n_randint(state, 2000);
acb_rsqrt(b, a, prec);
acb_inv(c, b, prec);
acb_mul(c, c, c, prec);
if (!acb_contains(c, a))
{
flint_printf("FAIL: containment\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_rsqrt(a, a, prec);
if (!acb_equal(a, b))
{
flint_printf("FAIL: aliasing\n\n");
flint_printf("a = "); acb_print(a); flint_printf("\n\n");
flint_printf("b = "); acb_print(b); flint_printf("\n\n");
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("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(void)
{
int i, j, result;
flint_rand_t state;
flint_printf("get/set_coeff_acb....");
fflush(stdout);
flint_randinit(state);
for (i = 0; i < 100; i++)
{
acb_poly_t a;
acb_t x1, x2;
slong coeff, len;
acb_poly_init(a);
acb_init(x1);
acb_init(x2);
len = n_randint(state, 100) + 1;
for (j = 0; j < 100; j++)
{
acb_randtest(x1, state, 2 + n_randint(state, 200), 10);
coeff = n_randint(state, len);
acb_poly_set_coeff_acb(a, coeff, x1);
acb_poly_get_coeff_acb(x2, a, coeff);
result = (acb_equal(x1, x2));
if (!result)
{
flint_printf("FAIL:\n");
flint_printf("x1 = "), acb_print(x1), flint_printf("\n");
flint_printf("x2 = "), acb_print(x2), flint_printf("\n");
flint_printf("coeff = %wd, length = %wd\n", coeff, len);
flint_abort();
}
}
acb_clear(x1);
acb_clear(x2);
acb_poly_clear(a);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return 0;
}
int
acb_mat_equal(const acb_mat_t mat1, const acb_mat_t mat2)
{
slong i, j;
if ((acb_mat_nrows(mat1) != acb_mat_nrows(mat2)) ||
(acb_mat_ncols(mat1) != acb_mat_ncols(mat2)))
return 0;
for (i = 0; i < acb_mat_nrows(mat1); i++)
for (j = 0; j < acb_mat_ncols(mat1); j++)
if (!acb_equal(acb_mat_entry(mat1, i, j),
acb_mat_entry(mat2, i, j)))
return 0;
return 1;
}
int
main(void)
{
int i, result;
flint_rand_t state;
printf("get_coeff_ptr....");
fflush(stdout);
flint_randinit(state);
for (i = 0; i < 1000; i++)
{
acb_poly_t A;
acb_t a;
long n = n_randint(state, 100);
acb_poly_init(A);
acb_poly_randtest(A, state, n_randint(state, 100), 100, 10);
acb_init(a);
acb_poly_get_coeff_acb(a, A, n);
result = n < acb_poly_length(A) ?
acb_equal(a, acb_poly_get_coeff_ptr(A, n)) :
acb_poly_get_coeff_ptr(A, n) == NULL;
if (!result)
{
printf("FAIL:\n");
printf("A = "), acb_poly_printd(A, 10), printf("\n\n");
printf("a = "), acb_print(a), printf("\n\n");
printf("n = %ld\n\n", n);
abort();
}
acb_poly_clear(A);
acb_clear(a);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return 0;
}
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;
}
void
acb_hypgeom_chebyshev_t(acb_t res, const acb_t n, const acb_t z, slong prec)
{
acb_t t;
if (acb_is_int(n) &&
arf_cmpabs_2exp_si(arb_midref(acb_realref(n)), FLINT_BITS - 1) < 0)
{
slong k = arf_get_si(arb_midref(acb_realref(n)), ARF_RND_DOWN);
acb_chebyshev_t_ui(res, FLINT_ABS(k), z, prec);
return;
}
if (acb_is_zero(z))
{
acb_mul_2exp_si(res, n, -1);
acb_cos_pi(res, res, prec);
return;
}
if (acb_is_one(z))
{
acb_one(res);
return;
}
acb_init(t);
acb_set_si(t, -1);
if (acb_equal(t, z))
{
acb_cos_pi(res, n, prec);
}
else
{
acb_sub_ui(t, z, 1, prec);
if (arf_cmpabs_2exp_si(arb_midref(acb_realref(t)), -2 - prec / 10) < 0 &&
arf_cmpabs_2exp_si(arb_midref(acb_imagref(t)), -2 - prec / 10) < 0)
{
acb_t a, c;
acb_init(a);
acb_init(c);
acb_neg(a, n);
acb_one(c);
acb_mul_2exp_si(c, c, -1);
acb_neg(t, t);
acb_mul_2exp_si(t, t, -1);
acb_hypgeom_2f1(res, a, n, c, t, 0, prec);
acb_clear(a);
acb_clear(c);
}
else if (arb_is_nonnegative(acb_realref(t)))
{
acb_acosh(t, z, prec);
acb_mul(t, t, n, prec);
acb_cosh(res, t, prec);
}
else
{
acb_acos(t, z, prec);
acb_mul(t, t, n, prec);
acb_cos(res, t, prec);
}
}
acb_clear(t);
}
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("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("mul_naive....");
fflush(stdout);
flint_randinit(state);
/* test aliasing of c and a */
for (iter = 0; iter < 100000 * arb_test_multiplier(); 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_mul_naive(c, a, b, prec);
acb_mul_naive(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 * arb_test_multiplier(); 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_mul_naive(c, a, b, prec);
acb_mul_naive(b, a, b, prec);
if (!acb_equal(b, c))
{
flint_printf("FAIL: aliasing b, 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 a, a */
for (iter = 0; iter < 100000 * arb_test_multiplier(); 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_mul_naive(c, a, a, prec);
acb_mul_naive(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 * arb_test_multiplier(); 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_mul_naive(c, a, b, prec);
acb_mul_naive(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*b + a*c */
for (iter = 0; iter < 100000 * arb_test_multiplier(); 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, b, c, 2 + n_randint(state, 200));
acb_mul_naive(e, a, d, 2 + n_randint(state, 200));
acb_mul_naive(d, a, b, 2 + n_randint(state, 200));
acb_mul_naive(f, a, 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*b + a*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;
}
