int main()
{
slong iter;
flint_rand_t state;
flint_printf("tan_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 2000 * arb_test_multiplier(); iter++)
{
slong m, n, rbits1, rbits2;
acb_poly_t a, b, c, d, e;
rbits1 = 2 + n_randint(state, 100);
rbits2 = 2 + n_randint(state, 100);
if (n_randint(state, 10) == 0)
{
m = 1 + n_randint(state, 50);
n = 1 + n_randint(state, 50);
}
else
{
m = 1 + n_randint(state, 20);
n = 1 + n_randint(state, 20);
}
acb_poly_init(a);
acb_poly_init(b);
acb_poly_init(c);
acb_poly_init(d);
acb_poly_init(e);
acb_poly_randtest(a, state, m, rbits1, 10);
acb_poly_tan_series(b, a, n, rbits2);
/* check tan(x) = 2*tan(x/2)/(1-tan(x/2)^2) */
acb_poly_scalar_mul_2exp_si(c, a, -1);
acb_poly_tan_series(c, c, n, rbits2);
acb_poly_mullow(d, c, c, n, rbits2);
acb_poly_one(e);
acb_poly_sub(e, e, d, rbits2);
acb_poly_div_series(c, c, e, n, rbits2);
acb_poly_scalar_mul_2exp_si(c, c, 1);
if (!acb_poly_overlaps(b, c))
{
flint_printf("FAIL\n\n");
flint_printf("bits2 = %wd\n", rbits2);
flint_printf("a = ");
acb_poly_printd(a, 15);
flint_printf("\n\n");
flint_printf("b = ");
acb_poly_printd(b, 15);
flint_printf("\n\n");
flint_printf("c = ");
acb_poly_printd(c, 15);
flint_printf("\n\n");
abort();
}
acb_poly_tan_series(a, a, n, rbits2);
if (!acb_poly_equal(a, b))
{
flint_printf("FAIL (aliasing)\n\n");
abort();
}
acb_poly_clear(a);
acb_poly_clear(b);
acb_poly_clear(c);
acb_poly_clear(d);
acb_poly_clear(e);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
void
acb_hypgeom_bessel_k_0f1_series(acb_poly_t res,
const acb_poly_t nu, const acb_poly_t z,
slong len, slong prec)
{
acb_poly_t s, u, A, B;
acb_poly_struct b[2];
arb_t c;
slong wlen;
int singular;
acb_poly_init(s);
acb_poly_init(u);
acb_poly_init(A);
acb_poly_init(B);
acb_poly_init(b + 0);
acb_poly_init(b + 1);
arb_init(c);
singular = (nu->length == 0) || acb_is_int(nu->coeffs);
wlen = len + (singular != 0);
/* A = (z/2)^nu, B = 1/A */
acb_poly_scalar_mul_2exp_si(A, z, -1);
acb_poly_pow_series(A, A, nu, wlen, prec);
acb_poly_inv_series(B, A, wlen, prec);
acb_poly_mullow(u, z, z, wlen, prec);
acb_poly_scalar_mul_2exp_si(u, u, -2);
acb_poly_one(b + 1);
acb_poly_add_si(b + 0, nu, 1, prec);
acb_hypgeom_pfq_series_direct(s, NULL, 0, b, 2, u, 1, -1, wlen, prec);
acb_poly_mullow(A, A, s, wlen, prec);
acb_poly_add_si(b + 0, nu, -1, prec);
acb_poly_neg(b + 0, b + 0);
acb_hypgeom_pfq_series_direct(s, NULL, 0, b, 2, u, 1, -1, wlen, prec);
acb_poly_mullow(B, B, s, wlen, prec);
acb_poly_sub(A, B, A, prec);
acb_poly_scalar_mul_2exp_si(A, A, -1);
/* multiply by pi csc(pi nu) */
acb_poly_sin_pi_series(B, nu, wlen, prec);
if (singular)
{
acb_poly_shift_right(A, A, 1);
acb_poly_shift_right(B, B, 1);
}
acb_poly_div_series(res, A, B, len, prec);
arb_const_pi(c, prec);
_acb_vec_scalar_mul_arb(res->coeffs, res->coeffs, res->length, c, prec);
acb_poly_clear(s);
acb_poly_clear(u);
acb_poly_clear(A);
acb_poly_clear(B);
acb_poly_clear(b + 0);
acb_poly_clear(b + 1);
arb_clear(c);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("get_unique_fmpz_poly....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
slong prec, c;
fmpz_poly_t A, B, C;
acb_poly_t a, b;
fmpz_poly_init(A);
fmpz_poly_init(B);
fmpz_poly_init(C);
acb_poly_init(a);
acb_poly_init(b);
fmpz_poly_randtest(A, state, 1 + n_randint(state, 10), 1 + n_randint(state, 1000));
fmpz_poly_randtest(B, state, 1 + n_randint(state, 10), 1 + n_randint(state, 1000));
fmpz_poly_randtest(C, state, 1 + n_randint(state, 10), 1 + n_randint(state, 1000));
c = 1 + n_randint(state, 1000);
prec = 2 + n_randint(state, 100);
for ( ; ; )
{
acb_poly_set_fmpz_poly(a, A, prec);
acb_poly_set2_fmpz_poly(b, B, C, prec);
acb_poly_scalar_mul_2exp_si(b, b, -c);
acb_poly_add(a, a, b, prec);
acb_poly_sub(a, a, b, prec);
if (acb_poly_get_unique_fmpz_poly(B, a))
{
if (!fmpz_poly_equal(A, B))
{
flint_printf("FAIL\n\n");
flint_printf("A = "); fmpz_poly_print(A); flint_printf("\n\n");
flint_printf("B = "); fmpz_poly_print(B); flint_printf("\n\n");
flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n");
abort();
}
break;
}
else
{
prec *= 2;
}
}
fmpz_poly_clear(A);
fmpz_poly_clear(B);
fmpz_poly_clear(C);
acb_poly_clear(a);
acb_poly_clear(b);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
