void
acb_digamma(acb_t y, const acb_t x, long prec)
{
int reflect;
long r, n, wp;
acb_t t, u, v;
wp = prec + FLINT_BIT_COUNT(prec);
acb_gamma_stirling_choose_param(&reflect, &r, &n, x, 1, 1, wp);
acb_init(t);
acb_init(u);
acb_init(v);
/* psi(x) = psi((1-x)+r) - h(1-x,r) - pi*cot(pi*x) */
if (reflect)
{
acb_sub_ui(t, x, 1, wp);
acb_neg(t, t);
acb_cot_pi(v, x, wp);
arb_const_pi(acb_realref(u), wp);
acb_mul_arb(v, v, acb_realref(u), wp);
acb_rising2_ui(y, u, t, r, wp);
acb_div(u, u, y, wp);
acb_add(v, v, u, wp);
acb_add_ui(t, t, r, wp);
acb_gamma_stirling_eval(u, t, n, 1, wp);
acb_sub(y, u, v, wp);
}
else
{
acb_add_ui(t, x, r, wp);
acb_gamma_stirling_eval(u, t, n, 1, wp);
acb_rising2_ui(y, t, x, r, wp);
acb_div(t, t, y, wp);
acb_sub(y, u, t, prec);
}
acb_clear(t);
acb_clear(u);
acb_clear(v);
}
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;
}
