void
_acb_hypgeom_m_1f1(acb_t res, const acb_t a, const acb_t b, const acb_t z,
int regularized, slong prec, slong gamma_prec, int kummer)
{
if (regularized)
{
/* Remove singularity */
if (acb_is_int(b) && arb_is_nonpositive(acb_realref(b)) &&
arf_cmpabs_2exp_si(arb_midref(acb_realref(b)), 30) < 0)
{
acb_t c, d, t, u;
slong n;
n = arf_get_si(arb_midref(acb_realref(b)), ARF_RND_DOWN);
acb_init(c);
acb_init(d);
acb_init(t);
acb_init(u);
acb_sub(c, a, b, prec);
acb_add_ui(c, c, 1, prec);
acb_neg(d, b);
acb_add_ui(d, d, 2, prec);
_acb_hypgeom_m_1f1(t, c, d, z, 0, prec, gamma_prec, kummer);
acb_pow_ui(u, z, 1 - n, prec);
acb_mul(t, t, u, prec);
acb_rising_ui(u, a, 1 - n, prec);
acb_mul(t, t, u, prec);
arb_fac_ui(acb_realref(u), 1 - n, prec);
acb_div_arb(res, t, acb_realref(u), prec);
acb_clear(c);
acb_clear(d);
acb_clear(t);
acb_clear(u);
}
else
{
acb_t t;
acb_init(t);
acb_rgamma(t, b, gamma_prec);
_acb_hypgeom_m_1f1(res, a, b, z, 0, prec, gamma_prec, kummer);
acb_mul(res, res, t, prec);
acb_clear(t);
}
return;
}
/* Kummer's transformation */
if (kummer)
{
acb_t u, v;
acb_init(u);
acb_init(v);
acb_sub(u, b, a, prec);
acb_neg(v, z);
_acb_hypgeom_m_1f1(u, u, b, v, regularized, prec, gamma_prec, 0);
acb_exp(v, z, prec);
acb_mul(res, u, v, prec);
acb_clear(u);
acb_clear(v);
return;
}
if (acb_is_one(a))
{
acb_hypgeom_pfq_direct(res, NULL, 0, b, 1, z, -1, prec);
}
else
{
acb_struct c[3];
c[0] = *a;
c[1] = *b;
acb_init(c + 2);
acb_one(c + 2);
acb_hypgeom_pfq_direct(res, c, 1, c + 1, 2, z, -1, prec);
acb_clear(c + 2);
}
}
void
acb_hypgeom_m(acb_t res, const acb_t a, const acb_t b, const acb_t z, int regularized, long prec)
{
long m = LONG_MAX;
long n = LONG_MAX;
if (acb_is_int(a) &&
arf_cmpabs_2exp_si(arb_midref(acb_realref(a)), 30) < 0)
{
m = arf_get_si(arb_midref(acb_realref(a)), ARF_RND_DOWN);
}
if (acb_is_int(b) &&
arf_cmpabs_2exp_si(arb_midref(acb_realref(b)), 30) < 0)
{
n = arf_get_si(arb_midref(acb_realref(b)), ARF_RND_DOWN);
}
/* terminating */
if (m <= 0 && m < n && m > -10 * prec && (n > 0 || !regularized))
{
acb_hypgeom_m_1f1(res, a, b, z, regularized, prec);
return;
}
/* large */
if (acb_hypgeom_u_use_asymp(z, prec))
{
acb_hypgeom_m_asymp(res, a, b, z, regularized, prec);
return;
}
/* remove singularity */
if (n <= 0 && n > -10 * prec && regularized)
{
acb_t c, d, t, u;
acb_init(c);
acb_init(d);
acb_init(t);
acb_init(u);
acb_sub(c, a, b, prec);
acb_add_ui(c, c, 1, prec);
acb_neg(d, b);
acb_add_ui(d, d, 2, prec);
acb_hypgeom_m_1f1(t, c, d, z, 0, prec);
acb_pow_ui(u, z, 1 - n, prec);
acb_mul(t, t, u, prec);
acb_rising_ui(u, a, 1 - n, prec);
acb_mul(t, t, u, prec);
arb_fac_ui(acb_realref(u), 1 - n, prec);
acb_div_arb(res, t, acb_realref(u), prec);
acb_clear(c);
acb_clear(d);
acb_clear(t);
acb_clear(u);
}
else
{
acb_hypgeom_m_1f1(res, a, b, z, regularized, prec);
}
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("rising_ui....");
fflush(stdout);
flint_randinit(state);
/* check functional equation */
for (iter = 0; iter < 1000; iter++)
{
acb_t x, xn, y, z;
ulong n, m;
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));
acb_rising_ui(y, x, n, 2 + n_randint(state, 4000));
acb_rising_ui(z, xn, m, 2 + n_randint(state, 4000));
acb_mul(y, y, z, 2 + n_randint(state, 4000));
acb_rising_ui(z, x, n + m, 2 + n_randint(state, 4000));
if (!acb_overlaps(y, z))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("n = %wu\n", n);
flint_printf("m = %wu\n", m);
flint_printf("x = "); acb_print(x); flint_printf("\n\n");
flint_printf("xn = "); acb_print(xn); flint_printf("\n\n");
flint_printf("y = "); acb_print(y); flint_printf("\n\n");
flint_printf("z = "); acb_print(z); flint_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;
slong prec;
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);
prec = 2 + n_randint(state, 4000);
acb_rising_ui(y, x, n, prec);
acb_rising_ui(x, x, n, prec);
if (!acb_equal(x, y))
{
flint_printf("FAIL: aliasing\n\n");
flint_printf("x = "); acb_print(x); flint_printf("\n\n");
flint_printf("y = "); acb_print(y); flint_printf("\n\n");
flint_printf("n = %wu\n", n);
abort();
}
acb_clear(x);
acb_clear(y);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
