void
acb_hypgeom_pfq_sum_bs_invz(acb_t s, acb_t t,
acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong n, slong prec)
{
acb_t u, v, w;
if (n < 4)
{
acb_init(u);
acb_inv(u, z, prec);
acb_hypgeom_pfq_sum_forward(s, t, a, p, b, q, u, n, prec);
acb_clear(u);
return;
}
acb_init(u);
acb_init(v);
acb_init(w);
bsplit(u, v, w, a, p, b, q, z, 0, n, prec, 1);
acb_div(t, u, w, prec);
acb_div(s, v, w, prec);
acb_clear(u);
acb_clear(v);
acb_clear(w);
}
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;
}
void
acb_hypgeom_pfq_sum_fme(acb_t s, acb_t t,
acb_srcptr a, slong p, acb_srcptr b, slong q,
const acb_t z, slong n, slong prec)
{
acb_poly_t A, B, C;
acb_ptr ks, As, Bs, Cs;
acb_t u, v;
acb_ptr * tree;
slong i, k, m, w;
/* we compute to n-1 instead of n to avoid dividing by 0 in the
denominator when computing a hypergeometric polynomial
that terminates right before a pole */
if (n > 4)
{
m = n_sqrt(n - 1) / 4; /* tuning parameter */
w = (n - 1) / FLINT_MAX(m, 1);
}
else
{
m = w = 0;
}
if (m < 1 || w < 1 || p > 3 || q > 3)
{
acb_hypgeom_pfq_sum_forward(s, t, a, p, b, q, z, n, prec);
return;
}
acb_poly_init(A);
acb_poly_init(B);
acb_poly_init(C);
acb_init(u);
acb_init(v);
ks = _acb_vec_init(w);
As = _acb_vec_init(w);
Bs = _acb_vec_init(w);
Cs = _acb_vec_init(w);
bsplit(A, B, C, a, p, b, q, z, 0, m, prec);
for (i = 0; i < w; i++)
acb_set_ui(ks + i, i * m);
tree = _acb_poly_tree_alloc(w);
_acb_poly_tree_build(tree, ks, w, prec);
_acb_poly_evaluate_vec_fast_precomp(As, A->coeffs, A->length, tree, w, prec);
_acb_poly_evaluate_vec_fast_precomp(Bs, B->coeffs, B->length, tree, w, prec);
_acb_poly_evaluate_vec_fast_precomp(Cs, C->coeffs, C->length, tree, w, prec);
_acb_poly_tree_free(tree, w);
/* todo: use binary splitting here for improved numerical stability */
for (i = 1; i < w; i++)
{
acb_mul(Cs, Cs, Bs + i, prec);
acb_addmul(Cs, As, Cs + i, prec);
acb_mul(As, As, As + i, prec);
acb_mul(Bs, Bs, Bs + i, prec);
}
acb_div(s, Cs, Bs, prec);
acb_div(t, As, Bs, prec);
for (k = w * m; k < n && !acb_is_zero(t); k++)
{
acb_add(s, s, t, prec);
if (p > 0)
{
acb_add_ui(u, a, k, prec);
for (i = 1; i < p; i++)
{
acb_add_ui(v, a + i, k, prec);
acb_mul(u, u, v, prec);
}
acb_mul(t, t, u, prec);
}
if (q > 0)
{
acb_add_ui(u, b, k, prec);
for (i = 1; i < q; i++)
{
acb_add_ui(v, b + i, k, prec);
acb_mul(u, u, v, prec);
}
acb_div(t, t, u, prec);
}
acb_mul(t, t, z, prec);
}
acb_clear(u);
acb_clear(v);
_acb_vec_clear(ks, w);
_acb_vec_clear(As, w);
_acb_vec_clear(Bs, w);
_acb_vec_clear(Cs, w);
acb_poly_clear(A);
acb_poly_clear(B);
acb_poly_clear(C);
}
