void
fmpz_poly_evaluate_horner_fmpz(fmpz_t res, const fmpz_poly_t f, const fmpz_t a)
{
if (res == a)
{
fmpz_t t;
fmpz_init(t);
_fmpz_poly_evaluate_horner_fmpz(t, f->coeffs, f->length, a);
fmpz_swap(res, t);
fmpz_clear(t);
}
else
_fmpz_poly_evaluate_horner_fmpz(res, f->coeffs, f->length, a);
}
void
_fmpz_poly_evaluate_fmpz(fmpz_t res, const fmpz * f, long len, const fmpz_t a)
{
if (len <= 50)
_fmpz_poly_evaluate_horner_fmpz(res, f, len, a);
else
_fmpz_poly_evaluate_divconquer_fmpz(res, f, len, a);
}
void
gamma_rising_fmprb_ui_delta(fmprb_t y, const fmprb_t x, ulong n, ulong m, long prec)
{
fmprb_ptr xs;
fmprb_t t, u, v;
ulong i, k, rem;
fmpz_t c, h;
fmpz *s, *d;
long wp;
if (n == 0)
{
fmprb_one(y);
return;
}
if (n == 1)
{
fmprb_set_round(y, x, prec);
return;
}
wp = FMPR_PREC_ADD(prec, FLINT_BIT_COUNT(n));
fmprb_init(t);
fmprb_init(u);
fmprb_init(v);
fmpz_init(c);
fmpz_init(h);
if (m == 0)
{
ulong m1, m2;
m1 = 0.2 * pow(wp, 0.4);
m2 = n_sqrt(n);
m = FLINT_MIN(m1, m2);
}
m = FLINT_MIN(m, n);
m = FLINT_MAX(m, 1);
xs = _fmprb_vec_init(m + 1);
d = _fmpz_vec_init(m * m);
s = _fmpz_vec_init(m + 1);
_fmprb_vec_set_powers(xs, x, m + 1, wp);
rising_difference_polynomial(s, d, m);
/* tail */
rem = m;
while (rem + m <= n)
rem += m;
fmprb_one(y);
for (k = rem; k < n; k++)
{
fmprb_add_ui(t, xs + 1, k, wp);
fmprb_mul(y, y, t, wp);
}
/* initial rising factorial */
fmprb_zero(t);
for (i = 1; i <= m; i++)
fmprb_addmul_fmpz(t, xs + i, s + i, wp);
fmprb_mul(y, y, t, wp);
/* the leading coefficient is always the same */
fmprb_mul_fmpz(xs + m - 1, xs + m - 1, d + m - 1 + 0, wp);
for (k = 0; k + 2 * m <= n; k += m)
{
for (i = 0; i < m - 1; i++)
{
fmpz_set_ui(h, k);
_fmpz_poly_evaluate_horner_fmpz(c, d + i * m, m - i, h);
if (i == 0)
fmprb_add_fmpz(t, t, c, wp);
else
fmprb_addmul_fmpz(t, xs + i, c, wp);
}
fmprb_add(t, t, xs + m - 1, wp);
fmprb_mul(y, y, t, wp);
}
fmprb_set_round(y, y, prec);
fmprb_clear(t);
fmprb_clear(u);
fmprb_clear(v);
_fmprb_vec_clear(xs, m + 1);
_fmpz_vec_clear(d, m * m);
_fmpz_vec_clear(s, m + 1);
fmpz_clear(c);
fmpz_clear(h);
}
