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/*
Copyright (C) 2012, 2016 Fredrik Johansson
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include <math.h>
#include "arith.h"
#include "arb.h"
/* The constant factor is nearly optimal up to at least 300000 bits. */
static double
euler_product_cutoff(double prec)
{
if (prec > 200 && prec < 15000) /* This range has a slight "bulge". */
return 0.39 * pow(prec, 0.8);
else
return 7 + 0.535 * prec / log(prec);
}
void
arb_zeta_ui(arb_t x, ulong n, slong prec)
{
if (n == 0)
{
arb_set_si(x, -1);
arb_mul_2exp_si(x, x, -1);
}
else if (n == 1)
{
arb_indeterminate(x);
}
/* fast detection of asymptotic case */
else if (n > 0.7 * prec)
{
arb_zeta_ui_asymp(x, n, prec);
}
else
{
/* even */
if (n % 2 == 0)
{
if (((prec < 10000) && (n < 40 + 0.11*prec)) ||
((prec >= 10000) && (arith_bernoulli_number_size(n) * 0.9 < prec)))
{
arb_zeta_ui_bernoulli(x, n, prec);
}
else
{
arb_zeta_ui_euler_product(x, n, prec);
}
}
else
{
if (n == 3)
{
arb_const_apery(x, prec);
}
else if (n < prec * 0.0006)
{
/* small odd n, extremely high precision */
arb_zeta_ui_borwein_bsplit(x, n, prec);
}
else if (n > euler_product_cutoff(prec))
{
/* large n */
arb_zeta_ui_euler_product(x, n, prec);
}
else
{
/* fallback */
arb_zeta_ui_vec_borwein(x, n, 1, 0, prec);
}
}
}
}