mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
99 lines
2 KiB
C
99 lines
2 KiB
C
/*
|
|
Copyright (C) 2014 Fredrik Johansson
|
|
|
|
This file is part of Arb.
|
|
|
|
Arb 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 2.1 of the License, or
|
|
(at your option) any later version. See <http://www.gnu.org/licenses/>.
|
|
*/
|
|
|
|
#include "mag.h"
|
|
|
|
void
|
|
mag_polylog_tail(mag_t u, const mag_t z, slong sigma, ulong d, ulong N)
|
|
{
|
|
mag_t TN, UN, t;
|
|
|
|
if (N < 2)
|
|
{
|
|
mag_inf(u);
|
|
return;
|
|
}
|
|
|
|
mag_init(TN);
|
|
mag_init(UN);
|
|
mag_init(t);
|
|
|
|
if (mag_cmp_2exp_si(z, 0) >= 0)
|
|
{
|
|
mag_inf(u);
|
|
}
|
|
else
|
|
{
|
|
/* Bound T(N) */
|
|
mag_pow_ui(TN, z, N);
|
|
|
|
/* multiply by log(N)^d */
|
|
if (d > 0)
|
|
{
|
|
mag_log_ui(t, N);
|
|
mag_pow_ui(t, t, d);
|
|
mag_mul(TN, TN, t);
|
|
}
|
|
|
|
/* multiply by 1/k^s */
|
|
if (sigma > 0)
|
|
{
|
|
mag_set_ui_lower(t, N);
|
|
mag_pow_ui_lower(t, t, sigma);
|
|
mag_div(TN, TN, t);
|
|
}
|
|
else if (sigma < 0)
|
|
{
|
|
mag_set_ui(t, N);
|
|
mag_pow_ui(t, t, -sigma);
|
|
mag_mul(TN, TN, t);
|
|
}
|
|
|
|
/* Bound U(N) */
|
|
mag_set(UN, z);
|
|
|
|
/* multiply by (1 + 1/N)**S */
|
|
if (sigma < 0)
|
|
{
|
|
mag_binpow_uiui(t, N, -sigma);
|
|
mag_mul(UN, UN, t);
|
|
}
|
|
|
|
/* multiply by (1 + 1/(N log(N)))^d */
|
|
if (d > 0)
|
|
{
|
|
ulong nl;
|
|
|
|
/* rounds down */
|
|
nl = mag_d_log_lower_bound(N) * N * (1 - 1e-13);
|
|
|
|
mag_binpow_uiui(t, nl, d);
|
|
mag_mul(UN, UN, t);
|
|
}
|
|
|
|
/* T(N) / (1 - U(N)) */
|
|
if (mag_cmp_2exp_si(UN, 0) >= 0)
|
|
{
|
|
mag_inf(u);
|
|
}
|
|
else
|
|
{
|
|
mag_one(t);
|
|
mag_sub_lower(t, t, UN);
|
|
mag_div(u, TN, t);
|
|
}
|
|
}
|
|
|
|
mag_clear(TN);
|
|
mag_clear(UN);
|
|
mag_clear(t);
|
|
}
|
|
|