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/*
Copyright (C) 2014 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 "mag.h"
void
mag_exp_tail(mag_t z, const mag_t x, ulong N)
{
if (N == 0 || mag_is_inf(x))
{
mag_exp(z, x);
}
else if (mag_is_zero(x))
{
mag_zero(z);
}
else
{
mag_t t;
mag_init(t);
mag_set_ui_2exp_si(t, N, -1);
/* bound by geometric series when N >= 2*x <=> N/2 >= x */
if (mag_cmp(t, x) >= 0)
{
/* 2 c^N / N! */
mag_pow_ui(t, x, N);
mag_rfac_ui(z, N);
mag_mul(z, z, t);
mag_mul_2exp_si(z, z, 1);
}
else
{
mag_exp(z, x);
}
mag_clear(t);
}
}