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/*=============================================================================
This file is part of FLINT.
FLINT is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License,or
(at your option) any later version.
FLINT is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with FLINT; if not,write to the Free Software
Foundation,Inc.,51 Franklin St,Fifth Floor,Boston,MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2010 Fredrik Johansson
******************************************************************************/
#include <gmp.h>
#include "flint.h"
#include "ulong_extras.h"
void n_nth_prime_bounds(mp_limb_t *lo, mp_limb_t *hi, ulong n)
{
int bits, ll;
double llo, lhi;
/* Lower and upper bounds for ln(n) */
bits = FLINT_BIT_COUNT(n);
llo = (bits-1) * 0.6931471;
lhi = bits * 0.6931472;
/* Lower bound for ln(ln(n)) */
if (n < 16) ll = 0;
else if (n < 1619) ll = 1;
else if (n < 528491312) ll = 2;
else ll = 3;
*lo = (mp_limb_t) (n * (llo + ll - 1));
*hi = (mp_limb_t) (n * (lhi + (ll+1) - (n >= 15985 ? 0.9427 : 0.0)));
}
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