50 lines
1.7 KiB
C
50 lines
1.7 KiB
C
/*=============================================================================
|
|
|
|
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)));
|
|
}
|