1 /*
2     Copyright (C) 2010 Fredrik Johansson
3 
4     This file is part of FLINT.
5 
6     FLINT is free software: you can redistribute it and/or modify it under
7     the terms of the GNU Lesser General Public License (LGPL) as published
8     by the Free Software Foundation; either version 2.1 of the License, or
9     (at your option) any later version.  See <http://www.gnu.org/licenses/>.
10 */
11 
12 #include <gmp.h>
13 #include "flint.h"
14 #include "ulong_extras.h"
15 
16 
n_nth_prime_bounds(mp_limb_t * lo,mp_limb_t * hi,ulong n)17 void n_nth_prime_bounds(mp_limb_t *lo, mp_limb_t *hi, ulong n)
18 {
19     int bits, ll;
20     double llo, lhi;
21 
22     /* Lower and upper bounds for ln(n) */
23     bits = FLINT_BIT_COUNT(n);
24     llo = (bits-1) * 0.6931471;
25     lhi = bits * 0.6931472;
26 
27     /* Lower bound for ln(ln(n)) */
28     if      (n < 16)        ll = 0;
29     else if (n < 1619)      ll = 1;
30     else if (n < 528491312) ll = 2;
31     else                    ll = 3;
32 
33     *lo = (mp_limb_t) (n * (llo + ll - 1));
34     *hi = (mp_limb_t) (n * (lhi + (ll+1) - (n >= 15985 ? 0.9427 : 0.0)));
35 }
36