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