/*
    Copyright (C) 2009 William Hart
    Copyright (C) 2010, 2013 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 2.1 of the License, or
    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
*/

#include <gmp.h>
#include "flint.h"
#include "ulong_extras.h"

extern const unsigned char FLINT_PRIME_PI_ODD_LOOKUP[];

void n_prime_pi_bounds(ulong *lo, ulong *hi, mp_limb_t n)
{
    if (n < FLINT_PRIME_PI_ODD_LOOKUP_CUTOFF)
    {
        if (n < 3)
            *lo = *hi = (n == 2);
        else
            *lo = *hi = FLINT_PRIME_PI_ODD_LOOKUP[(n-1)/2];
    }
    else
    {
        /* 14/10 < 1/log(2)*/
        *lo = (n / (10 * FLINT_CLOG2(n))) * 14;
        /* 19/10 > 1.25506/log(2) */
        *hi = (n / (10 * FLINT_FLOG2(n)) + 1) * 19;
    }
}