/*
    Copyright (C) 2009 William Hart

    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/>.
*/

#define ulong ulongxx /* interferes with system includes */
#include <stdlib.h>
#include <stdio.h>
#undef ulong
#include <gmp.h>
#include "flint.h"
#include "ulong_extras.h"

mp_limb_t flint_pseudosquares[] = {17, 73, 241, 1009, 2641, 8089, 18001, 
          53881, 87481, 117049, 515761, 1083289, 3206641, 3818929, 9257329, 
          22000801, 48473881, 48473881, 175244281, 427733329, 427733329, 
          898716289u, 2805544681u, 2805544681u, 2805544681u
#ifndef FLINT64          
          };
#else
          , 10310263441u, 23616331489u, 85157610409u, 85157610409u, 
          196265095009u, 196265095009u, 2871842842801u, 2871842842801u, 
          2871842842801u, 26250887023729u, 26250887023729u, 112434732901969u, 
          112434732901969u, 112434732901969u, 178936222537081u, 
          178936222537081u, 696161110209049u, 696161110209049u,
          2854909648103881u, 6450045516630769u, 6450045516630769u, 
          11641399247947921u, 11641399247947921u, 190621428905186449u,
          196640248121928601u, 712624335095093521u, 1773855791877850321u };
#endif

#if FLINT64
#define FLINT_NUM_PSEUDOSQUARES 52
#else
#define FLINT_NUM_PSEUDOSQUARES 25
#endif

int n_is_prime_pseudosquare(mp_limb_t n)
{
    unsigned int i, j, m1;
    mp_limb_t p, B, NB, exp, mod8;
    const mp_limb_t * primes;
    const double * inverses;

    if (n < UWORD(2)) return 0;

    if ((n & UWORD(1)) == UWORD(0))
    {
        return (n == UWORD(2));
    }

    primes = n_primes_arr_readonly(FLINT_PSEUDOSQUARES_CUTOFF+1);
    inverses = n_prime_inverses_arr_readonly(FLINT_PSEUDOSQUARES_CUTOFF+1);

    for (i = 0; i < FLINT_PSEUDOSQUARES_CUTOFF; i++)
    {
        double ppre;
        p = primes[i];
        if (p*p > n) return 1;
        ppre = inverses[i];
        if (!n_mod2_precomp(n, p, ppre)) return 0;
    }

    B  = primes[FLINT_PSEUDOSQUARES_CUTOFF];
    NB = (n - 1)/B + 1;
    m1 = 0;

    for (i = 0; i < FLINT_NUM_PSEUDOSQUARES; i++)
    {
        if (flint_pseudosquares[i] > NB) break;
    }

    exp = (n - 1)/2;

    for (j = 0; j <= i; j++)
    {
        mp_limb_t mod = n_powmod2(primes[j], exp, n);
        if ((mod != UWORD(1)) && (mod != n - 1)) return 0;
        if (mod == n - 1) m1 = 1;
    }

    mod8 = n % 8;

    if ((mod8 == 3) || (mod8 == 7)) return 1;

    if (mod8 == 5)
    {
        mp_limb_t mod = n_powmod2(UWORD(2), exp, n);
        if (mod == n - 1) return 1;
        flint_printf("Whoah, %wu is a probable prime, but not prime, please report!!\n", n);
        flint_abort();
    }
    else
    {
        if (m1) return 1;
        for (j = i + 1; j < FLINT_NUM_PSEUDOSQUARES + 1; j++)
        {
            mp_limb_t mod = n_powmod2(primes[j], exp, n);
            if (mod == n - 1) return 1;
            if (mod != 1)
            {
                flint_printf("Whoah, %wu is a probable prime, but not prime, please report!!\n", n);
                flint_abort();
            }
        }
        flint_printf("Whoah, %wu is a probable prime, but not prime, please report!!\n", n);
        flint_abort();
    }

    return 0;  /* not reached, but silence the compiler */
}