/*
    Copyright (C) 2009 Thomas Boothby
    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/>.
*/

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

int n_is_perfect_power235(mp_limb_t n)
{
    static unsigned char mod63[63] = {7,7,4,0,5,4,0,5,6,5,4,4,0,4,4,0,5,4,5,4,
                              4,0,5,4,0,5,4,6,7,4,0,4,4,0,4,6,7,5,4,0,4,4,0,5,
                              4,4,5,4,0,5,4,0,4,4,4,6,4,0,5,4,0,4,6};
    static unsigned char mod61[61] = {7,7,0,3,1,1,0,0,2,3,0,6,1,5,5,1,1,0,0,1,
                              3,4,1,2,2,1,0,3,2,4,0,0,4,2,3,0,1,2,2,1,4,3,1,0,
                              0,1,1,5,5,1,6,0,3,2,0,0,1,1,3,0,7};
    static unsigned char mod44[44] = {7,7,0,2,3,3,0,2,2,3,0,6,7,2,0,2,3,2,0,2,
                              3,6,0,6,2,3,0,2,2,2,0,2,6,7,0,2,3,3,0,2,2,2,0,6};
    static unsigned char mod31[31] = {7,7,3,0,3,5,4,1,3,1,1,0,0,0,1,2,3,0,1,1,
                              1,0,0,2,0,5,4,2,1,2,6};

    unsigned char t;
    
    t = mod31[n%31];
    if (!t) return 0;

    t &= mod44[n%44];
    if (!t) return 0;

    t &= mod61[n%61];
    if (!t) return 0;

    t &= mod63[n%63];
    
    if (t & 1) 
    {
        double x = sqrt((double) n);
        mp_limb_t y = (mp_limb_t) (x + 0.5);
        if (n == n_pow(y, 2)) return 1;
    }

    if (t & 2) 
    {
        double x = pow((double) n, 1.0 / 3.0);
        mp_limb_t y = (mp_limb_t) (x + 0.5);
        if (n == n_pow(y, 3)) return 1;
    }

    if (t & 4) 
    {
        double x = pow((double) n, 1.0 / 5.0);
        mp_limb_t y = (mp_limb_t) (x + 0.5);
        if (n == n_pow(y, 5)) return 1;
    }

    return 0;
}