<?php

set_include_path(get_include_path().PATH_SEPARATOR.dirname(__FILE__).DIRECTORY_SEPARATOR.'libpy2php');
require_once 'libpy2php.php';
class PrimeModule
{
    public function __construct()
    {
        $this->smallprimeset = array_unique($this->primesbelow(100000));
        $this->_smallprimeset = 100000;
        $this->primesbelowtwo(10000);
        $this->smallprimes = $this->primesbelow(10000);
    }
    /*
def primesbelow(N):
    # http://stackoverflow.com/questions/2068372/fastest-way-to-list-all-primes-below-n-in-python/3035188#3035188
    #""" Input N>=6, Returns a list of primes, 2 <= p < N """
    correction = N % 6 > 1
    N = {0:N, 1:N-1, 2:N+4, 3:N+3, 4:N+2, 5:N+1}[N%6]
    sieve = [True] * (N // 3)
    sieve[0] = False
    for i in range(int(N ** .5) // 3 + 1):
        if sieve[i]:
            k = (3 * i + 1) | 1
            print(len(sieve[k*k // 3::2*k]))
            print(((N // 6 - (k*k)//6 - 1)//k +1))
            sieve[k*k // 3::2*k] = [False] * ((N//6 - (k*k)//6 - 1)//k + 1)
            sieve[(k*k + 4*k - 2*k*(i%2)) // 3::2*k] = [False] * ((N // 6 - (k*k + 4*k - 2*k*(i%2))//6 - 1) // k + 1)
    return [2, 3] + [(3 * i + 1) | 1 for i in range(1, N//3 - correction) if sieve[i]]
    */
    public function primesbelowtwo($N) {
        $correction = posmod($N, 6) > 1;
        $N = [$N, $N - 1, $N + 4, $N + 3, $N + 2, $N + 1][$N%6];
        $sieve = array_fill(0, floor($N/3), true);
        $sieve[0] = false;
        foreach (range(0, floor(floor(pow($N, 0.5)) / 3) + 1) as $i) {
            if($sieve[$i]) {
                $k = (3 * $i + 1) | 1;
                array_walk($sieve, function (&$val, $key, $range) { if(in_array($key, $range)) $val = false; }, pyjslib_range(floor(($k*$k) / 3), count($sieve), 2*$k));
                array_walk($sieve, function (&$val, $key, $range) { if(in_array($key, $range)) $val = false; }, pyjslib_range(floor((($k*$k) + (4*$k) - (2*$k*posmod($i, 2))) / 3), count($sieve), 2*$k));
            }
        }
        var_dump($sieve);
    }
    public function primesbelow($N)
    {
        $res = [];
        for ($i = 2; $i <= $N; $i++) {
            if ($i % 2 != 1 && $i != 2) {
                continue;
            }
            $d = 3;
            $x = sqrt($i);
            while ($i % $d != 0 && $d < $x) {
                $d += 2;
            }
            if ((($i % $d == 0 && $i != $d) * 1) == 0) {
                $res[] = $i;
            }
        }

        return $res;
    }

    public function isprime($n, $precision = 7)
    {
        if (($n == 1) || (($n % 2) == 0)) {
            return false;
        } elseif (($n < 1)) {
            throw new Exception('Out of bounds, first argument must be > 0');
        } elseif (($n < $this->_smallprimeset)) {
            return in_array($n, $this->smallprimeset);
        }
        $d = ($n - 1);
        $s = 0;
        while (($d % 2) == 0) {
            $d = floor($d / 2);
            $s += 1;
        }
        foreach (pyjslib_range($precision) as $repeat) {
            $a = rand(2, ($n - 2));
            $x = posmod(pow($a, $d), $n);
            if (($x == 1) || ($x == ($n - 1))) {
                continue;
            }
            foreach (pyjslib_range(($s - 1)) as $r) {
                $x = posmod(pow($x, 2), $n);
                if (($x == 1)) {
                    return false;
                }
                if (($x == ($n - 1))) {
                    break;
                }
            }
        }

        return true;
    }

    public function pollard_brent($n)
    {
        if ((($n % 2) == 0)) {
            return 2;
        }
        if ((($n % 3) == 0)) {
            return 3;
        }
        list($y, $c, $m) = [rand(1, ($n - 1)), rand(1, ($n - 1)), rand(1, ($n - 1))];
        list($g, $r, $q) = [1, 1, 1];
        while (($g == 1)) {
            $x = $y;
            foreach (pyjslib_range($r) as $i) {
                $y = ((posmod(pow($y, 2), $n) + $c) % $n);
            }
            $k = 0;
            while (($k < $r) && ($g == 1)) {
                $ys = $y;
                foreach (pyjslib_range(min($m, ($r - $k))) as $i) {
                    $y = ((posmod(pow($y, 2), $n) + $c) % $n);
                    $q = (($q * abs(($x - $y))) % $n);
                }
                $g = $this->gcd($q, $n);
                $k += $m;
            }
            $r *= 2;
        }
        if (($g == $n)) {
            while (true) {
                $ys = ((posmod(pow($ys, 2), $n) + $c) % $n);
                $g = $this->gcd(abs(($x - $ys)), $n);
                if (($g > 1)) {
                    break;
                }
            }
        }

        return $g;
    }

    public function primefactors($n, $sort = false)
    {
        $factors = [];
        $limit = ((int) (pow($n, 0.5)) + 1);
        foreach ($this->smallprimes as $checker) {
            if (($checker > $limit)) {
                break;
            }
            while (($n % $checker) == 0) {
                $factors[] = $checker;
                $n = floor($n / $checker);
                $limit = ((int) (pow($n, 0.5)) + 1);
                if (($checker > $limit)) {
                    break;
                }
            }
        }
        if (($n < 2)) {
            return $factors;
        }
        while (($n > 1)) {
            if ($this->isprime($n)) {
                $factors[] = $n;
                break;
            }
            $factor = $this->pollard_brent($n);
            $factors[] = $this->primefactors($factor);
            $n = floor($n / $factor);
        }
        if ($sort) {
            $factors = sort($factors);
        }

        return $factors;
    }

    public function factorization($n)
    {
        $factors = [];
        foreach (primefactors($n) as $p1) {
            if (isset($factors[$p1])) {
                $factors[$p1] += 1;
            } else {
                $factors[$p1] = 1;
            }
        }

        return $factors;
    }

    public function totient($n)
    {
        $totients = [];
        if (($n == 0)) {
            return 1;
        }
        if (isset($totients[$n])) {
            return $totients[$n];
        }
        $tot = 1;
        foreach (factorization($n) as $p => $exp) {
            $tot *= (($p - 1) * pow($p, ($exp - 1)));
        }
        $totients[$n] = $tot;

        return $tot;
    }

    public function gcd($a, $b)
    {
        if (($a == $b)) {
            return $a;
        }
        while (($b > 0)) {
            list($a, $b) = [$b, ($a % $b)];
        }

        return $a;
    }

    public function lcm($a, $b)
    {
        return floor(abs(($a * $b)) / $this->gcd($a, $b));
    }

/*
function pqPrimeLeemon ($what) {
  $minBits = 64;
  $minLen = ceil($minBits / $bpe) + 1;
  $it = 0
  $a = new Array(minLen)
  $b = new Array(minLen)
  $c = new Array(minLen)
  $g = new Array(minLen)
  $z = new Array(minLen)
  $x = new Array(minLen)
  $y = new Array(minLen)

  for ($i = 0; $i < 3; $i++) {
    $q = (nextRandomInt(128) & 15) + 17
    copyInt_(x, nextRandomInt(1000000000) + 1)
    copy_(y, x)
    lim = 1 << (i + 18)

    for (j = 1; j < lim; j++) {
      ++it
      copy_(a, x)
      copy_(b, x)
      copyInt_(c, q)

      while (!isZero(b)) {
        if (b[0] & 1) {
          add_(c, a)
          if (greater(c, what)) {
            sub_(c, what)
          }
        }
        add_(a, a)
        if (greater(a, what)) {
          sub_(a, what)
        }
        rightShift_(b, 1)
      }

      copy_(x, c)
      if (greater(x, y)) {
        copy_(z, x)
        sub_(z, y)
      } else {
        copy_(z, y)
        sub_(z, x)
      }
      eGCD_(z, what, g, a, b)
      if (!equalsInt(g, 1)) {
        break
      }
      if ((j & (j - 1)) == 0) {
        copy_(y, x)
      }
    }
    if (greater(g, one)) {
      break
    }
  }

  divide_(what, g, x, y)

  if (greater(g, x)) {
    P = x
    Q = g
  } else {
    P = g
    Q = x
  }

  // console.log(dT(), 'done', bigInt2str(what, 10), bigInt2str(P, 10), bigInt2str(Q, 10))

  return [bytesFromLeemonBigInt(P), bytesFromLeemonBigInt(Q), it]
}*/
}