<?php
/******************************************************
* Prime number checking and generation
* @version 2.0
* Adapted from: Tzuly <tzulac@gmail.com> v1.0
* @author cpks
* @license Public Domain
* @package prime
*/
/**
* Set of prime numbers
*
* Outputs:
* - return whether a number is prime;
* - construct a list of prime numbers;
* - return biggest prime smaller than a number.
*
*************
* Use: *
*************
* - for finding if a number is prime: prime::is_prime($number);
* - for biggest prime number smaller than x:
* prime::smallerPrime($x);
* - for list of prime numbers smaller than x:
* $p = new prime($x);
* OR, using sieve of Eratosthenes:
* $e = new erato_prime($x);
* OR, using Atkin's sieve (a little slower):
* $a = new atkin_prime($x);
* OR, using sieve of Sundaram (uses half as much memory):
* $s = new sundaram_prime($x);
* @package prime
* @todo add an iterator to access the list and make primelist member private
*/
class prime {
/*
* @var int[] array contains list of prime numbers
*/
public $primelist = array();
/**
* return whether a number is prime
*
* @param int $number
* @return boolean
* @throws InvalidArgumentException
*/
static public function is_prime($number) {
if ($number < 2)
throw new InvalidArgumentException('Prime numbers start at 2.');
$number = (int)$number;
for ($i = 2; $i < floor(sqrt($number) + 1); ++$i) {
if (!($number % $i))
return FALSE;
}
return TRUE;
}
/**
* calculate biggest prime number smaller than $number
*
* @param int $number upper bound
* @return int
* @throws InvalidArgumentException
*/
static public function smallerPrime($number) {
if ($number <= 2)
throw new InvalidArgumentException('2 is smallest prime number');
for ($i = $number - 1; $i > 1; --$i)
if (self::is_prime($i)) return $i;
}
/**
* generate list of prime numbers, computed by calculating if every number
* from list is prime
*
* @param int $number upper bound
* @throws InvalidArgumentException
*/
private function generate($number) {
$this->primelist[] = 2;
$this->primelist[] = 3;
for ($i = 5; $i < $number; $i += 2) { // (BUG: was originally =+2)
if (self::is_prime($i)) $this->primelist[] = $i;
}
}
/**
* Construct as a list of primes up to number supplied
*
* Use the generate method for the class
* @param int $number upper bound
* @throws InvalidArgumentException if upper bound < 3
*/
public function __construct($number) {
if ($number <= 2)
throw new InvalidArgumentException('2 is smallest prime number');
$this->generate($number);
}
/**
* Compare with another instance
* @param prime $other
* @return bool TRUE if same
*/
public function same_as(prime $other) {
return $this->primelist == $other->primelist;
}
/**
* Dump to stdout for debug purposes
*/
public function dump() {
echo implode(',', $this->primelist) . PHP_EOL;
}
}
require_once 'bitvec.php';
/**
* Override generation to use the Eratosthenes sieve algorithm
* @package prime
*/
class erato_prime extends prime {
/**
* generate list of prime numbers, computed with Eratosthenes sieve algorithm
*
* @param int $number
*/
private function generate($number) {
$erat = new bitvec($number);
$erat->setall();
for ($i = 2; $i < $number; ++$i) {
if ($erat[$i]) {
for ($j = 2; $j * $i < $number; ++$j) $erat[$i * $j] = 0;
}
}
for ($i = 2; $i < $number; ++$i) {
if ($erat[$i]) $this->primelist[] = $i;
}
}
}
/**
* Override generation to use the Atkin sieve algorithm
* @package prime
*/
class atkin_prime extends prime {
/**
* generate list of prime numbers, computed with atkin sieve algorithm
*
* @param int $number
*/
private function generate($number) {
$atkin = new bitvec($number);
for ($i = 1; $i < sqrt($number); ++$i) {
for ($j = 1; $j < sqrt($number); ++$j) {
$x = 4 * $i * $i + $j * $j;
if ($x < $number && ($x % 12 == 1 || $x % 12 == 5))
$atkin[$x] = 1;
$x = 3 * $i * $i + $j * $j;
if ($x < $number && $x % 12 == 7)
$atkin[$x] = 1;
$x = 3 * $i * $i - $j * $j;
if ($i > $j && $x < $number && $x % 12 == 11)
$atkin[$x] = 1;
}
}
for ($i = 5; $i < sqrt($number); ++$i) {
$x = $i * $i;
$j = 1;
while ($j * $x < $number) {
$atkin[$j * $x] = 0;
++$j;
}
}
$atkin[2] = $atkin[3] = 1;
for ($i = 2; $i < $number; ++$i) {
if ($atkin[$i]) $this->primelist[] = $i;
}
}
}
/**
* Override generation to use the Sundaram sieve algorithm
* @package prime
*/
class sundaram_prime extends prime {
/**
* generate list of prime numbers, computed with Sundaram sieve algorithm
*
* @param int $number
*/
private function generate($number) {
$number >>= 1;
$sunda = new bitvec($number);
$sunda->setall();
for ($i = 1; $i < $number; ++$i) {
$denominator = ($i << 1) + 1;
$maxVal = ($number - $i) / $denominator;
for ($j = $i; $j < $maxVal; ++$j) $sunda[$i + $j * $denominator] = 0;
}
$this->primelist[] = 2;
for ($i = 1; $i < $number; ++$i) if ($sunda[$i]) $this->primelist[] = ($i << 1) + 1;
}
}
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