MadelineProto/prime.php
danogentili 2b31699ffd update
2016-07-20 20:23:26 +02:00

277 lines
6.6 KiB
PHP

<?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->smallprimes = $this->primesbelow(10000);
}
public function primesbelow($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++;
}
$break = false;
foreach (pyjslib_range($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))) {
$break = true;
}
}
if(!$break) return false;
}
return true;
}
public function pollard_brent($n)
{
if ((($n % 2) == 0)) {
return 2;
}
if ((($n % 3) == 0)) {
return 3;
}
$big = new \phpseclib\Math\BigInteger();
$max = new \phpseclib\Math\BigInteger($n - 1);
$min = new \phpseclib\Math\BigInteger(1);
list($y, $c, $m) = [(int)$big->random($min, $max)->toString(), (int)$big->random($min, $max)->toString(), (int)$big->random($min, $max)->toString()];
list($g, $r, $q) = [1, 1, 1];
while ($g == 1) {
$x = $y;
foreach (pyjslib_range($r) as $i) {
$y = posmod((posmod(pow($y, 2), $n) + $c), $n);
}
$k = 0;
while (($k < $r) && ($g == 1)) {
$ys = $y;
foreach (pyjslib_range(min($m, ($r - $k))) as $i) {
$y = posmod((posmod(pow($y, 2), $n) + $c), $n);
$q = posmod(($q * abs($x - $y)), $n);
}
$g = $this->gcd($q, $n);
$k += $m;
}
$r *= 2;
}
if (($g == $n)) {
while (true) {
$ys = posmod((posmod(pow($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, posmod($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]
}*/
}