292 lines
7.8 KiB
PHP
292 lines
7.8 KiB
PHP
<?php
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set_include_path(get_include_path().PATH_SEPARATOR.dirname(__FILE__).DIRECTORY_SEPARATOR.'libpy2php');
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require_once 'libpy2php.php';
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class PrimeModule
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{
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public function __construct()
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{
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$this->smallprimeset = array_unique($this->primesbelow(100000));
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$this->_smallprimeset = 100000;
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$this->smallprimes = $this->primesbelow(10000);
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}
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public function primesbelow($N)
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{
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$res = [];
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for ($i = 2; $i <= $N; $i++) {
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if ($i % 2 != 1 && $i != 2) {
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continue;
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}
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$d = 3;
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$x = sqrt($i);
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while ($i % $d != 0 && $d < $x) {
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$d += 2;
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}
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if ((($i % $d == 0 && $i != $d) * 1) == 0) {
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$res[] = $i;
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}
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}
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return $res;
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}
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public function isprime($n, $precision = 7)
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{
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if (($n == 1) || (($n % 2) == 0)) {
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return false;
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} elseif (($n < 1)) {
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throw new Exception('Out of bounds, first argument must be > 0');
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} elseif (($n < $this->_smallprimeset)) {
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return in_array($n, $this->smallprimeset);
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}
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$d = ($n - 1);
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$s = 0;
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while (($d % 2) == 0) {
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$d = floor($d / 2);
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$s++;
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}
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$break = false;
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foreach (pyjslib_range($precision) as $repeat) {
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$a = rand(2, ($n - 2));
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$x = posmod(pow($a, $d), $n);
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if (($x == 1) || ($x == ($n - 1))) {
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continue;
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}
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foreach (pyjslib_range($s - 1) as $r) {
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$x = posmod(pow($x, 2), $n);
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if (($x == 1)) {
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return false;
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}
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if (($x == ($n - 1))) {
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$break = true;
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}
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}
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if (!$break) {
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return false;
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}
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}
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return true;
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}
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public function pollard_brent($n)
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{
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$zero = new \phpseclib\Math\BigInteger(0);
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$one = new \phpseclib\Math\BigInteger(1);
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$two = new \phpseclib\Math\BigInteger(2);
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$three = new \phpseclib\Math\BigInteger(3);
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if ($n->powMod($one, $two)->toString() == '0') {
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return 2;
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}
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if ($n->powMod($one, $three)->toString() == '0') {
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return 3;
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}
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$big = new \phpseclib\Math\BigInteger();
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$max = $n->subtract($one);
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list($y, $c, $m) = [new \phpseclib\Math\BigInteger(87552211475113995), new \phpseclib\Math\BigInteger(330422027228888537), new \phpseclib\Math\BigInteger(226866727920975483)];
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//[$big->random($one, $max), $big->random($one, $max), $big->random($one, $max)];
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list($g, $r, $q) = [$one, $one, $one];
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while ($g->equals($one)) {
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$x = $y;
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$params = ["y" => $y, "two" => $two, "c" => $c, "one" => $one, "n" => $n];
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$r->loopforeach(function ($i, $params) {
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$params["y"] = $params["y"]->powMod($params["two"], $params["n"])->add($params["c"])->powMod($params["one"], $params["n"]);
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}, $params);
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each($params);
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$k = $zero;
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while ($k->compare($r) == -1 && $g->equals($one)) {
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$ys = $y;
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$params = ["x" => $x, "y" => $y, "two" => $two, "c" => $c, "one" => $one, "n" => $n, "q" => $q];
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$m->min($r->subtract($k))->loopforeach(function ($i, $params) {
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$params["y"] = $params["y"]->powMod($params["two"], $params["n"])->add($params["c"])->powMod($params["one"], $params["n"]);
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$params["q"] = $params["q"]->multiply($params["x"]->subtract($params["y"])->abs())->powMod($params["one"], $params["n"]);
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}, $params);
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each($params);
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$g = $q->gcd($n);
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$k = $k->add($m);
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}
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$r = $r->multiply($two);
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}
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die;
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if ($g->equals($n)) {
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while (true) {
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$ys = $ys->powMod($two, $n)->add($c)->powMod($one, $n);
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$g = $x->subtract($ys)->abs()->gcd($n);
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if ($g->compare($one) == 1) {
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break;
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}
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}
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}
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return $g;
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}
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public function primefactors($n, $sort = false)
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{
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$factors = [];
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$n = new \phpseclib\Math\BigInteger(1724114033281923457);
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$one = new \phpseclib\Math\BigInteger(1);
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$two = new \phpseclib\Math\BigInteger(2);
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$limit = $n->root()->add($one);
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foreach ($this->smallprimes as $checker) {
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$checker = new \phpseclib\Math\BigInteger($checker);
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if ($limit->compare($checker) == -1) {
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break;
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}
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while ($n->modPow($one, $checker)->toString() == '0') {
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$factors[] = $checker;
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$n = $n->divide($checker)[0];
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$limit = $n->root()->add($one);
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if ($limit->compare($checker) == -1) {
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break;
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}
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}
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}
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if ($n->compare($two) == -1) {
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return $factors;
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}
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while ($n->compare($two) == 1) {
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if ($n->isprime()) {
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$factors[] = $n;
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break;
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}
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$factor = $this->pollard_brent($n);
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$factors[] = $this->primefactors($factor);
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$n = floor($n / $factor);
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}
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if ($sort) {
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$factors = sort($factors);
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}
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return $factors;
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}
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public function factorization($n)
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{
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$factors = [];
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foreach (primefactors($n) as $p1) {
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if (isset($factors[$p1])) {
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$factors[$p1] += 1;
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} else {
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$factors[$p1] = 1;
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}
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}
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return $factors;
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}
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public function totient($n)
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{
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$totients = [];
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if (($n == 0)) {
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return 1;
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}
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if (isset($totients[$n])) {
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return $totients[$n];
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}
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$tot = 1;
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foreach (factorization($n) as $p => $exp) {
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$tot *= (($p - 1) * pow($p, ($exp - 1)));
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}
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$totients[$n] = $tot;
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return $tot;
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}
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public function gcd($a, $b)
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{
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if (($a == $b)) {
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return $a;
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}
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while (($b > 0)) {
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list($a, $b) = [$b, posmod($a, $b)];
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}
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return $a;
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}
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public function lcm($a, $b)
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{
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return floor(abs(($a * $b)) / $this->gcd($a, $b));
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}
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/*
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function pqPrimeLeemon ($what) {
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$minBits = 64;
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$minLen = ceil($minBits / $bpe) + 1;
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$it = 0
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$a = new Array(minLen)
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$b = new Array(minLen)
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$c = new Array(minLen)
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$g = new Array(minLen)
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$z = new Array(minLen)
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$x = new Array(minLen)
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$y = new Array(minLen)
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for ($i = 0; $i < 3; $i++) {
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$q = (nextRandomInt(128) & 15) + 17
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copyInt_(x, nextRandomInt(1000000000) + 1)
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copy_(y, x)
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lim = 1 << (i + 18)
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for (j = 1; j < lim; j++) {
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++it
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copy_(a, x)
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copy_(b, x)
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copyInt_(c, q)
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while (!isZero(b)) {
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if (b[0] & 1) {
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add_(c, a)
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if (greater(c, what)) {
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sub_(c, what)
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}
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}
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add_(a, a)
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if (greater(a, what)) {
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sub_(a, what)
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}
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rightShift_(b, 1)
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}
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copy_(x, c)
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if (greater(x, y)) {
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copy_(z, x)
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sub_(z, y)
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} else {
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copy_(z, y)
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sub_(z, x)
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}
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eGCD_(z, what, g, a, b)
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if (!equalsInt(g, 1)) {
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break
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}
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if ((j & (j - 1)) == 0) {
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copy_(y, x)
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}
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}
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if (greater(g, one)) {
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break
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}
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}
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divide_(what, g, x, y)
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if (greater(g, x)) {
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P = x
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Q = g
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} else {
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P = g
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Q = x
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}
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// console.log(dT(), 'done', bigInt2str(what, 10), bigInt2str(P, 10), bigInt2str(Q, 10))
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return [bytesFromLeemonBigInt(P), bytesFromLeemonBigInt(Q), it]
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}*/
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}
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