MadelineProto/prime.php
2016-07-14 09:15:50 -04:00

247 lines
6.3 KiB
PHP

<?php
set_include_path(get_include_path().PATH_SEPARATOR.dirname(__FILE__).DIRECTORY_SEPARATOR.'libpy2php');
require_once 'libpy2php.php';
function everynth($array, $n)
{
$result = [];
$i = -1;
foreach ($array as $key => $value) {
if ($i++ == $n) {
$i = 0;
}
if ($i == 0) {
$result[$key] = $value;
}
}
return $result;
}
function array_merge_ignore_keys($array1, $array2)
{
if (count($array1) == count($array2)) {
$i = -1;
foreach ($array1 as $key => $val) {
$array1[$key] = $array2[$i++];
}
} else {
return;
}
return $array1;
}
function primesbelow($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)];
$sieve = array_fill(0, floor($N / 3), true);
$sieve[0] = false;
foreach (pyjslib_range((floor(pyjslib_int(pow($N, 0.5)) / 3) + 1)) as $i) {
if ($sieve[$i]) {
$k = ((3 * $i) + 1) | 1;
$sieve = array_merge(
$sieve, array_merge(
everynth(
array_splice(
$sieve, floor(
(
$k * $k + 4 * $k - 2 * $k * ($i % 2)
) / 3
)
), 2 * $k
),
(
array_fill(
0,
(
floor(
(
(
floor(
$N / 6
) - floor(
(
(
($k * $k) + (4 * $k)
) - (
(2 * $k) * ($i % 2)
)
) / 6
)
) - 1
) / $k
) + 1
),
false
)
)
)
);
}
}
return [2, 3] + array_map(function ($i, $sieve) {
if ($sieve[$i]) {
return (3 * $i + 1) | 1;
}
}, pyjslib_range(1, (($N / 3) - $correction)), $sieve);
}
$smallprimeset = array_unique(primesbelow(100000));
$_smallprimeset = 100000;
function isprime($n, $precision = 7)
{
if (($n == 1) || (($n % 2) == 0)) {
return false;
} elseif (($n < 1)) {
throw new $ValueError('Out of bounds, first argument must be > 0');
} elseif (($n < $_smallprimeset)) {
return in_array($n, $smallprimeset);
}
$d = ($n - 1);
$s = 0;
while ((($d % 2) == 0)) {
$d = floor($d / 2);
$s += 1;
}
foreach (pyjslib_range($precision) as $repeat) {
$a = random::randrange(2, ($n - 2));
$x = pow($a, $d, $n);
if (($x == 1) || ($x == ($n - 1))) {
continue;
}
foreach (pyjslib_range(($s - 1)) as $r) {
$x = pow($x, 2, $n);
if (($x == 1)) {
return false;
}
if (($x == ($n - 1))) {
break;
}
}
}
return true;
}
function pollard_brent($n)
{
if ((($n % 2) == 0)) {
return 2;
}
if ((($n % 3) == 0)) {
return 3;
}
list($y, $c, $m) = [random::randint(1, ($n - 1)), random::randint(1, ($n - 1)), random::randint(1, ($n - 1))];
list($g, $r, $q) = [1, 1, 1];
while (($g == 1)) {
$x = $y;
foreach (pyjslib_range($r) as $i) {
$y = ((pow($y, 2, $n) + $c) % $n);
}
$k = 0;
while (($k < $r) && ($g == 1)) {
$ys = $y;
foreach (pyjslib_range(min($m, ($r - $k))) as $i) {
$y = ((pow($y, 2, $n) + $c) % $n);
$q = (($q * abs(($x - $y))) % $n);
}
$g = gcd($q, $n);
$k += $m;
}
$r *= 2;
}
if (($g == $n)) {
while (true) {
$ys = ((pow($ys, 2, $n) + $c) % $n);
$g = gcd(abs(($x - $ys)), $n);
if (($g > 1)) {
break;
}
}
}
return $g;
}
$smallprimes = primesbelow(10000);
function primefactors($n, $sort = false)
{
global $smallprimes;
$factors = [];
$limit = (pyjslib_int(pow($n, 0.5)) + 1);
foreach ($smallprimes as $checker) {
if (($checker > $limit)) {
break;
}
while ((($n % $checker) == 0)) {
$factors[] = $checker;
$n = floor($n / $checker);
$limit = (pyjslib_int(pow($n, 0.5)) + 1);
if (($checker > $limit)) {
break;
}
}
}
if (($n < 2)) {
return $factors;
}
while (($n > 1)) {
if (isprime($n)) {
$factors[] = $n;
break;
}
$factor = pollard_brent($n);
$factors->extend(primefactors($factor));
$n = floor($n / $factor);
}
if ($sort) {
$factors->sort();
}
return $factors;
}
function factorization($n)
{
$factors = [];
foreach (primefactors($n) as $p1) {
try {
$factors[$p1] += 1;
} catch (KeyError $e) {
$factors[$p1] = 1;
}
}
return $factors;
}
$totients = [];
function totient($n)
{
if (($n == 0)) {
return 1;
}
try {
return $totients[$n];
} catch (KeyError $e) {
}
$tot = 1;
foreach (factorization($n)->items() as list($p, $exp)) {
$tot *= (($p - 1) * pow($p, ($exp - 1)));
}
$totients[$n] = $tot;
return $tot;
}
function gcd($a, $b)
{
if (($a == $b)) {
return $a;
}
while (($b > 0)) {
list($a, $b) = [$b, ($a % $b)];
}
return $a;
}
function lcm($a, $b)
{
return floor(abs(($a * $b)) / gcd($a, $b));
}