Code to calculate Pi using the BBP formula

The BBP formula claims to be able to directly obtain the Nth result of Pi. Originally, I thought that the acquisition speed would be the same at any position, but download one from bellard's homepage (http://bellard.org/pi/) After testing the improved C program, I found that the larger N, the longer the calculation time. After I converted it to PHP code, it would take more than 1 minute to calculate the 1Kth digit. The calculation of the original C program was also very slow.

This program will only output 9 numbers at a time (囧rz, I don’t know how to change it to output more numbers)

/**
 * Pi calculation (BBP)
 * @author Moyo
 * @url http://moyo.uuland.org/code/php-pi-calc/
 * @version 1.0
 * @ date 2013.01.12
*/

class pi
{
 public static function calc($__N__)
 {
 $n = (int)$__N__;
 $av = $ a = $vmax = $N = $num = $den = $k = $kq = $kq2 = $t = $v = $s = $i = 0;
 $sum = 0.0;
 $N = (int) (($n + 20) * log(10) / log(2));
 $sum = 0;
 for ($a = 3; $a <= (2 * $N); $a = self: :next_prime($a))
 {
 $vmax = (int)(log(2 * $N) / log($a));
 $av = 1;
 for ($i = 0; $i < $vmax; $i ++)
 {
 $av = ($av * $a);
 }
 $s = 0;
 $num = 1;
 $den = 1;
 $v = 0;
 $ kq = 1;
 $kq2 = 1;
 for ($k = 1; $k <= $N; $k ++)
 {
 $t = $k;
 if ($kq >= $a )
 {
 do
 {
 $t = (int)($t / $a);
 $v --;
 }
 while (($t % $a) == 0);
 $kq = 0 ;
 }
 $kq ++;
 $num = self::mul_mod($num, $t, $av);
 $t = (2 * $k -1);
 if ($kq2 >= $ a)
 {
 if ($kq2 == $a)
 {
 do
 {
 $t = (int)($t / $a);
 $v ++;
 }
 while (($t % $a) == 0);
 }
 $kq2 -= $a;
 }
 $den = self::mul_mod($den, $t, $av);
 $kq2 += 2;
 if ($ v > 0)
 {
 $t = self::inv_mod($den, $av);
 $t = self::mul_mod($t, $num, $av);
 $t = self::mul_mod ($t, $k, $av);
 for ($i = $v; $i < $vmax; $i ++)
 {
 $t = self::mul_mod($t, $a, $ av);
 }
 $s += $t;
 if ($s >= $av)
 {
 $s -= $av;
 }
 }
 }
 $t = self::pow_mod(10 , ($n - 1), $av);
 $s = self::mul_mod($s, $t, $av);
 $sum = (double)fmod((double)$sum + (double)$ s / (double)$av, 1.0);
 }
 return array(
 'n' => $n,
 'v' => sprintf('%09d', (int)($sum * 1e9) )
 );
 }
 private static function next_prime($n)
 {
 do
 {
 $n ++;
 }
 while (!self::is_prime($n));
 return $n;
 }
 private static function is_prime($n)
 {
 $r = $i = 0;
 if (($n % 2) == 0)
 {
 return 0;
 }
 $r = (int)(sqrt ($n));
 for ($i = 3; $i <= $r; $i += 2)
 {
 if (($n % $i) == 0)
 {
 return 0;
 }
 }
 return 1;
 }
 private static function mul_mod($a, $b, $m)
 {
 return fmod((double)$a * (double)$b, $m);
 }
 private static function inv_mod($x, $y)
 {
 $q = $u = $v = $a = $c = $t = 0;
 $u = $x;
 $v = $y;
 $ c = 1;
 $a = 0;
 do
 {
 $q = (int)($v / $u);
 $t = $c;
 $c = $a - $q * $c;
 $a = $t;
 $t = $u;
 $u = $v - $q * $u;
 $v = $t;
 }
 while ($u != 0);
 $a = $ a % $y;
 if ($a < 0)
 {
 $a = $y + $a;
 }
 return $a;
 }
 private static function pow_mod($a, $b, $m)
 {
 $r = $aa = 0;
 $r = 1;
 $aa = $a;
 while (1)
 {
 if ($b & 1)
 {
 $r = self::mul_mod( $r, $aa, $m);
 }
 $b = $b >> 1;
 if ($b == 0)
 {
 break;
 }
 $aa = self::mul_mod($ aa, $aa, $m);
 }
 return $r;
 }
}

?>