使用BBP公式計算Pi的程式碼

BBP公式号称可以直接获取Pi的第N位结果，本来我以为这种获取的速度在任意一个位置都是相同的呢，但是从bellard的主页（http://bellard.org/pi/）下载一个改进的C程序测试后发现N越大，计算时间越长，我转换成php代码后，计算第1K位时会超过1分钟的时间，原C程序计算的时候也是很慢

这个程序一次只会输出9个数字（囧rz，不知道怎样改能多输出几位）

/**
 * 圆周率计算(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;
	}
}

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