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使用BBP公式计算Pi的代码

时间：2021-07-01 10:21:17 帮助过：22人阅读

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;
}
}
?>

使用BBP公式计算Pi的代码

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