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New version of Pi calculator, break the speed bound!

Posted February 2nd, 2007 by Mgccl

in

You think use PHP to calculate the 2000 places after pi in 8 seconds is fast? you haven't see anything yet. This is the 3rd last attempt of finding pi (at least till 2020). I still have 2 more algorithms going to try. This one uses Borwein's quartic convergence algorithm on pi finding.

Borwein's quartic convergence algorithm in pi finding

You want to know the speed right? It uses less than 4 second to find the 2000th place of pi! and it is only slightly slower than the older pi calculator when precision is very low(between 1 to 30).

Feel free to check the source.
This was modified to be part of the BCext class I am working on right now.

function bcpi($precision){
	bcscale($precision+6);
	$a = bcsqrt(2);
	$b = 0;
	$p = bcadd(2, $a);
	$i = 0;
	$count = ceil(log($precision+6)/log(2))-1;
	while($i < $count){
		$sqrt_a = bcsqrt($a);
		$a1 = $a;
		$a = bcdiv(bcadd($sqrt_a,bcdiv(1,$sqrt_a)),2);
		$b_up = bcmul($sqrt_a,bcadd(1,$b));
		$b_down = bcadd($a1,$b);
		$b = bcdiv($b_up, $b_down);
		$p_up = bcmul(bcmul($p,$b),bcadd(1,$a));
		$p_down = bcadd(1, $b);
		$p = bcdiv($p_up, $p_down);
		++$i;
	}
 
return bcadd($p,0,$precision);
}