PHP: Calculate Pi, revisited

Posted January 23rd, 2007 by Mgccl
in

Note: Even Faster pi calculation is here
The Pi calculation system I released previously was very slow, 180 digits could cost about 30 seconds. That's why I have to release a much faster system.
Especially after I find out that Yonatan Naamad have produced a faster script that calculate 200 digits of pi in 10 seconds.
So here is the newest release of bcpi, it generated 1000 digits of pi in 5 seconds! Should be the fastest one alive. Why is it fast? well it follows Chudnovsky brothers's Chudnovsky algorithm.
The Chudnovsky algorithm
Each time k plus one, 14 of pi's digit will be find, so this is much more efficient than the old one.
The new function:

function bcfact($n){
  return ($n == 0 || $n== 1) ? 1 : bcmul($n,bcfact($n-1));
}
function bcpi($precision){
	$num = 0;$k = 0;
	bcscale($precision+3);
$limit = ($precision+3)/14;
while($k < $limit){
	$num = bcadd($num, bcdiv(bcmul(bcadd('13591409',bcmul('545140134', $k)),bcmul(bcpow(-1, $k), bcfact(6*$k))),bcmul(bcmul(bcpow('640320',3*$k+1),bcsqrt('640320')), bcmul(bcfact(3*$k), bcpow(bcfact($k),3)))));
	++$k;
}
return bcdiv(1,(bcmul(12,($num))),$precision);
}
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[...] PHP: Calculate Pi,

On Jan/24/2007 00:48:23 WebDevLogs - Place where Web Developing Abstracts + Concluti (not verified) says:

[...] PHP: Calculate Pi, revisited [...]

[...] PHP: Calculate Pi,

On Jan/23/2007 16:55:31 WebDevLogs &raquo; PHP: Calculate PI (not verified) says:

[...] PHP: Calculate Pi, revisited [...]

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