Pi help with Php (mass looping)

Question

My primary question is: Is this alot of loops?

while ($decimals < 50000 and $remainder != "0") {
$number = floor($remainder/$currentdivider); //Always round down! 10/3 =3, 10/7 = 1
$remainder = $remainder%$currentdivider; // 10%3 =1, 10%1
$thisnumber = $thisnumber . $number;
$remainder = $remainder . 0; //10
$decimals += 1;
}

Or could I fit more into it? -without the server crashing/lagging.

I'm just wondering, Also is there a more effiecent way of doing the above? (e.g. finidng out that 1/3 = 0.3 to 50,000 decimals.)

Finally:

I'm doing this for a pi formulae the (1 - 1/3 + 1/5 - 1/7 etc.) one,

And i'm wondering if there is a better one. (In php) I have found one that finds pi to 2000 in 4 seconds.

But thats not what I want. I want an infinite series that converges closer to Pi

so every refresh, users can view it getting closer...

But obv. converging using the above formulae takes ALONG time.

Is there any other 'loop' like Pi formulaes (workable in php) that converge faster?

Thanks alot...

Answer 1

Here you have several formulas for calculating Pi:

http://mathworld.wolfram.com/PiFormulas.html

All of them are "workable" in PHP, like in any other programming language. A different question is how fast they are or how difficult they are to implement.

If the formulas converge faster or slower, it's a Math question, not about programming, so I can't help you. I can tell you that as a rule of a thumb, the less nested loops you put, the faster will be your algorithm (this is a general rule, don't take it as the absolute truth!)

Anyway, since the digits of Pi are known until a certain digit, why don't you copy it into a file and then just index it? That will be extremely fast :)

You can check previous answers to similar questions: http://stackoverflow.com/questions/1788519/calculating-pi-through-php http://stackoverflow.com/questions/3045020/which-is-the-best-formulae-to-find-pi

Answer 2

Check http://mathworld.wolfram.com/PiIterations.html (taken from the last answer). Those formulaes are using iterations and can therefor be implemented using a loop. You should use google and search for "php implementation xxxxxxx" (where xxxxxx stands for the algorithm name you want to search for).

EDIT: Here is an implementation of Vietas formula using a while-loop in php.