Calculating number Pi digits in C

[AliGh]

Hi
I was thinking about calculating Pi digits (for example up to 1000) using C programming
Unfortunately there seems to be no one in our university to know how (even teachers)
I know that i have to use arrays but i don't know how
And i don't know what is the best way to do it ?
-4 times the integration of (1-x^2)^(1/2) for 0 to 1
- Leibniz's series
-Wallis's series
- or ...

 

[Integrand]

Check out https://en.wikipedia.org/wiki/Bailey–Borwein–Plouffe_formula

There are very many methods available. What qualifies as "best" for you?

Incidentally, that no teachers in your university know how to calculate digits of pi seems a little implausible, don't you think? :)

 

[DrClaude]

I like the Monte Carlo approach to calculating π. See for instance http://www.eveandersson.com/pi/monte-carlo-circle

 

[AliGh]

Check out https://en.wikipedia.org/wiki/Bailey–Borwein–Plouffe_formula

There are very many methods available. What qualifies as "best" for you?

Incidentally, that no teachers in your university know how to calculate digits of pi seems a little implausible, don't you think? :)

No , the teacher connected his laptop to projector while he was teaching C his typing speed wasn't much different of a beginner ... I think he was two-finger typing
Still seems implausible ? FYI I am from iran.

 

[HallsofIvy]

What does typing speed have to do with knowing how to find the digits of pi? And the question was about all the teachers at your school so why refer to just one?

 

[AliGh]

What does typing speed have to do with knowing how to find the digits of pi? And the question was about all the teachers at your school so why refer to just one?

This is university ... The teacher (or should i call university teachers professor ?) got his degree from the best university in Iran .. it shows that he doesn't have much experience ... Just ask him intermediate questions and he can't answer more than half of them
I asked fifth semester students they couldn't

 

[HallsofIvy]

This is university ... The teacher (or should i call university teachers professor ?) got his degree from the best university in Iran .. it shows that he doesn't have much experience ... Just ask him intermediate questions and he can't answer more than half of them
I asked fifth semester students they couldn't

Perhaps this is a language problem- you did not respond to either of my questions.

 

[DrClaude]

I think we should stick to the topic of the thread, discussing numerical methods to calculate π.

 

[AliGh]

What does typing speed have to do with knowing how to find the digits of pi? And the question was about all the teachers at your school so why refer to just one?

First that typing faster means you had more experience coding (and you wrote a bigger variety of programs) but this one is way beyond slow
Second that I'm first semester i don't know any other teachers and they won't answer unless they know me

 

[AliGh]

Check out https://en.wikipedia.org/wiki/Bailey–Borwein–Plouffe_formula

There are very many methods available. What qualifies as "best" for you?

Incidentally, that no teachers in your university know how to calculate digits of pi seems a little implausible, don't you think? :)

How is that formula can calculate Nth digit of Pi i don't get it

 

[willem2]

To get the N't hexadecimal digit you still need to sum n terms (and a few more to prevent roundoff errors), but it's easy to get the nth hexadecimal digit of a single term. The factors of 1/16 will only shift the term 1 digit to the right, the numbers like 4/(8k+1) are rational numbers with a repeating hexadecimal expansion.
You only need to calculate the digits N through N+20 or so from all the terms to produce the Nth digit of the sum. For the billionth digit you still need to sum a billion terms, but the calculations involve only numbers of 20 digits.

 

[AliGh]

To get the N't hexadecimal digit you still need to sum n terms (and a few more to prevent roundoff errors), but it's easy to get the nth hexadecimal digit of a single term. The factors of 1/16 will only shift the term 1 digit to the right, the numbers like 4/(8k+1) are rational numbers with a repeating hexadecimal expansion.
You only need to calculate the digits N through N+20 or so from all the terms to produce the Nth digit of the sum. For the billionth digit you still need to sum a billion terms, but the calculations involve only numbers of 20 digits.

Sorry still confused .. can you write algorithm ?

 

[Svein]

What you need is much more complicated than an algorithm (I can direct you to several). You need a way to represent multi-digit numbers with associated arithmetic operations in a consistent way. Fortunately, somebody else has seen the need and created the appropriate definitions and libraries - see http://mpir.org/.

 

[AliGh]

What you need is much more complicated than an algorithm (I can direct you to several). You need a way to represent multi-digit numbers with associated arithmetic operations in a consistent way. Fortunately, somebody else has seen the need and created the appropriate definitions and libraries - see http://mpir.org/.

What i actually need is way to deal with the fact that i can't work with great numbers in C i don't know what the problem is
The Leibniz's series i said up there , is a summation . I couldn't calculate it because double variable types had limited digits ... i tried multiplying by 10^n and result%10 so that i could get nth digit but it didn't work ...
Is there any possibility that i can use arrays to solve the problem ? or it takes too much memory ?
Or any not very complicated way that i can at least understand ?

 

[rcgldr]

You need to use arrays. There are advanced methods for dealing with large numbers. One of them is a library that includes source code and the website explains some of what is involved.

http://www.apfloat.org

The formulas for fast computation of pi to large number of digits also gets complicated:

http://en.wikipedia.org/wiki/Pi#Rapidly_convergent_series

 

[Svein]

What i actually need is way to deal with the fact that i can't work with great numbers in C i don't know what the problem is

Follow the link! Those people have defined numbers with more than a million digits - the record for π is more than 13 trillion digits (see https://en.wikipedia.org/wiki/Approximations_of_π).