How do i calculate pie as a computer programmer?

Comments

• fred-w

  June 2021

  This comes up again and again...

  The google-fu is not strong with you...

  So, I get to amuse myself. Here is a program to compute PI. It is written in TECO (Text Editor and COrrector), which is an editor that dates back to 1962. TECO macros are very powerful; this is just for fun (can your editor compute PI?).

  [user@ariel ~]$ cat `locate pi.tec`

  GZ0J\UNQN"E 40UN ' BUH BUV HK

  QN< J BUQ QN*10/3UI

  QI< \+2*10+(QQ*QI)UA B L K QI*2-1UJ QA/QJUQ

  QA-(QQ*QJ)-2\ 10@I// -1%I >

  QQ/10UT QH+QT+48UW QW-58"E 48UW %V ' QV"N QV^T ' QWUV QQ-(QT*10)UH >

  QV^T @^A/

  /HKEX

  Note that the macro actually ends in 2 ESC characters. And, to show that it actually works... (MUNG is the macro executor, stands for Mangle Until No Good):

  [user@ariel ~]$ MUNG pi

  3141592653589793238462643383279502884197

  [user@ariel ~]$

  Now, for your answer (not a very good answer -- but it should give you an idea, first answer that comes up in google for the query "calculate pi in c++"):

  http://www.cplusplus.com/forum/beginner/1149/

  And, in case you don't want to bother clicking:

  #include <iostream>

  #include <iomanip>

  int main() {

  unsigned int decP;

  unsigned int denom=3;

  float ourPi=4.0f;

  bool addFlop=true;

  cout << "How many loop iterations? ";

  cin >> decP;

  for (unsigned int i=1;i<=decP;i++) {

  if (addFlop) {

  ourPi-=(4.0/denom);

  addFlop=false;

  denom+=2;

  } else {

  ourPi+=(4.0/denom);

  addFlop=true;

  denom+=2;

  }

  }

  cout << setiosflags(ios::showpoint) << setiosflags(ios::fixed) << setprecision(9);

  cout << "Pi calculated with " << decP << " iterations is: ";

  cout << ourPi << endl;

  }

  And now for a PI program in Scheme:

  ;; Program to calulate the decimal expansion of pi

  ;; This function calculates the arc cotan of a value scaled by the scale

  ;; factor. It uses scaled integer arithmetic to get more precision.

  (define (scaled-acot x scale n value)

  (define (calc-term x n)

  (define two-n-minus-1 (- (* n 2) 1))

  (quotient

  (* (if (odd? n) 1 -1) scale)

  (* (expt x two-n-minus-1) two-n-minus-1)))

  (let ((term (calc-term x n)))

  (if (< (abs term) 1)

  value

  (scaled-acot x scale (+ n 1) (+ value term)))))

  ;; This function sums up the arc cotan function values of the odd terms

  ;; in the Fibonacci sequence to produce an approximation of pi/4

  (define (sum-acot-even-fibonacci F_even F_odd scale sum)

  (let ((term (scaled-acot F_odd scale 1 0)))

  (if (< (abs term) 1)

  sum

  (sum-acot-even-fibonacci

  (+ F_even F_odd) ;; i.e. Fn+1

  (+ F_odd F_even F_odd) ;; equivalent to (+ Fn+1 Fn), i.e., Fn+2

  scale

  (+ sum term)))))

  (define (calc-extra-digits precision)

  (define (log10 x)

  (/ (log x) (log 10)))

  (inexact->exact

  (+ 2

  (ceiling

  (log10 (* 3 precision))))))

  (define (calc-pi precision)

  (let*

  ((extra-digits (calc-extra-digits precision))

  (scale (expt 10 (+ precision extra-digits))))

  ;; Add a couple of extra decimal places to the precision to take

  ;; accumulation of error in lower order terms into account. Scale

  ;; back down for the output

  (quotient

  (* 4 (sum-acot-even-fibonacci 1 2 scale 0))

  (expt 10 extra-digits))))

  (begin

  (display (calc-pi 1000))

  (display "\n"))

  Now, lets run that one (to 1000 places):

  [user@ariel projects]$ gsi pi.scm

  314159265358979323846264

  338327950288419716939937

  510582097494459230781640

  628620899862803482534211

  ...and so on...
• anonymous

  June 2021

  In Linux there is a nice program called Schnell Pi but it just calculates Pi to a specified amount of digits
• mdigitale

  June 2021

  There are many ways to calculate pi. Google can provide you with many mathematical approaches. Some of the methods are outlined here: http://documents.wolfram.com/v5/Demos/Notebooks/Ca...
• scootermacgyver

  June 2021

  http://en.wikipedia.org/wiki/Pi#Estimating_.CF.80