pi a la modulus

Edit 0 1 …
Pi.bas

This is a small routine to print pi, the ratio of a circle's circumference
to its diameter, to as many places as you wish.

It uses integer math for all values and calculations.
It'll crank out the first 100 digits in a few seconds.
After a minute it is upto about 200 digits, and reaches
300 digits after about 4 minutes but it can go much much
longer. I've let it run for an hour without crashing
and it was still churning out digits. :-)

It's output has been compared to John Fisher's pi program
and they are the same to 1500 digits. John's, much faster,
trigonometry program can be found at his website:
<http://atschool.eduweb.co.uk/taunton/LB/indexlb.html>

As mentioned above, this program does slow down.
To see why, change desiredprecision = 50, then
print a, a1, b, b1 or better yet, just print their sizes.
Each one will be more than a googul (10^100).
The longer you let it run, the larger they get.
After printing 300 digits a, b, a1, b1 are over
1000 digits long. That's insane.

LB's ability to handle such enormous integers is truly remarkable!

t0 = time$("ms")
k = 2 : a = 4 : b = 1 : a1 = 12 : b1 = 4
digits = 0 ; desiredprecision = 300
 
while digits<desiredprecision
' Next approximation
  p = k*k
  q = 2*k+1
  k = k+1
 
  olda1 = a1 : oldb1 = b1
  a1 = p*a+q*a1 : b1 = p*b+q*b1
  a = olda1 : b = oldb1
 
' Print common digits
  d = int(a / b)
  d1 = int(a1 / b1)
  while d = d1
    print d;
    digits = digits + 1
    if digits mod 50=0 then print
    a = 10*(a mod b) : a1 = 10*(a1 mod b1)
    d = int(a/b) : d1 = int(a1/b1)
  wend
wend
t1 = time$("ms")
print
print "Elapsed time was "; (t1-t0)/1000; " seconds."
end

Take care,