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identification division.
program-id. pibow.
* Berechnung von PI nach der Formel
* U=2*PI*r
* am Viertelkreis
author. "JD".
date-written. 15.8.2007.
date-compiled.
data division.
working-storage section.
77 n pic 9(4).
77 i pic 9(4).
77 c pic 9(4)V9(4).
77 u pic 9(4)V9(4).
77 xi pic 9(4)V9(4).
77 lyi pic 9(4)V9(4).
77 yi pic 9(4)V9(4).
77 bi pic 9(4)V9(4).
78 eps pic 9(4)V9(4) value 0.001.
77 x pic 9(4)V9(4).
77 a pic 9(4)V9(4).
linkage section.
77 pi pic 9(4)V9(4).
procedure division returning pi.
* computes pi = summ of all secants on the
* quarter circle, xi = breadth, yi=height
compute n=1/eps
move 0 to u
move 1 to lyi
perform varying i from 1 by 1 until i=n
compute xi=i*eps
compute x=1-xi*xi
perform root
move a to yi
compute bi=(yi-lyi)*eps
compute x=bi
perform root
add a to u
end-perform
add 1 to n
compute pi=4*u
stop run.
root.
move x to a
subtract x from 1 giving c
perform until c<=eps
* a*a=x*(1-c), c>=0
compute a = a*(1+0.5*c)
compute c = c*c*(0.75+0.25*c)
end-perform.
* x*(1-eps)/x<=a*a<x.
end-program pibow.
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