SIMSCRIPT II.5 Programming Language

SIMSCRIPT II.5 Programming Language
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Figure 5-7. A Rectangular Coordinates System
If we generate N points (i,j) within the square in a random fashion, some of the points will fall within
the circle, and some will not. In fact, the proportion of those falling within the circle will be approximately
π/4 of all the points. If M is the total number of those that fall within the circle, then
M/N is approximately equal to π/4. We can estimate the value of π as 4M/N. The accuracy of this
estimate improves as N increases, and is proportional to √N.
The program shown below uses the function uniform.f to generate points (i,j) that are randomly
distributed within a square of side R. It does this by generating random numbers between 0 and
R and assigning them in pairs to i and j.
Each such point (i,j) lies somewhere inside the square. If i 2 + j 2 ≤ r 2 , the point also lies within
the circle, and 1 is added to M to record this fact. This procedure is repeated N times. Each time, a
different i and j are generated and used to determine if the point (i,j) lies within the circle. At
the end of N point generations, the approximation to π is printed.
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main
normally mode is real
define HIT, I and NO.SAMPLES as integer variables
read RADIUS and NO.SAMPLES
let RADSQ = RADIUS**2
let HIT = 0
for I = 1 to NO.SAMPLES,
do
let XSAMPLE = uniform.f(0.0, RADIUS, 1)
let YSAMPLE = uniform.f(0.0, RADIUS, 1)
if XSAMPLE**2 + YSAMPLE**2 le RADSQ, '' within circle
add 1 to HIT
always
loop
let APPROX.PI = 4 * HIT/NO.SAMPLES
print 1 line with NO.SAMPLES, APPROX.PI as follows
THE ESTIMATED VALUE OF PI AFTER *** SAMPLES IS *.*****
stop
end
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