'Estimate PI with Monte Carlo Simulation

MODE 1,8  ' default screen settings

CLS

CONST POINTS = 100000  ' number of points to simulate.  More = higher accuracy and slower
CONST LENGTH = 450     ' length of square and radius of circle

text 250,25, "Monte Carlo Simulation to estimate PI"

BOX  ((800-LENGTH)/2)-5 ,(600-LENGTH)/2-4,LENGTH+10,LENGTH+10,4   ' bounding box, slightly larger than the area to draw in

ARC  (800-LENGTH)/2,(LENGTH+(600-LENGTH)/2),LENGTH-1,LENGTH,0,90   ' 1/4 circle, with same radius as square side

inside = 0   ' Reset counter for points inside circle


FOR i = 0 TO POINTS       ' iterate through the points
 x=INT(RND*(LENGTH+1))   ' random between 0 and Length (int rounds down)
 y=INT(RND*(LENGTH+1))
 d=SQR(x^2+y^2)          ' calculate the radius

 IF d <= LENGTH THEN    '  if inside the circle
   inside = inside +1
   PIXEL (x+(800-LENGTH)/2),(600-LENGTH)/2+LENGTH-y,RGB(red)
 ELSE
   PIXEL (x+(800-LENGTH)/2),(600-LENGTH)/2+LENGTH-y,RGB(green)
 ENDIF
NEXT i

header$="After " + STR$(POINTS) + " Iterations"
header2$="PI approximately = " + STR$(inside/POINTS * 4)

TEXT 300, 40, header$,,,,RGB(RED)
TEXT 280, 55, header2$,,,,RGB(GREEN)

DIM as FLOAT  X =0
DIM as FLOAT  Y =0
DIM as FLOAT fInsideCircle = 0
DIM as FLOAT  fTotal = 0
DIM as FLOAT  f_Pi
DIM as FLOAT fError

Do
X = RND()
Y = RND()
if sqr(X^2 + Y^2) <= 1.0 then fInsideCircle = fInsideCircle + 1
fTotal = fTotal + 1
f_Pi = 4.0 * (fInsideCircle/ fTotal)
fError = PI - f_Pi
Loop while inkey$ = ""

how many digits? 100
Started at 07:39:44
11.043mS so far
26.692mS so far
starting atan52()
atan52() step 2
atan52() step 3
46.259mS so far

pi = 3.1415926535 8979323846 2643383279 5028841971 6939937510      50
      5820974944 5923078164 0628620899 8628034825 3421170679     100

Total computation time:   48 mS
Time to format and print: 4 mS at 07:39:45

>

x=RND*LENGTH   ' random between 0 and Length
y=RND*LENGTH
d=SQR(x^2+y^2)          ' calculate the radius