![]() We have tested these files with ADW Modula-2, Stony Brook Modula-2 and XDS modula-2. The download EstimatePi.zip contains the program's source files, and Peter Moylan's slightly modified Rand module, taken from his freeware Numerical Analysis library (ISO version). The code as shown yields the following output: WriteString("PI by Monte Carlo simulation = ") Pi_est:=4.0*VAL(LONGREAL,cIn)/VAL(LONGREAL,cTot) MODULE EstimatePi įROM STextIO IMPORT WriteString,WriteLn,ReadChar,SkipLine Our estimate of Pi is then 4 times the number of points in the quadrant divided by the total number of random points. If x 2 + y 2 is less than or equal to 1, then the point given by x,y is inside the quadrant. We pick random coordinates x,y in the range. Modula-2 programĪs a random number generator, we use a module from the Numerical Analysis library of Peter Moylan. Now suppose we pick at random a large number of points inside the square, then the ratio of total points (inside the square) divided by the number of points inside the quadrant, will give us an estimate of Pi/4. The ratio of the area of the square and the quadrant therefore is Pi/4. ![]() The area of a circle is given by r 2Pi, so the quadrant's area is r 2Pi/4. It shows a square with one quadrant of a circle.Īs we all know, the area of the square is given by r 2. ![]() A common illustration is the estimation (rather than calculation) of Pi. Monte Carlo estimation of Pi For ISO Modula-2īy Frank Schoonjans Carlo methods are methods that use random numbers and probability statistics to solve problems. ![]()
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