Q28150: RND and RANDOMIZE Alternatives for Generating Random Numbers

Article: Q28150
Product(s): See article
Version(s): 1.00 1.01 1.02 2.00 2.01 3.00 4.00 4.00b 4.50
Operating System(s): MS-DOS
Keyword(s): ENDUSER | B_BasicCom B_BasicInt B_GWBasicI B_MQuickB | mspl13_basic
Last Modified: 26-JUN-1989

If you would like a substitute for RND and RANDOMIZE, you can use your
own equation to generate random numbers as shown below.

Microsoft BASIC offers the RND function to return random
single-precision numbers between 0.000000 and 1.000000. The RANDOMIZE
statement can be used to reseed (or initially start) a given sequence
returned by RND. Microsoft BASIC uses the linear-congruential method
for random-number generation in the RND function.

This article applies to the following products:

1. Microsoft BASIC Compiler Versions 6.00 and 6.00b for MS-DOS and MS
   OS/2

2. Microsoft QuickBASIC Compiler Versions 1.00, 1.01, 1.02, 2.00, 2.01,
   3.00, 4.00, 4.00b, and 4.50 for the IBM PC

3. Microsoft GW-BASIC Interpreter Versions 3.20, 3.22, and 3.23 for
   MS-DOS

4. Microsoft QuickBASIC Compiler for the Apple Macintosh

5. Most other Microsoft BASIC interpreters and compilers for Apple
   Macintosh, MS-DOS, MS OS/2, XENIX, and CP/M-80

Microsoft BASIC uses the linear-congruential method for random-number
generation in the RND function. The following is an example of the
linear-congruential method formula, similar to that used by RND in
Microsoft BASIC:

   x1 = ( x0 * a + c ) MOD 2^24

In the above example, the variables equal the following:

   x1=new number
   x0=previous number
   a=214013
   c=2531011

(Note: the MOD operator in the formula above returns the integer
remainder after an integer division.)

The expression x1/(2^24) returns a floating-point number between 0.0
and 1.0. Please refer to Code Examples 1 and 2 below for an
illustration.

For more random number generation algorithms, see Pages 353-364 of
"Microsoft QuickBASIC Programmer's Toolbox," by John C. Craig,
published by Microsoft Press (1988). Seven random number subprograms
are documented, and a companion disk in MS-DOS format is also
available from Microsoft Press.

The programs in Craig's book are written for QuickBASIC Version 4.00
for the IBM PC. Some programs, such as the random number programs, are
general and can easily be modified to run in Microsoft QuickBASIC for
the Apple Macintosh. When you run these programs, you may wish to
reseed the random number sequence regularly (such as every few hundred
invocations) for greater uniformity.

Code Example 1
--------------

The following is an example of the linear congruential method for
generating pseudo-random numbers:

DEFDBL A-Z  ' Requires double-precision intermediate variables.
a = 214013
c = 2531011
z = 2 ^ 24
INPUT "Input any seed value: ", x0
FOR count = 1 TO 25   ' print 25 random numbers between 0.0 and 1.0:
  temp = x0 * a + c
' Calculate (temp MOD z) and assign to x1:
  temp = temp / z
  x1 = (temp - FIX(temp)) * z
' Print the result as value between 0.0000000 and 1.0000000:
  result = x1 / z
  PRINT result
' Reseed the calculation before the next iteration:
  x0 = x1   ' x0 and x1 range from 0 to 16777216 (2^24)
NEXT

Code Example 2
--------------

The following is the same as Example 1, except the random numbers are
plotted to illustrate their uniform distribution:

DEFDBL A-Z     ' Requires double-precision intermediate variables.
SCREEN 2  ' Remove this SCREEN statement to work in Macintosh BASIC
a = 214013
c = 2531011
z = 2 ^ 24
INPUT "Input seed value: ", x0
FOR count = 1 TO 5000
  temp = x0 * a + c
  ' Calculate (temp MOD z) and assign to x1:
  temp = temp / z
  x1 = (temp - FIX(temp)) * z
  result = x1 / z  ' Result is between 0.000000 and 1.000000
  GOSUB 100       ' Plot Result
  x0 = x1   ' x0 and x1 range from 0 to 16777216 (2^24)
NEXT
END
' Plot the random points to see their uniform distribution:
100 y = y + 1
    IF y > 200 THEN y = 0   ' Wrap plot at y=200 pixels.
    x = result * 500   ' Assumes screen mode <= 500 pixels wide.
    PSET (x, y)   ' PSET requires a graphics screen mode.
    RETURN

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