|BASIC Non-Random Numbers|
Beware of GW-BASIC's Random Number Generator
The so-called random-number generators (RNG's) are a topic of great study and
debate. I say
so-called, because their output is only
pseudo-random. There are those touting "true RNGs," but
others claim that any series of numbers that can be programmed or
repeated — anything created within a computer — cannot
be truly random. The controversy rages.
Of course, randomness could be achieved by incorporating a seed based upon external input, such as the stereo set or static electricity from the household cat. Needless to say, that option has been deemed impractical.
Do we care about absolute randomness? Generally not, but it depends upon
the scope of a project. The
GW-BASIC random-number generator
starts repeating its series after 2^24, or 16.8 million, accesses.
That limitation presents big problems for someone such attempting a project such
as the random creation of any of the 635 billion possible bridge hands.
A WORD OF CAUTION
The manuals readily explain that in order to create a repeatable series of random numbers, one seeds the RNG with a negative integer. Care is essential in doing this, however, because there is a serious anomaly in BASIC's RNG relating to the powers of two. Try running this line of code:
10 FOR X=1 TO 20: PRINT RND(-3*X),: NEXT
What happens? A lot of the numbers are the same! Now try changing
-3 to any other negative number. What happens?
The actual values change, but the pattern remains:
The 1st, 2nd,
4th, 8th, and
16th numbers match.
The 3rd, 6th, and 12th numbers match.
The 5th, 10th, and 20th numbers match.
The 9th and 18th numbers match.
Some randomness, eh? Only one of my three BASIC manuals mentions this
matter, saying that the duplication occurs when the absolute value of the random
expression becomes a power of two; but that is
incorrect — or rather,
incomplete. In fact, duplication occurs for all numbers of the form
-k*2^n, where k is any value and need not be an integer.
Try it; change the -3 to something such as -sin(1.618).
So what is to be done? Note that when x is odd, there are no matching lower values. The only matches are at 2x, 4x, 8x, etc. An odd number cannot be a double of any integer. So to be safe, simply:
Use only odd-numbered negative integers for random seeds.
Have a random day!