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
the to any other negative number. What happens?
The actual values change, but the pattern remains:*-3*

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 or rather,
incomplete. In fact, duplication occurs for **incorrect** —**all** numbers of the form
where **-k*2^n**,**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!