[Coco] Tandy Color Computer 3 RND Function

[William Astle]

On 2020-03-26 11:09 a.m., Arthur Flexser wrote:
>   But, I wonder if a truly random function would pass
> this test?:  There might well be some bunching of points purely due to
> chance, with a finite number of dots.  Just like with random coin flips
> generating apparently long runs of heads or tails every now and then.

This is exactly right. Randomness is lumpy. Something that is truly 
random with equal probability for all outcomes will eventually arrive at 
a basically uniform distribution, but that requires a very large number 
of data points for that pattern to start to emerge and it's very 
unlikely that you will get a truly uniform distribution even then 
compared to something with at least a tiny bit of variation. (If you 
play around with calculating the relative probabilities, you may be able 
to convince yourself of that.)

If you run a relatively small number of tests and get a uniform 
distribution, then you don't have a good random number source. It really 
should be lumpy. It *feels* more random to many of us if we see a 
uniform distribution, but it really isn't.

All that said, RND() is a *pseudo* random number generator and is 
completely deterministic. That means if you run through its period (how 
long before the sequence repeats), you may not end up with an even 
distribution. In fact, you probably don't. Different pseudo-random 
generators have different characteristics. I don't know how good the 
algorithm used by RND() actually is, but for a great many things, it's 
good enough, especially if you can seed it with something a bit random 
so you don't know where in the sequence you're starting.

Note that its range is a great deal larger than the 10 bits needed to 
get to 640 so you'll probably get better overall randomness with 10 bit 
values than you will using the entire range (probably 32 bits, actually, 
given the mantissa size of floating point numbers in Color Basic).