Random number generators discussion

Seems your program can't generate all valid float in [0,1).

Like the smallest float (32 bits) is 2^-126, seems your program can only generate 2^-32?

Thanks!

You have a choice between the resolutions 2^-32, 2^-52, and 2^-63 = 10^-19. That's more than enough for any application you could ever think of.

I think you are confusing range and resolution. The range of floating point numbers is defined by the minimum/maximum exponent. The resolution is defined by the maximum number of decimals. A double can distinguish between 0 and 10^-307, but not between 1 and 1+10^-307.

f=1.xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

and returns f-1.0. This is equal to random()/2^32 mathematically (with full
scale computation, certainly). The problem is, if random() outputs a small number,
say 127, we can write the output float as this:

1.111111(in binary)x2^-25

The problem here is, the mantissa has only 6 bits. The precision is very bad.
Single precision float format can have 2^22 different numbers in [2^-25,2^-24),
but your program can only gives 2^6 = 64 of them.

You may argue the probability is very low, but with my test,
it hits 2^-27 in less than 30 secons, and hits 0 about 9 times in one hour.
I use your B generator to do the test on a Pentium 4 2GHz CPU.
The smallest positive number your program can give is 2^-32 and I met this
number in the one-hour test. This number will given as the entire mantissa
field equals 0.

Even though it is possible to represent extremely small values 2^(-x) in a float or double or long double, it's not possible to store the value 1-2^(-x). A random number generator that can generate 2^(-x) but not 1-2^(-x) will obviously not have a perfect uniform distribution. Therefore, x is limited by the resolution, not the range.