Generating random numbers on open-open interval (0,1) efficiently

Question

I'm looking for an efficient way to generate random floating-point numbers on the open-open interval (0,1). I currently have an RNG that generates random integers on the closed-closed interval of [0, (2^32)-1]. I've already created a half-open floating point RNG on the interval [0,1) by simply multiplying my result from the integer RNG by 1/((2^32)-1) rather than dividing by (2^32)-1 since it's inefficient.

The way I'm currently going about generating numbers on the interval (0,1) is with a conditional statement like the one below:

float open_open_flt = (closed_open_flt==0) ? closed_open_flt : FLT_MIN; 

Unfortunately, this is rather inefficient since it is control code and I feel like it introduces some bias.

Can anybody suggest an alternative?

Answer 1

You are already there.

The smallest distance between two floats your current generator produces is 1/(2^32).

So, your generator is efectively producing [0,1-1/(2^32)].

1/(2^32) is greater than FLT_MIN.

Thus if you add FLT_MIN to your generator,

float open_open_flt = FLT_MIN + closed_open_flt;

you'll get [FLT_MIN,1-(1/(2^32))+FLT_MIN], which works as a (0,1) generator.

Answer 2

Since the probability of actually observing 0 probability is very small, and checking if a number is equal to 0 is least expensive (as compared to addition or multiplication), I would regenerate the random number repeatedly until it is not equal to 0.