# Perfect and Fast Random Floating Point Numbers

While working on the Make It Random library for Unity, I took up an engineering challenge: generation of random floating point numbers between zero and one quickly and with perfect uniform distribution. The most common method, dividing a random integer by the full range of possible integers, has a few substantial flaws that I hoped to avoid:

• First, it involves a division operation, which could naturally slow things down a bit.
• Secondly, although the distribution on a high level is uniform, it’s more clumpy for higher numbers closer to one, and more diffusely spread for lower numbers closer to zero, so the uniformity is imperfect.
• Third, the quantity of possible integers generated rarely maps cleanly to the possible number of floating point values available, and so different floating point values are likely to have at least slightly different probabilities of occurring, further weakening the uniformity.
• And fourth, even when the mapping from integers to floating point values is carefully managed, if the range of values needed is not a power of two, this adds further problems to any attempt to get perfect uniformity without sacrificing performance, due to how typical random engines generate data as chunks of bits.

With the help of various sources around the internet plus some clever use of probability mathematics, I was able to conquer all of these difficulties, providing perfectly uniform and fast generation of floating point numbers in the unit range. This includes all four variants of whether the lower and upper bounds are inclusive or exclusive. The techniques involved are explained below.

The first two are not at all new, but are included because I have not seen them discussed as often as I think they deserve, and because they help build the context for the third technique. This last technique is something I devised on my own, and although I have no doubt other smart people have already discovered it or something similar, I never ran across it while researching, so I’m eager to share it with others in this post. Plus, I suspect that the general technique can be usefully applied to other random value generation beyond just floating point numbers, so the more people are aware of it, the better. (more…)