How do you generate uniformly distributed random integers?

Question

I need a function which would generate a random integer in a given range (including boundary values). I don't have unreasonable quality/randomness requirements; I have four requirements: - I need it to be fast. My project needs to generate millions (or sometimes even tens of millions) of random numbers and my current generator function has proven to be a bottleneck. - I need it to be reasonably uniform (use of rand() is perfectly fine). - the minimum-maximum ranges can be anything from <0, 1> to <-32727, 32727>. - it has to be seedable. I currently have the following C++ code: ``` output = min + (rand() * (int)(max - min) / RAND_MAX) ``` The problem is that it is not really uniform - max is returned only when rand() = RAND_MAX (for Visual C++ it is 1/32727). This is a major issue for small ranges like <-1, 1>, where the last value is almost never returned. So I grabbed pen and paper and came up with following formula (which builds on the (int)(n + 0.5) integer rounding trick): ``` ( (…

Accepted Answer

A fast, somewhat better than yours, but still not properly uniform distributed solution is

```
output = min + (rand() % static_cast<int>(max - min + 1))
```

Except when the size of the range is a power of 2, this method produces biased non-uniform distributed numbers regardless the quality of `rand()`. For a comprehensive test of the quality of this method, please read this.

How do you generate uniformly distributed random integers?

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