● Covered by 1 source · 1 reportLow impact1 neutral
Modulo Operator Can Cause Non-Uniform Distribution in Random Selections
Key points
- Modulo operator with random numbers can create non-uniform distributions.
- Some choices are selected more often than intended.
- Example shows 40% chance for one item, 30% for others.
- Use `random_between(l, h)` for uniform selection.
The Problem with Modulo for Random Selection
A common programming pattern involves selecting a random item from a set by generating a large random number and then using the modulo operator to clamp it to the size of the set. For example, `choices[random_u64() % 10]` is often used to pick one of ten items. This method is intuitive and frequently implemented, especially in languages like C or Haskell where standard libraries might offer limited random number generation functions.
Non-Uniform Distribution Explained
The issue with this approach is that it does not preserve a uniform distribution. While the initial `random_u64()` might be uniformly distributed, the modulo operation can introduce bias. If the range of the input random number is not an exact multiple of the number of choices, some choices will have more input values mapping to them than others.
Consider selecting from 3 objects using a random number from 0 to 9. Object #1 would be chosen if the input is 0, 3, 6, or 9 (4 times). Object #2 would be chosen for 1, 4, 7 (3 times), and Object #3 for 2, 5, 8 (3 times). This results in Object #1 being picked 40% of the time, while Objects #2 and #3 are picked only 30% of the time, deviating from the desired 33.3% uniform chance.
Correcting for Uniformity
To ensure a truly uniform distribution when selecting from a specific range, developers should use functions designed for this purpose, such as `random_between(l, h)`. These functions correctly handle the mapping of a large random input to a smaller, specific range while maintaining an even probability for each possible outcome.
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Primary sources
GitHub python/cpythonReporting from
Using the modulo operator with a large random number to select from a smaller set of choices can lead to a non-uniform distribution, where some choices are picked more frequently than others. This occurs because the modulo operation does not evenly distribute the input range across the output range when the input range size is not a multiple of the output range size. Developers should use functions like `random_between(l, h)` to ensure uniform distribution when selecting from a range.