How Can We Generate Truly Uniformly Distributed Random Integers in a Specified Range?

Generating Uniformly Distributed Random Integers

In many programming applications, generating random integers within a specified range is a common requirement. However, ensuring that these integers are uniformly distributed presents a challenge. This article explores various approaches to achieving uniform distribution.

Existing Code and Limitations

The code provided by the user leverages the rand() function to generate random numbers within a given range. However, this approach suffers from a lack of uniformity, particularly for small ranges like <0, 1>. This is attributed to the low probability of rand() returning RAND_MAX, the maximum value.

Proposed Formula

To address this issue, the user devised a new formula:

( (max - min) * rand() + (RAND_MAX / (2 * (max - min))) ) / RAND_MAX

While this formula aims to improve uniformity, it still falls short, as evidenced by sampling data.

C Standard Library Solution

The C standard library provides an elegant and reliable solution to this problem. The std::random header includes a set of random number generators and distributions that can generate random numbers with uniform distribution.

#include <random>

// Initialize random-number engine with a seed
std::random_device rd;
std::mt19937 rng(rd());

// Define uniform integer distribution
std::uniform_int_distribution<int> uni(min, max);

// Generate random integer within range
auto random_integer = uni(rng);

This approach leverages well-tested and optimized code, ensuring uniform distribution and efficiency. It eliminates the need for reinventing the wheel and concerns about bias or seed values.

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