Generate random numbers uniformly over an entire range


I need to generate random numbers within a specified interval, [max;min].

Also, the random numbers should be uniformly distributed over the interval, not located to a particular point.

Currenly I am generating as:

for(int i=0; i<6; i++)
    DWORD random = rand()%(max-min+1) + min;

From my tests, random numbers are generated around one point only.

min = 3604607;
max = 7654607;

Random numbers generated:


From answers below: OK, RAND_MAX is 32767. I am on C++ Windows platform. Is there any other method to generate random numbers with a uniform distribution?

8/1/2013 6:11:51 PM

Accepted Answer

Why rand is a bad idea

Most of the answers you got here make use of the rand function and the modulus operator. That method may not generate numbers uniformly (it depends on the range and the value of RAND_MAX), and is therefore discouraged.

C++11 and generation over a range

With C++11 multiple other options have risen. One of which fits your requirements, for generating a random number in a range, pretty nicely: std::uniform_int_distribution. Here's an example:

const int range_from  = 0;
const int range_to    = 10;
std::random_device                  rand_dev;
std::mt19937                        generator(rand_dev());
std::uniform_int_distribution<int>  distr(range_from, range_to);

std::cout << distr(generator) << '\n';

And here's the running example.

Other random generators

The <random> header offers innumerable other random number generators with different kind of distributions including Bernoulli, Poisson and normal.

How can I shuffle a container?

The standard provides std::shuffle, which can be used as follows:

std::vector<int> vec = {4, 8, 15, 16, 23, 42};

std::random_device random_dev;
std::mt19937       generator(random_dev());

std::shuffle(vec.begin(), vec.end(), generator);

The algorithm will reorder the elements randomly, with a linear complexity.


Another alternative, in case you don't have access to a C++11+ compiler, is to use Boost.Random. Its interface is very similar to the C++11 one.

12/8/2018 12:35:22 PM

[edit] Warning: Do not use rand() for statistics, simulation, cryptography or anything serious.

It's good enough to make numbers look random for a typical human in a hurry, no more.

See @Jefffrey's reply for better options, or this answer for crypto-secure random numbers.

Generally, the high bits show a better distribution than the low bits, so the recommended way to generate random numbers of a range for simple purposes is:

((double) rand() / (RAND_MAX+1)) * (max-min+1) + min

Note: make sure RAND_MAX+1 does not overflow (thanks Demi)!

The division generates a random number in the interval [0, 1); "stretch" this to the required range. Only when max-min+1 gets close to RAND_MAX you need a "BigRand()" function like posted by Mark Ransom.

This also avoids some slicing problems due to the modulo, which can worsen your numbers even more.

The built-in random number generator isn't guaranteed to have a the quality required for statistical simulations. It is OK for numbers to "look random" to a human, but for a serious application, you should take something better - or at least check its properties (uniform distribution is usually good, but values tend to correlate, and the sequence is deterministic). Knuth has an excellent (if hard-to-read) treatise on random number generators, and I recently found LFSR to be excellent and darn simple to implement, given its properties are OK for you.

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