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Skip to comments (9) Random numbers with a good uniform distribution
Posted by Erik on Jan 10 2006 @ 14:18  :: 6077 unique visits

C/C++

In lots of projects, including my own old projects, I see people getting random numbers the following way.
number between min and max:

This is very wrong because (most of the time) the modulo (%) operator will destroy the uniform distribution of the numers that rand() returnes.

A simple example:
Let's assume the rand() implementation you are using gives you numbers between 0 and 15 (inclusive).
If you would want a number between 0 and 10 this would lead to the following code:

In this case the numbers 0 up to 4 would be returned twice as much as the numbers 5 up to 10.
This because the % 11 will convert the numbers 11 up to 15 into 0 up to 4
11 % 11 = 0
12 % 11 = 1
...


A better method which leaves the distribution in tact is the following:

Note: RAND_MAX is a macro in C/C++ which defines the maximum value that can be returned by the rand() function.

PHP

In PHP you can specify a min and max parameter to the rand function. This function returns numbers with a uniform distribution.

Javascript

With javascript the story is a little different. Javascript has the Math.random() function which returns a number between 0 and 1 only never 1 (so 0 >= n < 1). If you would want a number between lets say 0 and 2 most people would write something like this:


This will randomly return 0, 1 or 2 but the distribution isn't unifom anymore because of the way Math.round() rounds the numbers. The number 1 will be returned twice as much as 0 and 2.
This because the range of numbers which is rounded to 1 is twice as big as for 0 and 2:
0.0 to 0.5 is rounded to 0
0.5 to 1.5 is rounded to 1 and
1.5 to 2.0 is rounded to 2

This can be fixed using Math.floor() which will always round a number to the lowest whole number:

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