By Julienne Walker
License: Public Domain

There is nothing wrong with rand() per se, though it is notorious for being implemented poorly such that the low order bits tend to cycle in uncomfortably short amounts. These days that problem has been largely corrected, but despite this, rand() is still not recommended if one wants a reasonable sequence of random numbers. For many applications, rand() will perform admirably when used correctly, but with the current sad state of affairs, rand() is very rarely used correctly.

The problem is that of distribution. A random number generator is designed to distribute numbers evenly across a range such that the probability of any newly generated number being any number in the range is 1/p. This is called the “uniform” distribution. Everything is great so far, but nine times out of ten, a programmer will want to define the range. When rolling a six sided die, it just does not do for the random number generator to give you 1845373. The typical solution for this is to use C and C++'s remainder operator to force the range down to whatever is desired. For example, to shrink the range into [0..N), one might do this:

1 int r = rand() % N;

To instead add a lower bound and set the range to [M..N), one might do this:

1 int r = M + rand() % ( N - M );

Anyone who does this will be rewarded with a seemingly random sequence and be thrilled that their clever solution worked. Unfotunately, this does not work. The first solution only works when N evenly divides into RAND_MAX. The second solution isn't any better. The reason is because forcing the range in this way eliminates any chance of having a uniform distribution. Now, this is okay if you care nothing about some numbers being more probable than others, but to be correct, you must work with the distribution instead of destroy it.

Most experienced C and C++ programmers will tell you that using remainder with random numbers is bad, but not many of them will be able to tell you why. This is similar to the goto issue, where beginners are taught to blindly believe that any code with a goto statement is spaghetti code and any use of goto is evil. The solution suggested to get around the remainder issue is usually division by RAND_MAX. For a range of [0..N), you would do something like this:

1 int r = rand() / ( RAND_MAX / N + 1 );

To get a more flexible range, you would do something more like this:

1 int r = M + rand() / ( RAND_MAX / ( N - M ) + 1 );

Once again, this produces a seemingly random sequence. The seasoned community is happy because you are not using the remainder operator with rand, and you are happy because you got your random numbers and foiled the evils of rand(). But wait! This solution is not a fix all for rand()'s problems. In fact, the problem of distribution is still there. The trick of dividing by RAND_MAX uses the high order bits of a random number produced by rand(), thus alleviating the old problem of poor rand() implementations with non-random low order bits. But as I said, these days that problem has been largely fixed by library vendors, so the only thing you have managed to do is make the code more complicated. It buys you nothing, and before you start thinking that doing the same thing with floating-point will help, I assure you that it will not. Floating-point can be used to solve the problem, but probably not the way you were thinking.

A real fix is to work with the distribution rather than try to circumvent it. Simply call rand() until you get a number that fits within your selected range:

1 int r; 2 3 do 4 r = rand(); 5 while ( r < low || high < r );

Not only does this fix the distribution problem, it also avoids the low order bit problem entirely. The down side to this solution is that the performance is dictated by the range. A small range could potentially call rand() many times. If you are worried about that possible performance hit, an alternative is to create a uniform deviate from the random number. This floating-point value in the range [0..1) can then be multiplied to fix the range. The uniform deviate would be used like so for [0..N):

1 double uniform_deviate ( int seed ) 2 { 3 return seed * ( 1.0 / ( RAND_MAX + 1.0 ) ); 4 } 5 6 int r = uniform_deviate ( rand() ) * N;

For a more flexible range, the code is simple:

1 int r = M + uniform_deviate ( rand() ) * ( N - M );

Uniform deviates may incur a performance penalty if floating-point operations are significantly slower on the machine than integer operations. Also note that this uniform deviate does not have perfect uniform distribution (despite the name). Unfortunately, the only correct solution to the distribution problem is calling rand() multiple times.

It should be kept in mind that these distribution problems are consistent with all random number generators that return a ranged integer, not just rand(). So please do not read this article as me harping on rand(), rather read it as me harping on the majority of programmers who use it incorrectly.

 

Seeding rand()

Probably the most vexing problem with how people use rand() is how the generator is seeded. The usual solution is to get the system time using the time() function. In theory, this is a great idea because not only does it seed the random number generator with an ever changing value, but it is also portable:

1 srand ( (unsigned int)time ( NULL ) );

Right? Well no, not really. The issue is that time_t is a restricted type, and may not be meaningfully converted to unsigned int. That is not a terribly big issue as I have yet to see a system where it would fail to work correctly, and I do not know anyone who has either. But subtle lingering portability issues should leave a sour taste in the mouth. Fortunately, there is a way to use the result of time() portably as a seed for rand(); just hash the bytes of a time_t:

1 unsigned time_seed() 2 { 3 time_t now = time ( 0 ); 4 unsigned char *p = (unsigned char *)&now; 5 unsigned seed = 0; 6 size_t i; 7 8 for ( i = 0; i < sizeof now; i++ ) 9 seed = seed * ( UCHAR_MAX + 2U ) + p[i]; 10 11 return seed; 12 } 13 14 srand ( time_seed() );

A hash will take advantage of the way the system time changes. Even better, the C and C++ standards guarantee that type punning is a portable operation for simple types, and time_t is a simple type. So hashing the system time and seeding rand() with it is a portable solution with desirable properties.

Of course, one might wonder why we should go to all of the trouble when time_t is extremely likely to work. The uncertainty of being able to use time_t alone should be a good enough reason to avoid directly seeding rand with one.

 

Conclusion

There is really nothing wrong with rand(), despite what you may be told. The problem is with the people who use it, and how they use it incorrectly and without having all of the facts. Another problem is that one can use rand() incorrectly and still get seemingly random results, so the incorrect use appears to work as expected.

Now for the big question: Does any of this matter to you? Yes, of course it does. A keen understanding of how things work will give you insight into writing good code. Will you encounter these problems in everyday programming? Probably not. Pseudorandom numbers are typically expected to be sufficiently random for the application but no more. As such, most people who use rand() will either not see, or not care, about distribution issues. In fact, these issues are generally not noticeable except on a very large scale.

An article on rand() isn't complete without the usual caveat that rand() isn't required to be a strong random number generator. In fact, it's usually pretty weak. For little things that don't need a good random number generator, rand() will do fine. For everything else, a much stronger algorithm with more guarantees, such as the Mersenne Twister, is recommended. In other words, for a dice rolling school project, rand() is just peachy. But for a slot machine in Las Vegas, you need the very best you can get, and rand() isn't it.

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From the twisted mind of Julienne Walker
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