Daniel Lemire's blog

, 3 min read

Doubling the speed of std::uniform_int_distribution in the GNU C++ library (libstdc++)

The standard way in C++ to generate a random integer in a range is to call the std::uniform_int_distribution function. The current implementation of std::uniform_int_distribution in the GNU C++ library (libstdc++) to generate an integer in the interval [0,range] looks as follows.

scaling = random_range / range;
limit = range * scaling;
   answer = random;
while ( answer >= limit);
return  answer / scaling;

where random generate a 32-bit or 64-bit integer at random. Typically, it requires two divisions by invocation. Even on recent processors, integer division is relatively expensive.

We can achieve the same algorithmic result with at most one division, and typically no division at all without requiring more calls to the random number generator. It speeds things up on various systems. It was recently added to Swift language.

Travis Downs suggested that someone should try to fix the GNU C++ implementation. So I prepared and submitted a patch. It is currently under review.

The main challenge is that we need to be able to compute the “full” product. E.g., given two 64-bit integers, we want the 128-bit result; given two 32-bit integers we want the 64-bit result. This is fast on common processors.

The 128-bit product is not natively supported in C/C++ but can be achieved with the __int128 128-bit integer extension when it is available. Thankfully, we can check for __int128 support, and when the support is lacking, we can fall back on another approach. The 128-bit integer extension appears in many compilers (LLMV clang, GNU GCC, Intel icc), but even within a given compiler (say GNU GCC), you cannot rely on the extension being always present, since the compiler implementation might be system specific.

The code I ended up with is somewhat ugly, but it works:

      __product = (unsigned __int128)(__urng() - __urngmin) * __uerange;
      uint64_t __lsb = uint64_t(__product);
      if(__lsb < __uerange)
        uint64_t __threshold = -uint64_t(__uerange) % uint64_t(__uerange);
        while (__lsb < __threshold)
          __product = (unsigned __int128)(__urng() - __urngmin) * __uerange;
          __lsb = uint64_t(__product);
      __ret = __product >> 64;

It mostly avoids divisions. I designed a simple random shuffling benchmark that mostly just calls std::shuffle which, in turn, relies on std::uniform_int_distribution. Given an array of one million elements, I get the following timings on a skylake processor with GNU GCC 8.3:

before patch 15 ns/value
after patch 8 ns/value

For fun, let us compare with the implementation that is present in the Swift standard library:

     var random: T = next()
     var m = random.multipliedFullWidth(by: upperBound)
     if m.low < upperBound {
       let t = (0 &- upperBound) % upperBound
       while m.low < t {
         random = next()
         m = random.multipliedFullWidth(by: upperBound)
     return m.high

I think it is more readable in part because the Swift language has built in support for the full multiplication. It is somewhat puzzling that the C++ language does not see fit to make it easy to compute the full product between two integers.

Update: This optimization was merged into libstdc++ by Jonathan Wakely on October 9, 2020.

Reference: Fast Random Integer Generation in an Interval, ACM Transactions on Modeling and Computer Simulation 29 (1), 2019