Notes for Intel® oneAPI Math Kernel Library Vector Statistics

ID 772987
Date 12/04/2020
Document Table of Contents


The following factors influence the performance of an RNG of a given distribution:

  1. architecture and configuration of the hardware and software

  2. performance of the underlying BRNG

  3. method of transformation

  4. number of random numbers to be generated (size of the output vector)

  5. parameters of a given probability distribution

VS random number generators are optimized for Intel® Xeon® Processor X7560 and Intel® Xeon® Processor X5670. For more details on performance, see Vector Statistics (VS) Performance Data document available at For earlier Intel processors, VS generators are fully functional, but not specifically optimized.

The value of Clocks Per Element (CPE), which is independent from the processor clock rate, is selected as a unit of measurement.

For example, if the generator performance is equal to 10 CPE and the processor rate is 1 GHz, then the generator produces 108 random numbers per second.

The VS BRNGs differ from each other in speed, therefore data on performance of general (discrete and continuous) distribution generators is given separately for each BRNG used as an underlying generator to produce uniformly distributed random numbers.

Performance of a general distribution generator also depends on a method chosen for transforming a uniform distribution to a given non-uniform one. This requires specifying the applied transformation method as well.

The length of a generated vector is another factor influencing the performance of the VS vector type generators. Calling generators on short vector lengths may prove highly ineffective. See the figure for the typical interdependence between the generator performance and the vector length.

Finally, the generator performance may vary according to probability distribution parameters. The tables provide performance data only for fixed parameter values (or fixed intervals of parameter variations). Table footnotes contain parameters with which a given performance is obtained. For some transformation methods the performance is approximately the same on a wide range of parameters, such methods being called uniformly fast, while for others the performance may vary considerably with variation in the distribution parameters, for example, in PTPE method for an RNG of Poisson distribution. When the latter is the case, graphs of interdependence between the performance and the distribution parameters are provided.