Notes for Intel® oneAPI Math Kernel Library Vector Statistics

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

About This Document

Product and Performance Information

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Performance varies by use, configuration and other factors. Learn more at

Notice revision #20201201

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This document includes a conceptual overview of random number generation problems and the product capabilities, with the focus on interpretation of results and the related figures of merit of VS Random Number Generators (RNGs). In contrast to the Intel® Math Kernel Library Reference Manual, VS Notes expand on the concept of random number generation and its application. The document provides extensive comparative analysis of the library generators and describes the basic tests applied. Apart from the VS distribution generators and service subroutines, the VS Notes describe testing of distribution generators.

If you are interested in general issues related to random number generators, their quality and applications in computer simulation, see Randomness and Scientific Experiment, Random Numbers and Figures of Merit for Random Number Generators sections that briefly cover the relevant matters and provide references for further studies.

To learn about the factors that help optimize the VS generators for Intel® processors, see the VS Structure section, which covers the concept underlying VS, its structure and potential for functionality enhancement. This section gives special attention to VS ease of use and other advantages in parallel programming.

For information on tests for the VS generators of various probability distributions, see the Testing of Basic Random Number Generators and Testing of Distribution Random Number Generators sections. You can see the latest test results in the Vector Statistics (VS) Performance Data document published at


This document does not cover the fundamentals of the mathematical statistics, probability theory, or the theory of numbers and statistical simulation. You can find this information in books and articles listed in the Bibliography section.