- Hiroshi Haramoto
- Automation of Statistical Tests on Randomness to Obtain Clearer Conclusion
- Monte Carlo and Quasi-Monte Carlo Methods 2008
- 2009
- Springer
- 411--421
- DOI:10.1007/978-3-642-04107-5_26

Statistical testing of pseudorandom number generators (PRNGs) is indispensable for their evaluation. A common difficulty among statistical tests is how we consider the resulting probability values (p-values). When we observe a small p-value such as 10−3, it is unclear whether it is due to a defect of the PRNG, or merely by chance. At the evaluation stage, we apply some hundred of different statistical tests to a PRNG. Even a good PRNG may produce some suspicious p-values in the results of a battery of tests. This may make the conclusions of the test battery unclear. This paper proposes an adaptive modification of statistical tests: once a suspicious p-value is observed, the adaptive statistical test procedure automatically increases the sample size, and tests the PRNG again. If the p-value is still suspicious, the procedure again increases the size, and re-tests. The procedure stops when the p-value falls either in an acceptable range, or in a clearly rejectable range. We implement such adaptive modifications of some statistical tests, in particular some of those in the Crush battery of TestU01. Experiments show that the evaluation of PRNGs becomes clearer and easier, and the sensitivity of the test is increased, at the cost of additional computation time.

Following codes require TestU01.

Functions for users

- void bbattery_Adaptive_Crush(unif01_Gen *)
- void bbattery_Repeat_Adaptive_Crush (unif01_Gen * gen, int Rep[])

Compile sample

```
````gcc example_adaptive_crush.c adaptive_crush.c -o example_adaptive_crush -ltestu01 -lprobdist`

Copyright (c) 2012 Hiroshi Haramoto, Hiroshima University. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. * Neither the name of the Hiroshima University nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.