TOPIC: A SCALABLE LIBRARY FOR PSEUDORANDOM NUMBER GENERATION: THEORY AND PRACTICE

Goals for creating a Scalable PRNG Tool for Parallel Monte Carlo are :

1.) Use new results in pseudorandom number generation to create an easy and effective new tool.

a. That make using the random number generator on parallel machines as easy as it is in serial machines.
b. That offer similar guarantees for the parallel generators as are given for serial generators.

2.) Create a tool that facilitates experimental Monte Carlo computations the on scalable platforms.

a. To ensure portability on several machines.
b. To allow for absolute reproducibility.
c. To allow for statistically significant new results.
d. To allow the PRNG 's impact to be isolated.

3.) Assemble a package with the following components :

a. Several different generation schemes.
b. User modified parallel generators.
c. Testing routines.

New Results in PRNGs using Distinct Parameterized Streams in Parallel are :

1.) Default generator : additive lagged-Fibonacci :

This generator is very efficient, good empirical quality and very easy to produce distinct parallel streams.

2.) Alternative generator #1 : prime modulus LCG :

This generator is less efficient than lagged-Fibonacci but provably good quality.

3.) Alternative generator #2 : parameterized shift-register:

This generator is also less efficient than lagged-Fibonacci and of provably good quality.

Advantages of having more than one generator are :

1.) An application may stumble on a given generator and so one can try alternatives
2.) Generators based on different recursions allow comparison to rule out spurious results.
3.) Makes the generators real experimental tools.