Last Wednesday, Dr. Mascagni gave us a wonderful seminar-- A Scaleable Library for pseudorandom number generator: Theory and Practice. Random numbers are very useful in many computer application areas, such as Monte Carlo method to estimate a many-dimensional integral by sampling and integrand.

Dr. Mascagni began his topic with the desired properties of Random Number Generator:

• Randomness
• Reproducibility
• Speed
• Large cycle length
• Parallelization

Dr. Mascagni mainly discussed the properties of large cycle length and parallelization. In order to gain the higher speed, Monte Carlo applications make extensive use of parallel computer. A common way to parallelize Monte Carlo is to put identical "clone" on various processors; only the random number sequences are different. A pseudo number generator is a finite machine with at most 2 to p power states, where p is the number of bits that represents the state. The smallest number of steps after which the generator starts repeating itself is called cycle. Any PRNGs should satisfied three properties: randomness, repeatability, and portability.

Dr. Mascagni then talked about some important schemes to realize the Parallelization. These schemes are the following:

• Central Server
• Cycle Division
• Cycle Parameterization
• Parameterized Iteration.

Dr. Mascagni also talked about the methods for random number generation. The methods are:

• Linear Congruential Generators.
• Power of 2 Modulus
• Prime Modulus
• Shift-Register Generators.
• Lagged-Fibonacci Generators.
• Inversive Congruential Generators.
• Combination Generators.