Random-Number Generation - Washington University in St. Louis
Random-Number Generation
Raj Jain Washington University Saint Louis, MO 63130
Jain@cse.wustl.edu
Audio/Video recordings of this lecture are available at:
Washington University in St. Louis
CSE574s
26-1
?2008 Raj Jain
Overview
! Desired properties of a good generator ! Linear-congruential generators ! Tausworthe generators ! Survey of random number generators ! Seed selection ! Myths about random number generation
Washington University in St. Louis
CSE574s
26-2
?2008 Raj Jain
Random-Number Generation
! Random Number = Uniform (0, 1) ! Random Variate = Other distributions
= Function(Random number)
Washington University in St. Louis
CSE574s
26-3
?2008 Raj Jain
A Sample Generator
! For example,
! Starting with x0=5:
! The first 32 numbers obtained by the above procedure 10, 3, 0, 1, 6, 15, 12, 13, 2, 11, 8, 9, 14, 7, 4, 5 10, 3, 0, 1, 6, 15, 12, 13, 2, 11, 8, 9, 14, 7, 4, 5.
! By dividing x's by 16: 0.6250, 0.1875, 0.0000, 0.0625, 0.3750, 0.9375, 0.7500, 0.8125, 0.1250, 0.6875, 0.5000, 0.5625, 0.8750, 0.4375, 0.2500, 0.3125, 0.6250, 0.1875, 0.0000, 0.0625, 0.3750, 0.9375, 0.7500, 0.8125, 0.1250, 0.6875, 0.5000, 0.5625, 0.8750, 0.4375, 0.2500, 0.3125.
Washington University in St. Louis
CSE574s
26-4
?2008 Raj Jain
Terminology
! Seed = x0 ! Pseudo-Random: Deterministic yet would pass randomness
tests ! Fully Random: Not repeatable ! Cycle length, Tail, Period
Washington University in St. Louis
CSE574s
26-5
?2008 Raj Jain
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