Random Numbers

1
Random Numbers

• Dick Steflik

2
Pseudo Random Numbers

• In most cases we do not want truly random numbers
• most applications need the idea of repeatability
  to be able to debug
• if we used truly random numbers how would we be
  able to debug a program, every time we would run
  the program it would be a different problem
• What we really want is something that will appear
  to be random but will be able to reproduce a
  sequence

3
Generation Uniform Random Numbers

• Consider a methos for generating a sequence of
  random fractions (Random real numbers ) Un
• uniformly distributed between 0 and 1
• Since a computer can only represent a real number
  with finite accuracy well actually generate
  integers Xn between 0 and some number m
• The fraction Un Xn / m
• will always be between 0 and 1
• Usually m is the word size of the computer so
  that Xn can be regarded as the integer content of
  of a computer word with the radix point assumed
  at the far-right.
• Un can be regarded as the contents of the same
  word with the radix point at the far-left.

4
The Linear Congruential Method
By far the most popular random number generators
in use today are special cases of the following
scheme, introduced by D.H.Lehmer in 1949.
Choose 4 magic numbers m, the modulus m gt
0 a, the multiplier 0 lt a lt m c, the
increment 0 lt c lt m X0 the Starting value 0
lt Xo lt m
The desired sequence is then Xn1 (aXn c)
mod m, n gt 0
This is called a linear congruential sequence
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Example
For m 10 X0 a c 7 the sequence is 7, 6,
9, 0, 7, 6, 9, 0 notice that the sequence has
a period of 4 I.e. it repeats and will do so
forever. This will happen for any linear
congruential generator.
6
Sample
include ltiostream.hgtint seed int random() int
num (13seed11) 11 seed num return
num int main() cout ltlt "input a seed
number " cin gtgt seed cout ltlt "\n"
for int j 0 j lt 20 j) cout ltlt
random() ltlt " "