Random Numbers Dick Steflik

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

Generation Uniform Random Numbers Consider a methos for generating a sequence of random fractions (Random real numbers ) U n uniformly distributed between 0 and 1 Since a computer can only represent a real number with finite accuracy we’ll actually generate integers X n between 0 and some number m The fraction U n = X n / m – will always be between 0 and 1 Usually m is the word size of the computer so that X n 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.

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 Choose 4 “magic numbers: m,the modulus;m > 0 a,the multiplier;0 <= a < m c,the increment;0 <= c < m X 0 the Starting value;0 <= Xo < m The desired sequence is then: X n+1 = (aX n + c) mod m,n >= 0 This is called a linear congruential sequence

Example For m = 10 ; X 0 = 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.

Sample #include int seed; int random() { int num = (13*seed+11) % 11; seed = num; return num; } int main() { cout << "input a seed number = "; cin >> seed; cout << "\n"; for int j = 0 ; j < 20 ; j++) cout << random() << " "; }