Mathematical Notation

The following notation is used throughout the text:

N

The set of natural numbers N = {1, 2, 3 ...}.

Z

The set of integers Z = {... -3, -2, -1, 0, 1, 2, 3 ...}.

R

The set of real numbers.

Equation

The floor of a (the largest integer less than or equal to a).

or xor

Bitwise exclusive OR.

Equation

Binomial coefficient or combination (αR, α 0; kN {0}).


Equation

For αk binomial coefficient is defined as


Equation

If α < k, then

Equation

Φ(x)

Cumulative Gaussian distribution function


Equation

defined over - < x < + .

Φ(-) = 0, Φ(+) = 1.

Γ(α)

The complete gamma function


Equation

where α > 0.

B(p, q)

The complete beta function


Equation

where p>0 and q>0.

LCG(a,c, m)

Linear Congruential Generator xn+1 = (axn + c) mod m, where a is called the multiplier, c is called the increment, and m is called the modulus of the generator.

MCG(a,m)

Multiplicative Congruential Generator xn+1 = (axn) mod m is a special case of Linear Congruential Generator, where the increment c is taken to be 0.

GFSR(p, q)

Generalized Feedback Shift Register Generator

xn  = xn-p xn-q.

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