Visible to Intel only — GUID: GUID-546B52C9-6420-4328-B3C4-5C80FDEC976C
Visible to Intel only — GUID: GUID-546B52C9-6420-4328-B3C4-5C80FDEC976C
Random Number Generators 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. |
The floor of a (the largest integer less than or equal to a). |
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⊕ or xor |
Bitwise exclusive OR. |
Binomial coefficient or combination (α∈R, α≥ 0; k∈N∪{0}). For α≥k binomial coefficient is defined as If α < k, then |
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Φ(x) |
Cumulative Gaussian distribution function defined over - ∞ < x < + ∞. Φ(-∞) = 0, Φ(+∞) = 1. |
Γ(α) |
The complete gamma function where α > 0. |
B(p, q) |
The complete beta function 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. |