Other random results

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The following routines return true with the given probability

Definitions of routines returning booleans

routine	probability
Boolean()	1/2
Prob<NumericType>(NumericType p)	p
Prob<NumericType>(NumericType m, NumericType n)	m/n

Prob accepts both real and integer types. However, typically the one-argument version (the Bernoulli distribution) would be used with a real argument and the two-argument version would be used with integer arguments. Prob<NumericType>(NumericType p) is false if p ≤ 0 and true if p ≥ 1. Prob<NumericType>(NumericType m, NumericType n) returns false if m ≤ 0 or n < 0 and true if m ≥ n. The results of Prob are exact. In particular, Prob<double>(x, y) returns true with probability x/y even if x/y cannot be exactly represented as a double (e.g., it underflows to zero).

Equivalences between routines returning booleans

Function	Equivalent
Boolean()	Integer<bool>()
Boolean()	Prob(1, 2)
Boolean()	Prob(0.5)
Prob<RealType>(x)	Float<RealType>() < x
Prob<RealType>(x)	FloatU<RealType>() ≤ x

Finally, Bits<n>() returns n random bits in a std::bitset<n>. For example

RandomLib::Random r; r.Reseed();
std::cout << "Generate 20 random bits: " << r.Bits<20>() << "\n"; 

might produce

  Generate 20 random bits: 10110101000101001001

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