[rand.util.canonical] (original) (raw)

29 Numerics library [numerics]

29.5 Random number generation [rand]

29.5.8 Utilities [rand.util]

29.5.8.2 Function template generate_canonical [rand.util.canonical]

template<class RealType, size_t digits, class URBG> RealType generate_canonical(URBG& g);

Let

• r be numeric_limits<RealType>​::​radix,
• R be ,
• d be the smaller ofdigits and numeric_limits<RealType>​::​digits,246
• k be the smallest integer such that , and
• x be .

An attempt is k invocations of g()to obtain values , respectively, and the calculation of a quantity S given by Formula 29.1:

Effects: Attempts are made until .

[Note 1:

When R is a power of r, precisely one attempt is made.

— _end note_]

Returns: .

[Note 2:

The return value c satisfies.

— _end note_]

Throws: What and when g throws.

Complexity: Exactly k invocations of g per attempt.

[Note 3:

If the values produced by g are uniformly distributed, the instantiation's results are distributed as uniformly as possible.

Obtaining a value in this way can be a useful step in the process of transforming a value generated by a uniform random bit generator into a value that can be delivered by a random number distribution.

— _end note_]

[Note 4:

When R is a power of r, an implementation can avoid using an arithmetic type that is wider than the output when computing S.

— _end note_]