28 Numerics library [numerics]

28.5 Random number generation [rand]

28.5.8 Utilities [rand.util] Function template generate_canonical [rand.util.canonical]

template<class RealType, size_t digits, class URBG> RealType generate_canonical(URBG& g);
  • r be numeric_limits<RealType>​::​radix,
  • R be ,
  • d be the smaller of digits and numeric_limits<RealType>​::​digits,226
  • 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
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]
d is introduced to avoid any attempt to produce more bits of randomness than can be held in RealType.