29 Numerics library [numerics]

29.6 Random number generation [rand]

29.6.7 Utilities [rand.util]

29.6.7.2 Function template generate_­canonical [rand.util.canonical]

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Each function instantiated from the template described in this section [rand.util.canonical] maps the result of one or more invocations of a supplied uniform random bit generator g to one member of the specified RealType such that, if the values gi produced by g are uniformly distributed, the instantiation's results tj, 0≤tj<1, are distributed as uniformly as possible as specified below.

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[ Note: 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 ]

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

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Complexity: Exactly k=max(1,⌈b/log2R⌉) invocations of g, where b273 is the lesser of numeric_­limits<RealType>​::​digits and bits, and R is the value of g.max()−g.min()+1.

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Effects: Invokes g() k times to obtain values g0,…,gk−1, respectively. Calculates a quantity

S=k−1∑i=0(gi−g.min())⋅Ri

using arithmetic of type RealType.

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Returns: S/Rk.

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Throws: What and when g throws.

273)

b is introduced to avoid any attempt to produce more bits of randomness than can be held in RealType.