[rand.util.canonical]

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

Let

(1.1)
r be numeric_limits<RealType>::radix,
(1.2)
R be $g.max() - g.min() + 1,$
(1.3)
d be the smaller of digits and numeric_limits<RealType>::digits,237
(1.4)
k be the smallest integer such that ${R k \geq {r d, and}^{d, and}}^{k \geq {r d, and}^{d, and}}$
(1.5)
x be $⌊ {R k / {r d ⌋ .}^{d ⌋ .}}^{k / {r d ⌋ .}^{d ⌋ .}}$

An attempt is k invocations of g() to obtain values

{g 0, \dots, {g k - 1, respectively, and the calculation of a quantity S given by Formula 29.1 : \begin{matrix} S = k - 1 \sum i = 0 ({g i - g.min()) \cdot {R i (29.1)}^{i}}_{i - g.min()) \cdot {R i (29.1)}^{i}} \end{matrix}}_{k - 1, respectively, and the calculation of a quantity S given by Formula 29.1 : \begin{matrix} S = k - 1 \sum i = 0 ({g i - g.min()) \cdot {R i (29.1)}^{i}}_{i - g.min()) \cdot {R i (29.1)}^{i}} \end{matrix}}}_{0, \dots, {g k - 1, respectively, and the calculation of a quantity S given by Formula 29.1 : \begin{matrix} S = k - 1 \sum i = 0 ({g i - g.min()) \cdot {R i (29.1)}^{i}}_{i - g.min()) \cdot {R i (29.1)}^{i}} \end{matrix}}_{k - 1, respectively, and the calculation of a quantity S given by Formula 29.1 : \begin{matrix} S = k - 1 \sum i = 0 ({g i - g.min()) \cdot {R i (29.1)}^{i}}_{i - g.min()) \cdot {R i (29.1)}^{i}} \end{matrix}}}

Returns:

⌊ S / x ⌋ / {r d .}^{d .}

[Note 2:

The return value c satisfies

0 \leq c < 1 .

— end note]

[Note 3:

If the values

{g i produced by g are uniformly distributed, the instantiation's results are distributed as uniformly as possible .}_{i 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]

237)237)

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

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]