[rand.req.urng]

# 29 Numerics library [[numerics]](./#numerics)

## 29.5 Random number generation [[rand]](rand#req.urng)

### 29.5.3 Requirements [[rand.req]](rand.req#urng)

#### 29.5.3.3 Uniform random bit generator requirements [rand.req.urng]

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L1771)

A [*uniform random bit generator*](#def:uniform_random_bit_generator)g of type G is a function object
returning unsigned integer values
such that each value
in the range of possible results
has (ideally) equal probability
of being returned[.](#1.sentence-1)

[*Note [1](#note-1)*:

The degree to which g's results
 approximate the ideal
 is often determined statistically[.](#1.sentence-2)

â *end note*]

template<class G>concept [uniform_random_bit_generator](#concept:uniform_random_bit_generator "29.5.3.3 Uniform random bit generator requirements [rand.req.urng]") =[invocable](concept.invocable#concept:invocable "18.7.2 Concept invocable [concept.invocable]")<G&> && [unsigned_integral](concepts.arithmetic#concept:unsigned_integral "18.4.7 Arithmetic concepts [concepts.arithmetic]")<invoke_result_t<G&>> &&requires {{ G::min() } -> [same_as](concept.same#concept:same_as "18.4.2 Concept same_­as [concept.same]")<invoke_result_t<G&>>; { G::max() } -> [same_as](concept.same#concept:same_as "18.4.2 Concept same_­as [concept.same]")<invoke_result_t<G&>>; requires bool_constant<(G::min() < G::max())>::value; };

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L1797)

Let g be an object of type G[.](#2.sentence-1)

G models[uniform_random_bit_generator](#concept:uniform_random_bit_generator "29.5.3.3 Uniform random bit generator requirements [rand.req.urng]") only if

- [(2.1)](#2.1)

G​::​min() <= g(),

- [(2.2)](#2.2)

g() <= G​::​max(), and

- [(2.3)](#2.3)

g() has amortized constant complexity[.](#2.sentence-2)

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L1808)

A class G meets the [*uniform random bit generator*](#def:uniform_random_bit_generator) requirements ifG models [uniform_random_bit_generator](#concept:uniform_random_bit_generator "29.5.3.3 Uniform random bit generator requirements [rand.req.urng]"),invoke_result_t<G&> is an unsigned integer type ([[basic.fundamental]](basic.fundamental "6.9.2 Fundamental types")),
andG provides a nested [*typedef-name*](dcl.typedef#nt:typedef-name "9.2.4 The typedef specifier [dcl.typedef]") result_type that denotes the same type as invoke_result_t<G&>[.](#3.sentence-1)
