[rand.general]

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

## 29.5 Random number generation [[rand]](rand#general)

### 29.5.1 General [rand.general]

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L1279)

Subclause [[rand]](rand "29.5 Random number generation") defines a facility
for generating (pseudo-)random numbers[.](#1.sentence-1)

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L1283)

In addition to a few utilities,
four categories of entities are described:[*uniform random bit generators*](#def:uniform_random_bit_generators),[*random number engines*](#def:random_number_engines),[*random number engine adaptors*](#def:random_number_engine_adaptors),
and[*random number distributions*](#def:random_number_distributions)[.](#2.sentence-1)

These categorizations are applicable
to types that meet the corresponding requirements,
to objects instantiated from such types,
and to templates producing such types when instantiated[.](#2.sentence-2)

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

These entities are specified in such a way
 as to permit the binding
 of any uniform random bit generator object e as the argument
 to any random number distribution object d,
 thus producing a zero-argument function object
 such as given by bind(d,e)[.](#2.sentence-3)

— *end note*]

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L1306)

Each of the entities specified in [[rand]](rand "29.5 Random number generation") has an associated arithmetic type ([[basic.fundamental]](basic.fundamental "6.9.2 Fundamental types"))
identified as result_type[.](#3.sentence-1)

With T as the result_type thus associated with such an entity,
that entity is characterized:

- [(3.1)](#3.1)

as [*boolean*](#def:boolean) or equivalently as [*boolean-valued*](#def:boolean-valued),
 if T is bool;

- [(3.2)](#3.2)

otherwise
 as [*integral*](#def:integral) or equivalently as [*integer-valued*](#def:integer-valued),
 if numeric_limits<T>​::​is_integer is true;

- [(3.3)](#3.3)

otherwise
 as [*floating-point*](#def:floating-point) or equivalently as [*real-valued*](#def:real-valued)[.](#3.sentence-2)

If integer-valued,
an entity may optionally be further characterized as[*signed*](#def:signed) or [*unsigned*](#def:unsigned),
according to numeric_limits<T>​::​is_signed[.](#3.sentence-3)

[4](#4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L1331)

Unless otherwise specified,
all descriptions of calculations
in [[rand]](rand "29.5 Random number generation") use mathematical real numbers[.](#4.sentence-1)

[5](#5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L1337)

Throughout [[rand]](rand "29.5 Random number generation"),
the operatorsbitand, bitor, and xor denote the respective conventional bitwise operations[.](#5.sentence-1)

Further:

- [(5.1)](#5.1)

the operator rshift denotes a bitwise right shift
 with zero-valued bits appearing in the high bits of the result, and

- [(5.2)](#5.2)

the operator lshiftw denotes a bitwise left shift
 with zero-valued bits appearing in the low bits of the result,
 and whose result is always taken modulo 2w[.](#5.sentence-2)