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[bit.byteswap]
# 22 General utilities library [[utilities]](./#utilities)
## 22.11 Bit manipulation [[bit]](bit#byteswap)
### 22.11.4 byteswap [bit.byteswap]
[🔗](#lib:byteswap)
`template<class T>
constexpr T byteswap(T value) noexcept;
`
[1](#1)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15760)
*Constraints*: T models [integral](concepts.arithmetic#concept:integral "18.4.7Arithmetic concepts[concepts.arithmetic]")[.](#1.sentence-1)
[2](#2)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15764)
*Mandates*: T does not have padding bits ([[basic.types.general]](basic.types.general "6.9.1General"))[.](#2.sentence-1)
[3](#3)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15768)
Let the sequence R comprise
the bytes of the object representation of value in reverse order[.](#3.sentence-1)
[4](#4)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15772)
*Returns*: An object v of type T such that each byte in the object representation of v is equal to
the byte in the corresponding position in R[.](#4.sentence-1)

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[bit.cast]
# 22 General utilities library [[utilities]](./#utilities)
## 22.11 Bit manipulation [[bit]](bit#cast)
### 22.11.3 Function template bit_cast [bit.cast]
[🔗](#lib:bit_cast)
`template<class To, class From>
constexpr To bit_cast(const From& from) noexcept;
`
[1](#1)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15691)
*Constraints*:
- [(1.1)](#1.1)
sizeof(To) == sizeof(From) is true;
- [(1.2)](#1.2)
is_trivially_copyable_v<To> is true; and
- [(1.3)](#1.3)
is_trivially_copyable_v<From> is true[.](#1.sentence-1)
[2](#2)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15699)
*Mandates*: Neither To nor From are consteval-only types ([[expr.const]](expr.const "7.7Constant expressions"))[.](#2.sentence-1)
[3](#3)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15703)
*Constant When*: To, From, and the types of all subobjects
of To and From are types T such that:
- [(3.1)](#3.1)
is_union_v<T> is false;
- [(3.2)](#3.2)
is_pointer_v<T> is false;
- [(3.3)](#3.3)
is_member_pointer_v<T> is false;
- [(3.4)](#3.4)
is_volatile_v<T> is false; and
- [(3.5)](#3.5)
T has no non-static data members of reference type[.](#3.sentence-1)
[4](#4)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15715)
*Returns*: An object of type To[.](#4.sentence-1)
Implicitly creates objects nested within the result ([[intro.object]](intro.object "6.8.2Object model"))[.](#4.sentence-2)
Each bit of the value representation of the result
is equal to the corresponding bit in the object representation
of from[.](#4.sentence-3)
Padding bits of the result are unspecified[.](#4.sentence-4)
For the result and each object created within it,
if there is no value of the object's type corresponding to the
value representation produced, the behavior is undefined[.](#4.sentence-5)
If there are multiple such values, which value is produced is unspecified[.](#4.sentence-6)
A bit in the value representation of the result is indeterminate if
it does not correspond to a bit in the value representation of from or
corresponds to a bit
for which the smallest enclosing object is not within its lifetime or
has an indeterminate value ([[basic.indet]](basic.indet "6.8.5Indeterminate and erroneous values"))[.](#4.sentence-7)
A bit in the value representation of the result is erroneous
if it corresponds to a bit
for which the smallest enclosing object has an erroneous value[.](#4.sentence-8)
For each bit b in the value representation of the result
that is indeterminate or erroneous,
let u be the smallest object containing that bit enclosing b:
- [(4.1)](#4.1)
If u is of unsigned ordinary character type or std::byte type,u has an indeterminate value
if any of the bits in its value representation are indeterminate, or
otherwise has an erroneous value[.](#4.1.sentence-1)
- [(4.2)](#4.2)
Otherwise, if b is indeterminate, the behavior is undefined[.](#4.2.sentence-1)
- [(4.3)](#4.3)
Otherwise, the behavior is erroneous, and the result is as specified above[.](#4.3.sentence-1)
The result does not otherwise contain any indeterminate or erroneous values[.](#4.sentence-10)

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[bit.count]
# 22 General utilities library [[utilities]](./#utilities)
## 22.11 Bit manipulation [[bit]](bit#count)
### 22.11.7 Counting [bit.count]
[1](#1)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15920)
In the following descriptions,
let N denote numeric_limits<T>::digits[.](#1.sentence-1)
[🔗](#itemdecl:1)
`template<class T>
constexpr int countl_zero(T x) noexcept;
`
[2](#2)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15931)
*Constraints*: T is an unsigned integer type ([[basic.fundamental]](basic.fundamental "6.9.2Fundamental types"))[.](#2.sentence-1)
[3](#3)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15935)
*Returns*: The number of consecutive 0 bits in the value of x,
starting from the most significant bit[.](#3.sentence-1)
[*Note [1](#note-1)*:
Returns N if x == 0[.](#3.sentence-2)
— *end note*]
[🔗](#itemdecl:2)
`template<class T>
constexpr int countl_one(T x) noexcept;
`
[4](#4)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15951)
*Constraints*: T is an unsigned integer type ([[basic.fundamental]](basic.fundamental "6.9.2Fundamental types"))[.](#4.sentence-1)
[5](#5)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15955)
*Returns*: The number of consecutive 1 bits in the value of x,
starting from the most significant bit[.](#5.sentence-1)
[*Note [2](#note-2)*:
Returns N if x == numeric_limits<T>::max()[.](#5.sentence-2)
— *end note*]
[🔗](#itemdecl:3)
`template<class T>
constexpr int countr_zero(T x) noexcept;
`
[6](#6)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15971)
*Constraints*: T is an unsigned integer type ([[basic.fundamental]](basic.fundamental "6.9.2Fundamental types"))[.](#6.sentence-1)
[7](#7)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15975)
*Returns*: The number of consecutive 0 bits in the value of x,
starting from the least significant bit[.](#7.sentence-1)
[*Note [3](#note-3)*:
Returns N if x == 0[.](#7.sentence-2)
— *end note*]
[🔗](#itemdecl:4)
`template<class T>
constexpr int countr_one(T x) noexcept;
`
[8](#8)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15991)
*Constraints*: T is an unsigned integer type ([[basic.fundamental]](basic.fundamental "6.9.2Fundamental types"))[.](#8.sentence-1)
[9](#9)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15995)
*Returns*: The number of consecutive 1 bits in the value of x,
starting from the least significant bit[.](#9.sentence-1)
[*Note [4](#note-4)*:
Returns N if x == numeric_limits<T>::max()[.](#9.sentence-2)
— *end note*]
[🔗](#itemdecl:5)
`template<class T>
constexpr int popcount(T x) noexcept;
`
[10](#10)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L16011)
*Constraints*: T is an unsigned integer type ([[basic.fundamental]](basic.fundamental "6.9.2Fundamental types"))[.](#10.sentence-1)
[11](#11)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L16015)
*Returns*: The number of 1 bits in the value of x[.](#11.sentence-1)

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[bit.endian]
# 22 General utilities library [[utilities]](./#utilities)
## 22.11 Bit manipulation [[bit]](bit#endian)
### 22.11.8 Endian [bit.endian]
[1](#1)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L16022)
Two common methods of byte ordering in multibyte scalar types are big-endian
and little-endian in the execution environment[.](#1.sentence-1)
Big-endian is a format for
storage of binary data in which the most significant byte is placed first,
with the rest in descending order[.](#1.sentence-2)
Little-endian is a format for storage of
binary data in which the least significant byte is placed first, with the rest
in ascending order[.](#1.sentence-3)
This subclause describes the endianness of the scalar types
of the execution environment[.](#1.sentence-4)
[🔗](#lib:endian)
`enum class endian {
little = see below,
big = see below,
native = see below
};
`
[2](#2)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L16044)
If all scalar types have size 1 byte, then all of endian::little,endian::big, and endian::native have the same value[.](#2.sentence-1)
Otherwise, endian::little is not equal to endian::big[.](#2.sentence-2)
If all scalar types are big-endian, endian::native is
equal to endian::big[.](#2.sentence-3)
If all scalar types are little-endian, endian::native is
equal to endian::little[.](#2.sentence-4)
Otherwise, endian::native is not equal
to either endian::big or endian::little[.](#2.sentence-5)

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[bit.general]
# 22 General utilities library [[utilities]](./#utilities)
## 22.11 Bit manipulation [[bit]](bit#general)
### 22.11.1 General [bit.general]
[1](#1)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15628)
The header <bit> provides components to access,
manipulate and process both individual bits and bit sequences[.](#1.sentence-1)

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[bit.pow.two]
# 22 General utilities library [[utilities]](./#utilities)
## 22.11 Bit manipulation [[bit]](bit#pow.two)
### 22.11.5 Integral powers of 2 [bit.pow.two]
[🔗](#lib:has_single_bit)
`template<class T>
constexpr bool has_single_bit(T x) noexcept;
`
[1](#1)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15788)
*Constraints*: T is an unsigned integer type ([[basic.fundamental]](basic.fundamental "6.9.2Fundamental types"))[.](#1.sentence-1)
[2](#2)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15792)
*Returns*: true if x is an integral power of two;false otherwise[.](#2.sentence-1)
[🔗](#lib:bit_ceil)
`template<class T>
constexpr T bit_ceil(T x);
`
[3](#3)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15806)
Let N be the smallest power of 2 greater than or equal to x[.](#3.sentence-1)
[4](#4)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15809)
*Constraints*: T is an unsigned integer type ([[basic.fundamental]](basic.fundamental "6.9.2Fundamental types"))[.](#4.sentence-1)
[5](#5)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15813)
*Preconditions*: N is representable as a value of type T[.](#5.sentence-1)
[6](#6)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15817)
*Returns*: N[.](#6.sentence-1)
[7](#7)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15821)
*Throws*: Nothing[.](#7.sentence-1)
[8](#8)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15825)
*Remarks*: A function call expression
that violates the precondition in the *Preconditions*: element
is not a core constant expression ([[expr.const]](expr.const "7.7Constant expressions"))[.](#8.sentence-1)
[🔗](#lib:bit_floor)
`template<class T>
constexpr T bit_floor(T x) noexcept;
`
[9](#9)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15839)
*Constraints*: T is an unsigned integer type ([[basic.fundamental]](basic.fundamental "6.9.2Fundamental types"))[.](#9.sentence-1)
[10](#10)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15843)
*Returns*: If x == 0, 0;
otherwise the maximal value y such that has_single_bit(y) is true and y <= x[.](#10.sentence-1)
[🔗](#lib:bit_width)
`template<class T>
constexpr int bit_width(T x) noexcept;
`
[11](#11)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15858)
*Constraints*: T is an unsigned integer type ([[basic.fundamental]](basic.fundamental "6.9.2Fundamental types"))[.](#11.sentence-1)
[12](#12)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15862)
*Returns*: If x == 0, 0;
otherwise one plus the base-2 logarithm of x,
with any fractional part discarded[.](#12.sentence-1)

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[bit.rotate]
# 22 General utilities library [[utilities]](./#utilities)
## 22.11 Bit manipulation [[bit]](bit#rotate)
### 22.11.6 Rotating [bit.rotate]
[1](#1)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15872)
In the following descriptions,
let N denote numeric_limits<T>::digits[.](#1.sentence-1)
[🔗](#itemdecl:1)
`template<class T>
constexpr T rotl(T x, int s) noexcept;
`
[2](#2)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15883)
*Constraints*: T is an unsigned integer type ([[basic.fundamental]](basic.fundamental "6.9.2Fundamental types"))[.](#2.sentence-1)
[3](#3)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15887)
Let r be s % N[.](#3.sentence-1)
[4](#4)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15890)
*Returns*: If r is 0, x;
if r is positive, (x << r) | (x >> (N - r));
if r is negative, rotr(x, -r)[.](#4.sentence-1)
[🔗](#itemdecl:2)
`template<class T>
constexpr T rotr(T x, int s) noexcept;
`
[5](#5)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15904)
*Constraints*: T is an unsigned integer type ([[basic.fundamental]](basic.fundamental "6.9.2Fundamental types"))[.](#5.sentence-1)
[6](#6)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15908)
Let r be s % N[.](#6.sentence-1)
[7](#7)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15911)
*Returns*: If r is 0, x;
if r is positive, (x >> r) | (x << (N - r));
if r is negative, rotl(x, -r)[.](#7.sentence-1)

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[bit.syn]
# 22 General utilities library [[utilities]](./#utilities)
## 22.11 Bit manipulation [[bit]](bit#syn)
### 22.11.2 Header <bit> synopsis [bit.syn]
// all freestandingnamespace std {// [[bit.cast]](bit.cast "22.11.3Function template bit_­cast"), bit_casttemplate<class To, class From>constexpr To bit_cast(const From& from) noexcept; // [[bit.byteswap]](bit.byteswap "22.11.4byteswap"), byteswaptemplate<class T>constexpr T byteswap(T value) noexcept; // [[bit.pow.two]](bit.pow.two "22.11.5Integral powers of 2"), integral powers of 2template<class T>constexpr bool has_single_bit(T x) noexcept; template<class T>constexpr T bit_ceil(T x); template<class T>constexpr T bit_floor(T x) noexcept; template<class T>constexpr int bit_width(T x) noexcept; // [[bit.rotate]](bit.rotate "22.11.6Rotating"), rotatingtemplate<class T>constexpr T rotl(T x, int s) noexcept; template<class T>constexpr T rotr(T x, int s) noexcept; // [[bit.count]](bit.count "22.11.7Counting"), countingtemplate<class T>constexpr int countl_zero(T x) noexcept; template<class T>constexpr int countl_one(T x) noexcept; template<class T>constexpr int countr_zero(T x) noexcept; template<class T>constexpr int countr_one(T x) noexcept; template<class T>constexpr int popcount(T x) noexcept; // [[bit.endian]](bit.endian "22.11.8Endian"), endianenum class endian { little = *see below*,
big = *see below*,
native = *see below*};}