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[bit]
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# 22 General utilities library [[utilities]](./#utilities)
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## 22.11 Bit manipulation [bit]
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### [22.11.1](#general) General [[bit.general]](bit.general)
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[1](#general-1)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15628)
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The header <bit> provides components to access,
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manipulate and process both individual bits and bit sequences[.](#general-1.sentence-1)
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### [22.11.2](#syn) Header <bit> synopsis [[bit.syn]](bit.syn)
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// all freestandingnamespace std {// [[bit.cast]](#cast "22.11.3 Function template bit_cast"), bit_casttemplate<class To, class From>constexpr To bit_cast(const From& from) noexcept; // [[bit.byteswap]](#byteswap "22.11.4 byteswap"), byteswaptemplate<class T>constexpr T byteswap(T value) noexcept; // [[bit.pow.two]](#pow.two "22.11.5 Integral 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]](#rotate "22.11.6 Rotating"), rotatingtemplate<class T>constexpr T rotl(T x, int s) noexcept; template<class T>constexpr T rotr(T x, int s) noexcept; // [[bit.count]](#count "22.11.7 Counting"), 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]](#endian "22.11.8 Endian"), endianenum class endian { little = *see below*,
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big = *see below*,
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native = *see below*};}
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### [22.11.3](#cast) Function template bit_cast [[bit.cast]](bit.cast)
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[ð](#lib:bit_cast)
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`template<class To, class From>
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constexpr To bit_cast(const From& from) noexcept;
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`
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[1](#cast-1)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15691)
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*Constraints*:
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- [(1.1)](#cast-1.1)
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sizeof(To) == sizeof(From) is true;
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- [(1.2)](#cast-1.2)
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is_trivially_copyable_v<To> is true; and
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- [(1.3)](#cast-1.3)
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is_trivially_copyable_v<From> is true[.](#cast-1.sentence-1)
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[2](#cast-2)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15699)
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*Mandates*: Neither To nor From are consteval-only types ([[expr.const]](expr.const "7.7 Constant expressions"))[.](#cast-2.sentence-1)
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[3](#cast-3)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15703)
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*Constant When*: To, From, and the types of all subobjects
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of To and From are types T such that:
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- [(3.1)](#cast-3.1)
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is_union_v<T> is false;
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- [(3.2)](#cast-3.2)
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is_pointer_v<T> is false;
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- [(3.3)](#cast-3.3)
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is_member_pointer_v<T> is false;
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- [(3.4)](#cast-3.4)
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is_volatile_v<T> is false; and
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- [(3.5)](#cast-3.5)
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T has no non-static data members of reference type[.](#cast-3.sentence-1)
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[4](#cast-4)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15715)
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*Returns*: An object of type To[.](#cast-4.sentence-1)
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Implicitly creates objects nested within the result ([[intro.object]](intro.object "6.8.2 Object model"))[.](#cast-4.sentence-2)
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Each bit of the value representation of the result
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is equal to the corresponding bit in the object representation
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of from[.](#cast-4.sentence-3)
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Padding bits of the result are unspecified[.](#cast-4.sentence-4)
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For the result and each object created within it,
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if there is no value of the object's type corresponding to the
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value representation produced, the behavior is undefined[.](#cast-4.sentence-5)
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If there are multiple such values, which value is produced is unspecified[.](#cast-4.sentence-6)
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A bit in the value representation of the result is indeterminate if
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it does not correspond to a bit in the value representation of from or
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corresponds to a bit
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for which the smallest enclosing object is not within its lifetime or
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has an indeterminate value ([[basic.indet]](basic.indet "6.8.5 Indeterminate and erroneous values"))[.](#cast-4.sentence-7)
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A bit in the value representation of the result is erroneous
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if it corresponds to a bit
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for which the smallest enclosing object has an erroneous value[.](#cast-4.sentence-8)
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For each bit b in the value representation of the result
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that is indeterminate or erroneous,
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let u be the smallest object containing that bit enclosing b:
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- [(4.1)](#cast-4.1)
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If u is of unsigned ordinary character type or std::byte type,u has an indeterminate value
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if any of the bits in its value representation are indeterminate, or
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otherwise has an erroneous value[.](#cast-4.1.sentence-1)
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- [(4.2)](#cast-4.2)
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Otherwise, if b is indeterminate, the behavior is undefined[.](#cast-4.2.sentence-1)
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- [(4.3)](#cast-4.3)
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Otherwise, the behavior is erroneous, and the result is as specified above[.](#cast-4.3.sentence-1)
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The result does not otherwise contain any indeterminate or erroneous values[.](#cast-4.sentence-10)
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### [22.11.4](#byteswap) byteswap [[bit.byteswap]](bit.byteswap)
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[ð](#lib:byteswap)
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`template<class T>
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constexpr T byteswap(T value) noexcept;
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`
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[1](#byteswap-1)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15760)
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*Constraints*: T models [integral](concepts.arithmetic#concept:integral "18.4.7 Arithmetic concepts [concepts.arithmetic]")[.](#byteswap-1.sentence-1)
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[2](#byteswap-2)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15764)
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*Mandates*: T does not have padding bits ([[basic.types.general]](basic.types.general "6.9.1 General"))[.](#byteswap-2.sentence-1)
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[3](#byteswap-3)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15768)
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Let the sequence R comprise
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the bytes of the object representation of value in reverse order[.](#byteswap-3.sentence-1)
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[4](#byteswap-4)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15772)
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*Returns*: An object v of type T such that each byte in the object representation of v is equal to
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the byte in the corresponding position in R[.](#byteswap-4.sentence-1)
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### [22.11.5](#pow.two) Integral powers of 2 [[bit.pow.two]](bit.pow.two)
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[ð](#lib:has_single_bit)
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`template<class T>
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constexpr bool has_single_bit(T x) noexcept;
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`
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[1](#pow.two-1)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15788)
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*Constraints*: T is an unsigned integer type ([[basic.fundamental]](basic.fundamental "6.9.2 Fundamental types"))[.](#pow.two-1.sentence-1)
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[2](#pow.two-2)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15792)
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*Returns*: true if x is an integral power of two;false otherwise[.](#pow.two-2.sentence-1)
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[ð](#lib:bit_ceil)
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`template<class T>
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constexpr T bit_ceil(T x);
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`
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[3](#pow.two-3)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15806)
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Let N be the smallest power of 2 greater than or equal to x[.](#pow.two-3.sentence-1)
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[4](#pow.two-4)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15809)
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*Constraints*: T is an unsigned integer type ([[basic.fundamental]](basic.fundamental "6.9.2 Fundamental types"))[.](#pow.two-4.sentence-1)
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[5](#pow.two-5)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15813)
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*Preconditions*: N is representable as a value of type T[.](#pow.two-5.sentence-1)
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[6](#pow.two-6)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15817)
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*Returns*: N[.](#pow.two-6.sentence-1)
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[7](#pow.two-7)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15821)
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*Throws*: Nothing[.](#pow.two-7.sentence-1)
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[8](#pow.two-8)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15825)
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*Remarks*: A function call expression
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that violates the precondition in the *Preconditions*: element
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is not a core constant expression ([[expr.const]](expr.const "7.7 Constant expressions"))[.](#pow.two-8.sentence-1)
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[ð](#lib:bit_floor)
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`template<class T>
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constexpr T bit_floor(T x) noexcept;
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`
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[9](#pow.two-9)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15839)
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*Constraints*: T is an unsigned integer type ([[basic.fundamental]](basic.fundamental "6.9.2 Fundamental types"))[.](#pow.two-9.sentence-1)
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[10](#pow.two-10)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15843)
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*Returns*: If x == 0, 0;
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otherwise the maximal value y such that has_single_bit(y) is true and y <= x[.](#pow.two-10.sentence-1)
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[ð](#lib:bit_width)
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`template<class T>
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constexpr int bit_width(T x) noexcept;
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`
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[11](#pow.two-11)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15858)
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*Constraints*: T is an unsigned integer type ([[basic.fundamental]](basic.fundamental "6.9.2 Fundamental types"))[.](#pow.two-11.sentence-1)
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[12](#pow.two-12)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15862)
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*Returns*: If x == 0, 0;
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otherwise one plus the base-2 logarithm of x,
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with any fractional part discarded[.](#pow.two-12.sentence-1)
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### [22.11.6](#rotate) Rotating [[bit.rotate]](bit.rotate)
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[1](#rotate-1)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15872)
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In the following descriptions,
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let N denote numeric_limits<T>::digits[.](#rotate-1.sentence-1)
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|
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[ð](#rotate-itemdecl:1)
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`template<class T>
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constexpr T rotl(T x, int s) noexcept;
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`
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[2](#rotate-2)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15883)
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|
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*Constraints*: T is an unsigned integer type ([[basic.fundamental]](basic.fundamental "6.9.2 Fundamental types"))[.](#rotate-2.sentence-1)
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[3](#rotate-3)
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|
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15887)
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Let r be s % N[.](#rotate-3.sentence-1)
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[4](#rotate-4)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15890)
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*Returns*: If r is 0, x;
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if r is positive, (x << r) | (x >> (N - r));
|
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if r is negative, rotr(x, -r)[.](#rotate-4.sentence-1)
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[ð](#rotate-itemdecl:2)
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`template<class T>
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constexpr T rotr(T x, int s) noexcept;
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`
|
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|
||||
[5](#rotate-5)
|
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|
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15904)
|
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|
||||
*Constraints*: T is an unsigned integer type ([[basic.fundamental]](basic.fundamental "6.9.2 Fundamental types"))[.](#rotate-5.sentence-1)
|
||||
|
||||
[6](#rotate-6)
|
||||
|
||||
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15908)
|
||||
|
||||
Let r be s % N[.](#rotate-6.sentence-1)
|
||||
|
||||
[7](#rotate-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)[.](#rotate-7.sentence-1)
|
||||
|
||||
### [22.11.7](#count) Counting [[bit.count]](bit.count)
|
||||
|
||||
[1](#count-1)
|
||||
|
||||
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15920)
|
||||
|
||||
In the following descriptions,
|
||||
let N denote numeric_limits<T>::digits[.](#count-1.sentence-1)
|
||||
|
||||
[ð](#count-itemdecl:1)
|
||||
|
||||
`template<class T>
|
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constexpr int countl_zero(T x) noexcept;
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`
|
||||
|
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[2](#count-2)
|
||||
|
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15931)
|
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|
||||
*Constraints*: T is an unsigned integer type ([[basic.fundamental]](basic.fundamental "6.9.2 Fundamental types"))[.](#count-2.sentence-1)
|
||||
|
||||
[3](#count-3)
|
||||
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15935)
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||||
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*Returns*: The number of consecutive 0 bits in the value of x,
|
||||
starting from the most significant bit[.](#count-3.sentence-1)
|
||||
|
||||
[*Note [1](#count-note-1)*:
|
||||
|
||||
Returns N if x == 0[.](#count-3.sentence-2)
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||||
|
||||
â *end note*]
|
||||
|
||||
[ð](#count-itemdecl:2)
|
||||
|
||||
`template<class T>
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constexpr int countl_one(T x) noexcept;
|
||||
`
|
||||
|
||||
[4](#count-4)
|
||||
|
||||
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15951)
|
||||
|
||||
*Constraints*: T is an unsigned integer type ([[basic.fundamental]](basic.fundamental "6.9.2 Fundamental types"))[.](#count-4.sentence-1)
|
||||
|
||||
[5](#count-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[.](#count-5.sentence-1)
|
||||
|
||||
[*Note [2](#count-note-2)*:
|
||||
|
||||
Returns N if x == numeric_limits<T>::max()[.](#count-5.sentence-2)
|
||||
|
||||
â *end note*]
|
||||
|
||||
[ð](#count-itemdecl:3)
|
||||
|
||||
`template<class T>
|
||||
constexpr int countr_zero(T x) noexcept;
|
||||
`
|
||||
|
||||
[6](#count-6)
|
||||
|
||||
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15971)
|
||||
|
||||
*Constraints*: T is an unsigned integer type ([[basic.fundamental]](basic.fundamental "6.9.2 Fundamental types"))[.](#count-6.sentence-1)
|
||||
|
||||
[7](#count-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[.](#count-7.sentence-1)
|
||||
|
||||
[*Note [3](#count-note-3)*:
|
||||
|
||||
Returns N if x == 0[.](#count-7.sentence-2)
|
||||
|
||||
â *end note*]
|
||||
|
||||
[ð](#count-itemdecl:4)
|
||||
|
||||
`template<class T>
|
||||
constexpr int countr_one(T x) noexcept;
|
||||
`
|
||||
|
||||
[8](#count-8)
|
||||
|
||||
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L15991)
|
||||
|
||||
*Constraints*: T is an unsigned integer type ([[basic.fundamental]](basic.fundamental "6.9.2 Fundamental types"))[.](#count-8.sentence-1)
|
||||
|
||||
[9](#count-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[.](#count-9.sentence-1)
|
||||
|
||||
[*Note [4](#count-note-4)*:
|
||||
|
||||
Returns N if x == numeric_limits<T>::max()[.](#count-9.sentence-2)
|
||||
|
||||
â *end note*]
|
||||
|
||||
[ð](#count-itemdecl:5)
|
||||
|
||||
`template<class T>
|
||||
constexpr int popcount(T x) noexcept;
|
||||
`
|
||||
|
||||
[10](#count-10)
|
||||
|
||||
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L16011)
|
||||
|
||||
*Constraints*: T is an unsigned integer type ([[basic.fundamental]](basic.fundamental "6.9.2 Fundamental types"))[.](#count-10.sentence-1)
|
||||
|
||||
[11](#count-11)
|
||||
|
||||
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/utilities.tex#L16015)
|
||||
|
||||
*Returns*: The number of 1 bits in the value of x[.](#count-11.sentence-1)
|
||||
|
||||
### [22.11.8](#endian) Endian [[bit.endian]](bit.endian)
|
||||
|
||||
[1](#endian-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[.](#endian-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[.](#endian-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[.](#endian-1.sentence-3)
|
||||
|
||||
This subclause describes the endianness of the scalar types
|
||||
of the execution environment[.](#endian-1.sentence-4)
|
||||
|
||||
[ð](#lib:endian)
|
||||
|
||||
`enum class endian {
|
||||
little = see below,
|
||||
big = see below,
|
||||
native = see below
|
||||
};
|
||||
`
|
||||
|
||||
[2](#endian-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[.](#endian-2.sentence-1)
|
||||
|
||||
Otherwise, endian::little is not equal to endian::big[.](#endian-2.sentence-2)
|
||||
|
||||
If all scalar types are big-endian, endian::native is
|
||||
equal to endian::big[.](#endian-2.sentence-3)
|
||||
|
||||
If all scalar types are little-endian, endian::native is
|
||||
equal to endian::little[.](#endian-2.sentence-4)
|
||||
|
||||
Otherwise, endian::native is not equal
|
||||
to either endian::big or endian::little[.](#endian-2.sentence-5)
|
||||
Reference in New Issue
Block a user