[valarray.syn]

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

## 29.6 Numeric arrays [[numarray]](numarray#valarray.syn)

### 29.6.1 Header <valarray> synopsis [valarray.syn]

[ð](#header:%3cvalarray%3e)

#include <initializer_list> // see [[initializer.list.syn]](initializer.list.syn "17.11.2 Header <initializer_­list> synopsis")namespace std {template<class T> class valarray; // An array of type Tclass slice; // a BLAS-like slice out of an arraytemplate<class T> class slice_array; class gslice; // a generalized slice out of an arraytemplate<class T> class gslice_array; template<class T> class mask_array; // a masked arraytemplate<class T> class indirect_array; // an indirected arraytemplate<class T> void swap(valarray<T>&, valarray<T>&) noexcept; template<class T> valarray<T> operator* (const valarray<T>&, const valarray<T>&); template<class T> valarray<T> operator* (const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<T> operator* (const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<T> operator/ (const valarray<T>&, const valarray<T>&); template<class T> valarray<T> operator/ (const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<T> operator/ (const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<T> operator% (const valarray<T>&, const valarray<T>&); template<class T> valarray<T> operator% (const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<T> operator% (const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<T> operator+ (const valarray<T>&, const valarray<T>&); template<class T> valarray<T> operator+ (const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<T> operator+ (const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<T> operator- (const valarray<T>&, const valarray<T>&); template<class T> valarray<T> operator- (const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<T> operator- (const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<T> operator^ (const valarray<T>&, const valarray<T>&); template<class T> valarray<T> operator^ (const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<T> operator^ (const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<T> operator& (const valarray<T>&, const valarray<T>&); template<class T> valarray<T> operator& (const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<T> operator& (const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<T> operator| (const valarray<T>&, const valarray<T>&); template<class T> valarray<T> operator| (const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<T> operator| (const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<T> operator<<(const valarray<T>&, const valarray<T>&); template<class T> valarray<T> operator<<(const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<T> operator<<(const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<T> operator>>(const valarray<T>&, const valarray<T>&); template<class T> valarray<T> operator>>(const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<T> operator>>(const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<bool> operator&&(const valarray<T>&, const valarray<T>&); template<class T> valarray<bool> operator&&(const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<bool> operator&&(const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<bool> operator||(const valarray<T>&, const valarray<T>&); template<class T> valarray<bool> operator||(const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<bool> operator||(const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<bool> operator==(const valarray<T>&, const valarray<T>&); template<class T> valarray<bool> operator==(const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<bool> operator==(const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<bool> operator!=(const valarray<T>&, const valarray<T>&); template<class T> valarray<bool> operator!=(const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<bool> operator!=(const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<bool> operator< (const valarray<T>&, const valarray<T>&); template<class T> valarray<bool> operator< (const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<bool> operator< (const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<bool> operator> (const valarray<T>&, const valarray<T>&); template<class T> valarray<bool> operator> (const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<bool> operator> (const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<bool> operator<=(const valarray<T>&, const valarray<T>&); template<class T> valarray<bool> operator<=(const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<bool> operator<=(const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<bool> operator>=(const valarray<T>&, const valarray<T>&); template<class T> valarray<bool> operator>=(const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<bool> operator>=(const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<T> abs (const valarray<T>&); template<class T> valarray<T> acos (const valarray<T>&); template<class T> valarray<T> asin (const valarray<T>&); template<class T> valarray<T> atan (const valarray<T>&); template<class T> valarray<T> atan2(const valarray<T>&, const valarray<T>&); template<class T> valarray<T> atan2(const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<T> atan2(const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<T> cos (const valarray<T>&); template<class T> valarray<T> cosh (const valarray<T>&); template<class T> valarray<T> exp (const valarray<T>&); template<class T> valarray<T> log (const valarray<T>&); template<class T> valarray<T> log10(const valarray<T>&); template<class T> valarray<T> pow(const valarray<T>&, const valarray<T>&); template<class T> valarray<T> pow(const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<T> pow(const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<T> sin (const valarray<T>&); template<class T> valarray<T> sinh (const valarray<T>&); template<class T> valarray<T> sqrt (const valarray<T>&); template<class T> valarray<T> tan (const valarray<T>&); template<class T> valarray<T> tanh (const valarray<T>&); template<class T> *unspecified*1 begin(valarray<T>& v); template<class T> *unspecified*2 begin(const valarray<T>& v); template<class T> *unspecified*1 end(valarray<T>& v); template<class T> *unspecified*2 end(const valarray<T>& v);}

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L7123)

The header [<valarray>](#header:%3cvalarray%3e "29.6.1 Header <valarray> synopsis [valarray.syn]") defines five class templates
(valarray,slice_array,gslice_array,mask_array,
andindirect_array),
two classes (slice andgslice),
and a series of related
function templates
for representing
and manipulating arrays of values[.](#1.sentence-1)

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L7139)

Thevalarray array classes
are defined to be free of certain forms of aliasing, thus allowing
operations on these classes to be optimized[.](#2.sentence-1)

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L7146)

Any function returning avalarray<T> is permitted to return an object of another type, provided all the
const member functions ofvalarray<T> are also applicable to this type[.](#3.sentence-1)

This return type shall not add
more than two levels of template nesting over the most deeply nested
argument type[.](#3.sentence-2)[247](#footnote-247 "[implimits] recommends a minimum number of recursively nested template instantiations. This requirement thus indirectly suggests a minimum allowable complexity for valarray expressions.")

[4](#4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L7164)

Implementations introducing such replacement types shall provide
additional functions and operators as follows:

- [(4.1)](#4.1)

for every function taking aconst valarray<T>& other than[begin](valarray.range#lib:begin,valarray "29.6.10 valarray range access [valarray.range]") and[end](valarray.range#lib:end,valarray "29.6.10 valarray range access [valarray.range]"),
identical functions taking the replacement types shall be added;

- [(4.2)](#4.2)

for every function taking twoconst valarray<T>& arguments, identical functions taking every combination ofconst valarray<T>& and replacement types shall be added[.](#4.sentence-1)

[5](#5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L7182)

In particular, an implementation shall allow avalarray<T> to be constructed from such replacement types and shall allow assignments
and compound assignments of such types tovalarray<T>,slice_array<T>,gslice_array<T>,mask_array<T> andindirect_array<T> objects[.](#5.sentence-1)

[6](#6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L7195)

These library functions are permitted to throw a[bad_alloc](bad.alloc "17.6.4.1 Class bad_­alloc [bad.alloc]") exception if there are not sufficient resources available
to carry out the operation[.](#6.sentence-1)

Note that the exception is not mandated[.](#6.sentence-2)

[247)](#footnote-247)[247)](#footnoteref-247)

[[implimits]](implimits "Annex B (informative) Implementation quantities") recommends a minimum number
of recursively nested template
instantiations[.](#footnote-247.sentence-1)

This requirement thus indirectly suggests a minimum
allowable complexity for valarray expressions[.](#footnote-247.sentence-2)
