operator+,-,*,/,%,&,|,^,<<,>>,&&,|| (std::valarray)

From cppreference.com
< cpplrm; | numericlrm; | valarray
Defined in header <valarray>
template <class T>

std::valarray<T> operator+ (const std::valarray<T>& lhs, const std::valarray<T>& rhs);
template <class T>
std::valarray<T> operator- (const std::valarray<T>& lhs, const std::valarray<T>& rhs);
template <class T>
std::valarray<T> operator* (const std::valarray<T>& lhs, const std::valarray<T>& rhs);
template <class T>
std::valarray<T> operator/ (const std::valarray<T>& lhs, const std::valarray<T>& rhs);
template <class T>
std::valarray<T> operator% (const std::valarray<T>& lhs, const std::valarray<T>& rhs);
template <class T>
std::valarray<T> operator& (const std::valarray<T>& lhs, const std::valarray<T>& rhs);
template <class T>
std::valarray<T> operator| (const std::valarray<T>& lhs, const std::valarray<T>& rhs);
template <class T>
std::valarray<T> operator^ (const std::valarray<T>& lhs, const std::valarray<T>& rhs);
template <class T>
std::valarray<T> operator<<(const std::valarray<T>& lhs, const std::valarray<T>& rhs);
template <class T>
std::valarray<T> operator>>(const std::valarray<T>& lhs, const std::valarray<T>& rhs);
template <class T>
std::valarray<bool> operator&&(const std::valarray<T>& lhs, const std::valarray<T>& rhs);
template <class T>

std::valarray<bool> operator||(const std::valarray<T>& lhs, const std::valarray<T>& rhs);
(1)
template <class T>

std::valarray<T> operator+ (const typename std::valarray<T>::value_type & val,
const std::valarray<T>& rhs);
template <class T>
std::valarray<T> operator- (const typename std::valarray<T>::value_type & val,
const std::valarray<T>& rhs);
template <class T>
std::valarray<T> operator* (const typename std::valarray<T>::value_type & val,
const std::valarray<T>& rhs);
template <class T>
std::valarray<T> operator/ (const typename std::valarray<T>::value_type & val,
const std::valarray<T>& rhs);
template <class T>
std::valarray<T> operator% (const typename std::valarray<T>::value_type & val,
const std::valarray<T>& rhs);
template <class T>
std::valarray<T> operator& (const typename std::valarray<T>::value_type & val,
const std::valarray<T>& rhs);
template <class T>
std::valarray<T> operator| (const typename std::valarray<T>::value_type & val,
const std::valarray<T>& rhs);
template <class T>
std::valarray<T> operator^ (const typename std::valarray<T>::value_type & val,
const std::valarray<T>& rhs);
template <class T>
std::valarray<T> operator<<(const typename std::valarray<T>::value_type & val,
const std::valarray<T>& rhs);
template <class T>
std::valarray<T> operator>>(const typename std::valarray<T>::value_type & val,
const std::valarray<T>& rhs);
template <class T>
std::valarray<bool> operator&&(const typename std::valarray<T>::value_type & val,
const std::valarray<T>& rhs);
template <class T>
std::valarray<bool> operator||(const typename std::valarray<T>::value_type & val,

const std::valarray<T>& rhs);
(2)
template <class T>

std::valarray<T> operator+ (const std::valarray<T>& lhs,
const typename std::valarray<T>::value_type & val);
template <class T>
std::valarray<T> operator- (const std::valarray<T>& lhs,
const typename std::valarray<T>::value_type & val);
template <class T>
std::valarray<T> operator* (const std::valarray<T>& lhs,
const typename std::valarray<T>::value_type & val);
template <class T>
std::valarray<T> operator/ (const std::valarray<T>& lhs,
const typename std::valarray<T>::value_type & val);
template <class T>
std::valarray<T> operator% (const std::valarray<T>& lhs,
const typename std::valarray<T>::value_type & val);
template <class T>
std::valarray<T> operator& (const std::valarray<T>& lhs,
const typename std::valarray<T>::value_type & val);
template <class T>
std::valarray<T> operator| (const std::valarray<T>& lhs,
const typename std::valarray<T>::value_type & val);
template <class T>
std::valarray<T> operator^ (const std::valarray<T>& lhs,
const typename std::valarray<T>::value_type & val);
template <class T>
std::valarray<T> operator<<(const std::valarray<T>& lhs,
const typename std::valarray<T>::value_type & val);
template <class T>
std::valarray<T> operator>>(const std::valarray<T>& lhs,
const typename std::valarray<T>::value_type & val);
template <class T>
std::valarray<bool> operator&&(const std::valarray<T>& lhs,
const typename std::valarray<T>::value_type & val);
template <class T>
std::valarray<bool> operator||(const std::valarray<T>& lhs,

const typename std::valarray<T>::value_type & val);
(3)

Apply binary operators to each element of two valarrays, or a valarray and a value.

1) The operators works on valarrays of the same size and returns a valarray with the same size as the parameters with the operation applied to every elements of the two arguments.
2,3) Applies the operator between each element of the valarray and the scalar.

Parameters

rhs - a numeric array
lhs - a numeric array
val - a value of type T

Return value

A valarray with the same size as the parameter.

Note

The behaviour is undefined when the two arguments are valarrays with different sizes.

The function can be implemented with the return type different from std::valarray. In this case, the replacement type has the following properties:

Defect reports

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

DR Applied to Behavior as published Correct behavior
LWG 3074 C++98 T is deduced from both the scalar and the valarray for (2-3), disallowing mixed-type calls only deduce T from the valarray

Example

Finds real roots of multiple quadratic equations.

#include <valarray>
#include <iostream>

int main()
{
    std::valarray<double> a(1, 8);
    std::valarray<double> b{1, 2, 3, 4, 5, 6, 7, 8};
    std::valarray<double> c = -b;
    // literals must also be of type T (double in this case)
    std::valarray<double> d = std::sqrt((b * b - 4.0 * a * c));
    std::valarray<double> x1 = (-b - d) / (2.0 * a);
    std::valarray<double> x2 = (-b + d) / (2.0 * a);
    std::cout << "quadratic equation    root 1,  root 2" << "\n";
    for (size_t i = 0; i < a.size(); ++i) {
        std::cout << a[i] << "x\u00B2 + " << b[i] << "x + " << c[i] << " = 0   ";
        std::cout << x1[i] << ", " << x2[i] << "\n";
    }
}

Output:

quadratic equation    root 1,  root 2
1x + 1x + -1 = 0   -1.61803, 0.618034
1x + 2x + -2 = 0   -2.73205, 0.732051
1x + 3x + -3 = 0   -3.79129, 0.791288
1x + 4x + -4 = 0   -4.82843, 0.828427
1x + 5x + -5 = 0   -5.8541, 0.854102
1x + 6x + -6 = 0   -6.87298, 0.872983
1x + 7x + -7 = 0   -7.88748, 0.887482
1x + 8x + -8 = 0   -8.89898, 0.898979