std::sinh(std::valarray)

template< class T >
valarray<T> sinh( const valarray<T>& va );

For each element in va computes hyperbolic sine of the value of the element.

Parameters

Return value

Value array containing hyperbolic sine of the values in va.

Notes

Unqualified function (sinh) is used to perform the computation. If such function is not available, std::sinh is used due to argument-dependent lookup.

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

• All const member functions of std::valarray are provided.
• std::valarray, std::slice_array, std::gslice_array, std::mask_array and std::indirect_array can be constructed from the replacement type.
• All functions accepting an argument of type const std::valarray& except begin() and end() (since C++11) should also accept the replacement type.
• All functions accepting two arguments of type const std::valarray& should accept every combination of const std::valarray& and the replacement type.
• The return type does not add more than two levels of template nesting over the most deeply-nested argument type.

Possible implementation

template< class T >
valarray<T> sinh( const valarray<T>& va )
{
    valarray<T> other = va;
    for (T &i : other)
        i = sinh(i);
 
    return other; // proxy object may be returned
}

Example

#include <cmath>
#include <iomanip>
#include <iostream>
#include <valarray>
#include <complex>
 
template<typename T>
void show(char const* title, const std::valarray<T>& va)
{
    std::cout << title << " : " << std::right;
    for (T x : va) {
        std::cout << std::fixed << x << " ";
    }
    std::cout << '\n';
}
 
template<typename T>
void sinh_for(std::valarray<T> const& z)
{
    // Hyperbolic sine is sinh(z) = (eᶻ - e⁻ᶻ) / 2.
 
    const std::valarray<T> sinh_z { std::sinh(z) };
    const std::valarray<T> e_z { std::exp(z) };
    const std::valarray<T> e_neg_z { std::exp(-z) };
    const std::valarray<T> sinh_def { (e_z - e_neg_z) / 2.0f };
 
    show("n         ", z);
    show("sinh(n)   ", sinh_z);
    show("(eⁿ-e⁻ⁿ)/2", sinh_def);
 
    std::cout.put('\n');
}
 
int main()
{
    sinh_for(std::valarray<float>{ -.2f, -.1f, 0.f, .1f, .2f, INFINITY });
    sinh_for(std::valarray<std::complex<double>>{ {-.2,-.1}, {.2,.1} });
}

n          : -0.200000 -0.100000 0.000000 0.100000 0.200000 inf 
sinh(n)    : -0.201336 -0.100167 0.000000 0.100167 0.201336 inf 
(eⁿ-e⁻ⁿ)/2 : -0.201336 -0.100167 0.000000 0.100167 0.201336 inf 
 
n          : (-0.200000,-0.100000) (0.200000,0.100000) 
sinh(n)    : (-0.200330,-0.101837) (0.200330,0.101837) 
(eⁿ-e⁻ⁿ)/2 : (-0.200330,-0.101837) (0.200330,0.101837)

See also