# std::sinh(std::valarray)

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< cpp‎ | numeric‎ | valarray

Defined in header `<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

va | - | value array to apply the operation to

### 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

Run this code

    #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} });
    }

Output:

    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

cosh(std::valarray) | applies the function std::cosh to each element of valarray (function template)
tanh(std::valarray) | applies the function std::tanh to each element of valarray (function template)
sinh sinhf sinhl (C++11)(C++11) | computes hyperbolic sine (\({\small\sinh{x} }\)sinh(x)) (function)
sinh(std::complex) | computes hyperbolic sine of a complex number (\({\small\sinh{z} }\)sinh(z)) (function template)

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