std::sinh(std::valarray)(3)

NAME
std::sinh(std::valarray) - std::sinh(std::valarray)

Synopsis
   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 computes hyperbolic sine (\({\small\sinh{x} }\)sinh(x))
   sinhl (function)
   (C++11)
   (C++11)
                       computes hyperbolic sine of a complex number (\({\small\sinh{z}
   sinh(std::complex) }\)sinh(z))
                       (function template)