cosh

kyosu::cosh = eve::functor<cosh_t>

inlineconstexpr

Computes the hyperbolic cosine of the argument.

Header file

#include <kyosu/functions.hpp>

Callable Signatures

namespace kyosu
{
   template<eve::floating_ordered_value T>     constexpr T cosh(T z) noexcept; //1
   template<kyosu::concepts::complex T>        constexpr T cosh(T z) noexcept; //2
   template<kyosu::concepts::cayley_dickson T> constexpr T cosh(T z) noexcept; //3
}

Parameters

• z: Value to process.

Return value

1. returns eve::cosh(z)
2. Returns elementwise the complex value of the hyperbolic cosine of the input.
   • for every z: cosh(conj(z)) == conj(cosh(z))
   • for every z: cosh(-z) == cosh(z)
   • If z is \(0\), the result is \(1\)
   • If z is \(i \infty\), the result is \(\textrm{NaN}\)
   • If z is \(i \textrm{NaN}\), the result is \(\textrm{NaN}\)
   • If z is \(x+i \infty\) (for any finite non-zero x), the result is \(\textrm{NaN}+i \textrm{NaN}\)
   • If z is \(x+i \textrm{NaN}\) (for any finite non-zero x), the result is \(\textrm{NaN}+i \textrm{NaN}\)
   • If z is \(\infty+i 0\), the result is \(\infty+i 0\)
   • If z is \(\infty,y\) (for any finite non-zero y), the result is \(\infty e^{iy}\)
   • If z is \(\infty+i \infty\), the result is \(\pm \infty+i \textrm{NaN}\) (the sign of the real part is unspecified)
   • If z is \(\infty+i \textrm{NaN}\), the result is \(\infty+i \textrm{NaN}\)
   • If z is \(\textrm{NaN}\), the result is \(\textrm{NaN}\)
   • If z is \(\textrm{NaN}+i y\) (for any finite non-zero y), the result is \(\textrm{NaN}+i \textrm{NaN}\)
   • If z is \(\textrm{NaN}+i \textrm{NaN}\), the result is \(\textrm{NaN}+i \textrm{NaN}\)
3. Is semantically equivalent to (exp(z)+exp(-z))/2.

External references

• C++ standard reference: complex cosh
• Wolfram MathWorld: Hyperbolic Cosine
• Wikipedia: hyperbolic functions

Example

#include <kyosu/kyosu.hpp>
#include <eve/wide.hpp>
#include <iostream>
 
int main()
{
  using kyosu::cos;
  using kyosu::complex_t;
  using kyosu::quaternion_t;
  using e_t = float;
  using c_t = kyosu::complex_t<float>;
  using q_t = kyosu::quaternion_t<float>;
  using we_t = eve::wide<e_t, eve::fixed<2>>;
  using wc_t = eve::wide<c_t, eve::fixed<2>>;
  using wq_t = eve::wide<q_t, eve::fixed<2>>;
 
  std::cout << "Real:        \n";
  e_t e(2.9f);
  we_t we = we_t(e);
  std::cout << e << " -> " << cos(e) << "\n";
  std::cout << we << " -> " << cos(we) << "\n";
  std::cout               << cos(c_t(e))<< "\n";
  std::cout               << cos(q_t(e))<< "\n";
  std::cout               << cos(wc_t(e))<< "\n";
  std::cout               << cos(wq_t(e))<< "\n";
 
  std::cout << "Complex:     \n";
  c_t c(3.5f,-2.9f);
  wc_t wc = wc_t(c);
  std::cout << c << " -> " << cos(c) << "\n";
  std::cout << wc << " -> " << cos(wc) << "\n";
  std::cout               << cos(q_t(c))<< "\n";
  std::cout               << cos(wq_t(c))<< "\n";
 
  std::cout << "Quaternion:  \n";
  q_t q(3.5f,-2.9f, 2.1f, 3.2f);
  wq_t wq = wq_t(q);
  std::cout << q << " -> " << cos(q) << "\n";
  std::cout << wq << " -> " << cos(wq) << "\n";
 
  return 0;
}