sinh

kyosu::sinh = eve::functor<sinh_t>

inlineconstexpr

Computes the hyperbolic sine of the argument.

Header file

#include <kyosu/functions.hpp>

Callable Signatures

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

Parameters

• z: Value to process.

Return value

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

External references

• C++ standard reference: complex sinh
• Wolfram MathWorld: Hyperbolic Sine
• Wikipedia: hyperbolic functions

Example

#include <kyosu/kyosu.hpp>
#include <eve/wide.hpp>
#include <iostream>
 
int main()
{
  using kyosu::sinh;
  using kyosu::complex_t;
  using kyosu::quaternion_t;
 
  std::cout << "Real:        ";
  std::cout << 72.9f << " -> " << sinh(72.9f) << "\n";
 
  std::cout << "Complex:     ";
  std::cout << kyosu::complex_t<float>(3.5f,-2.9f) << " -> " << sinh(kyosu::complex_t<float>(3.5f,-2.9f)) << "\n";
 
  std::cout << "Quaternion:  ";
  std::cout << kyosu::quaternion_t<double>(1.,2.,3.,4.) << " -> " << sinh(kyosu::quaternion_t<double>(1.,2.,3.,4.)) << "\n";
 
  std::cout << "SIMD:        ";
  using wc_t = eve::wide<kyosu::complex_t<double>, eve::fixed<2>>;
  std::cout << wc_t(kyosu::complex_t<double>(1.3,-3.7)) << " -> " << sinh(wc_t(kyosu::complex_t<double>(1.3,-3.7))) << "\n";
 
  return 0;
}