proj

kyosu::proj = {}

inlineconstexpr

Callable object computing proj(x), the projection of the cayley_dickson number z onto the (hyper) Riemann sphere.

Defined in Header

#include <kyosu/functions.hpp>

Callable Signatures

namespace kyosu
{
   template<kyosu::concepts::cayley_dickson T> constexpr T proj(T z) noexcept;
   template<eve::floating_ordered_value T>     constexpr T proj(T z) noexcept;
}

Parameters

• z: Value to project.

Return value

• For most z, proj(z)==z, but all infinities, even the numbers where one component is infinite and the other is NaN, become positive real
  infinity, (inf, 0...) or (inf, -0...).
  The sign of the pure (zero) components are the signs of the components of pure(z).

Example

#include <kyosu/kyosu.hpp>
#include <eve/wide.hpp>
#include <iostream>
 
int main()
{
  using kyosu::proj;
  using kyosu::complex_t;
  using kyosu::quaternion_t;
  auto inf = eve::inf(eve::as<float>());
 
  std::cout << "Real:        \n";
  std::cout << "    " <<  72.9f << " -> " << proj(72.9f) << "\n";
  std::cout << "    " <<  inf   << " -> " << proj(inf) << "\n";
  std::cout << "    " <<  -inf  << " -> " << proj(-inf) << "\n";
 
  std::cout << "Complex:     \n";
  std::cout << "    " << kyosu::complex_t<float>(3.5f,-2.9f) << " -> " << proj(kyosu::complex_t<float>(3.5f,-2.9f)) << "\n";
  std::cout << "    " <<  kyosu::complex_t<float>(3.5f,inf)   << " -> " << proj(kyosu::complex_t<float>(3.5f,inf)) << "\n";
  std::cout << "    " <<  kyosu::complex_t<float>(3.5f,-inf) << " -> " << proj(kyosu::complex_t<float>(3.5f,-inf)) << "\n";
  std::cout << "    " <<  kyosu::complex_t<float>(inf,-2.9f) << " ->  " << proj(kyosu::complex_t<float>(inf,-2.9f)) << "\n";
  std::cout << "    " <<  kyosu::complex_t<float>(inf, 2.9f) << " ->  " << proj(kyosu::complex_t<float>(inf,2.9f)) << "\n";
 
  std::cout << "Quaternion:  \n";
  std::cout << "    " <<  kyosu::quaternion_t<double>(1.f,2.f,3.f,4.f) << " -> " << proj(kyosu::quaternion_t<double>(1.f,2.f,3.f,4.f)) << "\n";
  std::cout << "    " <<  kyosu::quaternion_t<double>(-1.f,inf,3.f,-4.f) << " -> " << proj(kyosu::quaternion_t<double>(-1.f,inf,3.f,-4.f)) << "\n";
 
  using T =  eve::wide < float, eve::fixed < 2 > >;
  using c_t = kyosu::quaternion_t<T>;
  auto g = c_t(32, 44, 55, 34);
  std::cout << g << std::endl;
  return 0;
}