proj

auto kyosu::proj = eve::functor<proj_t>

inlineconstexpr

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

Header file

#include <kyosu/functions.hpp>

Callable Signatures

namespace kyosu
{
   template<kyosu::concepts::cayley_dickson 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 of the form:
  infinity, (inf, 0...) or (inf, -0...).
  The sign of the pure (zero) components are the signs of the components of pure(z).

Example

#include <eve/wide.hpp>
#include <iostream>
#include <kyosu/kyosu.hpp>
 
int main()
{
  using kyosu::complex_t;
  using kyosu::proj;
  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;
}