log_gamma

auto kyosu::log_gamma = eve::functor<log_gamma_t>

inlineconstexpr

Computes \(\log(\Gamma(z))\).

Header file

#include <kyosu/functions.hpp>

Callable Signatures

namespace kyosu
{
  //  regular call
  template<concepts::cayley_dickson_like Z> constexpr complexify_t<Z> log_gamma(Z z) noexcept;
  template<kyosu::concepts::cayley_dickson_like T> constexpr complexify_t<T> log(T z eve::value n) noexcept;
 
  // semantic modifyers
  template<concepts::real Z> constexpr complexify_t<Z> log_gamma[real_only](Z z) noexcept;
}

Parameters

• z : Value to process.

Return value

• A real typed input z is treated as if complex(z) was entered, unless the option real_only is used in which case the result will the same as to an eve::log_gamma call implying a Nan result if the input is not greater than zero.

Returns \(\Gamma(z)\).

• with two parameters use the nth branch of the logarithm.

External references

• Wolfram MathWorld: Gamma Function
• Wikipedia: Gamma function

Example

#include <eve/wide.hpp>
#include <iostream>
#include <kyosu/kyosu.hpp>
 
int main()
{
 
  using wide_ft = eve::wide<float, eve::fixed<4>>;
  wide_ft ref1 = {3.0f, 2.0f, 1.0f, 0.5f};
  wide_ft imf1 = {2.0f, -1.0, -5.0, 0.0};
  wide_ft ref2 = {0.0, 1.0, 2.0, 3.0};
  auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
 
  std::cout << "---- simd" << std::endl
            << "<- zc            = " << zc << std::endl
            << "-> log_gamma(zc)      = " << kyosu::log_gamma(zc) << std::endl
            << "-> log_gamma(ref2)    = " << kyosu::log_gamma(ref2) << std::endl;
 
  return 0;
}