log_gamma

auto eve::log_gamma = functor<log_gamma_t>

inlineconstexpr

Header file

#include <eve/module/special.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
   constexpr auto log_gamma(floating_value auto x)                          noexcept; // 1
 
   // Lanes masking
   constexpr auto log_gamma[raw](floating_value auto x)                     noexcept; // 2
   constexpr auto log_gamma[fast](floating_value auto x)                    noexcept; // 2
   constexpr auto log_gamma[conditional_expr auto c](floating_value auto x) noexcept; // 3
   constexpr auto log_gamma[logical_value auto m](floating_value auto x)    noexcept; // 3
}

Parameters

• x: strictly positive real floating argument.
• c: Conditional expression masking the operation.
• m: Logical value masking the operation.

Return value

1. The value of the logarithm of the \(\Gamma\) function is returned. this callable returns NaN if eve::gamma(x) is less than zero.
2. faster computations at accuracy price based on "An accurate approximation formula for gamma function" of Zhen-Hang Yang and Jing-Feng Tian.
3. The operation is performed conditionnaly.

External references

• [Wolfram MathWorld: Log Gamma Function](https://mathworld.wolfram.com/LogGammaFunction.html
• Zhen-Hang Yang & al.

Example

// revision 1
#include <eve/module/special.hpp>
#include <iostream>
 
int main()
{
  eve::wide<float> wf([](auto i, auto c)->float{ return 2*(i+c/2);});
  eve::wide bads{0.0, -0.0, -1.0, -2.5};
  std::cout << "<- wf   = " << wf << "\n";
  std::cout << "<- bads = " << bads << "\n";
 
  std::cout << "-> log_gamma(wf)                = " << eve::log_gamma(wf) << "\n";
  std::cout << "-> log_gamma[ignore_last(2)](wf)= " << eve::log_gamma[eve::ignore_last(2)](wf) << "\n";
  std::cout << "-> log_gamma[wf != 12.0f](wf)   = " << eve::log_gamma[wf != 12.0f](wf) << "\n";
  std::cout << "-> log_gamma(bads)              = " << eve::log_gamma(bads)<< "\n";
}