stirling

eve::stirling = functor<stirling_t>

inlineconstexpr

Header file

#include <eve/module/special.hpp>

Callable Signatures

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

Parameters

• x: floating value.
• c: Conditional expression masking the operation.
• m: Logical value masking the operation.

Return value

1. The value of an approximation of the \(\Gamma\) function by \(\displaystyle \Gamma(x) \approx \sqrt{2 \pi} x^{x-\frac12} e^{-x} \left( 1 + \frac1{x} P(\frac1{x})\right)\), where \(P\) is a polynomial, is returned.
2. The operation is performed conditionnaly.

External references

• Wikipedia: Stirling approximation
• Wolfram MathWorld: Stirling's Approximation

Example

// revision 1
#include <eve/module/special.hpp>
#include <iostream>
 
 
int main()
{
  eve::wide<float> wf([](auto i, auto c)->float{ return 2*(i+float(c)/3);});
  std::cout << "<- wf = " << wf << "\n";
 
  std::cout << "-> stirling(wf)                = " << eve::stirling(wf) << "\n";
  std::cout << "-> stirling[ignore_last(2)](wf)= " << eve::stirling[eve::ignore_last(2)](wf) << "\n";
  std::cout << "-> stirling[wf != 6.0f](wf)    = " << eve::stirling[wf != 6.0f](wf) << "\n";
}