gamma_p

auto eve::gamma_p = functor<gamma_p_t>

inlineconstexpr

Header file

#include <eve/module/special.hpp>

Callable Signatures

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

Parameters

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

Return value

1. The value of the normalized lower incomplete \(\Gamma\) function: \(\displaystyle \frac{1}{\Gamma(x)}\int_0^{y} t^{x-1}e^{-t}\mbox{d}t\) is returned.
2. The operation is performed conditionnaly.

External references

• Wikipedia: Incomplete gamma function
• DLMF

Example

// revision 1
#include <eve/module/special.hpp>
#include <iostream>
 
int main()
{
 
  eve::wide wk = {1.0e-3, 0.3, 0.75, 5.5};
  eve::wide wp = {10.0, 0.5, 20.7, 1.0};
 
  std::cout << "<- wk                             = " << wk << "\n";
  std::cout << "<- wp                             = " << wp << "\n";
 
  std::cout << "-> gamma_p(wk, wp)                = " << eve::gamma_p(wk, wp) << "\n";
  std::cout << "-> gamma_p[ignore_last(2)](wk, wp)= " << eve::gamma_p[eve::ignore_last(2)](wk, wp) << "\n";
  std::cout << "-> gamma_p[wk > 0.5](wk, wp)      = " << eve::gamma_p[wk > 0.5](wk, wp) << "\n";
}