digamma

auto eve::digamma = functor<digamma_t>

inlineconstexpr

Header file

#include <eve/module/special.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
   constexpr auto digamma(floating_value auto x)                          noexcept; // 1
 
   // Lanes masking
   constexpr auto digamma[conditional_expr auto c](floating_value auto x) noexcept; // 2
   constexpr auto digamma[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 the Digamma function: \(\psi(x) = \frac{\Gamma'(x)}{\Gamma(x)}\) is returned.
2. The operation is performed conditionnaly.

External references

• DLMF: Gamma and Psi Functions
• Wolfram MathWorld: Digamma Function

Example

// revision 1
#include <eve/module/special.hpp>
#include <iostream>
 
int main()
{
  eve::wide wf = {0.5, -1.5, 0.1, -1.0, 19.0, 25.0, 21.5, 10000.0};
 
  std::cout << "<- wf                         = " << wf << "\n";
 
  std::cout << "-> digamma(wf)                = " << eve::digamma(wf) << "\n";
  std::cout << "-> digamma[ignore_last(2)](wf)= " << eve::digamma[eve::ignore_last(2)](wf) << "\n";
  std::cout << "-> digamma[wf > 0.0f](wf)     = " << eve::digamma[wf >  0.0](wf) << "\n";
}