zeta

auto eve::zeta = functor<zeta_t>

inlineconstexpr

Header file

#include <eve/module/special.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
   constexpr auto zeta(floating_value auto x)                          noexcept; // 1
 
   // Lanes masking
   constexpr auto zeta[conditional_expr auto c](floating_value auto x) noexcept; // 2
   constexpr auto zeta[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 Riemann function defined as \(\displaystyle \zeta(s)=\sum_{n=0}^\infty \frac1{n^s}\) for \(s > 1\) and using analytic continuation elsewhere, is returned.
2. The operation is performed conditionnaly.

External references

• Wikipedia: Riemann zeta function
• Wolfram MathWorld: Riemann Zeta Function

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);});
 
  std::cout << "<- wf = " << wf << "\n";
 
  std::cout << "-> zeta(wf)                = " << eve::zeta(wf) << "\n";
  std::cout << "-> zeta[ignore_last(2)](wf)= " << eve::zeta[eve::ignore_last(2)](wf) << "\n";
  std::cout << "-> zeta[wf != -2.0f](wf)   = " << eve::zeta[wf != -2.0f](wf) << "\n";
}