sinc

auto eve::sinc = functor<sinc_t>

inlineconstexpr

Header file

#include <eve/module/math.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
   constexpr auto sinc(floating_value auto x)                          noexcept; // 1
 
   // Lanes masking
   constexpr auto sinc[conditional_expr auto c](floating_value auto x) noexcept; // 2
   constexpr auto sinc[logical_value auto m](floating_value auto x)    noexcept; // 2
 
   // Semantic options
   constexpr auto sinc[radpi](floating_value auto x)                    noexcept; // 1.c
   constexpr auto sinc[quarter_circle](floating_value auto x)           noexcept; // 3.a
   constexpr auto sinc[half_circle](floating_value auto x)              noexcept; // 3.b
   constexpr auto sinc[full_circle](floating_value auto x)              noexcept; // 3.c
   constexpr auto sinc[raw](floating_value auto x)                      noexcept; // 4.a
   constexpr auto sinc[fast] (floating_value auto x)                    noexcept; // 4.b
   constexpr auto sinc[radpi](floating_value auto x)                      noexcept; // 5
}

Parameters

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

Return value

1. Returns the elementwise sine of the input divided by the input. In particular:
   • If the element is \(\pm0\), \(1\) is returned.
   • If the element is \(\pm\infty\), 0 is returned.
   • If the element is a Nan, NaN is returned.
2. The operation is performed conditionally.
3. These are optimized calls providing a balance between speed and range limitation.
   1. assumes that the inputs elements belong to \([-\pi/4,\pi/4]\) and return NaN outside.
   2. assumes that the inputs elements belong to \([-\pi/2,\pi/2]\) and return NaN outside.
   3. assumes that the inputs elements belong to \([-\pi,\pi]\) and return NaN outside. these options can be combined with the previous ones with ranges adapted to the chosen unity.
4. returns \(\frac{\sin \pi x}{\pi x}\)

   External references

• Wikipedia
• Wolfram MathWorld

Example

// revision 1
#include <eve/module/math.hpp>
#include <iostream>
 
int main()
{
  eve::wide wf = {0.0, 1.0, 2.0, 20.0, 100.0, 1000.0,
                  eve::inf(eve::as<double>()), eve::nan(eve::as<double>())};
 
  std::cout << "<- wf                      = " << wf << "\n";
 
  std::cout << "-> sinc(wf)                = " << eve::sinc(wf) << "\n";
  std::cout << "-> sinc[ignore_last(2)](wf)= " << eve::sinc[eve::ignore_last(2)](wf) << "\n";
  std::cout << "-> sinc[wf != 2.0f](wf)    = " << eve::sinc[wf != 2.0f](wf) << "\n";
}