epsilon

auto eve::epsilon = functor<epsilon_t>

inlineconstexpr

Header file

#include <eve/module/core.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
   constexpr auto epsilon(value auto x)                          noexcept; // 1
 
   // Lanes masking
   constexpr auto epsilon[conditional_expr auto c](value auto x) noexcept; // 2
   constexpr auto epsilon[logical_value auto m](value auto x)    noexcept; // 2
 
   // Semantic options
   constexpr auto abs[downward](value auto x)                    noexcept; // 1
   constexpr auto abs[upward](value auto x)                      noexcept; // 3
}

Parameters

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

Return value

1. The distance of abs(x) to the next representable element in the type of x. (Kahan-Harrisson definition)
2. The operation is performed conditionnaly.
3. The distance of abs(x) to the previous representable element in the type of x. (Goldberg definition)

External references

• wikipedia
• HAL: On the definition of ulp(x)

Example

// revision 0
#include <eve/module/core.hpp>
#include <iostream>
 
int main()
{
  eve::wide wf0{0.0, 1.0, 2.0, 3.0, -1.0, -2.0, -3.0, -4.0};
  eve::wide wi0{0, 1, 2, 3, -1, -2, -3, -4};
  eve::wide wu0{0u, 1u, 2u, 3u, 4u, 5u, 6u, 7u};
 
  std::cout << "<- wf0                          = " << wf0 << "\n";
  std::cout << "<- wi0                          = " << wi0 << "\n";
  std::cout << "<- wu0                          = " << wu0 << "\n";
                                                
  std::cout << "-> epsilon(wf0)                 = " << eve::epsilon(wf0) << "\n";
  std::cout << "-> epsilon[ignore_last(2)](wf0) = " << eve::epsilon[eve::ignore_last(2)](wf0) << "\n";
  std::cout << "-> epsilon[wf0 != 0](wf0)       = " << eve::epsilon[wf0 != 0](wf0) << "\n";
  std::cout << "-> epsilon(wu0)                 = " << eve::epsilon(wu0) << "\n";
  std::cout << "-> epsilon[ignore_last(2)](wu0) = " << eve::epsilon[eve::ignore_last(2)](wu0) << "\n";
  std::cout << "-> epsilon[wu0 != 0](wu0)       = " << eve::epsilon[wu0 != 0](wu0) << "\n";
  std::cout << "-> epsilon(wi0)                 = " << eve::epsilon(wi0) << "\n";
  std::cout << "-> epsilon[ignore_last(2)](wi0) = " << eve::epsilon[eve::ignore_last(2)](wi0) << "\n";
  std::cout << "-> epsilon[wi0 != 0](wi0)       = " << eve::epsilon[wi0 != 0](wi0) << "\n";
}